Patent Publication Number: US-11638933-B2

Title: Injection molded screening apparatuses and methods

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of U.S. patent application Ser. No. 16/837,716, filed Apr. 1, 2020, which is a continuation-in-part of U.S. patent application Ser. No. 16/269,656, filed Feb. 7, 2019, now U.S. Pat. No. 10,843,230, which is a continuation of U.S. patent application Ser. No. 15/965,195, filed on Apr. 27, 2018, now U.S. Pat. No. 10,576,502, which claims priority to U.S. Provisional Application No. 62/648,771, filed Mar. 27, 2018, and is also a continuation-in-part of U.S. patent application Ser. No. 15/851,099, filed Dec. 21, 2017, now U.S. Pat. No. 10,259,013, which is a divisional of U.S. patent application Ser. No. 15/201,865, filed Jul. 5, 2016, now U.S. Pat. No. 9,884,344, which is a continuation of U.S. patent application Ser. No. 14/268,101, filed May 2, 2014, now U.S. Pat. No. 9,409,209, which is a continuation-in-part of U.S. patent application Ser. No. 13/800,826, filed Mar. 13, 2013, now U.S. Pat. No. 10,046,363, which claims the benefit of U.S. Provisional Patent Application Serial Nos. 61/652,039 filed May 25, 2012, and 61/714,882 filed Oct. 17, 2012, the entire contents of which are incorporated herein by reference. 
    
    
     FIELD 
     The present disclosure relates generally to material screening. More particularly, the present disclosure relates to screening members, screening assemblies, methods for fabricating screening members and assemblies and methods for screening materials. 
     BACKGROUND 
     Material screening includes the use of vibratory screening machines. Vibratory screening machines provide the capability to excite an installed screen such that materials placed upon the screen may be separated to a desired level. Oversized materials are separated from undersized materials. Over time, screens wear and require replacement. As such, screens are designed to be replaceable. 
     Replacement screen assemblies must be securely fastened to a vibratory screening machine and are subjected to large vibratory forces. Replacement screens may be attached to a vibratory screening machine by tensioning members, compression members or clamping members. 
     Replacement screen assemblies are typically made of metal or a thermoset polymer. The material and configuration of the replacement screens are specific to a screening application. For example, due to their relative durability and capacity for fine screening, metal screens are frequently used for wet applications in the oil and gas industry. Traditional thermoset polymer type screens (e.g., molded polyurethane screens), however, are not as durable and would likely not withstand the rough conditions of such wet applications and are frequently utilized in dry applications, such as applications in the mining industry. 
     Fabricating thermoset polymer type screens is relatively complicated, time consuming and prone to errors. Typical thermoset type polymer screens that are used with vibratory screening machines are fabricated by combining separate liquids (e.g., polyester, polyether and a curative) that chemically react and then allowing the mixture to cure over a period of time in a mold. When fabricating screens with fine openings, e.g., approximately 43 microns to approximately 100 microns, this process can be extremely difficult and time consuming. Indeed, to create fine openings in a screen, the channels in the molds that the liquid travels through have to be very small (e.g., on the order of 43 microns) and all too often the liquid does not reach all the cavities in the mold. As a result, complicated procedures are often implemented that require close attention to pressures and temperatures. Since a relatively large single screen (e.g., two feet by three feet or larger) is made in a mold, one flaw (e.g., a hole, i.e., a place where the liquid did not reach) will ruin the entire screen. Thermoset polymer screens are typically fabricated by molding an entire screen assembly structure as one large screening piece and the screen assembly may have openings ranging from approximately 43 microns to approximately 4000 microns in size. The screening surface of conventional thermoset polymer screens normally has a uniform flat configuration. 
     Thermoset polymer screens are relatively flexible and are often secured to a vibratory screening machine using tensioning members that pull the side edges of the thermoset polymer screen away from each other and secure a bottom surface of the thermoset polymer screen against a surface of a vibratory screening machine. To prevent deformation when being tensioned, thermoset polymer assemblies may be molded with aramid fibers that run in the tensioning direction (see, e.g., U.S. Pat. No. 4,819,809). If a compression force were applied to the side edges of the typical thermoset polymer screens it would buckle or crimp, thereby rendering the screening surface relatively ineffective. 
     In contrast to thermoset polymer screens, metal screens are rigid and may be compressed or tensioned onto a vibratory screening machine. Metal screen assemblies are often fabricated from multiple metal components. The manufacture of metal screen assemblies typically includes: fabricating a screening material, often three layers of a woven wire mesh; fabricating an apertured metal backing plate; and bonding the screening material to apertured metal backing plate. The layers of wire cloth may be finely woven with openings in the range of approximately 30 microns to approximately 4000 microns. The entire screening surface of conventional metal assemblies is normally a relatively uniform flat configuration or a relatively uniform corrugated configuration. 
     Critical to screening performance of screen assemblies (thermoset polymer assemblies and metal type assemblies) for vibratory screening machines are the size of the openings in the screening surface, structural stability and durability of the screening surface, structural stability of the entire unit, chemical properties of the components of the unit and ability of the unit to perform in various temperatures and environments. Drawbacks to conventional metal assemblies include lack of structural stability and durability of the screening surface formed by the woven wire mesh layers, blinding (plugging of screening openings by particles) of the screening surface, weight of the overall structure, time and cost associated with the fabrication or purchase of each of the component members, and assembly time and costs. Because wire cloth is often outsourced by screen manufacturers, and is frequently purchased from weavers or wholesalers, quality control can be extremely difficult and there are frequently problems with wire cloth. Flawed wire cloth may result in screen performance problems and constant monitoring and testing is required. 
     One of the biggest problems with conventional metal assemblies is blinding. A new metal screen may initially have a relatively large open screening area but over time, as the screen is exposed to particles, screening openings plug (i.e., blind) and the open screening area, and effectiveness of the screen itself, is reduced relatively quickly. For example, a 140 mesh screen assembly (having three layers of screen cloth) may have an initial open screening area of 20-24%. As the screen is used, however, the open screening area may be reduced by 50% or more. 
     Conventional metal screen assemblies also lose large amounts of open screening area because of their construction, which includes adhesives, backing plates, plastic sheets bonding layers of wire cloth together, etc. 
     Another major problem with conventional metal assemblies is screen life. Conventional metal assemblies don&#39;t typically fail because they get worn down but instead fail due to fatigue. That is, the wires of the woven wire cloth often actually break due to the up and down motion they are subject to during vibratory loading. 
     Drawbacks to conventional thermoset polymer screens also include lack of structural stability and durability. Additional drawbacks include inability to withstand compression type loading and inability to withstand high temperatures (e.g., typically a thermoset polymer type screen will begin to fail or experience performance problems at temperatures above 130° F., especially screens with fine openings, e.g., approximately 43 microns to approximately 100 microns). Further, as discussed above, fabrication is complicated, time consuming and prone to errors. Also, the molds used to fabricate thermoset polymer screens are expensive and any flaw or the slightest damage thereto will ruin the entire mold and require replacement, which may result in costly downtime in the manufacturing process. 
     Another drawback to both conventional metal and thermoset polymer screens is the limitation of screen surface configurations that are available. Existing screening surfaces are fabricated with relatively uniform opening sizes throughout and a relatively uniform surface configuration throughout, whether the screening surface is flat or undulating. 
     The conventional polymer type screens referenced in U.S. Provisional Application No. 61/652,039 (also referred to therein as traditional polymer screens, existing polymer screens, typical polymer screens or simply polymer screens) refer to the conventional thermoset polymer screens described in U.S. Provisional Patent Application Ser. No. 61/714,882 and the conventional thermoset polymer screens described herein (also referred to herein and in U.S. Provisional Patent Application Ser. No. 61/714,882 as traditional thermoset polymer screens, existing thermoset polymer screens, typical thermoset polymer screens or simply thermoset screens). Accordingly, the conventional polymer type screens referenced in U.S. Provisional Application No. 61/652,039 are the same conventional thermoset polymer screens referenced herein, and in U.S. Provisional Patent Application Ser. No. 61/714,882, and may be fabricated with extremely small screening openings (as described herein and in U.S. Provisional Patent Application Ser. No. 61/714,882) but have all the drawbacks (as described herein and in U.S. Provisional Patent Application Ser. No. 61/714,882) regarding conventional thermoset polymer screens, including lack of structural stability and durability, inability to withstand compression type loading, inability to withstand high temperatures and complicated, time consuming, error prone fabrication methods. 
     There is a need for versatile and improved screening members, screening assemblies, methods for fabricating screening members and assemblies and methods for screening materials for vibratory screening machines that incorporate the use of injection molded materials (e.g., thermoplastics) having improved mechanical and chemical properties. 
     SUMMARY 
     The present disclosure is an improvement over existing screen assemblies and methods for screening and fabricating screen assemblies and parts thereof. The present invention provides extremely versatile and improved screening members, screening assemblies, methods for fabricating screening members and assemblies and methods for screening materials for vibratory screening machines that incorporate the use of injection molded materials having improved properties, including mechanical and chemical properties. In certain embodiments of the present invention a thermoplastic is used as the injection molded material. The present invention is not limited to thermoplastic injection molded materials and in embodiments of the present invention other materials may be used that have similar mechanical and/or chemical properties. In embodiments of the present invention, multiple injection molded screen elements are securely attached to subgrid structures. The subgrids are fastened together to form the screen assembly structure, which has a screening surface including multiple screen elements. Use of injection molded screen elements with the various embodiments described herein provide, inter alia, for: varying screening surface configurations; fast and relatively simple screen assembly fabrication; and a combination of outstanding screen assembly mechanical, chemical and electrical properties, including toughness, wear and chemical resistance. 
     Embodiments of the present invention include screen assemblies that are configured to have relatively large open screening areas while having structurally stable small screening openings for fine vibratory screening applications. In embodiments of the present invention, the screening openings are very small (e.g., as small as approximately 43 microns) and the screen elements are large enough (e.g., one inch by one inch, one inch by two inches, two inches by three inches, etc.) to make it practical to assemble a complete screen assembly screening surface (e.g., two feet by three feet, three feet by four feet, etc.). Fabricating small screening openings for fine screening applications requires injection molding very small structural members that actually form the screening openings. These structural members are injection molded to be formed integrally with the screen element structure. Importantly, the structural members are small enough (e.g., in certain applications they may be on the order of approximately 43 microns in screening surface width) to provide an effective overall open screening area and form part of the entire screen element structure that is large enough (e.g., two inches by three inches) to make it practical to assemble a relatively large complete screening surface (e.g., two feet by three feet) therefrom. 
     In one embodiment of the present invention a thermoplastic material is injection molded to form screen elements. Previously thermoplastics have not been used with the fabrication of vibratory screens with fine size openings (e.g., approximately 43 microns to approximately 1000 microns) because it would be extremely difficult, if not impossible, to thermoplastic injection mold a single relatively large vibratory screening structure having fine openings and obtain the open screening area necessary for competitive performance in vibratory screening applications. 
     According to an embodiment of the present disclosure, a screen assembly is provided that: is structurally stable and can be subjected to various loading conditions, including compression, tensioning and clamping; can withstand large vibrational forces; includes multiple injection molded screen elements that, due to their relatively small size, can be fabricated with extremely small opening sizes (having dimensions as small as approximately 43 microns); eliminates the need for wire cloth; is lightweight; is recyclable; is simple and easy to assemble; can be fabricated in multiple different configurations, including having various screen opening sizes throughout the screen and having various screening surface configurations, e.g., various combinations of flat and undulating sections; and can be fabricated with application-specific materials and nanomaterials. Still further, each screen assembly may be customized to a specific application and can be simply and easily fabricated with various opening sizes and configurations depending on the specifications provided by an end user. Embodiments of the present disclosure may be applied to various applications, including wet and dry applications and may be applied across various industries. The present invention is not limited to the oil and gas industry and the mining industry. Disclosed embodiments may also be utilized in any industry that requires separation of materials using vibratory screenings machines, including pulp and paper, chemical, pharmaceuticals and others. 
     In an example embodiment of the present invention, a screen assembly is provided that substantially improves screening of materials using a thermoplastic injection molded screen element. Multiple thermoplastic polymer injection molded screen elements are securely attached to subgrid structures. The subgrids are fastened together to form the screen assembly structure, which has a screening surface including multiple screen elements. Each screen element and each subgrid may have different shapes and configurations. Thermoplastic injection molding individual screen elements allows for precise fabrication of screening openings, which may have dimensions as small as approximately 43 microns. The grid framework may be substantially rigid and may provide durability against damage or deformation under the substantial vibratory load burdens it is subjected to when secured to a vibratory screening machine. Moreover, the subgrids, when assembled to form the complete screen assembly, are strong enough not only to withstand the vibratory loading, but also the forces required to secure the screen assembly to the vibratory screening machine, including large compression loads, tension loads and/or clamping loads. Still further, the openings in the subgrids structurally support the screen elements and transfer vibrations from the vibratory screening machine to the elements forming the screening openings thereby optimizing screening performance. The screen elements, subgrids and/or any other component of the screen assembly may include nanomaterials and/or glass fibers that, in addition to other benefits, provide durability and strength. 
     According to an example embodiment of the present disclosure, a screen assembly is provided having a screen element including a screen element screening surface with a series of screening openings and a subgrid including multiple elongated structural members forming a grid framework having grid openings. The screen element spans at least one of the grid openings and is attached to a top surface of the subgrid. Multiple independent subgrids are secured together to form the screen assembly and the screen assembly has a continuous screen assembly screening surface having multiple screen element screening surfaces. The screen element includes substantially parallel end portions and substantially parallel side edge portions substantially perpendicular to the end portions. The screen element further includes a first screen element support member and a second screen element support member orthogonal to the first screen element support member. The first screen element support member extends between the end portions and is approximately parallel to the side edge portions. The second screen element support member extends between the side edge portions and is approximately parallel to the end portions. The screen element includes a first series of reinforcement members substantially parallel to the side edge portions and a second series of reinforcement members substantially parallel to the end portions. The screen element screening surface includes screen surface elements forming the screening openings. The end portions, side edge portions, first and second support members and first and second series of reinforcement members structurally stabilize screen surface elements and screening openings. The screen element is formed as a single thermoplastic injection molded piece. 
     The screening openings may be rectangular, square, circular, and oval or any other shape. The screen surface elements may run parallel to the end portions and form the screening openings. The screen surface elements may also run perpendicular to the end portions and form the screen openings. Different combinations of rectangular, square, circular and oval screening openings (or other shapes) may be incorporated together and depending on the shape utilized may run parallel and/or perpendicular to the end portions. 
     The screen surface elements may run parallel to the end portions and may be elongated members forming the screening openings. The screening openings may be elongated slots having a distance of approximately 43 microns to approximately 4000 microns between inner surfaces of adjacent screen surface elements. In certain embodiments, the screen openings may have a distance of approximately 70 microns to approximately 180 microns between inner surfaces of adjacent screen surface elements. In other embodiments, the screening openings may have a distance of approximately 43 microns to approximately 106 microns between inner surfaces of adjacent screen surface elements. In embodiments of the present invention, the screening openings may have a width and a length, the width may be about 0.043 mm to about 4 mm and the length may be about 0.086 mm to about 43 mm. In certain embodiments, the width to length ratio may be approximately 1:2 to approximately 1:1000. 
     Multiple subgrids of varying sizes may be combined to form a screen assembly support structure for screen elements. Alternatively, a single subgrid may be thermoplastic injection molded, or otherwise constructed, to form the entire screen assembly support structure for multiple individual screen elements. 
     In embodiments that use multiple subgrids, a first subgrid may include a first base member having a first fastener that is configured to mate with a second fastener of a second base member of a second subgrid, the first and second fasteners securing the first and second subgrids together. The first fastener may be a clip and the second fastener may be a clip aperture, wherein the clip snaps into the clip aperture and securely attaches the first and second subgrids together. 
     The first and second screen element support members and the screen element end portions may include a screen element attachment arrangement configured to mate with a subgrid attachment arrangement. The subgrid attachment arrangement may include elongated attachment members and the screen element attachment arrangement may include attachment apertures that mate with the elongated attachment members securely attaching the screen element to the subgrid. A portion of the elongated attachment members may be configured to extend through the screen element attachment apertures and slightly above the screen element screening surface. The attachment apertures may include a tapered bore or may simply include an aperture without any tapering. The portion of the elongated attachment members above the screening element screening surface may be melted and may fill the tapered bore, fastening the screen element to the subgrid. Alternatively, the portion of the elongated attachment members that extends through and above the aperture in screening element screening surface may be melted such that it forms a bead on the screening element screening surface and fastens the screen element to the subgrid. 
     The elongated structural members may include substantially parallel subgrid end members and substantially parallel subgrid side members substantially perpendicular to the subgrid end members. The elongated structural members may further include a first subgrid support member and a second subgrid support member orthogonal to the first subgrid support member. The first subgrid support member may extend between the subgrid end members and may be approximately parallel to the subgrid side members. The second subgrid support member may extend between the subgrid side members and may be approximately parallel to the subgrid end members, and substantially perpendicular to the subgrid edge members. 
     The grid framework may include a first and a second grid framework forming a first and a second grid opening. The screen elements may include a first and a second screen element. The subgrid may have a ridge portion and a base portion. The first and second grid frameworks may include first and second angular surfaces that peak at the ridge portion and extend downwardly from the peak portion to the base portion. The first and second screen elements may span the first and second angular surfaces, respectively. 
     According to an example embodiment of the present invention, a screen assembly is provided having a screen element including a screen element screening surface with a series of screening openings and a subgrid including multiple elongated structural members forming a grid framework having grid openings. The screen element spans at least one grid opening and is secured to a top surface of the subgrid. Multiple subgrids are secured together to form the screen assembly and the screen assembly has a continuous screen assembly screening surface comprised of multiple screen element screening surfaces. The screen element is a single thermoplastic injection molded piece. 
     The screen element may include substantially parallel end portions and substantially parallel side edge portions substantially perpendicular to the end portions. The screen element may further include a first screen element support member and a second screen element support member orthogonal to the first screen element support member. The first screen element support member may extend between the end portions and may be approximately parallel to the side edge portions. The second screen element support member may extend between the side edge portions and may be approximately parallel to the end portions. The screen element may include a first series of reinforcement members that are substantially parallel to the side edge portions and a second series of reinforcement members substantially parallel to the end portions. The screen element may include elongated screen surface elements running parallel to the end portions and forming the screening openings. The end portions, side edge portions, first and second support members, first and second series of reinforcement members may structurally stabilize the screen surface elements and the screening openings. 
     The first and second series of reinforcement members may have a thickness less than a thickness of the end portions, side edge portions and the first and second screen element support members. The end portions and the side edge portions and the first and second screen element support members may form four rectangular areas. The first series of reinforcement members and the second series of reinforcement members may form multiple rectangular support grids within each of the four rectangular areas. The screening openings may have a width of approximately 43 microns to approximately 4000 microns between inner surfaces of each of the screen surface elements. In certain embodiments, the screening openings may have a width of approximately 70 microns to approximately 180 microns between inner surfaces of each of the screen surface elements. In other embodiments, the screening openings may have a width of approximately 43 microns to approximately 106 microns between inner surfaces of each of the screen surface elements. In embodiments of the present invention, the screening openings may have a width of about 0.043 mm to about 4 mm and length of about 0.086 mm to about 43 mm. In certain embodiments, the width to length ratio may be approximately 1:2 to approximately 1:1000. 
     The screen elements may be flexible. 
     The subgrid end members, the subgrid side members and the first and second subgrid support members may form eight rectangular grid openings. A first screen element may span four of the grid openings and a second screen element may span the other four openings. 
     A central portion of the screening element screening surface may slightly flex when subject to a load. The subgrid may be substantially rigid. The subgrid may also be a single thermoplastic injection molded piece. At least one of the subgrid end members and the subgrid side members may include fasteners configured to mate with fasteners of other subgrids, which fasteners may be clips and clip apertures that snap into place and securely attach the subgrids together. 
     The subgrid may include: substantially parallel triangular end pieces, triangular middle pieces substantially parallel to the triangular end pieces, a first and second mid support substantially perpendicular to the triangular end pieces and extending between the triangular end pieces, a first and second base support substantially perpendicular to the triangular end pieces and extending the between the triangular end pieces and a central ridge substantially perpendicular to the triangular end pieces and extending the between the triangular end pieces. A first edge of the triangular end pieces, the triangular middle pieces, and the first mid support, the first base support and the central ridge may form a first top surface of the subgrid having a first series of grid openings. A second edge of the triangular end pieces, the triangular middle pieces, and the second mid support, the second base support and the central ridge may form a second top surface of the subgrid having a second series of grid openings. The first top surface may slope down from the central ridge to the first base support and the second top surface may slope down from the central ridge to the second base support. A first and a second screen element may span the first series and second series of grid openings, respectively. The first edges of the triangular end pieces, the triangular middle pieces, the first mid support, the first base support and the central ridge may include a first subgrid attachment arrangement configured to securely mate with a first screen element attachment arrangement of the first screen element. The second edges of the triangular end pieces, the triangular middle pieces, the second mid support, the second base support and the central ridge may include a second subgrid attachment arrangement configured to securely mate with a second screen element attachment arrangement of the second screen element. The first and second subgrid attachment arrangements may include elongated attachment members and the first and second screen element attachment arrangements may include attachment apertures that mate with the elongated attachment members thereby securely attaching the first and second screen elements to the first and second subgrids, respectively. A portion of the elongated attachment members may extend through the screen element attachment apertures and slightly above a first and second screen element screening surface. 
     The first and second screen elements each may include substantially parallel end portions and substantially parallel side edge portions substantially perpendicular to the end portions. The first and second screen elements may each include a first screen element support member and a second screen element support member orthogonal to the first screen element support member, the first screen element support member extending between the end portions and being approximately parallel to the side edge portions, the second screen element support member extending between the side edge portions and may be approximately parallel to the end portions. The first and second screen elements may each include a first series of reinforcement members substantially parallel to the side edge portions and a second series of reinforcement members substantially parallel to the end portions. The first and second screen elements may each include elongated screen surface elements running parallel to the end portions and forming the screening openings. The end portions, side edge portions, first and second support members, first and second series of reinforcement members may structurally stabilize screen surface elements and screening openings. 
     One of the first and second base supports may include fasteners that secure the multiple subgrids together, which fasteners may be clips and clip apertures that snap into place and securely attach subgrids together. 
     The screen assembly may include a first, a second, a third and a fourth screen element. The first series of grid openings may be eight openings formed by the first edge of the triangular end pieces, the triangular middle pieces, and the first mid support, the first base support and the central ridge. The second series of grid openings may be eight openings formed by the second edge of the triangular end pieces, the triangular middle pieces, the second mid support, the second base support and the central ridge. The first screen element may span four of the grid openings of the first series of grid openings and the second screen element may span the other four openings of the first series of grid openings. The third screen element may span four of the grid openings of the second series of grid openings and the fourth screen element may span the other four openings of the second series of grid openings. A central portion of the first, second, third and fourth screening element screening surfaces may slightly flex when subject to a load. The subgrid may be substantially rigid and may be a single thermoplastic injection molded piece. 
     According to an example embodiment of the present disclosure, a screen assembly is providing having a screen element including a screen element screening surface with screening openings and a subgrid including a grid framework with grid openings. The screen element spans the grid openings and is attached to a surface of the subgrid. Multiple subgrids are secured together to form the screen assembly and the screen assembly has a continuous screen assembly screening surface that includes multiple screen element screening surfaces. The screen element is a thermoplastic injection molded piece. 
     The screen assembly may also include a first thermoplastic injection molded screen element and a second thermoplastic injection molded screen element, and the grid framework may include a first and second grid framework forming a first grid opening and a second grid opening. The subgrid may include a ridge portion and a base portion, the first and second grid frameworks including first and second angular surfaces that peak at the ridge portion and extend downwardly from the peak portion to the base portion. The first and second screen elements may span the first and second angular surfaces, respectively. The first and second angular surfaces may include a subgrid attachment arrangement configured to securely mate with a screen element attachment arrangement. The subgrid attachment arrangement may include elongated attachment members and the screen element attachment arrangement may include apertures that mate with the elongated attachment members thereby securely attaching the screen elements to the subgrid. 
     The subgrid may be substantially rigid and may be a single thermoplastic injection molded piece. A section of the base portion may include a first and a second fastener that secure the subgrid to a third and a fourth fastener of another subgrid. The first and third fasteners may be clips and the second and fourth fasteners may be clip apertures. The clips may snap into clip apertures and securely attach the subgrid and then another subgrid together. 
     The subgrids may form a concave structure and the continuous screen assembly screening surface may be concave. The subgrids may form a flat structure and the continuous screen assembly screening surface may be flat. The subgrids may form a convex structure and the continuous screen assembly screening surface may be convex. 
     The screen assembly may be configured to form a predetermined concave shape when subjected to a compression force by a compression assembly of a vibratory screening machine against at least one side member of the vibratory screen assembly when placed in the vibratory screening machine. The predetermined concave shape may be determined in accordance with a shape of a surface of the vibratory screening machine. The screen assembly may have a mating surface mating the screen assembly to a surface of the vibratory screening machine, which mating surface may be rubber, metal (e.g., steel, aluminum, etc.), a composite material, a plastic material or any other suitable material. The screen assembly may include a mating surface configured to interface with a mating surface of a vibratory screening machine such that the screen assembly is guided into a fixed position on the vibratory screening machine. The mating surface may be formed in a portion of at least one subgrid. The screen assembly mating surface may be a notch formed in a corner of the screen assembly or a notch formed approximately in the middle of a side edge of the screen assembly. The screen assembly may have an arched surface configured to mate with a concave surface of the vibratory screening machine. The screen assembly may have a substantially rigid structure that does not substantially deflect when secured to the vibratory screening machine. The screen assembly may include a screen assembly mating surface configured such that it forms a predetermined concave shape when subjected to a compression force by a member of a vibratory screening machine. The screen assembly mating surface may be shaped such that it interfaces with a mating surface of the vibratory screening machine such that the screen assembly may be guided into a predetermined location on the vibratory screening machine. The screen assembly may include a load bar attached to an edge surface of the subgrid of the screen assembly. The load bar may be configured to distribute a load across a surface of the screen assembly. The screen assembly may be configured to form a predetermined concave shape when subjected to a compression force by a compression member of a vibratory screening machine against the load bar of the vibratory screen assembly. The screen assembly may have a concave shape and may be configured to deflect and form a predetermined concave shape when subjected to a compression force by a member of a vibratory screening machine. 
     A first set of the subgrids may be formed into center support frame assemblies having a first fastener arrangement. A second set of the subgrids may be formed into a first end support frame assembly having a second fastener arrangement. A third set of the subgrids may be formed into a second end support frame assembly having a third fastener arrangement. The first, second, and third fastener arrangements may secure the first and second end support frames to the center support assemblies. A side edge surface of the first end support frame assembly may form a first end of the screen assembly. A side edge surface of the second end support frame arrangement may form a second end of the screen assembly. An end surface of each of the first and second end support frame assemblies and center support frame assemblies may cumulatively form a first and a second side surface of the complete screen assembly. The first and second side surfaces of the screen assembly may be substantially parallel and the first and second end surfaces of the screen assembly may be substantially parallel and substantially perpendicular to the side surfaces of the screen assembly. The side surfaces of the screen assembly may include fasteners configured to engage at least one of a binder bar and a load distribution bar. The subgrids may include side surfaces such that when individual subgrids are secured together to form the first and second end support frame assemblies and the center support frame assembly that the first and second end support frame assemblies and the center support frame assembly each form a concave shape. The subgrids may include side surfaces shaped such that when individual subgrids are secured together to form the first and second end support frame assemblies and the center support frame assembly that the first and second end support frame assemblies and the center support frame assembly each form a convex shape. 
     The screen elements may be affixed to the subgrids by at least one of a mechanical arrangement, an adhesive, heat staking and ultrasonic welding. 
     According to an example embodiment of the present disclosure, a screen element is provided having: a screen element screening surface with screen surface elements forming a series of screening openings; a pair of substantially parallel end portions; a pair of substantially parallel side edge portions substantially perpendicular to the end portions; a first screen element support member; a second screen element support member orthogonal to the first screen element support member, the first screen element support member extending between the end portions and being approximately parallel to the side edge portions, the second screen element support member extending between the side edge portions and being approximately parallel to the end portions and substantially perpendicular to the side edge portions; a first series of reinforcement members substantially parallel to the side edge portions; and a second series of reinforcement members substantially parallel to the end portions. The screen surface elements run parallel to the end portions. The end portions, side edge portions, first and second support members, first and second series of reinforcement members structurally stabilize screen surface elements and screening openings, and the screen element is a single thermoplastic injection molded piece. 
     According to an example embodiment of the present disclosure, a screen element is provided having a screen element screening surface with screen surface elements forming a series of screening openings; a pair of substantially parallel end portions; and a pair of substantially parallel side edge portions substantially perpendicular to the end portions. The screen element is a thermoplastic injection molded piece. 
     The screen element may also have a first screen element support member; a second screen element support member orthogonal to the first screen element support member, the first screen element support member extending between the end portions and being approximately parallel to the side edge portions, the second screen element support member extending between the side edge portions and being approximately parallel to the end portions; a first series of reinforcement members substantially parallel to the side edge portions; and a second series of reinforcement members substantially parallel to the end portions. The screen surface elements may run parallel to the end portions. In certain embodiments, the screen surface elements may also be configured to run perpendicular to the end portions. The end portions, side edge portions, first and second support members, first and second series of reinforcement members may structurally stabilize screen surface elements and screening openings. 
     The screen element may also have a screen element attachment arrangement molded integrally with the screen element and configured to mate with a subgrid attachment arrangement. Multiple subgrids may form a screen assembly and the screen assembly may have a continuous screen assembly screening surface that includes multiple screen element screening surfaces. 
     According to an example embodiment of the present disclosure, a method for fabricating a screen assembly for screening materials is provided that includes: determining screen assembly performance specifications for the screen assembly; determining a screening opening requirement for a screen element based on the screen assembly performance specifications, the screen element including a screen element screening surface having screening openings; determining a screen configuration based on the screen assembly performance specifications, the screen configuration including having the screen elements arranged in at least one of flat configuration and a non-flat configuration; injection molding the screen elements with a thermoplastic material; fabricating a subgrid configured to support the screen elements, the subgrid having a grid framework with grid openings wherein at least one screen element spans at least one grid opening and is secured to a top surface of the subgrid, the top surface of each subgrid including at least one of a flat surface and a non-flat surface that receives the screen elements; attaching the screen elements to the subgrids; attaching multiple subgrid assemblies together to form end screen frames and center screen frames; attaching the end screen frames to the center screen frames to form a screen frame structure; attaching a first binder bar to a first end of the screen frame structure; and attaching a second binder bar to a second end of the screen frame structure to form the screen assembly, the screen assembly having a continuous screen assembly screening surface comprised of multiple screen element screening surfaces. 
     The screen assembly performance specifications may include at least one of dimensions, material requirements, open screening area, cut point, and capacity requirements for a screening application. A handle may be attached to the binder bar. A tag may be attached to the binder bar, which tag may include a performance description of the screen assembly. At least one of the screen element and the subgrid may be a single thermoplastic injection molded piece. The thermoplastic material may include a nanomaterial. The subgrid may include at least one base member having fasteners that mate with fasteners of other base members of other subgrids and secure the subgrids together. The fasteners may be clips and clip apertures that snap into place and securely attach the subgrids together. 
     According to an example embodiment of the present disclosure, a method for fabricating a screen assembly for screening materials is provided by injection molding a screen element with a thermoplastic material, the screen element including a screen element screening surface having screening openings; fabricating a subgrid that supports the screen element, the subgrid having a grid framework with grid openings, the screen element spanning at least one grid opening; securing the screen element to a top surface of the subgrid; and attaching multiple subgrid assemblies together to form the screen assembly, the screen assembly having a continuous screen assembly screening surface made of multiple screen element screening surfaces. The method may also include attaching a first binder bar to a first end of the screen assembly and attaching a second binder bar to a second end of the screen assembly. The first and second binder bars may bind the subgrids together. The binder bar may be configured to distribute a load across the first and second ends of the screen assembly. The thermoplastic material may include a nanomaterial. 
     According to an example embodiment of the present disclosure, a method for screening a material is provided by attaching a screen assembly to a vibratory screening machine, the screen assembly including a screen element having a series of screening openings forming a screen element screening surface and a subgrid including multiple elongated structural members forming a grid framework having grid openings. Screen elements span grid openings and are secured to a top surface of the subgrid. Multiple subgrids are secured together to form the screen assembly. The screen assembly has a continuous screen assembly screening surface comprised of multiple screen element screening surfaces. The screen element is a single thermoplastic injection molded piece. The material is screened using the screen assembly. 
     According to an example embodiment of the present disclosure, a method for screening a material is provided including attaching a screen assembly to a vibratory screening machine and forming a top screening surface of the screen assembly into a concave shape. The screen assembly includes a screen element having a series of screening openings forming a screen element screening surface and a subgrid including multiple elongated structural members forming a grid framework having grid openings. Screen elements span grid openings and are secured to a top surface of the subgrid. Multiple subgrids are secured together to form the screen assembly and the screen assembly has a continuous screen assembly screening surface comprised of multiple screen element screening surfaces. The screen element is a single thermoplastic injection molded piece. The material is screened using the screen assembly. 
     According to an example embodiment of the present disclosure, a screen assembly is provided, including: a screen element having a first adhesion arrangement; and a subgrid unit having a second adhesion arrangement. The first adhesion arrangement and the second adhesion arrangement may be different materials. At least one of the first adhesion arrangement and the second adhesion arrangement is excitable such that the screen element and the subgrid may be secured together. The screen element is a single thermoplastic injection molded piece. 
     The first adhesion arrangement may be a plurality of cavity pockets on a bottom surface of the screen element and the second adhesion arrangement may be a plurality of fusion bars a top surface of the subgrid. The screen element is micro molded and has screening openings between approximately 40 microns and approximately 1000 microns. The cavity pockets may be elongated pockets. The fusion bars may have a height slightly larger than a depth of the cavity pockets. The depth of the cavity pockets may be approximately 0.05 inches and the height of the fusion bars is approximately 0.056 inches. The fusion bars may have a width slightly smaller than a width of the cavity pockets. 
     The screen element may include thermoplastic polyurethane. The subgrid may include nylon. The screen assembly may include additional screen elements and subgrids secured together, wherein multiple subgrids are secured together. The screen element may have a plurality of screening openings being elongated slots with a width and a length, the width of the screening openings being approximately 43 microns to approximately 1000 microns between inner surfaces of each screen surface element. The screen element may be attached to the subgrid via laser welding. A weld between the screen element and the subgrid may include a mixture of materials from the screen element and the subgrid. 
     According to an example embodiment of the present disclosure, a screen assembly is provided, including: a screen element including a screen element screening surface having a series of screening openings; and a subgrid including multiple elongated structural members forming a grid framework having grid openings. The screen element spans at least one of the grid openings and is attached to a top surface of the subgrid. Multiple independent subgrids are secured together to form the screen assembly and the screen assembly has a continuous screen assembly screening surface having multiple screen element screening surfaces. The screen element includes substantially parallel end portions and substantially parallel side edge portions substantially perpendicular to the end portions. The screen element further includes a first screen element support member and a second screen element support member orthogonal to the first screen element support member, the first screen element support member extending between the end portions and being approximately parallel to the side edge portions, the second screen element support member extending between the side edge portions and being approximately parallel to the end portions. The screen element includes a first series of reinforcement members substantially parallel to the side edge portions, a second series of reinforcement members substantially parallel to the end portions. The screen element screening surface includes screen surface elements forming the screening openings. The end portions, side edge portions, first and second support members, first and second series of reinforcement members structurally stabilize screen surface elements and screening openings. The screen element is a single thermoplastic injection molded piece. The screen element includes a plurality of pocket cavities on a bottom surface of the screen element. The subgrid includes a plurality of fusion bars on the top surface of the subgrid. The plurality of fusion bars are configured to mate with the plurality of pocket cavities. 
     The screening openings may be elongated slots with a width and a length, the width of the screening openings being approximately 43 microns to approximately 1000 microns between inner surfaces of each screen surface element. The plurality of fusion bars may have a height slightly larger than a depth of the plurality of pocket cavities. The height of the plurality of fusion bars may be approximately 0.056 inches. The depth of the plurality of pocket cavities may be approximately 0.050 inches. Each of plurality of pocket cavities may have a width slightly larger than a width of each of the plurality of fusion bars. The plurality of fusion bars may be configured such that, when melted, a portion of the plurality of fusion bars fills the width of the plurality of pocket cavities. Material of the screen element may be fused with material of the subgrid. The screen element may be configured to allow a laser to pass through the screen element and contact the plurality of fusion bars. The laser may melt a portion of the plurality of fusion bars fusing the screen element to the subgrid. 
     The subgrid may be a single thermoplastic injection molded piece. The screen element may include a thermoplastic polyurethane material. The thermoplastic polyurethane may be at least one of a poly-ether based thermoplastic polyurethane and a polyester based thermoplastic polyurethane. The subgrid may include a nylon material. The fusion bars may include at least one of a carbon and a graphite material. The subgrid may include a screen element locator arrangement configured to locate a screen element upon the subgrid. The screen element may include a plurality of tapered counter bores on a top surface of the screen element along the side edge portions and the end portions between locator apertures of the locator arrangement. The fusion bars and the pocket cavities may be different materials. 
     The grid framework may include a first and second grid framework forming a first and a second grid opening, the screen elements including a first and a second screen element. The subgrid may include a ridge portion and a base portion, the first and second grid frameworks include first and second angular surfaces that peak at the ridge portion and extend downwardly from the peak portion to the base portion, wherein the first and second screen elements span the first and second angular surfaces, respectively. The screen assembly may include a secondary support framework spanning at least a portion of each grid opening. 
     According to an exemplary embodiment of the present invention a screen assembly is provided, including: a screen element including a screen element screening surface having a series of screening openings and a plurality of pocket cavities on a bottom surface of the screen element; and a subgrid including multiple elongated structural members forming a grid framework having grid openings and a plurality of fusion bars on a top surface of the subgrid. The screen element spans at least one grid opening and is secured to the top surface of the subgrid via fusing the plurality of fusion bars to the plurality of pocket cavities. Multiple subgrids are secured together to form the screen assembly and the screen assembly has a continuous screen assembly screening surface comprised of multiple screen element screening surfaces. The screen element is a single thermoplastic injection molded piece. The screen element in configured to allow a laser to pass through the screen element and contact the plurality of fusion bars. 
     The screening openings may be elongated slots with a width and a length, the width of the screening openings being approximately 43 microns to approximately 1000 microns between inner surfaces of each screen surface element. The screening openings may be elongated slots with a width and a length, the width of the screening openings being approximately 70 microns to approximately 180 microns between inner surfaces of each screen surface element. The screening openings may be elongated slots with a width and a length, the width of the screening openings being approximately 43 microns to approximately 106 microns between inner surfaces of each screen surface element. The screening openings may be elongated slots with a width and a length, the width being about 0.044 mm to about 4 mm and the length being about 0.088 mm to about 60 mm. 
     The subgrid may include substantially parallel triangular end pieces, triangular middle pieces substantially parallel to the triangular end pieces, a first and second mid support substantially perpendicular to the triangular end pieces and extending between the triangular end pieces, a first and second base support substantially perpendicular to the triangular end pieces and extending between the triangular end pieces and a central ridge substantially perpendicular to the triangular end pieces and extending between the triangular end pieces, a first edge of the triangular end pieces, the triangular middle pieces, the first mid support, the first base support and the central ridge form a first top surface of the subgrid having a first series of grid openings and a second edge of the triangular end pieces, the triangular middle pieces, the second mid support, the second base support and the central ridge form a second top surface of the subgrid having a second series of grid openings, the first top surface sloping from the central ridge to the first base support, the second top surface sloping from the central ridge to the second base support. A first and a second screen element may span the first series and second series of grid openings, respectively. 
     In exemplary embodiments of the present invention, a method of fabricating a screen assembly is provided, including: laser welding a screen element of a first material to a subgrid of a second material; and attaching multiple subgrids together to form the screen assembly. The first material and the second material are different materials. The first material and the second material are fused together at laser weld locations. 
     The screen assembly may have a first adhesion arrangement on a bottom surface of the screen element and the subgrid has a second adhesion arrangement on a top surface of the subgrid. The first adhesion arrangement may be a plurality of pocket cavities and the second adhesion arrangement is a plurality of fusion bars. The plurality of pocket cavities may be configured to mate with the plurality of fusion bars. 
     The method of fabricating a screen assembly may include locating the screen element upon the subgrid via location apertures in the screen element and location extensions on a top surface of the subgrid. The method for fabricating a screen assembly may include passing a laser through the screen element such that it contacts the plurality of fusion bars. The method for fabricating a screen assembly may include melting a portion of the plurality of fusion bars with the laser. The method for fabricating a screen assembly may include melting a portion of the first material with one of heat produced by the laser and heat transfer from the melted portions of the plurality of fusion bars. The method of fabricating a screen assembly may include removing the laser such that the melted portion of the first material and the melted portion of the fusion bars mix and return to a solid. 
     Example embodiments of the present disclosure are described in more detail below with reference to the appended Figures. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG.  1    is an isometric view of a screen assembly, according to an exemplary embodiment of the present invention. 
         FIG.  1 A  is an enlarged view of a break out portion of the screen assembly shown in  FIG.  1   . 
         FIG.  1 B  is a bottom isometric view of the screen assembly shown in  FIG.  1   . 
         FIG.  2    is an isometric top view of a screen element, according to an exemplary embodiment of the present invention. 
         FIG.  2 A  is a top view of the screen element shown in  FIG.  2   . 
         FIG.  2 B  is a bottom isometric view of the screen element shown in  FIG.  2   . 
         FIG.  2 C  is a bottom view of the screen element shown in  FIG.  2   . 
         FIG.  2 D  is an enlarged top view of a break out portion of the screen element shown in  FIG.  2   . 
         FIG.  3    is a top isometric view of an end subgrid, according to an exemplary embodiment of the present invention. 
         FIG.  3 A  is a bottom isometric view of the end subgrid shown in  FIG.  3   . 
         FIG.  4    is a top isometric view of a center subgrid, according to an exemplary embodiment of the present invention. 
         FIG.  4 A  is a bottom isometric view of the center subgrid shown in  FIG.  4   . 
         FIG.  5    is a top isometric view of a binder bar, according to an exemplary embodiment of the present invention. 
         FIG.  5 A  is a bottom isometric view of the binder bar shown in  FIG.  5   . 
         FIG.  6    is an isometric view of a screen subassembly, according to an exemplary embodiment of the present invention. 
         FIG.  6 A  is an exploded view of the subassembly shown in  FIG.  6   . 
         FIG.  7    is a top view of the screen assembly shown in  FIG.  1   . 
         FIG.  7 A  is an enlarged cross-section of Section A-A of the screen assembly shown in  FIG.  7   . 
         FIG.  8    is a top isometric view of a screen assembly partially covered with screen elements, according to an exemplary embodiment of the present invention. 
         FIG.  9    is an exploded isometric view of the screen assembly shown in  FIG.  1   . 
         FIG.  10    is an exploded isometric view of an end subgrid showing screen elements prior to attachment to the end subgrid, according to an exemplary embodiment of the present invention. 
         FIG.  10 A  is an isometric view of the end subgrid shown in  FIG.  10    having the screen elements attached thereto. 
         FIG.  10 B  is a top view of the end subgrid shown in  FIG.  10 A . 
         FIG.  10 C  is a cross-section of Section B-B of the end subgrid shown in  FIG.  10 A . 
         FIG.  11    is an exploded isometric view of a center subgrid showing screen elements prior to attachment to the center subgrid, according to an exemplary embodiment of the present invention. 
         FIG.  11 A  is an isometric view of the center subgrid shown in  FIG.  11    having the screen elements attached thereto. 
         FIG.  12    is an isometric view of a vibratory screening machine having screen assemblies with concave screening surfaces installed thereon, according to an exemplary embodiment of the present invention. 
         FIG.  12 A  is an enlarged isometric view of the discharge end of the vibratory screening machine shown in  FIG.  12   . 
         FIG.  12 B  is a front view of the vibratory screening machine shown in  FIG.  12   . 
         FIG.  13    is an isometric view of a vibratory screening machine with a single screening surface having screen assemblies with concave screening surfaces installed thereon, according to an exemplary embodiment of the present invention. 
         FIG.  13 A  is a front view of the vibratory screening machine shown in  FIG.  13   . 
         FIG.  14    is a front view of a vibratory screening machine having two separate concave screening surfaces with preformed screen assemblies installed upon the vibratory screening machine, according to an exemplary embodiment of the present invention. 
         FIG.  15    is a front view of a vibratory screening machine having a single screening surface with a preformed screen assembly installed upon the vibratory screening machine, according to an exemplary embodiment of the present invention. 
         FIG.  16    is an isometric view of an end support frame subassembly, according to an exemplary embodiment of the present invention. 
         FIG.  16 A  is an exploded isometric view of the end support frame subassembly shown in  FIG.  16   . 
         FIG.  17    is an isometric view of a center support frame subassembly, according to an exemplary embodiment of the present invention. 
         FIG.  17 A  is an exploded isometric view of the center support frame subassembly shown in  FIG.  17   . 
         FIG.  18    is an exploded isometric view of a screen assembly, according to an exemplary embodiment of the present invention. 
         FIG.  19    is a top isometric view of a flat screen assembly, according to an exemplary embodiment of the present invention. 
         FIG.  20    is a top isometric view of a convex screen assembly, according to an exemplary embodiment of the present invention. 
         FIG.  21    is an isometric view of a screen assembly having pyramidal shaped subgrids, according to an exemplary embodiment of the present invention. 
         FIG.  21 A  is an enlarged view of section D of the screen assembly shown in  FIG.  21   . 
         FIG.  22    is a top isometric view of a pyramidal shaped end subgrid, according to an exemplary embodiment of the present invention. 
         FIG.  22 A  is a bottom isometric view of the pyramidal shaped end subgrid shown in  FIG.  22   . 
         FIG.  23    is a top isometric view of a pyramidal shaped center subgrid, according to an exemplary embodiment of the present invention. 
         FIG.  23 A  is a bottom isometric view of the pyramidal shaped center subgrid shown in  FIG.  23   . 
         FIG.  24    is an isometric view of a pyramidal shaped subassembly, according to an exemplary embodiment of the present invention. 
         FIG.  24 A  is an exploded isometric view of the pyramidal shaped subassembly shown in  FIG.  24   . 
         FIG.  24 B  is an exploded isometric view of a pyramidal shaped end subgrid showing screen elements prior to attachment to the pyramidal shaped end subgrid. 
         FIG.  24 C  is an isometric view of the pyramidal shaped end subgrid shown in  FIG.  24 B  having the screen elements attached thereto. 
         FIG.  24 D  is an exploded isometric view of a pyramidal shaped center subgrid showing screen elements prior to attachment to the pyramidal shaped center subgrid, according to an exemplary embodiment of the present invention. 
         FIG.  24 E  is an isometric view of the pyramidal shaped center subgrid shown in  FIG.  24 D  having the screen elements attached thereto. 
         FIG.  25    is a top view of a screen assembly having pyramidal shaped subgrids, according to an exemplary embodiment of the present invention. 
         FIG.  25 A  is a cross-section view of Section C-C of the screen assembly shown in  FIG.  25   . 
         FIG.  25 B  is an enlarged view of Section C-C shown in  FIG.  25 A . 
         FIG.  26    is an exploded isometric view of a screen assembly having pyramidal shaped and flat subassemblies, according to an exemplary embodiment of the present invention. 
         FIG.  27    is an isometric view of a vibratory screening machine with two screening surfaces having assemblies with concave screening surfaces installed thereon wherein the screen assemblies include pyramidal shaped and flat subassemblies, according to an exemplary embodiment of the present invention. 
         FIG.  28    is a top isometric view of a screen assembly having pyramidal shaped and flat subgrids without screen elements, according to an exemplary embodiment of the present invention. 
         FIG.  29    is a top isometric view of the screen assembly shown in  FIG.  28    where the subgrids are partially covered with screen elements. 
         FIG.  30    is a front view of a vibratory screening machine with two screening surfaces having assemblies with concave screening surfaces installed thereon where the screen assemblies include pyramidal shaped and flat subgrids, according to an exemplary embodiment of the present invention. 
         FIG.  31    is a front view of a vibratory screening machine with a single screen surface having an assembly with a concave screening surface installed thereon where the screen assembly includes pyramidal shaped and flat subgrids, according to an exemplary embodiment of the present invention. 
         FIG.  32    is a front view of a vibratory screening machine with two screening surfaces having preformed screen assemblies with flat screening surfaces installed thereon where the screen assemblies include pyramidal shaped and flat subgrids, according to an exemplary embodiment of the present invention. 
         FIG.  33    is a front view of a vibratory screening machine with a single screening surface having a preformed screen assembly with a flat screening surface installed thereon where the screen assembly includes pyramidal shaped and flat subgrids, according to an exemplary embodiment of the present invention. 
         FIG.  34    is an isometric view of the end subgrid shown in  FIG.  3    having a single screen element partially attached thereto, according to an exemplary embodiment of the present invention. 
         FIG.  35    is an enlarged view of break out Section E of the end subgrid shown in  FIG.  34   . 
         FIG.  36    is an isometric view of a screen assembly having pyramidal shaped subgrids in a portion of the screen assembly, according to an exemplary embodiment of the present invention. 
         FIG.  37    is a flow chart of a screen assembly fabrication, according to an exemplary embodiment of the present invention. 
         FIG.  38    is a flow chart of a screen assembly fabrication, according to an exemplary embodiment of the present invention. 
         FIG.  39    an isometric view of a vibratory screening machine having a single screen assembly with a flat screening surface installed thereon with a portion of the vibratory machine cut away showing the screen assembly, according to an exemplary embodiment of the present invention. 
         FIG.  40    is an isometric top view of an individual screen element, according to an exemplary embodiment of the present invention. 
         FIG.  40 A  is an isometric top view of a screen element pyramid, according to an exemplary embodiment of the present invention. 
         FIG.  40 B  is an isometric top view of four of the screen element pyramids shown in  FIG.  40 A . 
         FIG.  40 C  is an isometric top view of an inverted screen element pyramid, according to an exemplary embodiment of the present invention. 
         FIG.  40 D  is a front view of the screen element shown in  FIG.  40 C . 
         FIG.  40 E  is an isometric top view of a screen element structure, according to an exemplary embodiment of the present invention. 
         FIG.  40 F  is a front view of the screen element structure shown in  FIG.  40 E . 
         FIGS.  41  to  43    are front cross-sectional profile views of screen elements, according to exemplary embodiments of the present invention. 
         FIG.  44    is an isometric top view of a prescreening structure with prescreen assemblies according to an exemplary embodiment of the present invention. 
         FIG.  44 A  is an isometric top view of the prescreen assembly shown in  FIG.  44   , according to an exemplary embodiment of the present invention. 
         FIG.  45    is a top view of a screen element above a portion of a subgrid, according to an exemplary embodiment of the present invention. 
         FIG.  45 A  is an exploded side view of cross section A-A showing the screen element above the portion of the subgrid of  FIG.  45   . 
         FIG.  45 B  is a side view of cross section A-A of the screen element and the portion of the subgrid of  FIG.  45    prior to attachment of the screen element to the subgrid, according to an exemplary embodiment of the present invention. 
         FIG.  45 C  is an enlarged view of section A of  FIG.  45 B . 
         FIG.  45 D  is a side view of cross section A-A of the screen element and the portion of the subgrid of  FIG.  45    after attachment of the screen element to the subgrid, according to an exemplary embodiment of the present invention. 
         FIG.  45 E  is an enlarged view of section B of  FIG.  45 D . 
         FIG.  46    is side cross section view of a portion of a screen element and a portion of a subgrid, according to an exemplary embodiment of the present invention. 
         FIG.  47    is a top isometric view of a portion of a screen assembly, according to an exemplary embodiment of the present invention. 
         FIG.  48    is an isometric top view of a screen element, according to an exemplary embodiment of the present invention. 
         FIG.  48 A  is a top view of the screen element shown in  FIG.  48   . 
         FIG.  48 B  is a bottom isometric view of the screen element shown in  FIG.  48   . 
         FIG.  48 C  is a bottom view of the screen element shown in  FIG.  48   . 
         FIG.  49    is a top isometric view of an end subgrid, according to an exemplary embodiment of the present invention. 
         FIG.  49 A  is a bottom isometric view of the end subgrid shown in  FIG.  49   . 
         FIG.  50    is a top isometric view of a center subgrid, according to an exemplary embodiment of the present invention. 
         FIG.  50 A  is a bottom isometric view of the center subgrid shown in  FIG.  50   . 
         FIG.  51    is an exploded isometric view of an end subgrid showing screen elements prior to attachment to the end subgrid, according to an exemplary embodiment of the present invention. 
         FIG.  51 A  is an isometric view of the end subgrid shown in  FIG.  51    having the screen elements attached thereto. 
         FIG.  52    is an exploded isometric view of a center subgrid showing screen elements prior to attachment to the center subgrid, according to an exemplary embodiment of the present invention. 
         FIG.  52 A  is an isometric view of the center subgrid shown in  FIG.  52    having the screen elements attached thereto. 
         FIG.  53    is a top isometric view of a pyramidal shaped end subgrid, according to an exemplary embodiment of the present invention. 
         FIG.  53 A  is a bottom isometric view of the pyramidal shaped end subgrid shown in  FIG.  53   . 
         FIG.  54    is a top isometric view of a pyramidal shaped center subgrid, according to an exemplary embodiment of the present invention. 
         FIG.  54 A  is a bottom isometric view of the pyramidal shaped center subgrid shown in  FIG.  54   . 
         FIG.  55    is an exploded isometric view of a pyramidal shaped end subgrid showing screen elements prior to attachment to the pyramidal shaped end subgrid, according to an exemplary embodiment of the present invention. 
         FIG.  55 A  is an isometric view of the pyramidal shaped end subgrid shown in  FIG.  55    having the screen elements attached thereto. 
         FIG.  56    is an exploded isometric view of a pyramidal shaped center subgrid showing screen elements prior to attachment to the pyramidal shaped center subgrid, according to an exemplary embodiment of the present invention. 
         FIG.  56 A  is an isometric view of the pyramidal shaped center subgrid shown in  FIG.  56    having the screen elements attached thereto. 
         FIG.  57    is an isometric view of the end subgrid shown in  FIG.  50    having a single screen element partially attached thereto, according to an exemplary embodiment of the present invention. 
         FIG.  57 A  is an enlarged view of section A of the end subgrid shown in  FIG.  57   . 
         FIG.  58    is a top isometric view of a portion of a screen assembly, according to an exemplary embodiment. 
         FIG.  59    is a top isometric view of an end subgrid, according to an exemplary embodiment. 
         FIG.  59 A  is a bottom isometric view of the end subgrid shown in  FIG.  59   . 
         FIG.  60    is a top isometric view of a center subgrid, according to an exemplary embodiment. 
         FIG.  60 A  is a bottom isometric view of the center subgrid shown in  FIG.  60   . 
         FIG.  61    is an exploded isometric view of an end subgrid showing screen elements prior to attachment to the end subgrid, according to an exemplary embodiment. 
         FIG.  61 A  is an isometric view of the end subgrid shown in  FIG.  61    having the screen elements attached thereto, according to an exemplary embodiment. 
         FIG.  62    is an exploded isometric view of a center subgrid showing screen elements prior to attachment to the center subgrid, according to an exemplary embodiment. 
         FIG.  62 A  is an isometric view of the center subgrid shown in  FIG.  62    having the screen elements attached thereto, according to an exemplary embodiment. 
         FIG.  63    is a top isometric view of a pyramidal shaped end subgrid, according to an exemplary embodiment. 
         FIG.  63 A  is a bottom isometric view of the pyramidal shaped end subgrid shown in  FIG.  63   . 
         FIG.  63 B  illustrates an isometric view of clip  42  of  FIGS.  3  and  3 A , according to an embodiment. 
         FIG.  63 C  illustrates an isometric view of clip  142  of  FIGS.  59 - 62 A , according to an embodiment. 
         FIG.  63 D  illustrates an isometric view of clip  242  of  FIGS.  63  and  63 A , according to an embodiment. 
         FIG.  64    is a top isometric view of an end subgrid, according to an exemplary embodiment. 
         FIG.  64 A  is a bottom isometric view of the end subgrid shown in  FIG.  64   . 
         FIG.  65    is a top isometric view of a center subgrid, according to an exemplary embodiment. 
         FIG.  65 A  is a bottom isometric view of the center subgrid shown in  FIG.  65   . 
         FIG.  66    is an isometric top view of a screen element, according to an exemplary embodiment of the present invention. 
         FIG.  66 A  is a top view of the screen element shown in  FIG.  66   . 
         FIG.  66 B  is a bottom isometric view of the screen element shown in  FIG.  66   . 
         FIG.  66 C  is a bottom view of the screen element shown in  FIG.  66   . 
         FIG.  67    is an exploded isometric view of an end subgrid showing a screen element prior to attachment to the end subgrid, according to an exemplary embodiment. 
         FIG.  67 A  is an isometric view of the end subgrid shown in  FIG.  67    having the screen element attached thereto, according to an exemplary embodiment. 
         FIG.  68    is an exploded isometric view of a center subgrid showing a screen element prior to attachment to the center subgrid, according to an exemplary embodiment. 
         FIG.  68 A  is an isometric view of the center subgrid shown in  FIG.  68    having the screen element attached thereto, according to an exemplary embodiment. 
         FIG.  69    is an isometric view of a screen assembly having pyramidal shaped subgrids, according to an exemplary embodiment of the present invention. 
         FIG.  69 A  is an enlarged view of section D of the screen assembly shown in  FIG.  69   . 
         FIG.  70    is a reproduction of  FIG.  66 C , illustrating a bottom view of a screen element, for comparison with the screen element of  FIG.  70 A . 
         FIG.  70 A  is a bottom view of a screen element having smaller features than the screen element of  FIGS.  70  and  66   . 
         FIG.  71    is a reproduction of  FIG.  65   , illustrating a top isometric view of a center subgrid, for comparison with the center subgrid of  FIG.  71 A . 
         FIG.  71 A  is a side isometric view of a center subgrid, according to an embodiment. 
         FIG.  71 B  is an enlarged view of region “A” of  FIG.  71 A , according to an embodiment. 
         FIG.  71 C  is a top down view of the center subgrid of  FIG.  71 A , according to an embodiment. 
         FIG.  71 D  is a side view of the center subgrid of  FIG.  71 A , according to an embodiment. 
         FIG.  71 E  illustrates features of a screen element in comparison with support features of an end subgrid, according to an embodiment. 
         FIG.  71 F  illustrates features of a further screen element in comparison with support features of a further end subgrid, according to an embodiment. 
         FIG.  72    illustrates a pyramidal shaped end subgrid similar to the pyramidal shaped end subgrid of  FIG.  63   , for comparison with the pyramidal shaped end subgrid of  FIG.  72 A . 
         FIG.  72 A  illustrates a pyramidal shaped end subgrid having a higher linear density of structural features than the  72 , according to an embodiment. 
         FIG.  72 B  illustrates features of a screen element in comparison with support features of a pyramidal shaped end subgrid, according to an embodiment. 
         FIG.  72 C  illustrates features of a further screen element in comparison with support features of a further pyramidal shaped end subgrid, according to an embodiment. 
         FIG.  73    illustrates a top-down view of a screen element, previously illustrated in  FIGS.  70 A,  71 F, and  72 C , in which a first cross section direction A-A and a second cross section direction C-C is defined, according to an embodiment. 
         FIG.  73 A  illustrates a first cross section, defined by the first cross section direction A-A of  FIG.  73   , according to an embodiment. 
         FIG.  73 B  illustrates an enlarged view of the first cross section illustrated in  FIG.  73 A , according to an embodiment. 
         FIG.  73 C  illustrates a second cross section of the screen element of  FIG.  73    defined by the second cross section direction C-C of  FIG.  73   , according to an embodiment. 
         FIG.  73 D  illustrates an enlarged view of the second cross section illustrated in  FIG.  73 C , according to an embodiment. 
         FIG.  74    illustrates a top-down view of the center screen subassembly similar to center screen subassembly of  FIG.  68 A , in which a cross section direction A-A is defined, according to an embodiment. 
         FIG.  74 A  illustrates a side view of the center screen subassembly of  FIG.  74   , according to an embodiment. 
         FIG.  74 B  illustrates a cross section, defined by the cross section direction A-A of  FIG.  74   , according to an embodiment. 
         FIG.  74 C  illustrates a first enlarged view of a first portion of the cross section of center screen subassembly of  FIG.  74 B , according to an embodiment. 
         FIG.  74 D  illustrates a second enlarged view of a second portion of the cross section of center screen subassembly of  FIG.  74 C , according to an embodiment. 
         FIG.  75 A  illustrates a screen assembly including screen elements that are configured to be attached to rectangular regions formed by a grid framework, according to an embodiment. 
         FIG.  75 B  illustrates top perspective view of a grid framework to which screen elements may be attached to form a screen assembly, according to an embodiment. 
         FIG.  75 C  illustrates a bottom perspective view of the grid framework of  FIG.  75 B , according to an embodiment. 
         FIG.  76    illustrates screen elements directly attached to a plate structure without the need to first attach the screen elements to subgrids, according to an embodiment. 
         FIG.  76 A  illustrates screen elements configured to be directly attached to a punched plate, according to an embodiment. 
         FIG.  76 B  illustrates screen elements configured to be directly attached to a corrugated punched plate, according to an embodiment. 
         FIG.  76 C  illustrates a frame having pockets to accommodate screen elements, according to an embodiment. 
         FIG.  77 A  illustrates an embodiment fusion bar that may serve as a location member, according to an embodiment. 
         FIG.  77 B  illustrates an embodiment cavity pocket that may serve as a location aperture, according to an embodiment. 
         FIG.  77 C  illustrates alignment of the fusion bar of  FIG.  77 A  with the cavity pocket of  FIG.  77 B . 
         FIG.  78 A  illustrates a side view of a compression assembly applying a compressive force to a screen assembly via a binder bar, according to an embodiment. 
         FIG.  78 B  illustrates a first perspective view of the binder bar of  FIG.  78 A , according to an embodiment. 
         FIG.  78 C  illustrates a second perspective view of the binder bar of  FIG.  78 A , according to an embodiment. 
         FIG.  78 D  illustrates an end view of the binder bar of  FIG.  78 A , according to an embodiment. 
         FIG.  78 E  illustrates a screen assembly installed in a vibratory screening machine and held by compressive forces generated by a compression assembly, according to an embodiment. 
         FIG.  79    illustrates an edge view of a surface of an uncompressed screen assembly, having a first radius of curvature, positioned over a mating surface of a vibratory screening machine having a second radius of curvature, according to an embodiment. 
         FIG.  80 A  illustrates a top view of a circular screen assembly, according to an embodiment. 
         FIG.  80 B  illustrates a perspective top view of the circular screen assembly of  FIG.  80 A , according to an embodiment. 
         FIG.  80 C  illustrates a perspective bottom view of the circular screen assembly of  FIG.  80 A , according to an embodiment. 
         FIG.  80 D  illustrates a top view of structural support components for a circular screen assembly, according to an embodiment. 
         FIG.  80 E  illustrates a top view of an example subgrid that may be combined with other similar subgrids to form a screen assembly, according to an embodiment. 
         FIG.  80 F  illustrates a top view of three subgrids that are combined in a staggered arrangement, according to an embodiment. 
         FIG.  80 G  illustrates a cross-sectional view of the staggered arrangement of subgrids shown in  FIG.  80 F , according to an embodiment. 
         FIG.  80 H  illustrates a triangular arrangement of subgrids used to generate a triangular screen assembly, according to an embodiment. 
         FIG.  80 I  illustrates a triangular screen assembly including a triangular support frame, according to an embodiment. 
         FIG.  80 J  illustrates an enlarged view of the triangular screen assembly of  FIG.  80 I , according to an embodiment. 
         FIG.  81    illustrates a top view of a screen element with various regions that may be laser welded to an underlying subgrid, according to an embodiment. 
         FIG.  82    illustrates a vibrational amplitude profile of a screen element that is partially bonded to a subgrid, according to an embodiment. 
         FIG.  83    illustrates an example attrition screening machine, according to an embodiment. 
         FIG.  84 A  illustrates a perspective exploded view of a screen assembly that is configured to facilitate screen de-blinding, according to an embodiment. 
         FIG.  84 B  illustrates an assembled view of the screen assembly of  FIG.  84 A , according to an embodiment. 
         FIG.  85 A  illustrates a perspective view of a support frame having a single internal support structure forming two internal compartments, according to an embodiment. 
         FIG.  85 B  illustrates a perspective view of a support frame having three internal support structures forming four internal compartments, according to an embodiment. 
         FIG.  85 C  illustrates a perspective view of a support frame having two crossed internal support structures forming four internal compartments, according to an embodiment. 
         FIG.  85 D  illustrates a perspective view of a support frame having four internal support structures forming eight internal compartments, according to an embodiment. 
         FIG.  85 E  illustrates a top view of a screen assembly having support frames and unsecured objects, according to an embodiment. 
         FIG.  86    is a flowchart illustrating a method of manufacturing a screening apparatus, according to an embodiment. 
         FIG.  87 A  illustrates a top perspective view of a screening assembly and a plug that may be installed in a damaged area of the screening assembly, according to an embodiment. 
         FIG.  87 B  illustrates the plug and screen assembly of  FIG.  87 A  with the plug in an installed configuration, according to an embodiment. 
         FIG.  88 A  illustrates a top perspective view of the plug of  FIGS.  87 A and  87 B , according to an embodiment. 
         FIG.  88 B  illustrates a bottom perspective view of the plug of  FIGS.  87 A and  87 B , according to an embodiment. 
         FIG.  89    illustrates an exploded view of the screening assembly and plug of  FIGS.  87 A and  87 B , according to an embodiment. 
         FIG.  90 A  illustrates a bottom perspective view of the plug and screen assembly of  FIGS.  87 A and  87 B  with the plug in an installed configuration, according to an embodiment. 
         FIG.  90 B  illustrates a bottom view of the plug and screen assembly of  FIGS.  87 A and  87 B  with the plug in an installed configuration, according to an embodiment. 
         FIG.  91 A  illustrates an exploded view of a screening assembly having a subgrid and a replaceable screen element, according to an embodiment. 
         FIG.  91 B  illustrates the screening assembly of  FIG.  91 A  with the replaceable screen element and the subgrid in an installed configuration, according to an embodiment. 
         FIG.  92 A  illustrates a perspective bottom view of a screening element having attachment arrangements configured as hooks, according to an embodiment. 
         FIG.  92 B  illustrates a close-up bottom perspective view of the screening element of  FIG.  92 A  showing details of the hooks, according to an embodiment. 
         FIG.  93 A  illustrates a top perspective view of a subgrid having hook apertures, according to an embodiment. 
         FIG.  93 B  illustrates a bottom view of the subgrid of  FIG.  93 A , according to an embodiment. 
         FIG.  94    illustrates close-up exploded view of the screening assembly of  FIG.  91 A  having a subgrid and a replaceable screen element, according to an embodiment. 
         FIG.  95 A  illustrates a bottom perspective view of the screening assembly of  FIG.  91 B  having a subgrid and a replaceable screen element in an installed configuration, according to an embodiment. 
         FIG.  95 B  illustrates a close-up bottom view of the screening assembly of  FIG.  95 A  having a subgrid and a replaceable screen element in an installed configuration, according to an embodiment. 
         FIG.  96 A  illustrates a top perspective exploded view of a three-piece screening assembly, according to an embodiment. 
         FIG.  96 B  illustrates a top perspective exploded view of the three-piece screening assembly of  FIG.  96 A  in which a screening element has been attached to a top subgrid, according to an embodiment. 
         FIG.  96 C  illustrates a top perspective view of the screening assembly of  FIGS.  96 A and  96 B  in an installed configuration, according to an embodiment. 
         FIG.  97 A  illustrates a top perspective view of the top subgrid of  FIGS.  96 A to  96 C , according to an embodiment. 
         FIG.  97 B  illustrates a bottom perspective view of the top subgrid of  FIGS.  96 A to  96 C , according to an embodiment. 
         FIG.  97 C  illustrates a screening sub-assembly including a screening element attached to a top subgrid, according to an embodiment. 
         FIG.  98 A  illustrates a top perspective view of the bottom subgrid of  FIGS.  96 A to  96 C , according to an embodiment. 
         FIG.  98 B  illustrates a bottom perspective view of the bottom subgrid of  FIG.  98 A , according to an embodiment. 
         FIG.  99 A  illustrates a bottom perspective exploded view of the three-piece screening assembly of  FIG.  96 B  in which a screening element has been attached to a top subgrid, according to an embodiment. 
         FIG.  99 B  illustrates a bottom perspective view of the screening assembly of  FIGS.  96 A to  96 C and  99 A  in an installed configuration, according to an embodiment. 
         FIG.  100 A  illustrates a top view of a screening element that includes screening openings having rounded corners, according to an embodiment. 
         FIG.  100 B  illustrates a side view of the screening element of  FIG.  100 A , according to an embodiment. 
         FIG.  100 C  illustrates a top exploded view of a surface region of the screening element of  FIG.  100 A  showing screening openings having rounded corners, according to an embodiment. 
         FIG.  101 A  illustrates a top view of a screening element that includes transversely aligned screening openings, according to an embodiment. 
         FIG.  101 B  illustrates an exploded top view of a portion of the screening element of  FIG.  101 A  showing details of transversely aligned screening openings, according to an embodiment. 
         FIG.  101 C  illustrates a top view of a screening element that includes longitudinally aligned screening openings, according to an embodiment. 
         FIG.  101 D  illustrates an exploded top view of a portion of the screening element of  FIG.  101 C  showing details of longitudinally aligned screening openings, according to an embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     Embodiments of the present invention provide a screen assembly that includes injection molded screen elements that are mated to a subgrid. Multiple subgrids are securely fastened to each other to form the vibratory screen assembly, which has a continuous screening surface and is configured for use on a vibratory screening machine. The entire screen assembly structure is configured to withstand rigorous loading conditions encountered when mounted and operated on a vibratory screening machine. Injection molded screen elements provide for many advantages in screen assembly manufacturing and vibratory screening applications. In certain embodiments of the present invention, screen elements are injection molded using a thermoplastic material. In certain embodiments of the present invention, screen elements may have a first adhesion arrangement configured to mate with a second adhesion arrangement on a subgrid. The first and second adhesion arrangements may include different materials and may be configured such that screen elements may be fused to the subgrid via laser welding. The first adhesion arrangement may be a plurality of pocket cavities and the second adhesion arrangement may be a plurality of fusion bars, which may be configured to melt when subjected to a laser. Screen elements may include a thermoplastic polyurethane, which may be polyester based, polycarbonate based, or poly-ether based. Embodiments of the present invention include screen elements secured to subgrids via a hardened mixture of separate materials. Embodiments of the present invention include methods of fabricating a screen assembly by fusing screen elements to subgrids via laser welding and attaching multiple subgrids together to form the screen assembly. 
     Embodiments of the present invention provide injection molded screen elements that are of a practical size and configuration for manufacture of vibratory screen assemblies and for use in vibratory screening applications. Several important considerations have been taken into account in the configuration of individual screen elements. Screen elements are provided that: are of an optimal size (large enough for efficient assembly of a complete screen assembly structure yet small enough to injection mold (micro-mold in certain embodiments) extremely small structures forming screening openings while avoiding freezing (i.e., material hardening in a mold before completely filling the mold)); have optimal open screening area (the structures forming the openings and supporting the openings are of a minimal size to increase the overall open area used for screening while maintaining, in certain embodiments, very small screening openings necessary to properly separate materials to a specified standard); have durability and strength, can operate in a variety of temperature ranges; are chemically resistant; are structural stable; are highly versatile in screen assembly manufacturing processes; and are configurable in customizable configurations for specific applications. 
     Embodiments of the present invention provide screen elements that are fabricated using extremely precise injection molding. The larger the screen element the easier it is to assemble a complete vibratory screen assembly. Simply put, the fewer pieces there are to put together, the easier the system will be to put together. However, the larger the screen element, the more difficult it is to injection mold extremely small structures, i.e. the structures forming the screening openings. It is important to minimize the size of the structures forming the screening openings so as to maximize the number of screening openings on an individual screen element and thereby optimize the open screening area for the screening element and thus the overall screen assembly. In certain embodiments, screen elements are provided that are large enough (e.g., one inch by one inch, one inch by two inches, two inches by three inches, etc.) to make it practical to assemble a complete screen assembly screening surface (e.g., two feet by three feet, three feet by four feet, etc.). The relatively “small size” (e.g., one inch by one inch, one inch by two inches, two inches by three inches, etc.) is fairly large when micro-molding extremely small structural members (e.g., opening sizes and structural members as small as 43 microns). The larger the size of the overall screen element and the smaller the size of the individual structural members forming the screening openings, the more prone the injection molding process is to errors such as freezing. Thus, the size of the screen elements must be practical for screen assembly manufacture while at the same time small enough to eliminate problems such as freezing when micro-molding extremely small structures. Sizes of screening elements may vary based on the material being injection molded, the size of the screening openings required and the overall open screening area desired. 
     Open screening area is a critical feature of vibratory screen assemblies. The average usable open screening area (i.e., actual open area after taking into account the structural steel of support members and bonding materials) for traditional 100 mesh to 200 mesh wire screen assemblies may be in the range of 16%. Specific embodiments of the present invention (e.g., screening assemblies with constructions described herein and having 100 mesh to 200 mesh screen openings) provide screen assemblies in the same range having a similar actual open screening areas. Traditional screens, however, blind fairly quickly in the field which results in the actual opening screening area being reduced fairly quickly. It is not uncommon for traditional metal screens to blind within the first 24 hours of use and to have the actual open screening area reduced by 50%. Traditional wire assemblies also frequently fail as a result of wires being subjected to vibratory forces which place bending loads of the wires. Injection molded screen assemblies, according to embodiments of the present invention, in contrast, are not subject to extensive blinding (thereby maintaining a relatively constant actual open screening area) and rarely fail because of the structural stability and configuration of the screen assembly, including the screen elements and subgrid structures. In fact, screen assemblies according to embodiments of the present invention have extremely long lives and may last for long periods of time under heaving loading. Screen assemblies according to the present invention have been tested for months under rigorous conditions without failure or blinding whereas traditional wire assemblies were tested under the same conditions and blinded and failed within days. As more fully discussed herein, traditional thermoset type assemblies could not be used in such applications. 
     In embodiments of the present invention a thermoplastic is used to injection mold screen elements. As opposed to thermoset type polymers, which frequently include liquid materials that chemically react and cure under temperature, use of thermoplastics is often simpler and may be provided, e.g., by melting a homogeneous material (often in the form of solid pellets) and then injection molding the melted material. Not only are the physical properties of thermoplastics optimal for vibratory screening applications but the use of thermoplastic liquids provides for easier manufacturing processes, especially when micro-molding parts as described herein. The use of thermoplastic materials in the present invention provides for excellent flexure and bending fatigue strength and is ideal for parts subjected to intermittent heavy loading or constant heavy loading as is encountered with vibratory screens used on vibratory screening machines. Because vibratory screening machines are subject to motion, the low coefficient of friction of the thermoplastic injection molded materials provides for optimal wear characteristics. Indeed, the wear resistance of certain thermoplastics is superior to many metals. Further, use of thermoplastics as described herein provides an optimal material when making “snap-fits” due to its toughness and elongation characteristics. The use of thermoplastics in embodiments of the present invention also provides for resistance to stress cracking, aging and extreme weathering. The heat deflection temperature of thermoplastics is in the range of 200° F. With the addition of glass fibers, this will increase to approximately 250° F. to approximately 300° F. or greater and increase rigidity, as measured by Flexural Modulus, from approximately 400,000 PSI to over approximately 1,000,000 PSI. All of these properties are ideal for the environment encountered when using vibratory screens on vibratory screening machines under the demanding conditions encounter in the field. 
     Embodiments of the present invention may incorporate various materials into subgrid units and/or the screen elements depending on the desired properties of the embodiments. Thermoplastic polyurethane (TPU) may be incorporated into embodiments of the present invention (e.g., screen elements), providing elasticity, transparency, and resistance to oil, grease, and abrasion. TPU also has high shear strength. These properties of TPU are beneficial when applied to embodiments of the present invention, which are subjected to high vibratory forces, abrasive materials and high load demands. Different types of TPU may be incorporated into embodiments depending on the material being screened. For example, polyester-based TPUs may be incorporated into screen assemblies used for oil and/or gas screening because the esters provide superior abrasion resistance, oil resistance, mechanical integrity, chemical resistance and adhesion strength. Poly-ether based TPUs may be incorporated into mining applications where hydrolysis resistance (a property of ether based TPUs) is important. Para-phenylene disocyanate (PPDI) may be incorporated into embodiments of the present invention. PPDI may provide high performance properties in a variety of screening applications. Materials for embodiments of the present invention may be selected or determined based upon a variety of factors, including performance properties of each material and costs associated with using the materials. 
     In embodiments of the present invention, materials for a screen element may be selected to have high temperature tolerance, chemical resistance, hydrolytic resistance, and/or abrasion resistance. Screen elements may incorporate materials, such as TPUs, providing the screen elements with a clear appearance. Clear screen elements may allow for efficient laser transmission through the screen elements for laser welding purposes. Subgrid materials may be different than the screen element material. In embodiments of the present invention, subgrids may be nylon. Subgrids may incorporate carbon or graphite. Different materials between screen elements and subgrids may be secured to each other via laser welding, which may provide a much stronger adhesion between the screen elements and the subgrids than alternative attachment methods. The stronger attachment of the screen element to the subgrid provides improved performance of the screen assemblies when subjected to the high vibratory forces of vibratory screening machines and the abrasive forces that occur on the surfaces of the screen elements during screening of materials. 
       FIG.  1    illustrates a screen assembly  10  for use with vibratory screening machines. Screen assembly  10  is shown having multiple screen elements  16  (See, e.g.,  FIGS.  2  and  2 A- 2 D ) mounted on subgrid structures. The subgrid structures include multiple independent end subgrid units  14  (See, e.g.,  FIG.  3   ) and multiple independent center subgrid units  18  (See, e.g.,  FIG.  4   ) that are secured together to form a grid framework having grid openings  50 . Each screen element  16  spans four grid openings  50 . Although screen element  16  is shown as a unit covering four grid openings, screen elements may be provided in larger or smaller sized units. For example, a screen element may be provided that is approximately one-fourth the size of screen element  16  such that it would span a single grid opening  50 . Alternatively, a screen element may be provided that is approximately twice the size of screen element  16  such that it would span all eight grid openings of subgrid  14  or  18 . Subgrids may also be provided in different sizes. For example, subgrid units may be provided that have two grid openings per unit or one large subgrid may be provided for the overall structure, i.e., a single subgrid structure for the entire screen assembly. In  FIG.  1   , multiple independent subgrids  14  and  18  are secured together to form the screen assembly  10 . Screen assembly  10  has a continuous screen assembly screening surface  11  that includes multiple screen element screening surfaces  13 . Each screen element  16  is a single thermoplastic injection molded piece. 
       FIG.  1 A  is an enlarged view of a portion of the screen assembly  10  having multiple end subgrids  14  and center subgrids  18 . As discussed below, the end subgrids  14  and center subgrids  18  may be secured together to form the screen assembly. Screen elements  16  are shown attached to the end subgrids  14  and center subgrids  18 . The size of the screen assembly may be altered by attaching more or less subgrids together to form the screen assembly. When installed in a vibratory screening machine, material may be fed onto the screen assembly  10 . See, e.g.,  FIGS.  12 ,  12 A,  12 B,  13 ,  13 A,  14 , and  15   . Material smaller than the screen openings of the screen element  16 , passes through the openings in screening element  16  and through the grid openings  50  thereby separating the material from that which is too big to pass through the screen openings of the screen elements  16 . 
       FIG.  1 B  shows a bottom view of the screen assembly  10  such that the grid openings  50  may be seen below the screen elements. Binder bars  12  are attached to sides of the grid framework. Binder bars  12  may be attached to lock subassemblies together creating the grid framework. Binder bars  12  may include fasteners that attach to fasteners on side members  38  of subgrid units ( 14  and  18 ) or fasteners on base member  64  of pyramidal subgrid units ( 58  and  60 ). Binder bars  12  may be provided to increase the stability of the grid framework and may distribute compression loads if the screen assembly is mounted to a vibratory screening machine using compression, e.g., using compression assemblies as described in U.S. Pat. No. 7,578,394 and U.S. patent application Ser. No. 12/460,200 (now U.S. Pat. No. 8,443,984). Binder bars may also be provided that include U-shaped members or finger receiving apertures, for undermount or overmount tensioning onto a vibratory screening machine, e.g., see mounting structures described in U.S. Pat. Nos. 5,332,101 and 6,669,027. The screen elements and subgrids are securely attached together, as described herein, such that, even under tensioning, the screen assembly screening surface and screen assembly maintain their structural integrity. 
     The screen assembly shown in  FIG.  1    is slightly concave, i.e., the bottom and top surfaces of the screen assembly have a slight curvature. Subgrids  14  and  18  are fabricated such that when they are assembled together this predetermined curvature is achieved. Alternatively, a screen assembly may be flat or convex (see, e.g.,  FIGS.  19  and  20   ). As shown in  FIGS.  12 ,  12 A,  13 , and  13 A , screen assembly  10  may be installed upon a vibratory screening machine having one or more screening surfaces. In one embodiment, screen assembly  10  may be installed upon a vibratory screening machine by placing screen assembly  10  on the vibratory screening machine such that the binder bars contact end or side members of the vibratory screening machine. Compression force is then applied to binder bar  12 . Binder bars  12  distribute the load from the compression force to the screen assembly. The screen assembly  10  may be configured such that it flexes and deforms into a predetermined concave shape when compression force is applied to binder bar  12 . The amount of deformation and range of concavity may vary according to use, compression forced applied, and shape of the bed support of the vibratory screening machine. Compressing screen assembly  10  into a concave shape when installed in a vibratory screening machine provides many benefits, e.g., easy and simple installation and removal, capturing and centering of materials to be screened, etc. Further benefits are enumerated in U.S. Pat. No. 7,578,394. Centering of material streams on screen assembly  10  prevents the material from exiting the screening surface and potentially contaminating previously segregated materials and/or creating maintenance concerns. For larger material flow volumes, screen assembly  10  may be placed in greater compression, thereby increasing the amount of arc of the screen assembly  10 . The greater the amount of arc in screen assembly  10  allows for greater retaining capability of material by screen assembly  10  and prevention of over spilling of material off edges of the screen assembly  10 . Screen assembly  10  may also be configured to deform into a convex shape under compression or remain substantially flat under compression or clamping. Incorporating binder bars  12  into the screen assembly  10  allows for a compression load from a vibratory screening machine to be distributed across the screen assembly  10 . Screen assembly  10  may include guide notches in the binder bars  12  to help guide the screen assembly  10  into place when installed upon a vibratory screening machine having guides. Alternatively, the screen assembly may be installed upon a vibratory screening machine without binder bars  12 . In the alternative embodiment, guide notches may be included in subgrid units. U.S. patent application Ser. No. 12/460,200 (now U.S. Pat. No. 8,443,984) is incorporated herein by reference and any embodiments disclosed therein may be incorporated into embodiments of the present invention described herein. 
       FIG.  2    shows a screen element  16  having substantially parallel screen element end portions  20  and substantially parallel screen element side portions  22  that are substantially perpendicular to the screen element end portions  20 . The screen element screening surface  13  includes surface elements  84  running parallel to the screen element end portions  20  and forming screening openings  86 . See  FIG.  2 D . Surface elements  84  have a thickness T, which may vary depending on the screening application and configuration of the screening openings  86 . T may be, e.g., approximately 43 microns to approximately 1000 microns depending on the open screening area desired and the width W of screening openings  86 . The screening openings  86  are elongated slots having a length L and a width W, which may be varied for a chosen configuration. The width may be a distance of approximately 43 microns to approximately 2000 microns between inner surfaces of each screen surface element  84 . The screening openings are not required to be rectangular but may be thermoplastic injection molded to any shape suitable to a particular screening application, including approximately square, circular and/or oval. For increased stability, the screen surface elements  84  may include integral fiber materials which may run substantially parallel to end portions  20 . The fiber may be an aramid fiber (or individual filaments thereof), a naturally occurring fiber or other material having a relatively high tensile strength. U.S. Pat. No. 4,819,809 and U.S. patent application Ser. No. 12/763,046 (now U.S. Pat. No. 8,584,866) are incorporated herein by reference and, as appropriate, the embodiments disclosed therein may be incorporated into the screen assemblies disclosed herein. 
     The screen element  16  may include attachment apertures  24  configured such that elongated attachment members  44  of a subgrid may pass through the attachment apertures  24 . The attachment apertures  24  may include a tapered bore that may be filled when a portion of the elongated attachment member  44  above the screening element screening surface is melted fastening screen element  16  to the subgrid. Alternatively, the attachment apertures  24  may be configured without a tapered bore allowing formation of a bead on the screening element screening surface when a portion of an elongated attachment member  44  above a screening element screening surface is melted fastening the screen element to the subgrid. Screen element  16  may be a single thermoplastic injection molded piece. Screen element  16  may also be multiple thermoplastic injection molded pieces, each configured to span one or more grid openings. Utilizing small thermoplastic injection molded screen elements  16 , which are attached to a grid framework as described herein, provides for substantial advantages over prior screen assemblies. Thermoplastic injection molding screen elements  16  allow for screening openings  86  to have widths W as small as approximately 43 microns. This allows for precise and effective screening. Arranging the screen elements  16  on subgrids, which may also be thermoplastic injection molded, allows for easy construction of complete screen assemblies with very fine screening openings. Arranging the screen elements  16  on subgrids also allows for substantial variations in overall size and/or configuration of the screen assembly  10 , which may be varied by including more or less subgrids or subgrids having different shapes. Moreover, a screen assembly may be constructed having a variety of screening opening sizes or a gradient of screening opening sizes simply by incorporating screen elements  16  with the different size screening openings onto subgrids and joining the subgrids in the desired configuration. 
       FIG.  2 B  and  FIG.  2 C  show a bottom of the screen element  16  having a first screen element support member  28  extending between the end portions  20  and being substantially perpendicular to the end portions  20 .  FIG.  2 B  also shows a second screen element support member  30  orthogonal to the first screen element support member  28  extending between the side edge portions  22  being approximately parallel to the end portions  20  and substantially perpendicular to the side portions  22 . The screen element may further include a first series reinforcement members  32  substantially parallel to the side edge portions  22  and a second series of reinforcement members  34  substantially parallel to the end portions  20 . The end portions  20 , the side edge portions  22 , the first screen element support member  28 , the second screen element support member  30 , the first series reinforcement members  32 , and the second series of reinforcement members  34  structurally stabilize the screen surface elements  84  and screening openings  86  during different loadings, including distribution of a compression force and/or vibratory loading conditions. 
       FIG.  3    and  FIG.  3 A  illustrate an end subgrid  14  unit. The end subgrid unit  14  includes parallel subgrid end members  36  and parallel subgrid side members  38  substantially perpendicular to the subgrid end members  36 . The end subgrid unit  14  has fasteners along one subgrid end member  36  and along the subgrid side members  38 . The fasteners may be clips  42  and clip apertures  40  such that multiple subgrid units  14  may be securely attached together. The subgrid units may be secured together along their respective side members  38  by passing the clip  42  into the clip aperture  40  until extended members of the clip  42  extend beyond clip aperture  40  and subgrid side member  38 . As the clip  42  is pushed into the clip aperture  40 , the clip&#39;s extended members will be forced together until a clipping portion of each extended member is beyond the subgrid side member  38  allowing the clipping portions to engage an interior portion of the subgrid side member  38 . When the clipping portions are engaged into the clip aperture, subgrid side members of two independent subgrids will be side by side and secured together. The subgrids may be separated by applying a force to the clip&#39;s extended members such that the extended members are moved together allowing for the clipping portions to pass out of the clip aperture. Alternatively, the clips  42  and clip apertures  40  may be used to secure subgrid end member  36  to a subgrid end member of another subgrid, such as a center subgrid ( FIG.  4   ). The end subgrid may have a subgrid end member  36  that does not have any fasteners. Although the fasteners shown in drawings are clips and clip apertures, alternative fasters and alternative forms of clips and apertures may be used, including other mechanical arrangements, adhesives, etc. 
     Constructing the grid framework from subgrids, which may be substantially rigid, creates a strong and durable grid framework and screen assembly  10 . Screen assembly  10  is constructed so that it can withstand heavy loading without damage to the screening surface and supporting structure. For example, the pyramidal shaped grid frameworks shown in  FIGS.  22  and  23    provide a very strong pyramid base framework that supports individual screen elements capable of very fine screening, having screening openings as small as 43 microns. Unlike the pyramidal screen assembly embodiment of the present invention described herein, existing corrugated or pyramid type wire mesh screen assemblies are highly susceptible to damage and/or deformation under heavy loading. Thus, unlike current screens, the present invention provides for screen assemblies having very small and very precise screening openings while simultaneously providing substantial structural stability and resistance to damage thereby maintaining precision screening under a variety of load burdens. Constructing the grid framework from subgrids also allows for substantial variation in the size, shape, and/or configuration of the screen assembly by simply altering the number and/or type of subgrids used to construct the grid framework. 
     End subgrid unit  14  includes a first subgrid support member  46  running parallel to subgrid side members  38  and a second subgrid support member  48  orthogonal to the first subgrid support member  46  and perpendicular to the subgrid side members  38 . Elongated attachment members  44  may be configured such that they mate with the screen element attachment apertures  24 . Screen element  16  may be secured to the subgrid  14  via mating the elongated attachment members  44  with screen element attachment apertures  24 . A portion of elongated attachment member  44  may extend slightly above the screen element screening surface when the screen element  16  is attached to the end subgrid  14 . The screen element attachment apertures  24  may include a tapered bore such that a portion of the elongated attachment members  44  extending above the screen element screening surface may be melted and fill the tapered bore. Alternatively, screen element attachment apertures  24  may be without a tapered bore and the portion of the elongated attachment members extending above the screening surface of the screening element  16  may be configured to form a bead on the screening surface when melted. See  FIGS.  34  and  35   . Once attached, the screen element  16  will span at least one grid opening  50 . Materials passing through the screening openings  86  will pass through grid opening  50 . The arrangement of elongated attachment members  44  and the corresponding arrangement of screen element attachment apertures  24  provide a guide for attachment of screen elements  16  to subgrids simplifying assembly of subgrids. The elongated attachment members  44  pass through the screen element attachment apertures  24  guiding the screen element into correct placement on the surface of the subgrid. Attachment via elongated attachment members  44  and screen element attachment apertures  24  further provides a secure attachment to the subgrid and strengthens the screening surface of the screen assembly  10 . 
       FIG.  4    shows a center subgrid  18 . As shown in  FIG.  1    and  FIG.  1 A , the center subgrid  18  may be incorporated into a screen assembly. The center subgrid  18  has clips  42  and clip apertures  40  on both subgrid end members  36 . The end subgrid  14  has clips  42  and clip apertures  40  on only one of two subgrid end members  36 . Center subgrids  18  may be secured to other subgrids on each of its subgrid end members and subgrid side members. 
       FIG.  5    shows a top view of binder bar  12 .  FIG.  5 A  shows a bottom view of binder bar  12 . Binder bars  12  include clips  42  and clip apertures  40  such that binder bar  12  may be clipped to a side of an assembly of screen panels (see  FIG.  9   ). As with subgrids, fasteners on the binder bar  12  are shown as clips and clip apertures but other fasteners may be utilized to engage fasteners of the subgrids. Handles may be attached to binder bars  12  (see, e.g.,  FIG.  7   ) which may simplify transportation and installation of a screen assembly. Tags and/or labels may also be attached to binder bars. As discussed above, binder bars  12  may increase the stability of the grid framework and may distribute compression loads of a vibratory screening machine if the screen assembly is placed under compression as shown in U.S. Pat. No. 7,578,394 and U.S. patent application Ser. No. 12/460,200 (now U.S. Pat. No. 8,443,984). 
     The screening members, screening assemblies and parts thereof, including connecting members/fasteners as described herein, may include nanomaterial dispersed therein for improved strength, durability and other benefits associated with the use of a particular nanomaterial or combination of different nanomaterials. Any suitable nanomaterial may be used, including, but not limited to nanotubes, nanofibers and/or elastomeric nanocomposites. The nanomaterial may be dispersed in the screening members and screening assemblies and parts thereof in varying percentages, depending on the desired properties of the end product. For example, specific percentages may be incorporated to increase member strength or to make a screening surface wear resistant. Use of a thermoplastic injection molded material having nanomaterials dispersed therein may provide for increased strength while using less material. Thus, structural members include subgrid framework supports and screen element supporting members may be made smaller and stronger and/or lighter. This is particularly beneficial when fabricating relatively small individual components that are built into a complete screen assembly. Also, instead of producing individual subgrids that clip together, one large grid structure having nanomaterials dispersed therein may be fabricated that is relatively light and strong. Individual screen elements, with or without nanomaterials, may then be attached to the single complete grid framework structure. Use of nanomaterials in a screen element will provide increased strength while reducing the weight and size of the element. This may be especially helpful when injection molding screen elements having extremely small openings as the openings are supported by the surrounding materials/members. Another advantage to incorporating nanomaterials into the screen elements is an improved screening surface that is durable and resistant to wear. Screen surfaces tend to wear out through heavy use and exposure to abrasive materials. Use of a thermoplastic and/or a thermoplastic having abrasive resistant nanomaterials provides a screening surface with a long life. 
       FIG.  6    shows a subassembly  15  of a row of subgrid units.  FIG.  6 A  is an exploded view of the subassembly in  FIG.  6    showing individual subgrids and direction of attachment to each other. The subassembly includes two end subgrid units  14  and three center subgrid units  18 . The end subgrid units  14  form the ends of the subassembly while the center subgrid units  18  are used to join the two end subgrid units  14  via connections between the clips  42  and clip apertures  40 . The subgrid units shown in  FIG.  6    are shown with attached screen elements  16 . By fabricating the screen assembly from subgrids and into the subassembly, each subgrid may be constructed to a chosen specification and the screen assembly may be constructed from multiple subgrids in a configuration required for the screening application. The screen assembly may be quickly and simply assembled and will have precise screening capabilities and substantial stability under load pressures. Because of the structure configuration of the grid framework and screen elements  16 , the configuration of multiple individual screen elements forming the screening surface of the screen assembly  10  and the fact that the screen elements  16  are thermoplastic injection molded, the openings in screen elements  16  are relatively stable and maintain their opening sizes for optimal screening under various loading conditions, including compression loads and concavity deflections and tensioning. 
       FIG.  7    shows a screen assembly  10  with binder bars  12  having handles attached to the binder bars  12 . The screen assembly is made up of multiple subgrid units secured to each other. The subgrid units have screen elements  16  attached to their top surfaces.  FIG.  7 A  is a cross-section of Section A-A of  FIG.  7    showing individual subgrids secured to screen elements forming a screening surface. As reflected in  FIG.  7 A , the subgrids may have subgrid support members  48  configured such that screen assembly has a slightly concave shape when the subgrid support members  48  are fastened to each other via clips  42  and clip apertures  40 . Because the screen assembly is constructed with a slightly concave shape it may be configured to deform to a desired concavity upon application of a compression load without having to guide the screen assembly into a concave shape. Alternatively, the subgrids may be configured to create a slightly convex screen assembly or a substantially flat screen assembly. 
       FIG.  8    is a top isometric view of a screen assembly partially covered with screen elements  16 . This figure shows end subgrid units  14  and center subgrid units  18  secured to form a screen assembly. The screening surface may be completed by attaching screen elements  16  to the uncovered subgrid units shown in the figure. Screen elements  16  may be attached to individual subgrids prior to construction of the grid framework or attached to subgrids after subgrids have been fastened to each other into the grid framework. 
       FIG.  9    is an exploded isometric view of the screen assembly shown in  FIG.  1   . 
     This figure shows eleven subassemblies being secured to each other via clips and clip apertures along subgrid end members of subgrid units in each subassembly. Each subassembly has two end subgrid units  14  and three center subgrid units  18 . Binder bars  12  are clipped at each side of the assembly. Different size screen assemblies may be created using different numbers of subassemblies or different numbers of center subgrid units in each subassembly. An assembled screen assembly has a continuous screen assembly screening surface made up of multiple screen element screening surfaces. 
       FIGS.  10  and  10 A  illustrate attachment of screen elements  16  to end subgrid unit  14 , according to an exemplary embodiment of the present invention. Screen elements  16  may be aligned with end subgrid unit  14  via the elongated attachment members  44  and the screen element attachment apertures  24  such that the elongated  20  attachment members  44  pass through the screen element attachment apertures  24  and extend slightly beyond the screen element screening surface. The elongated attachment members  44  may be melted to fill the tapered bores of the screen element attachment apertures  24  or, alternatively, to form beads upon the screen element screening surface, securing the screen element  16  to the subgrid unit  14 . Attachment via elongated attachment members  44  and screen element attachment apertures  24  is only one embodiment of the present invention. Alternatively, screen element  16  may be secured to end subgrid unit  14  via adhesive, fasteners and fastener apertures, laser welding, etc. Although shown having two screen elements for each subgrid, the present invention includes alternate configurations of one screen element per subgrid, multiple screen elements per subgrid, one screen element per subgrid opening, or having a single screen element cover multiple subgrids. The end subgrid  14  may be substantially rigid and may be formed as a single thermoplastic injection molded piece. 
       FIG.  10 B  is a top view of the end subgrid unit shown in  FIG.  10 A  with screen elements  16  secured to the end subgrid.  FIG.  10 C  is an enlarged cross-section of Section B-B of the end subgrid unit in  FIG.  10 B . Screen element  16  is placed upon the end subgrid unit such that elongated attachment member  44  passes through the attachment aperture and beyond a screening surface of the screen element. The portion of the elongated attachment member  44  passing through the attachment aperture and beyond the screening surface of the screen element may be melted to attach the screen element  16  to the end subgrid unit as described above. 
       FIG.  11    and  FIG.  11 A  illustrate attachment of screen elements  16  to center subgrid unit  18 , according to an exemplary embodiment of the present invention. Screen elements  16  may be aligned with center subgrid unit  18  via the elongated attachment members  44  and the screen element attachment apertures  24  such that the elongated attachment members  44  pass through the screen element attachment apertures  24  and extend slightly beyond the screen element screening surface. The elongated attachment members  44  may be melted to fill the tapered bores of the screen element attachment apertures  24  or, alternatively, to form beads upon the screen element screening surface, securing the screen element  16  to center subgrid unit  18 . Attachment via elongated attachment members  44  and screen element attachment apertures  24  is only one embodiment of the present invention. Alternatively, screen element  16  may be secured to center subgrid unit  14  via adhesive, fasteners and fastener apertures, etc. Although shown having two screen elements for each subgrid, the present invention includes alternate configurations of one screen element per subgrid, one screen element per subgrid opening, multiple screen elements per subgrid, or having a single screen element cover multiple subgrid units. The center subgrid unit  18  may be substantially rigid and may be a single thermoplastic injection molded piece. 
       FIGS.  12  and  12 A  show screen assemblies  10  installed on a vibratory screening machine having two screening surfaces. The vibratory screening machine may have compression assemblies on side members of the vibratory screening machine, as shown in U.S. Pat. No. 7,578,394. A compression force may be applied to a binder bar or a side member of the screen assembly such that the screen assembly deflects downward into a concave shape. A bottom side of the screen assembly may mate with a screen assembly mating surface of the vibratory screening machine as shown in U.S. Pat. No. 7,578,394 and U.S. patent application Ser. No. 12/460,200 (now U.S. Pat. No. 8,443,984). The vibratory screening machine may include a center wall member configured to receive a binder bar of a side member of the screen assembly opposite of the side member of the screen assembly receiving compression. The center wall member may be angled such that a compression force against the screen assembly deflects the screen assembly downward. The screen assembly may be installed in the vibratory screening machine such that it is configured to receive material for screening. The screen assembly may include guide notches configured to mate with guides of the vibratory screening machine such that the screen assembly may be guided into place during installation and may include guide assembly configurations as shown in U.S. patent application Ser. No. 12/460,200 (now U.S. Pat. No. 8,443,984). 
       FIG.  12 B  is a front view of the vibratory screening machine shown in  FIG.  12   .  FIG.  12 B  shows screen assemblies  10  installed upon the vibratory screening machine with compression applied to deflect the screen assemblies downward into a concave shape. Alternatively, the screen assembly may be pre-formed in a predetermined concave shape without compression force. 
       FIGS.  13  and  13 A  show installations of screen assembly  10  in a vibratory screening machine having a single screening surface. The vibratory screening machine may have a compression assembly on a side member of the vibratory screening machine. Screen assembly  10  may be placed into the vibratory screening machine as shown. A compression force may be applied to a binder bar or side member of the screen assembly such that the screen assembly deflects downward into a concave shape. A bottom side of the screen assembly may mate with a screen assembly mating surface of the vibratory screening machine as shown in U.S. Pat. No. 7,578,394 and U.S. patent application Ser. No. 12/460,200 (now U.S. Pat. No. 8,443,984). The vibratory screening machine may include a side member wall opposite of the compression assembly configured to receive a binder bar or a side member of the screen assembly. The side member wall may be angled such that a compression force against the screen assembly deflects the screen assembly downward. The screen assembly may be installed in the vibratory screening machine such that it is configured to receive material for screening. The screen assembly may include guide notches configured to mate with guides of the vibratory screening machine such that the screen assembly may be guided into place during installation. 
       FIG.  14    is a front view of screen assemblies  52  installed upon a vibratory screening machine having two screening surfaces, according to an exemplary embodiment of the present invention. Screen assembly  52  is an alternate embodiment where the screen assembly has been pre-formed to fit into the vibratory screening machine without applying a load to the screen assembly, i.e., screen assembly  52  includes a bottom portion  52 A that is formed such that it mates with a bed  83  of the vibratory screening machine. The bottom portion  52 A may be formed integrally with screen assembly  52  or maybe a separate piece. Screen assembly  52  includes similar features as screen assembly  10 , including subgrids and screen elements but also includes bottom portion  52 A that allows it to fit onto bed  83  without being compressed into a concave shape. A screening surface of screen assembly  52  may be substantially flat, concave or convex. Screen assembly  52  may be held into place by applying a compression force to a side member of screen assembly  52 . A bottom portion of screen assembly  52  may be pre-formed to mate with any type of mating surface of a vibratory screening machine. 
       FIG.  15    is a front view of screen assembly  53  installed upon a vibratory screening machine having a single screening surface, according to an exemplary embodiment of the present invention. Screen assembly  53  has similar features of screen assembly  52  described above, including a bottom portion  53 A that is formed such that it mates with a bed  87  of the vibratory screening machine. 
       FIG.  16    shows an end support frame subassembly and  FIG.  16 A  shows an exploded view of the end support frame subassembly shown in  FIG.  16   . The end support frame subassembly shown in  FIG.  16    incorporates eleven end subgrid units  14 . Alternate configurations having more or less end subgrid units may be utilized. The end subgrid units  14  are secured to each other via clips  42  and clip apertures  40  alongside members of the end subgrid units  14 .  FIG.  16 A  shows attachment of individual end subgrid units such that the end support frame subassembly is created. As shown, the end support frame subassembly is covered in screen elements  16 . Alternatively, the end support frame subassembly may be constructed from end subgrids prior to attachment of screen elements or partially from pre-covered subgrid units and partially from uncovered subgrid units. 
       FIG.  17    shows a center support frame assembly and  FIG.  17 A  shows an exploded view of the center support frame subassembly shown in  FIG.  17   . The center support frame assembly shown in  FIG.  17    incorporates eleven center subgrid units  18 . Alternate configurations having more or less center subgrid units may be utilized. The center subgrid units  18  are secured to each other via clips  42  and clip apertures  40  alongside members of the center subgrid units  18 .  FIG.  17 A  shows attachment of individual center subgrid units such that the center support frame subassembly is created. As shown, the center support frame subassembly is covered in screen elements  16 . Alternatively, the center support frame subassembly may be constructed from center subgrids prior to attachment of screen elements or partially from pre-covered subgrid units and partially from uncovered subgrid units. 
       FIG.  18    shows an exploded view of a screen assembly having three center support frame subassemblies and two end support frame subassemblies. The support frame assemblies are secured to each other via the clips  42  and clip apertures  40  on the subgrid end members. Each center subgrid unit is attached to two other subgrid units via end members. End members  36  of end subgrid units having no clips  42  or clip apertures  40  form the end edges of the screen assembly. The screen assembly may be made with more or less center support frames subassemblies or larger or smaller frame subassemblies. Binder bars may be added to side edges of the screen assembly. As shown, the screen assembly has screen elements installed upon the subgrid units prior to assembly. Alternatively, screen elements  16  may be installed after all or a portion of assembly. 
       FIG.  19    illustrates an alternative embodiment of the present disclosure where screen assembly  54  is substantially flat. Screen assembly  54  may be flexible such that it can be deformed into a concave or convex shape or may be substantially rigid. Screen assembly  54  may be used with a flat screening surface. See  FIG.  39   . As shown, screen assembly  54  has binder bars  12  attached to side portions of the screen assembly  54 . Screen assembly  54  may be configured with the various embodiments of the grid structures and screen elements described herein. 
       FIG.  20    illustrates an alternative embodiment of the present disclosure wherein screen assembly  56  is convex. Screen assembly  56  may be flexible such that it can be deformed into a more convex shape or may be substantially rigid. As shown, screen assembly  56  has binder bars  12  attached to side portions of the screen assembly. Screen assembly  56  may be configured with the various embodiments of the grid structures and screen elements described herein. 
     In alternative embodiments of the present disclosure, screen assembly  410  is provided having screen elements  416 , center subgrid units  418 , and end subgrid units  414 . See, e.g.,  FIG.  47   . Screen element  416  may be thermoplastic injection molded and may include all of the features of screen element  16  provided above. Screen element  416  may be incorporated into any of the screen assemblies disclosed herein (e.g., screen assemblies  10  and  52 - 54 , illustrated in  FIGS.  1 ,  14 ,  15 , and  19   , respectively) and is interchangeable with screen element  16 . Screen element  416  may include location apertures  424 , which may be located at a center of screen element  416  and at  10  each of the four corners of screen element  416 . See, e.g.,  FIGS.  48  and  48 A . More or less location apertures  424  may be provided on screen element  416  and multiple configurations may be provided. The location apertures  424  may be substantially the same as attachment apertures  24  and may be utilized to locate the screen element  416  on a subgrid. Alternatively, screen element  416  may be located without location apertures  424 . Screen element  416  may include a plurality of tapered counter bores  470 , which may facilitate extraction of screen element  416  from a mold, which mold may have ejector pins configured to push the screen element out of the mold. See, e.g.,  FIGS.  48  and  48 A . 
     On a bottom side of screen element  416 , a first adhesion arrangement may be incorporated, which may be a plurality of extensions, cavities or a combination of extensions and cavities. The first adhesion arrangement of screen element  416  may be configured to mate with a complementary second adhesion arrangement on a top surface of a subgrid unit. For example, in  FIGS.  48 B and  48 C  a plurality of cavity pockets  472  are provided. The plurality of cavity pockets  472  may be arranged along end portions  20  and side portions  22  between the location apertures  424 . Additional cavity pockets  272  may be arranged along all or a portion of first support screen element member  28  and along all or a portion of second screen element support member  30 . Although shown as elongated cavities, cavity pockets  472  may have a variety of configurations, sizes, and depths. Moreover, the first adhesion arrangement on screen element  416  may be extensions rather than cavities. The first adhesion arrangement of screen element  416  may be configured to mate with a complimentary second adhesion arrangement on a subgrid unit such that a portion of screen element  416  overlaps at least a portion the subgrid unit regardless of whether the screen element  416  or the subgrid unit has extensions or cavities. 
     End subgrid unit  414  and center subgrid unit  418  may be incorporated into screen assembly  410 . See, e.g.,  FIGS.  49 ,  49 A,  50 , and  50 A . End subgrid unit  414  and center subgrid unit  418  may be thermoplastic injection molded and may include all of the features of end subgrid unit  14  and center subgrid unit  18  discussed above. End subgrid unit  414  and center subgrid unit  418  may be interchangeably used wherever end subgrid unit  14  and center subgrid unit  18  are indicated. End subgrid unit  414  and center subgrid unit  418  may have a plurality elongated location members  444 , which may be substantially the same as attachment members  44 . The arrangement of location members  444  may correspond to the location apertures  424  of screen elements  416  such that screen elements  416  may be located onto end subgrid unit  414  and center subgrid unit  418  for attachment. 
     End subgrid unit  414  and center subgrid unit  418  may include a second adhesion arrangement on a top surface of each of end subgrid unit  414  and center subgrid unit  418 , which second adhesion arrangement may be complimentary to the first adhesion arrangement of screen element  416  such that the screen element may be mated to a subgrid unit via the mating of the first and second adhesion arrangements. In one embodiment of the present invention, the second adhesion arrangement may be a plurality of fusion bars  476  arranged along a top surface of subgrid side members  38  and subgrid end members  36 . End subgrid unit  414  and center subgrid unit  418  may also include a plurality of fusion bars  478 , which may be shortened fusion bars having heights less than heights of fusion bars  476 , arranged along a top surface of first subgrid support member  46  and second subgrid support member  48 . See, e.g.,  FIGS.  49  to  50 A . Although shown as elongated extensions, fusion bars  476  (and  478 ) may be various shapes and sizes and may be arranged in a variety of configurations. Alternatively, the second adhesion arrangement may be cavities, pockets, or similar and may be configured to receive extensions from a screen element. The second adhesion arrangement could include both extensions and cavities. 
     Each of the plurality of cavity pockets  472  is configured to receive fusion bars  476  and shorted fusion bars  478  arranged on subgrids ( 414 ,  418 ,  458 , and  460 ). See, e.g.,  FIGS.  45 A to  45 E and  46   . As shown in  FIGS.  45 B to  45 E , fusion bars  476  fit within the plurality of cavity pockets  472  when screen element  416  is placed upon a subgrid. Cavity pockets  472  may have a width C that is slightly larger than width D of fusion bar  476 . Cavity pocket  472  may have a depth A that is slightly smaller than a height B of fusion bar  476 . See, e.g.,  FIG.  47   . Height B of fusion bar  476  may be approximately 0.056 inches. Prior to melting of fusion bars  476 , screen element  416  may rest upon fusion bars  476  without contacting the rest of a subgrid. Screen element  416  and the subgrids may be bonded together via laser welding. Bonding may be accomplished through chemical bonding between the cavity pockets  472  and the fusion bars ( 476  or  478 ) or melting portions of the materials of each component such that the components harden together. In one embodiment, when screen element  416  is located on a subgrid, fusion bar  476  (or shortened fusion bar  478 ) may be melted, allowing for a melted portion of the fusion bar  476  to fill all or a portion of width C of the cavity pocket  472 . In certain embodiments approximately 0.006 inches of fusion bar  476  may be melted and allowed to fill all or a portion of the width of cavity pocket  472 . Melting of fusion bar  476  may be performed via laser welding, which may secure screen element  416  to a subgrid. A laser  500  may be configured and controlled to reach a specific depth of fusion bar  476 . 
     Fusion bars  476  (or shortened fusion bars  478 ) may include carbon, graphite or other materials configured to respond to a specific laser wavelength. The fusion bars may be further configured to correspond to a laser to be used for laser welding. Fusion bars may have specific lengths to correspond to a laser  500 . Although shown as elongated protrusions, other shapes and/or designs may be incorporated for fusion bars subject to the requirements of a chosen laser. In embodiments having fusion bars on subgrids, screen elements  416  typically do not include carbon or graphite. Screen element  416  and the fusion bars may be made of different materials such that a selected laser  500  may travel through screen element  416  without melting screen element  416  and contact the fusion bars. See, e.g.,  FIGS.  45 B  and C. Screen element  416  may be made of a TPU or similar material having performance properties desired for a screening application. Screen element  416  may be substantially clear. Subgrids ( 414  and  418 ) may be made from nylon or similar materials. The fusion bars may have a higher melting point than the material of screen element  416  such that, when the fusion bars are melted, a portion of the screen element  416  also melts, which may be accomplished by heat transfer from the melted portion of fusion bar  476  that contacts screen element  416  in the cavity pocket  472 . In this way, screen element  416  is welded to a subgrid. See, e.g.,  FIGS.  51 ,  51 A,  52 , and  52 A . 
     Laser welding is typically performed by focusing a laser beam toward a seam or area to transform material from a solid to a liquid, and after removal of the laser beam, the material return to a solid. Laser welding is a type of fusion welding and can be performed through conduction or penetration. Conduction welding relies upon conductivity of the material being welded to generate heat and melt the material. Laser welding of screen element  416  to a subgrid having fusion bars provides for laser welding of two different materials together. Typically, this cannot be accomplished with laser welding; however, applying the laser  500  through the screen element  416  to the fusion bars, which have conductive properties to generate heat upon the application of the selected laser  500 , may cause the fusion bars ( 476  or  478 ) to melt. Similarly, the heat produced by the conduction and/or from the melted fusion bar material causes a portion of the screen element to melt. The two liquid materials combine and create a strong solid attachment between the subgrid and the screen element when the laser is removed, and the combined materials return to a solid. By forming laser welded bonds between the screen element and the subgrids, the attachment between the components is very strong, which is essential for components of screen assemblies used in vibratory screening machines. The screen assemblies can be subjected to vibratory forces in excess of 8 G, abrasive materials and chemicals, and very high load requirements. Therefore, screen assemblies must be very strong and durable. Embodiments of the present invention provide screen assemblies made from multiple parts secured together. Creating screen assemblies from smaller subparts allows for micro injection molding of screen elements with very small openings, e.g. having a thickness of approximately 43 microns to approximately 1000 microns. The strength of the laser welding adds overall strength to the screen assemblies, allowing for the benefits of micro injection molding the screen elements while maintaining durable screen assemblies. Laser welding also provides a more efficient attachment procedure than other attachment procedures such as heat staking. In certain embodiments, laser welding may be accomplished in approximately 8 to 10 seconds where heat staking involving other embodiments may require approximately 1.5 minutes. 
     End subgrid unit  414  (or  14 ) and center subgrid unit  418  (or  18 ) may include secondary support framework  488  spanning across grid openings  50 . Secondary support framework  488  may span all or only a portion of a grid opening  50 . Secondary support framework  488  increases the strength and durability of end subgrid unit  414  (or  14 ) and center subgrid unit  418  (or  18 ). Secondary support framework  488  increases the overall strength of screen assembly  410  allowing it to withstand vibratory forces in excess of 8 G. 
       FIGS.  21  and  21 A  show an alternative embodiment of the present disclosure incorporating pyramidal shaped subgrid units. A screen assembly is shown with binder bars  12  attached. The screen assembly incorporates center and end subgrid units  14  and  18  (or  414  and  418 ) and center and end pyramidal shaped subgrid units  58  and  60  (or  458  and  460 ). By incorporating the pyramidal shaped subgrid units  58  and  60  into the screen assembly, an increased screening surface may be achieved. Additionally, material being screened may be controlled and directed. The screen assembly may be concave, convex, or flat. The screen assembly may be flexible and may be deformed into a concave or convex shape upon the application of a compression force. The screen assembly may include guide notches capable of mating with guide mating surfaces on a vibratory screening machine. Different configurations of subgrid units and pyramid subgrid units may be employed which may increase or decrease an amount of screening surface area and flow characteristics of the material being processed. Unlike mesh screens or similar technology, which may incorporate corrugations or other manipulations to increase surface area, the screen assembly shown is supported by the grid framework, which may be substantially rigid and capable of withstanding substantial loads without damage or destruction. Under heavy material flows, traditional screen assemblies with corrugated screening surfaces are frequently flattened or damaged by the weight of the material, thereby impacting the performance and reducing the screening surface area of such screen assemblies. The screen assemblies disclosed herein are difficult to damage because of the strength of the grid framework, and the benefits of increased surface area provided by incorporating pyramidal shaped subgrids may be maintained under substantial loads. 
     A pyramidal shaped end subgrid  58  is illustrated in  FIG.  22    and  FIG.  22 A . Pyramidal shaped end subgrid  58  includes a first and a second grid framework forming first and second sloped surface grid openings  74 . Pyramidal shaped end subgrid  58  includes a ridge portion  66 , subgrid side members/base members  64 , and first and second angular surfaces  70  and  72 , respectively, that peak at ridge portion  66  and extend downwardly to side member  64 . Pyramidal shaped subgrids  58  and  60  have triangular end members  62  and triangular middle support members  76 . Angles shown for first and second angular surface  70  and  72  are exemplary only. Different angles may be employed to increase or decrease surface area of screening surface. Pyramidal shaped end subgrid  58  has fasteners alongside members  64  and at least one triangle end member  62 . The fasteners may be clips  42  and clip apertures  40  such that multiple subgrid units  58  may be secured together. Alternatively, the clips  42  and clip apertures  40  may be used to secure pyramidal shaped end subgrid  58  to end subgrid  14 , center subgrid  18 , or pyramidal shaped center subgrid  60 . Elongated attachment members  44  may be configured on first and second sloped surfaces  70  and  72  such that they mate with the screen element attachment apertures  24 . Screen element  16  may be secured to pyramidal shaped end subgrid  58  via mating elongated attachment members  44  with the screen element attachment apertures  24 . A portion of the elongated attachment member  44  may extend slightly above the screen element screening surface when the screen element  16  is attached to pyramidal shaped end subgrid  58 . The screen element attachment apertures  24  may include a tapered bore such that a portion of the elongated attachment members  44  extending above the screen element screening surface may be melted and fill the tapered bore. Alternatively, the screen element attachment apertures  24  may be without a tapered bore and the portion of the elongated attachment members extending above the screening surface of the screening element  16  may be melted to form a bead on the screening surface. Once attached, screen element  16  may span first  74  and second sloped grid openings. Materials passing through the screening openings  86  will pass through the first  74  and second grid openings. 
     A pyramidal shaped center subgrid  60  is illustrated in  FIG.  23    and  FIG.  23 A . Pyramidal shaped center subgrid  60  includes a first and a second grid framework forming a first and second sloped surface grid opening,  74 . Pyramidal shaped center subgrid  60  includes a ridge portion  66 , a subgrid side members/base members  64 , and first and second angular surfaces  70  and  72  that peak at the ridge portion  66  and extend downwardly to the side member  64 . Pyramidal shaped center subgrid  60  has triangular end members  62  and triangular middle members  76 . Angles shown for first and second angular surface  70  and  72  are exemplary only. Different angles may be employed to increase or decrease surface area of screening surface. The pyramidal shaped center subgrid  60  has fasteners alongside members  64  and both triangle end members  62 . The fasters may be clips  42  and clip apertures  40  such that multiple pyramidal shaped center subgrids  60  may be secured together. Alternatively, the clips  42  and clip apertures  40  may be used to secure pyramidal shaped center subgrid  60  to end subgrid  14 , center subgrid  18 , or pyramidal shaped end subgrid  58 . Elongated attachment members  44  may be configured on first and second sloped surfaces  70  and  72  such that they mate with the screen element attachment apertures  24 . Screen element  16  may be secured to pyramidal shaped center subgrid  60  via mating elongated attachment members  44  with the screen element attachment apertures  24 . A portion of the elongated attachment member  44  may extend slightly above the screen element screening surface when the screen element  16  is attached to pyramidal shaped center subgrid  60 . The screen element attachment apertures  24  may include a tapered bore such that the portion of the elongated attachment members  44  extending above the screen element screening surface may be melted and fill the tapered bore. Alternatively, the screen element attachment apertures  24  may be without a tapered bore and the portion of the elongated attachment members extending above the screening surface of the screening element  16  may be melted to form a bead on the screening surface. Once attached, screen element  16  will span sloped grid opening  74 . Materials passing through the screening openings  86  will pass through the grid opening  74 . While pyramid and flat shaped grid structures are shown, it will be appreciated that various shaped subgrids and corresponding screen elements may be fabricated in accordance with the present disclosure. 
       FIG.  24    shows a subassembly of a row of pyramidal shaped subgrid units.  FIG.  24 A  is an exploded view of the subassembly in  FIG.  24    showing the individual pyramidal shaped subgrids and direction of attachment. The subassembly includes two pyramidal shaped end subgrids  58  and three pyramidal shaped center subgrids  60 . The pyramidal shaped end subgrids  58  form ends of the subassembly while pyramidal shaped center subgrids  60  are used to join the two end subgrids  58  via connections between the clips  42  and clip apertures  40 . The pyramidal subgrids shown in  FIG.  24    are shown with attached screen elements  16 . Alternatively, the subassembly may be constructed from subgrids prior to attachment of screen elements or partially from pre-covered pyramidal shaped subgrid units and partially from uncovered pyramidal shaped subgrid units. 
       FIGS.  24 B and  24 C  illustrate attachment of screen elements  16  to pyramidal shaped end subgrid  58 , according to an exemplary embodiment of the present invention. Screen elements  16  may be aligned with pyramidal shaped end subgrid  58  via elongated attachment members  44  and screen element attachment apertures  24  such that the elongated attachment members  44  pass through the screen element attachment apertures  24  may extend slightly beyond the screen element screening surface. The portion of elongated attachment members  44  extending beyond screen element screening surface may be melted to fill tapered bores of the screen element attachment apertures  24  or, alternatively, to form beads upon the screen element screening surface, securing the screen element  16  to pyramidal shaped subgrid  58 . Attachment via elongated attachment members  44  and screen element attachment apertures  24  is only one embodiment of the present invention. Alternatively, screen element  16  may be secured to pyramidal shaped end subgrid  58  via adhesive, fasteners and fastener apertures, etc. Although shown having four screen elements for each pyramidal shaped end subgrid  58 , the present invention includes alternate configurations of two screen elements per pyramidal shaped end subgrid  58 , multiple screen elements per pyramidal shaped end subgrid  58 , or having a single screen element cover a sloped surface of multiple pyramidal shaped subgrid units. Pyramidal shaped end subgrid  58  may be substantially rigid and may be a single thermoplastic injection molded piece. 
       FIGS.  24 D and  24 E  illustrate attachment of screen elements  16  to pyramidal shaped center subgrid  60 , according to an exemplary embodiment of the present invention. Screen elements  16  may be aligned with pyramidal shaped center subgrid  60  via elongated attachment members  44  and screen element attachment apertures  24  such that the elongated attachment members  44  may pass through the screen element attachment apertures  24  and may extend slightly beyond the screen element screening surface. The portion of the elongated attachment members  44  extending beyond screen element screening surface may be melted to fill tapered bores of the screen element attachment apertures  24  or, alternatively, to form beads upon the screen element screening surface, securing the screen element  16  to pyramidal shaped subgrid unit  60 . Attachment via elongated attachment members  44  and screen element attachment apertures  24  is only one embodiment of the present invention. Alternatively, screen element  16  may be secured to pyramidal shaped center subgrid  60  via adhesive, fasteners and fastener apertures, etc. Although shown having four screen elements for each pyramidal shaped center subgrid  60 , the present invention includes alternate configurations of two screen elements per pyramidal shaped center subgrid  60 , multiple screen elements per pyramidal shaped center subgrid  60 , or having a single screen element cover a sloped surface of multiple pyramidal shaped subgrids. Pyramidal shaped center subgrid  60  may be substantially rigid and may be a single thermoplastic injection molded piece. While pyramid and flat shaped grid structures are shown, it will be appreciated that various shaped subgrids and corresponding screen elements may be fabricated in accordance with the present disclosure. 
       FIGS.  53  to  56 A  show end and center pyramidal shaped subgrids  458  and  460 , respectively, according to exemplary embodiments of the present disclosure. End and center pyramidal shaped subgrids  458  and  460  may be thermoplastic injection molded and may have all of the features of end and center pyramidal shaped subgrids  58  and  60  discussed herein above. As with end subgrid unit  414  and center subgrid unit  418 , end and center pyramidal shaped subgrids  458  and  460  may have location members  444  corresponding to the location apertures  424  of screen element  416  such that screen elements  416  may be located onto end and center pyramidal shaped subgrids  458  and  460  for attachment. End and center pyramidal shaped subgrids  458  and  460  may have second adhesion arrangements such as a plurality of fusion bars  476  and shorted fusion bars  478 . The second adhesion arrangements may be configured to mate with complimentary first adhesion arrangements on screen elements  416  such as a plurality of pocket cavities. Screen elements  416  may be laser welded to the pyramidal subgrids. End and center pyramidal shaped subgrids  458  and  460  may include secondary support framework  488  spanning across grid openings  74 . Secondary support framework  488  may span all or only a portion of a grid opening  74 . Secondary support framework  488  increases the strength and durability of end and center pyramidal shaped subgrids  458  and  460 . End and center pyramidal shaped subgrids  458  and  460  may include a flattened ridge portion  465  and may have fixture locators  490  in ridge  66 . See, e.g.,  FIG.  53   . Flattened ridge portion  465  may allow for easier molding than rounded or pointed embodiments and may allow for easier release and/or extraction of the subgrids from molds. Embodiments may include one or more fixture locators  490  which may be utilized in alignment and/or assembly during laser welding. Fixtures may engage subgrids at fixture locators  490  allowing for alignment of laser welding. Flattened ridge portion  465  may provide easier engagement of the fixture locators  490 . 
       FIG.  25    is a top view of a screen assembly  80  having pyramidal shaped subgrids, which may be any of subgrids  14 ,  18 ,  414 , and  418 . As shown, the screen assembly  80  is formed from screen subassemblies attached to each other alternating from flat subassemblies to pyramidal shaped subassemblies. Alternatively, pyramidal shaped subassemblies may be attached to each other or less or more pyramidal shaped subassemblies may be used.  FIG.  25 A  is a cross-section of Section C-C of the screen assembly shown in  FIG.  25   . As shown, the screen assembly has five rows of pyramidal shaped subgrid units and six rows of flat subgrids, with the rows of flat subgrid units in between each row of the pyramidal shaped subgrids. Binder bars  12  are attached to the screen assembly. Any combination of flat subgrid rows and pyramidal shaped subgrid rows may be utilized.  FIG.  25 B  is a larger view of the cross-section shown in  FIG.  25 A . In  FIG.  25 B , attachment of each subgrid to another subgrid and/or binder bar  12  is visible via clips and clip apertures. 
       FIG.  26    is an exploded isometric view of a screen assembly having pyramidal shaped subgrid units. This figure shows eleven subassemblies being secured to each other via clips and clip apertures along subgrid side members of subgrid units in each subassembly. Each flat subassembly has two end subgrids ( 14  or  414 ) and three center subgrids ( 18  or  418 ). Each pyramidal shaped subassembly has two pyramidal shaped end subgrids ( 58  or  458 ) and three pyramidal shaped center subgrids ( 60  or  460 ). Binder bars  12  are fastened at each end of the assembly. Different size screen assemblies may be created using different numbers of subassemblies or different numbers of center subgrid units. Screening surface area may be increased by incorporating more pyramidal shaped subassemblies or decreased by incorporating more flat assemblies. An assembled screen assembly has a continuous screen assembly screening surface made up of multiple screen element screening surfaces. 
       FIG.  27    shows installation of screen assemblies  80  upon a vibratory screening machine having two screening surfaces.  FIG.  30    is a front view of the vibratory machine shown in  FIG.  27   . The vibratory screening machine may have compression assemblies on side members of the vibratory screening machine. The screen assemblies may be placed into the vibratory screening machine as shown. A compression force may be applied to a side member of the screen assembly such that the screen assembly deflects downward into a concave shape. A bottom side of the screen assembly may mate with a screen assembly mating surface of the vibratory screening machine as shown in U.S. Pat. No. 7,578,394 and U.S. patent application Ser. No. 12/460,200 (now U.S. Pat. No. 8,443,984). The vibratory screening machine may include a center wall member configured to receive a side member of the screen assembly opposite of the side member of the screen assembly receiving compression. The center wall member may be angled such that a compression force against the screen assembly deflects the screen assembly downward. The screen assembly may be installed in the vibratory screening machine such that it is configured to receive material for screening. The screen assembly may include guide notches configured to mate with guides of the vibratory screening machine such that the screen assembly may be guided into place during installation. 
       FIG.  28    shows an isometric view of a screen assembly having pyramidal shaped subgrids where screen elements have not been attached. The screen assembly shown in  FIG.  28    has a slightly concave shape; however, the screen assembly may be more concave, convex, or flat. The screen assembly may be made from multiple subassemblies, which may be any combination of flat subassemblies and pyramidal shaped subassemblies. As shown, eleven subassemblies are included, however, greater or fewer subassemblies may be included. The screen assembly is shown without screen elements  16  (or  416 ). The subgrids may be assembled together before or after attachment of screen elements to subgrids or any combination of subgrids having attached screen elements and subgrids without screen elements may be fastened together.  FIG.  29    shows the screen assembly of  FIG.  28    partially covered in screen elements. Pyramidal shaped subassemblies include pyramidal shaped end subgrids  58  and pyramidal shaped center subgrids  60 . Flat subassemblies include flat end subgrids  14  and flat center subgrids  18 . The subgrid units may be secured to each other via clips and clip apertures. 
       FIG.  31    shows installation of screen assembly  81  in a vibratory screening machine having a single screening surface, according to an exemplary embodiment of the present invention. Screen assembly  81  is similar in configuration to screen assembly  80  but includes additional pyramid and flat assemblies. The vibratory screening machine may have a compression assembly on a side member of the vibratory screening machine. Screen assembly  81  may be placed into the vibratory screening machine as shown. A compression force may be applied to a side member of screen assembly  81  such that screen assembly  81  deflects downward into a concave shape. A bottom side of the screen assembly may mate with a screen assembly mating surface of the vibratory screening machine as shown in U.S. Pat. No. 7,578,394 and U.S. patent application Ser. No. 12/460,200 (now U.S. Pat. No. 8,443,984). The vibratory screening machine may include a side member wall opposite of the compression assembly configured to receive a side member of the screen assembly. The side member wall may be angled such that a compression force against the screen assembly deflects the screen assembly downward. The screen assembly may be installed in the vibratory screening machine such that it is configured to receive material for screening. The screen assembly may include guide notches configured to mate with guides of the vibratory screening machine such that the screen assembly may be guided into place during installation. 
       FIG.  32    is a front view of screen assemblies  82  installed upon a vibratory screening machine having two screening surfaces, according to an exemplary embodiment of the present invention. Screen assembly  82  is an alternate embodiment where the screen assembly has been pre-formed to fit into the vibratory screening machine without applying a load to the screen assembly, i.e., screen assembly  82  includes a bottom portion  82 A that is formed such that it mates with a bed  83  of the vibratory screening machine. The bottom portion  82 A may be formed integrally with screen assembly  82  or it may be a separate piece. Screen assembly  82  includes similar features as screen assembly  80 , including subgrids and screen elements but also includes bottom portion  82 A that allows it to fit onto bed  83  without being compressed into a concave shape. A screening surface of screen assembly  82  may be substantially flat, concave or convex. Screen assembly  82  may be held into place by applying a compression force to a side member of screen assembly  82  or may simply be held in place. A bottom portion of screen assembly  82  may be pre-formed to mate with any type of mating surface of a vibratory screening machine. 
       FIG.  33    is a front view of screen assembly  85  installed upon a vibratory screening machine having a single screening surface, according to an exemplary embodiment of the present invention. Screen assembly  85  is an alternate embodiment where the screen assembly has been pre-formed to fit into the vibratory screening machine without applying a load to the screen assembly i.e., screen assembly  85  includes a bottom portion  85 A that is formed such that it mates with a bed  87  of the vibratory screening machine. The bottom portion  85 A may be formed integrally with screen assembly  85  or it may be a separate piece. Screen assembly  85  includes similar features as screen assembly  80 , including subgrids and screen elements but also includes bottom portion  85 A that allows it to fit onto bed  87  without being compressed into a concave shape. A screening surface of screen assembly  85  may be substantially flat, concave or convex. Screen assembly  85  may be held into place by applying a compression force to a side member of screen assembly  85  or may simply be held in place. A bottom portion of screen assembly  85  may be pre-formed to mate with any type of mating surface of a vibratory screening machine. 
       FIG.  34    is an isometric view of the end subgrid shown in  FIG.  3    having a single screen element partially attached thereto.  FIG.  35    is an enlarged view of break out section E of the end subgrid shown in  FIG.  34   . In  FIGS.  34  and  35   , screen element  16  is partially attached to end subgrid  38 . Screen element  16  is aligned with subgrid  38  via elongated attachment members  44  and screen element attachment apertures  24  such that the elongated attachment members  44  pass through the screen element attachment apertures  24  and extend slightly beyond the screen element screening surface. As shown along the end edge portion of screen element  16 , the portions of the elongated attachment members  44  extending beyond screen element screening surface are melted to form beads upon the screen element screening surface, securing the screen element  16  to end subgrid unit  38 . 
       FIG.  36    shows a slightly concave screen assembly  91  having pyramidal shaped subgrids incorporated into a portion of screen assembly  91  according to an exemplary embodiment of the present invention. A screening surface of the screen assembly may be substantially flat, concave or convex. The screen assembly  91  may be configured to deflect to a predetermined shape under a compression force. The screen assembly  91 , as shown in  FIG.  36   , incorporates pyramidal shaped subgrids in the portion of the screen assembly installed nearest the inflow of material on the vibratory screening machine. The portion incorporating the pyramidal shaped subgrids allows for increased screening surface area and directed material flow. A portion of the screen assembly installed nearest a discharge end of the vibratory screening machine incorporates flat subgrids. On the flat portion, an area may be provided such that material may be allowed to dry and/or cake on the screen assembly. Various combinations of flat and pyramidal subgrids may be included in the screen assembly depending on the configuration desired and/or the particular screening application. Further, vibratory screening machines that use multiple screen assemblies may have individual screen assemblies with varying configurations designed for use together on specific applications. For example, screen assembly  91  may be used with other screen assemblies such that it is positioned near the discharge end of a vibratory screening machine such that it provides for caking and/or drying of a material. 
       FIG.  37    is a flow chart showing steps to fabricate a screen assembly, according to an exemplary embodiment of the present invention. As shown in  FIG.  37   , a screen fabricator may receive screen assembly performance specifications for the screen assembly. The specifications may include at least one of a material requirement, open screening area, capacity and a cut point for a screen assembly. The fabricator may then determine a screening opening requirement (shape and size) for a screen element as described herein. The fabricator may then determine a screen configuration (e.g., size of assembly, shape and configuration of screening surface, etc.). For example, the fabricator may have the screen elements arranged in at least one of a flat configuration and a non-flat configuration. A flat configuration may be constructed from center subgrids ( 18  or  418 ) and end subgrids ( 14  or  414 ). A non-flat configuration may include at least a portion of pyramidal shaped center subgrids ( 60  or  460 ) and/or pyramidal shaped end subgrids ( 58  or  458 ). Screen elements may be injection molded. Subgrid units may also be injection molded but are not required to be injection molded. Screen elements and subgrids may include a nanomaterial, as described herein, dispersed within. After both screen elements and subgrid units have been created, screen elements may be attached to subgrid units. The screen elements and subgrids may be attached together using connection materials having a nanomaterial dispersed within. Screen elements may be attached to subgrids using laser welding. Multiple subgrid units may be attached together forming support frames. Center support frames are formed from center subgrids and end support frames are formed from end subgrids. Pyramidal shaped support frames may be created from pyramidal shaped subgrid units. Support frames may be attached such that center support frames are in a center portion of the screen assembly and end support frames are on an end portion of the screen assembly. Binder bars may be attached to the screen assembly. Different screening surface areas may be accomplished by altering the number of pyramidal shaped subgrids incorporated into the screen assembly. Alternatively, screen elements may be attached to subgrid units after attachment of multiple subgrids together or after attachment of multiple support frames together. Instead of multiple independent subgrids that are attached together to form a single unit, one subgrid structure may be fabricated that is the desired size of the screen assembly. Individual screen elements may then be attached to the one subgrid structure. 
       FIG.  38    is a flow chart showing steps to fabricate a screen assembly, according to an exemplary embodiment of the present invention. A thermoplastic screen element may be injection molded. Subgrids may be fabricated such that they are configured to receive the screen elements. Screen elements may be attached to subgrids and multiple subgrid assemblies may be attached, forming a screening surface. Alternatively, the subgrids may be attached to each other prior to attachment of screen elements. 
     In another exemplary embodiment, a method for screening a material is provided, including attaching a screen assembly to a vibratory screening machine and forming a top screening surface of the screen assembly into a concave shape, wherein the screen assembly includes a screen element having a series of screening openings forming a screen element screening surface and a subgrid including multiple elongated structural members forming a grid framework having grid openings. The screen elements span grid openings and are secured to a top surface of the subgrid. Multiple subgrids are secured together to form the screen assembly and the screen assembly has a continuous screen assembly screening surface comprised of multiple screen element screening surfaces. The screen element is a single thermoplastic injection molded piece. 
       FIG.  39    is an isometric view of a vibratory screening machine having a single screen assembly  89  with a flat screening surface installed thereon with a portion of the vibratory machine cut away showing the screen assembly. Screen assembly  89  is a single unit that includes a subgrid structure and screen elements as described herein. The subgrid structure may be one single unit or may be multiple subgrids attached together. While screen assembly  89  is shown as a generally flat type assembly, it may be convex or concave and may be configured to be deformed into a concave shape from a compression assembly or the like. It may also be configured to be tensioned from above or below or may be configured in another manner for attachment to different types of vibratory screening machines. While the embodiment of the screen assembly shown covers the entire screening bed of the vibratory screening machine, screen assembly  89  may also be configured in any shape or size desired and may cover only a portion of the screening bed. 
       FIG.  40    is an isometric view of a screen element  99  according to an exemplary embodiment of the present invention. Screen element  99  is substantially triangular in shape. Screen element  99  is a single thermoplastic injection molded piece and has similar features (including screening opening sizes) as screen elements  16  and  416  as described herein. Alternatively, the screen element may be rectangular, circular, triangular, square, etc. Any shape may be used for the screen element and any shape may be used for the subgrid as long as the subgrid has grid openings that correspond to the shapes of the screen elements. 
       FIGS.  40 A and  40 B  show screen element structure  101 , which may be a subgrid type structure, with screen elements  99  attached thereto forming a pyramid shape. In an alternative embodiment the complete pyramid structure of screen element structure  101  may be thermoplastic injection molded as a single screen element having a pyramid shape. In the configuration shown, the screen element structure has four triangular screen element screening surfaces. The bases of two of the triangular screening surfaces begin at the two side members of the screen element and the bases of the other two triangular screening surfaces begin at the two end members of the screen element. The screening surfaces all slope upward to a center point above the screen element end members and side members. The angle of the sloped screening surfaces may be varied. Screen element structure  101  (or alternatively single screen element pyramids) may be attached to a subgrid structure as described herein. 
       FIGS.  40 C and  40 D  show a screen element structures  105  with screen elements  99  attached and having a pyramidal shape dropping below side members and edge members of the screen element structure  105 . Alternatively, the entire pyramid may be thermoplastic injection molded as a single pyramid shaped screen element. In the configuration shown, individual screen elements  99  form four triangular screening surfaces. The bases of two of the triangular screening surfaces begin at the two side members of the screen element and the bases of the other two triangular screening surfaces begin at the two end members of the screen element. The screening surfaces all slope downward to a center point below the screen element end members and side members. The angle of the sloped screening surfaces may be varied. Screen element structure  105  (or alternatively single screen element pyramids) may be attached to a subgrid structure as described herein. 
       FIGS.  40 E and  40 F  show a screen element structure  107  having multiple pyramidal shapes dropping below and rising above the side members and edge members of screen element structure  107 . Each pyramid includes four individual screen elements  99  but may also be formed as single screen element pyramid. In the configuration shown, each screen element has sixteen triangular screening surfaces forming four separate pyramidal screening surfaces. The pyramidal screening surfaces may slope above or below the screen element end members and side members. Screen element structure  107  (or alternatively single screen element pyramids) may be attached to a subgrid structure as described herein.  FIGS.  40  through  40 F  are exemplary only as to the variations that may be used for the screen elements and screen element support structures. 
       FIGS.  41  to  43    show cross-sectional profile views of exemplary embodiments of thermoplastic injection molded screen element surface structures that may be incorporated into the various embodiments of the present invention discussed herein. The screen element is not limited to the shapes and configurations identified herein. Because the screen element is thermoplastic injection molded, multiple variations may be easily fabricated and incorporated into the various exemplary embodiments discussed herein. 
       FIG.  44    shows a prescreen structure  200  for use with vibratory screening machines. Prescreen structure  200  includes a support frame  300  that is partially covered with individual prescreen assemblies  210 . Prescreen assemblies  210  are shown having multiple prescreen elements  216  mounted on prescreen subgrids  218 . Although, prescreen assemblies  210  are shown including six prescreen subgrids  218  secured together, various numbers and types of subgrids may be secured together to form various shapes and sizes of prescreen assemblies  210 . The prescreen assemblies  210  are fastened to support frame  300  and form a continuous prescreening surface  213 . Prescreen structure  200  may be mounted over a primary screening surface. Prescreen assemblies  210 , prescreen elements  216  and the prescreen subgrids  218  may include any of the features of the various embodiments of screen assemblies, screen elements and subgrid structures described herein and may configured to be mounted on prescreen support frame  300 , which may have various forms and configurations suitable for prescreening applications. Prescreen structure  200 , prescreen assemblies  210 , prescreen elements  216  and the prescreen subgrids  218  may be configured to be incorporated into the prescreening technologies (e.g., compatible with the mounting structures and screen configurations) described in U.S. patent application Ser. No. 12/051,658 (now U.S. Pat. No. 8,439,203). 
       FIG.  44 A  shows an enlarged view of prescreen assembly  210 . 
       FIG.  58    is a top isometric view of a portion of a screen assembly  510 . Screen assembly  510  includes screen elements  416 , center subgrid units  518 , and end subgrid units  514 . Screen elements  416  were described in detail above with reference to  FIGS.  48 ,  48 A,  48 B, and  48 C . End subgrid units  514  are described in greater detail below with reference to  FIGS.  59  and  59 A , and center subgrid units  518  are described in greater detail below with reference to  FIGS.  60  and  60 A . Screen assembly  510  is similar to screen element  410  described above with reference to  FIG.  47   . Like screen assembly  410 , screen assembly includes binder bars  12  that are attached to ends of the screen assembly. 
     In further embodiments, screen assemblies similar to screen assembly  510  of  FIG.  58    (or screen assembly  410  of  FIG.  47   ) may be formed by mixing and matching various screen elements (e.g.,  416  of  FIGS.  48 - 48 C,  516    of  FIGS.  66 - 66 C, and  616    of  FIG.  70 A ) with various subgrid structures (e.g.,  14  of  FIGS.  3  and  3 A,  514    of  FIGS.  59  and  59 A,  818    of  FIGS.  65  and  65 A,  918    of  FIGS.  71 A- 71 D , etc.). As described in greater detail below, screen element  516  has similar features to screen element  416  but screen elements  516  and  416  have different sizes. In an example embodiment, screen element  416  may be a 2″×3″ screen element while screen elements  516  and  616  may be 1″×6″ screen elements. As described in greater detail below, screen element  616  has smaller features than screen element  516 . Further, the smaller width of screen elements  516  and  616 , and associated structures, allows smaller features to be manufactured. 
       FIG.  59    is a top isometric view of an end subgrid  514 , and  FIG.  59 A  is a bottom isometric view of end subgrid  514  shown in  FIG.  59   . End subgrid  514  is an alternative embodiment to end subgrid  414  shown in  FIGS.  49  and  49 A . End subgrid  514  may be thermoplastic (or other suitably chosen material) injection molded and may include all of the features of end subgrid unit  414  with the exception of clips  42  of end subgrid unit  414 . End subgrid unit  514  includes clips  142  as discussed in greater detail below. 
     With the exception of clips  142 , end subgrids  514  (e.g., see  FIGS.  59 ,  59 A,  61 , and  61 A ) include structural features similar to those found in end subgrids  414  (e.g., see  FIGS.  49 ,  49 A,  51 , and  51 A ). For example, end subgrid  514  includes a plurality elongated location members  444 , a secondary support framework  488  spanning across grid openings  50 , a plurality of fusion bars  476 , and a plurality of shortened fusion bars  478 . Further, end subgrid  514  includes parallel subgrid end members  36 , and parallel subgrid side members  38  that are substantially perpendicular to the subgrid end members  36 . 
     Screen elements  416  (e.g., see  FIGS.  61  and  61 A ) may be attached to end subgrids  514 , using methods similar to those described herein, including methods above with reference to  FIGS.  51  and  51 A  for attaching screen element  416  to end subgrids  414 . For example, as shown in  FIG.  61   , two screen elements  416  may be positioned over an end subgrid unit  514 . Fusion bars  476  and  478  may be melted (e.g., using laser welding, heat staking, etc.) to fuse the two screen elements  416  to end subgrid unit  514  to form the end subassembly  660  shown in  FIG.  61 A . Further details describing this technique of fusing a screen element to a subgrid unit are described above with reference to  FIGS.  51  and  51 A . In other embodiments, other methods may be used to fuse a screen element to a subgrid. For example, screen elements may be affixed to the subgrids by at least one of a mechanical arrangement, an adhesive, heat staking, and ultrasonic welding, as described above. 
       FIG.  60    is a top isometric view of a center subgrid  518 , and  FIG.  60 A  is a bottom isometric view of center subgrid  518  shown in  FIG.  60   . Center subgrid  518  is an alternative embodiment to center subgrid  418  shown in  FIGS.  50  and  50 A . Center subgrid  518  may be thermoplastic (or other suitably chosen material) injection molded and may include all of the features of center subgrid unit  418  with the exception of clips  42  of center subgrid unit  418 . Center subgrid unit  518  includes clips  142  as discussed in greater detail below. 
     Similarly, with the exception of clips  142 , center subgrids  518  (e.g., see  FIGS.  60 ,  60 A,  62 , and  62 A ) include structural features similar to those found in center subgrids  418  (e.g., see  FIGS.  50 ,  50 A,  52 , and  52 A ). For example, center subgrid  518  includes a plurality elongated location members  444 , a secondary support framework  488  spanning across grid openings  50 , a plurality of fusion bars  476 , and a plurality of shortened fusion bars  478 . Further, center subgrid  518  includes parallel subgrid end members  36 , and parallel subgrid side members  38  that are substantially perpendicular to the subgrid end members  36 . 
     Screen elements  416  (e.g., see  FIGS.  62  and  62 A ) may be attached to center subgrids  518 , using methods similar to those discussed above with reference to  FIGS.  52  and  52 A  for attaching screen element  416  to center subgrids  418 . For example, as shown in  FIG.  62   , two screen elements  416  may be positioned over a center subgrid unit  518 . Fusion bars  476  and  478  may be melted to fuse the two screen elements  416  to center subgrid unit  518  to form the center subassembly  760  shown in  FIG.  62 A , as described in greater detail above with reference to  FIGS.  52  and  52 A . Further details describing this technique of fusing a screen element to a subgrid unit are described above with reference to  FIGS.  52  and  52 A . 
     Clips  142  (e.g., see  FIGS.  59 ,  59 A,  60 ,  60 A, and  63 C ) include similar extended members to those of clips  42 . In addition to the two extended members of clips  42  (e.g. see  FIGS.  3 ,  3 A,  49 ,  49 A,  50  and  50 A ) clips  142  have an additional extended member for a total of three extended members (e.g., see  FIG.  63    and related discussion below). The presence of three extended members allows clips  142  to make a stronger and more rugged connection between end subgrid units  514  relative to the connection between end subgrid units  414  (e.g., see  FIGS.  49  and  49 A ) provided by clips  42 . Similarly, clips  142  provide stronger and more rugged connections between end subgrid units  514  and center subgrids  518 , and between neighboring center subgrid units  518 , relative to connections provided by clips  42 . 
     The use of clips  142  (e.g., see  FIGS.  59 ,  59 A,  60 ,  60 A, and  63 C ) is similar to the use of clips  42  (e.g. see  FIGS.  3 ,  3 A , and related discussion). In this regard, subgrid units (e.g., end subgrid units  514  and/or center subgrid units  518 ) may be secured together along their respective side members  38  by passing clip  142  into clip aperture  40  until the three extended members of clip  142  extend beyond clip aperture  40  and subgrid side member  38 . As clip  142  is pushed into clip aperture  40 , extended members of clip  142  will be forced together until a clipping portion of each extended member is beyond subgrid side member  38  allowing the clipping portions of clip  142  to engage an interior portion of subgrid side member  38 . 
     As described above with reference to  FIGS.  3  and  3 A , when the clipping portions of clip  142  are engaged into clip aperture  40 , subgrid side members of two independent end subgrids  514  will be side by side and secured together (e.g. see  FIGS.  3 ,  3 A , and related discussion). Similarly, when the clipping portions of clip  142  are engaged into the clip aperture  40 , subgrid side members of two independent center subgrids  518  will be side by side and secured together. An end member  36  of end subgrid  514  may similarly be secured to an end member  36  of a center subgrid  518 . Likewise end members  36  of two neighboring center subgrids  518  may be secured together. The subgrids may be separated by applying a force to the extended members of clip  142  such that the extended members are moved together allowing for the clipping portions to pass out of clip aperture  40 . 
     In further embodiments, clips  142  may be configured to form a permanent connection between subgrids that once connected cannot be disconnected without breaking the clips  142  or one or more of the subgrids. Such embodiments having clips  142  that may form permanent connections may be advantageous for generating screen assemblies that may be secured into a vibratory screening machine based on compressive forces as described, for example, in U.S. Pat. Nos. 7,578,394 and 9,027,760, the disclosure of each of which is incorporated herein by reference. In this regard, screen assemblies may be generated that can withstand compressive forces in a range of 2000-3000 lb applied to edges of screen assemblies. Further, such screen assemblies may be configured to operate in a vibratory screening machine with vibrational accelerations in a range of 3-9 G. 
       FIG.  63    is a top isometric view of a pyramidal shaped end subgrid  558 , and  FIG.  63 A  is a bottom isometric view of the pyramidal shaped end subgrid  558  shown in  FIG.  63   . Pyramidal shaped subgrid  558  of  FIGS.  63  and  63 A  is an alternative embodiment to pyramidal shaped end subgrid  458  shown in  FIGS.  53  and  53 A . Pyramidal shaped subgrid  558  may be thermoplastic (or other suitably chosen material) injection molded and may include all of the features of pyramidal shaped end subgrid  458  with the exception of clips  42  of pyramidal shaped end subgrid unit  458 . Pyramidal shaped subgrid  558  includes clips  242 . 
     Similarly, with the exception of clips  242 , pyramidal shaped subgrid  558  (e.g., see  FIGS.  63  and  63 A ) includes structural features similar to those found in pyramidal shaped end subgrid  458  (e.g., see  FIGS.  53  and  53 A . For example, pyramidal shaped end subgrid  558  includes a ridge portion  66 , subgrid side members/base members  64 , and angular surfaces  70  that peak at ridge portion  66  and extend downwardly to side member  64 . Pyramidal shaped subgrid  558  also has triangular end members  62 . Pyramidal shaped end subgrid  558  may have a plurality elongated location members  444 , and second adhesion arrangements such as a plurality of fusion bars  476  and shorted fusion bars  478 . Pyramidal shaped end subgrid  558  may include secondary support framework  488  spanning across grid openings, and may include a flattened ridge portion  465  and may have fixture locators  490  in ridge  66 . 
     Clips  242  are similar to clips  142  in that they have additional structure that provides for a stronger and more rugged connection between neighboring pyramidal shaped end subgrids  458 . For example, clips  242  have two similar extended members that are structurally similar to the two extended members of clips  42  and  142 . Clips  242  also have an additional central extended member (e.g., see  FIG.  63 D  below) that likewise engages an interior portion of subgrid side member  64 . 
     Clips  142  and  242  provide additional structure to form strong connections between subgrid units and may withstand compression forces in a range from 2000-3000 lb compression force on a screen assembly. Further, when screening subassemblies are formed into screening assemblies, the resulting assemblies that utilize clips  142  and  242  provide strong binding forces between subassemblies so that the resulting screen assembly may withstand large vibrational accelerations on the order of 3G to 9G. Disclosed screening assemblies are further designed to support abrasive materials (e.g., fluids having several percent to up to 65 percent abrasive solids) and high load demands (e.g., fluids having specific gravity up to 3 pounds per gallon), as described in greater detail below. 
       FIGS.  63 B,  63 C, and  63 D  compare structural features of clips  42  (e.g., see  FIGS.  3  and  3 A ),  142  (e.g. see  FIGS.  59 - 62 A ), and  242  (e.g., see  FIGS.  63  and  63 A ), respectively.  FIG.  63 B  illustrates an isometric view of clip  42 . As shown in  FIG.  63 B , clip  42  has first  42   a  and second  42   b  extended members that engage with a clipping aperture  40  (e.g., see  FIG.  59   ).  FIG.  63 C  illustrates an isometric view of clip  142 , which has first  142   a  and second  142   b  extended members that are similar to corresponding first  42   a  and second  42   b  extended members of clip  42  of  FIG.  63 B  (see also  FIGS.  3  and  3 A ). Clip  142 , however, provides third  142   c  extended member as shown in  FIG.  63 C . The three extended members,  142   a ,  142   b , and  142   c , of clip  142  provide a stronger and more rugged connection between subgrids, as described above. 
       FIG.  63 D  illustrates an isometric view of clip  242 . As shown in  FIG.  63 D , clip  142  has first  242   a  and second  242   b  extended members that are similar to first  42   a  and second  42   b  extended members of clip  42  (e.g., see  FIGS.  3 ,  3 A,  63 B ), and are similar to first  142   a  and second  142   b  extended members of clip  142  (e.g., see  FIG.  63 C ). As mentioned above, however, clip  142  of  FIG.  63 D  also has a central extended member  242   c  that engages with upper and lower edges of clip aperture  40  (e.g., see  FIG.  63   ). Clip  242  provides additional stability for connections between subgrids in that central extended member  242   c  hinders rotational motion about an axis  242   d  of two subgrids bound by clip  242 , as shown in  FIG.  63 D . 
     The above discussion may be generalized straightforwardly in that any structure having clips  42  may be generalized to a similar structure having clips  142  or  242  (e.g., see  FIGS.  63 C and  63 D ). For example, pyramidal shaped center subgrid  460  shown in  FIGS.  54  and  54 A  may similarly be generalized to a pyramidal shaped center subgrid structure having clips  142  or  242  (not shown). Similarly, the methods for attaching screening members  416  to such pyramidal shaped subgrids described above with reference to  FIGS.  55 ,  55 A,  56  and  56 A  may be employed to attach screening members  416  to the generalized pyramidal shaped center subgrids since clips  42 ,  142 , and  242  play no role in the process of attaching screening members  416 . 
       FIG.  64    is a top isometric view of an end subgrid  718 , and  FIG.  64 A  is a bottom isometric view of end subgrid  718  shown in  FIG.  64   . End subgrid  718  is an alternative embodiment to end subgrid  514  shown in  FIGS.  59  and  59 A . End subgrid  718  may be thermoplastic (or other suitably chosen material) injection molded and may include similar features to those found in end subgrid unit  514 . For example, end subgrid  718  includes a plurality elongated location members  444 , a secondary support framework  488  spanning across grid openings  50 , a plurality of fusion bars  476 , and a plurality of shortened fusion bars  478 . Further, end subgrid  718  includes parallel subgrid end members  136 , and parallel subgrid side members  138  that are substantially perpendicular to the subgrid end members  136 . End subgrid  718  may also have clips  242  similar to those of pyramidal shaped end subgrid  558  (e.g., see  FIGS.  63  and  63 A ). Alternatively, in an embodiment end subgrid  718  may employ other clips such as clips  142  of end subgrid  514  (e.g., see  FIGS.  59  and  59 A ) or clips  42  of end subgrid  14  (e.g., see  FIGS.  3  and  3 A ). 
     In contrast to end subgrid  514 , however, end subgrid  718  has about the same length as end subgrid  514  but about half the width of end subgrid  514 . In other words, a length measured along the parallel subgrid side members  138  for end subgrid  718  is substantially equal to a length measured along the parallel subgrid side members  38  for end subgrid  514 , but the a distance measured along parallel subgrid end member  136  for subgrid  718  is substantially equal to half the distance measured along the subgrid end member  36  of end subgrid  514 . The shorter width of end subgrid  718  provides an advantage in that it may support corresponding screen elements  516  (e.g., see  FIGS.  66 ,  66 A,  66 B, and  66 C ) having half the width of screen elements  416  (e.g., see  FIGS.  48 ,  48 A,  48 B, and  48 C ). Screen elements  516  having a shorter width allows manufacturing of screen elements  516  having smaller features such as smaller screening openings  86 , and smaller surface elements  84  (e.g., see  FIG.  2 D ), as described in greater detail below. 
       FIG.  65    is a top isometric view of a center subgrid  818 , and  FIG.  65 A  is a bottom isometric view of the center subgrid  818  shown in  FIG.  65   . Center subgrid  818  is an alternative embodiment to center subgrid  518  shown in  FIGS.  60  and  60 A . Center subgrid  818  may be thermoplastic (or other suitably chosen material) injection molded and may include similar features to those found in center subgrid unit  518 . For example, center subgrid  818  includes a plurality of elongated location members  444 , a secondary support framework  488  spanning across grid openings  50 , a plurality of fusion bars  476 , and a plurality of shortened fusion bars  478 . Further, center subgrid  818  includes parallel subgrid end members  136 , and parallel subgrid side members  138  that are substantially perpendicular to the subgrid end members  136 . Center subgrid  818  may also have clips  242  similar to those of pyramidal shaped center subgrid  558  (e.g., see  FIGS.  63  and  63 A ). Alternatively, in an embodiment center subgrid  818  may employ other clips such as clips  142  of center subgrid  518  (e.g., see  FIGS.  60  and  60 A ) or clips  42  of center subgrid  18  (e.g., see  FIGS.  4  and  4 A ). 
     In contrast to center subgrid  518 , however, center subgrid  818  has about the same length as center subgrid  518  but about half the width of center subgrid  518  (e.g., compare  FIGS.  65  and  65 A  with  FIGS.  60  and  60 A ). In other words, a length measured along parallel subgrid side members  138  for center subgrid  818  is substantially equal to a length measured along parallel subgrid side member  38  for center subgrid  518 , but a distance measured along parallel subgrid end members  136  for subgrid  818  is substantially equal to half a distance measured along the subgrid end members  36  of center subgrid  518 . The shorter width of center subgrid  818  provides an advantage in that it may support corresponding screen elements  516  (e.g., see  FIGS.  66 ,  66 A,  66 B, and  66 C ) having half the width of screen elements  416  (e.g., see  FIGS.  48 ,  48 A,  48 B, and  48 C ). Screen elements  516  having a shorter width allows manufacturing of screen elements  516  having smaller features such as smaller screening openings  86 , and smaller surface elements  84  (e.g., see  FIG.  2 D ), as described in greater detail below. 
     As described in greater detail below (e.g., with reference to  FIGS.  70 - 74 D ), screen elements (e.g., see  FIG.  70 A ) having smaller features such as smaller screening openings  86 , and smaller surface elements  84  (e.g., see  FIG.  2 D , and Tables I.-IV. below), are designed to be supported by corresponding subgrid structures having additional structural features (e.g., see  FIGS.  71 - 71 D,  72 , and  72 A ) that support corresponding reinforcement members (e.g., see  FIGS.  71 E,  71 F,  72 B,  72 C,  74 B, and  74 C ) of screening elements. The smaller screening features of screen elements that are supported by additional structure of the subgrids may be assembled into screening assemblies having increased open screening area. 
     In this way, screen elements are provided that: are of an optimal size (large enough for efficient assembly of a complete screen assembly structure yet small enough to injection mold (micro-mold in certain embodiments) extremely small structures forming screening openings while avoiding freezing (i.e., material hardening in a mold before completely filling the mold)); have optimal open screening area (the structures forming the openings and supporting the openings are of a minimal size to increase the overall open area used for screening while maintaining, in certain embodiments, very small screening openings necessary to properly separate materials to a specified standard); have durability and strength, can operate in a variety of temperature ranges; are chemically resistant; are structurally stable; are highly versatile in screen assembly manufacturing processes; and are configurable in customizable configurations for specific applications. 
     Further, screening elements, subgrids, and screen assemblies may have different shapes and sizes as long as structural support members of subgrids are provided to support corresponding reinforcement members of screening elements. Screens, subgrids, and screen assemblies are designed to withstand high vibratory forces (e.g., accelerations in a range of 3-9G), abrasive materials (e.g., fluids having several percent to up to 65 percent abrasive solids) and high load demands (e.g., fluids having specific gravity up to 3 pounds per gallon). Screen assemblies are also designed to withstand up to 2000-3000 lb compressive loading of screen assembly edges as described, for example, in U.S. Pat. Nos. 7,578,394 and 9,027,760, the entire disclosure of each of which is hereby incorporated by references. Further, the disclose screening assemblies are designed so that a size of screening openings is maintained under service conditions including the above-mentioned compressive loading, high vibratory forces, and in the presence of heavy fluids. 
       FIGS.  66 ,  66 A,  66 B, and  66 C  illustrate a screen element  516  that is similar to screen element  416  (e.g., see  FIGS.  48 ,  48 A,  48 B, and  48 C ). For example, screen element  516  may include location apertures  424 , which may be located at four corners of screen element  516  and at various places along end member  120  and side member  122  of screen element  516  (e.g., see  FIGS.  66  and  66 A ). Greater or fewer location apertures  424  may be provided on screen element  516  and multiple configurations may be provided. The location apertures  424  may be utilized to locate the screen element  516  on a subgrid (e.g., such as on end subgrid  718  of  FIGS.  64  and  64 A  or on center subgrid  818  of  FIGS.  65  and  65 A ). Screen element  516  may further include a center location aperture  524 . Alternatively, in an embodiment screen element  516  may be located without location apertures  424 . Screen element  516  may include a plurality of tapered counter bores  470 , which may facilitate extraction of screen element  516  from a mold, wherein the mold may have ejector pins configured to push the screen element out of the mold (e.g., see  FIGS.  66  and  66 A ). 
     In this example, screen elements  516  (e.g., see  FIGS.  66 - 66 C ) have twice the length of screen elements  416  but half the width of screen elements  416  (e.g., see  FIGS.  48 - 48 C ). For example, a distance measured alongside portion  122  of screen element  516  is substantially equal to twice a distance measured alongside portion  22  of screen element  416  (e.g., see  FIG.  48   ). However, a distance measured along end portion  120  of screen element  516  is substantially equal to half of a distance measured along end portion  20  of screen element  416  (e.g., see  FIG.  48   ). Choosing screen elements  516  to have a shorter width allows manufacturing of screen elements  516  having smaller features such as smaller screening openings  86 , and smaller surface elements  84  (e.g., see  FIG.  2 D ), as described in greater detail below. 
     Screen element  516  may have similar features to screen element  416  (e.g., see  FIGS.  48 B and  48 C ) on a bottom side of screen element  516 , as illustrated in  FIGS.  66 B and  66 C . For example, screen element  516  may have a plurality of cavity pockets  472  that may be arranged along end portions  120  and side portions  122  between the location apertures  424 . As with screen element  416 , the cavity pockets  472  (e.g., see  FIG.  66 C ) may serve as an adhesion arrangement of screen element  516  that may be configured to mate with a complementary second adhesion arrangement on a top surface of a subgrid unit (e.g., such as on end subgrid  718  of  FIGS.  64  and  64 A  or on center subgrid  818  of  FIGS.  65  and  65 A ). 
     As illustrated, for example, in  FIGS.  67  and  67 A , screen elements  516  may be attached to end subgrid  718  to generate end screen subassembly  860 , using methods similar to those described above used to attach screen elements  416  to end subgrid  514  to generate the end subassembly  660  (e.g., see  FIGS.  61  and  61 A ). For example, location apertures,  424  and  524 , of screen element  516  (e.g., see  FIG.  66 A ) may engage with location members  444  of end subgrid  718 . Fusion bars  476  and  478  may then be melted to fuse screen element  516  to end subgrid  718 , as described in greater detail above with reference to  FIGS.  51 ,  51 A,  61   , and  61 A. 
     In contrast to the situation illustrated in  FIG.  61   , in which two screen elements  416  span end subgrid  514 , as shown in  FIG.  67   , a single screen element  516  spans end subgrid  718 . This situation occurs because screen element  516  has twice the length and half the width of screen element  416  while end subgrid  718  has the same length but half the width of end subgrid  514 . The shorter width and longer length of screen element  516  allows smaller features, such as screening openings  86 , and smaller surface elements  84  (e.g., see  FIG.  2 D ), to be manufactured (e.g., via thermoplastic injection molding), as described in greater detail below. 
     As illustrated, for example, in  FIGS.  68  and  68 A , screen elements  516  may be attached to center subgrid  818  to generate center screen subassembly  960 , using methods similar to those described above used to attach screen elements  416  to center subgrid  518  to generate the center subassembly  760  (e.g., see  FIGS.  62  and  62 A ). For example, fusion bars  476  and  478  may be melted to fuse screen element  516  to center subgrid  818 , as described in greater detail above with reference to  FIGS.  52 ,  52 A,  62 , and  62 A . 
     In contrast to the situation illustrated in  FIG.  62   , in which two screen elements  416  span center subgrid  518 , as shown in  FIG.  68   , a single screen element  516  spans center subgrid  818 . This situation occurs because screen element  516  has twice the length and half the width of screen element  416  while center subgrid  818  has the same length but half the width of center subgrid  518 . The shorter width and longer length of screen element  516  allows smaller features, such as screening openings  86 , and smaller surface elements  84  (e.g., see  FIG.  2 D ), to be manufactured, as described in greater detail below. 
     As illustrated, for example, in  FIGS.  69  and  69 A , a screen assembly  80  may be formed by combining end screen subassemblies  860 , center screen subassemblies  960 , and screen subassemblies having pyramidal shaped subgrids, such as pyramidal shaped end subassemblies based on pyramidal end subgrids  58  and pyramidal shaped center subassemblies based on pyramidal center subgrids  60 , described above. Pyramidal shaped subassemblies may include screen elements  16  (e.g., see  FIGS.  2  to  2 C ),  416  (e.g., see  FIGS.  48  to  48 C ), or  516  (e.g., see  FIGS.  66  to  66 C ). By using end screen subassemblies  860  and center screen subassemblies  960 , which each have half the width of end subgrids  514  and center subgrids  518 , respectively, the pyramidal shaped subassemblies may be placed closer together than similar assemblies shown in other embodiments, such as the screen assemblies shown, for example, in  FIGS.  21  and  21 A . 
       FIGS.  70  and  70 A  compare screen element  516  (see  FIG.  70   ) with an alternative embodiment screen element  616  (see  FIG.  70 A ) having smaller features than those of screen element  516 . Screen element  616  is designed to support smaller features including smaller screening openings  86  and smaller surface elements  84  (e.g., see  FIG.  2 D ), as described in greater detail below. 
     Screen element  616  may be thermoplastic (or other suitably chosen material) injection molded and have similar features to those of screen element  516 . For example, screen element  616  may include location apertures  424 , which may be located at four corners of screen element  616  and at various places along end member  120  and side member  122  of screen element  616 . Greater or fewer location apertures  424  may be provided on screen element  616  and multiple configurations may be provided. The location apertures  424  may be utilized to locate the screen element  616  on a subgrid (e.g., such as on end subgrid  718  of  FIGS.  67  and  67 A  or on center subgrid  818  of  FIGS.  68  and  68 A ). Screen element  616  may further include a center location aperture  524 . Alternatively, in an embodiment, screen element  616  may be located without location apertures  424 . Screen element  616  may include a plurality of tapered counter bores  470 , which may facilitate extraction of screen element  616  from a mold, wherein the mold may have ejector pins configured to push the screen element out of the mold. 
     Screen element  616  may have a plurality of cavity pockets  472  that may be arranged along end portions  120  and side portions  122  between the location apertures  424 . As with screen element  516 , the cavity pockets  472  may serve as an adhesion arrangement of screen element  616  that may be configured to mate with a complementary second adhesion arrangement on a top surface of a subgrid unit. Screen element  616  may thus be attached to a subgrid using similar techniques as those described above for attaching screen element  516  to a subgrid. For example, fusion bars  476  and  478  (e.g., see  FIGS.  67  and  68   ) may be melted to fuse screen element  516  to a subgrid (e.g., end subgrid  718  of  FIG.  67    or center subgrid  818  of  FIG.  68   ). 
     Differences between screen element  516  (of  FIG.  70   ) and screen  616  (of  FIG.  70 A ) relate to support structures, as follows. Screen element  516  has a first series of reinforcement members  32  and screen  616  has a first series of reinforcement members  132 . The linear density of reinforcement members  132  of screen element  616  is higher than the linear density of reinforcement members  32  of screen element  516 . In this example, there are a total of ten reinforcement members  32  spanning a direction parallel to end member  120  for screen element  516 , while there are a total of fourteen reinforcement members  132  spanning a direction parallel to end member  120  for screen element  616 . The greater linear density of reinforcement members  132  of screen element  616  provides greater structural strength to screen element  616  in comparison to screen element  516 . Further, as described in greater detail below, the greater number of reinforcement members  132  allows for a greater number of screen surface elements  84  and screening openings  86 , both of which reside between reinforcement members  132 . 
     Screen element  516  has a second series of reinforcement members  34 . Screen element  616  also includes the second series of support members  34  along with an additional third series  134  of reinforcement members.  FIG.  70    illustrates two of the second series of support members  34  in screen element  516 .  FIG.  71    also illustrates a corresponding two of the second series of support members  34  of screen element  616 . The additional third series of reinforcement members  134  of screen element  616  are shown interposed between neighboring reinforcement members  34  of the second series of reinforcement members  34 . Collectively, the second series of reinforcement members  34  combined with the third series of reinforcement members  134  of screen element  616  represents a larger linear density of reinforcement members, in contrast to the linear density of second reinforcement members  34  of screen member  516 . As described above, regarding the case of the linear density of reinforcement members  132 , the greater linear density of reinforcement members,  34  and  132 , of screen element  616  provides greater structural strength to screen element  616  in comparison to screen element  516 . 
       FIGS.  71  and  71 A  compare center subgrid unit  818  (of  FIG.  71   ) with an alternative embodiment center subgrid unit  918  (of  FIG.  71 A ) having additional structural support features. The additional structural support features of center subgrid  918  correspond to and provide additional support for the third series of reinforcement members  134  of screen element  616 , as described in greater detail below. 
     Center subgrid  918  may be thermoplastic (or other suitably chosen material) injection molded and may include similar features to those found in center subgrid unit  818 . For example, center subgrid  918  includes a plurality of elongated location members  444 , a plurality of fusion bars  476 , and a plurality of shortened fusion bars  478 . Further, center subgrid  918  includes parallel subgrid end members  136 , and parallel subgrid side members  138  that are substantially perpendicular to the subgrid end members  136 . Center subgrid  918  may also have clips  242  similar to those of center subgrid  818  (e.g., see  FIG.  65   ) and to those of pyramidal shaped center subgrid  558  (e.g., see  FIGS.  63  and  63 A ). 
     Like center subgrid  818 , center subgrid  918  has a secondary support framework  488  spanning across grid openings  50  (e.g., see grid openings  50  of  FIG.  65 A ). In contrast to center subgrid  818 , however, center subgrid  918  has an additional tertiary support framework  588  as shown in greater detail in  FIGS.  71 B,  71 C,  71 D, and  71 F . 
       FIG.  71 B  shows an enlarged view of the region “A” of  FIG.  71 A . The view of  FIG.  71 B  illustrates two members of secondary support framework  488  that are parallel to end members  136  and two members of secondary framework  488  that are parallel to side members  138 . The additional tertiary support framework  588  includes members that are parallel to end members  136  and are interspersed between adjacent members of secondary framework  488  that are parallel to end members  136 . The combination of secondary framework  488  and tertiary framework  588  collectively results in a framework that has an increased linear density of support members along a direction parallel to side members  138 . The additional support members of tertiary support framework  588  correspond to, and provide support to the third series of reinforcement members  134  of screen element  616  (e.g., see  FIG.  70 A ), as described in greater detail below. Similarly, support members of secondary support framework  488  that are parallel to end members  136  support the corresponding second series of support members  34  of screen element  616 . 
       FIG.  71 C  illustrates a top-down view of center subgrid  918  and  FIG.  71 D  illustrates a side view of center subgrid  918 . Center subgrid  918  includes secondary support framework  488  as does center subgrid  818 . In contrast to center subgrid  818 , however, center subgrid  918  includes tertiary support framework  588 , as described above. Both  FIGS.  71 C and  71 D  show members of tertiary support framework  588  interspersed between adjacent members of secondary support framework  488  that are parallel to end members  136 . As mentioned above, the combination of secondary framework  488  and tertiary framework  588  collectively results in a framework that has an increased linear density of support members along a direction parallel to side members  138 . 
       FIGS.  71 E and  71 F  illustrate a correspondence between reinforcement members of screen elements  516  and  616  and corresponding members of support frameworks  488  and  588 , respectively. For clarity of comparison, screen  516  is placed next to center subgrid  818  in  FIG.  71 E , and screen  616  is placed next to center subgrid  918  in  FIG.  71 F . In  FIG.  71 E , two reinforcement members  34  of screen element  516  are shown to spatially align with corresponding members of secondary support network  488  of center subgrid  818 . Similarly, in  FIG.  71 F , two reinforcement members  34  of screen element  616  are shown to spatially align with corresponding members of secondary support network  488  of center subgrid  918 . Further,  FIG.  71 F  shows two members of third series of support members  134  that spatially align with corresponding members of tertiary support network  588  of center subgrid  918 . As mentioned above, the additional tertiary support framework  588  includes members that are parallel to end members  136  and are interspersed between adjacent members of secondary framework  488  that are parallel to end members  136 . As such, the combination of secondary framework  488  and tertiary framework  588  collectively results in a framework that has an increased linear density of support members along a direction parallel to side members  138 . 
     The above discussion regarding end subgrids  818  and  918  may be generalized to other subgrid structures, including end subgrids, as well as pyramidal center, and end subgrids. For example,  FIG.  72    illustrates pyramidal shaped end subgrid  558  having a grid framework with a first linear density of support members along a direction parallel to side member  64 . The support members in  FIGS.  72  and  72 A  are parallel to end member  62 .  FIG.  72 A  illustrates an alternate embodiment pyramidal shaped end subgrid  658  that includes a grid framework having a higher linear density of support members along a direction parallel to side member  64  in contrast to pyramidal shaped end subgrid  558  of  FIG.  72   . The additional support members of end subgrid  658  provide support for the reinforcement members of screen element  516  as follows. 
       FIG.  72 B  illustrates support members  688  of support framework of end subgrid  558  that spatially align with corresponding reinforcement members  34  of screen element  516 . This alignment between support members  688  of pyramidal shaped end subgrid  558  and reinforcement members  34  of screen element  516  is similar to the way that support members  488  of center subgrid  818  aligned with reinforcement members  34  of screen element  516  in  FIG.  71 E . 
     Similarly, pyramidal shaped end subgrid  658 , shown in  FIG.  71 F , has support members  688  that spatially align with corresponding reinforcement members  34  of screen element  616 . In contrast to pyramidal shaped end subgrid  558 , however, pyramidal shaped end subgrid  658  includes additional support members  788 . As shown in  FIG.  72 C , support members  788  of pyramidal shaped end subgrid  658  spatially align with reinforcement members  134  of screen element  616 . In this regard, pyramidal shaped end subgrid  658  provides additional structural support to screen element  516  than pyramidal shaped end subgrid  558  provides to screen element  416 . 
     The following discussion provides further details of screen element  616  with reference to  FIGS.  73  to  73 D and  74  to  74 D . As mentioned above, screen element  616  is similar to screen element  516  in that it is twice as long and half as wide as screen element  416  (e.g., compare relative dimensions of screen elements  416  in  FIG.  61    to screen element  516  in  FIG.  67   ). The smaller width allows manufacturing of screens  616  having smaller features such as smaller screening openings  86  and smaller surface elements  84  (e.g., see  FIG.  2 D ). 
       FIG.  73    illustrates a top-down view of a screen element  616 , previously illustrated, for example, in  FIGS.  70 A,  71 F, and  72 C .  FIG.  73    defines a first cross section direction A to A and a second cross section direction C to C.  FIG.  73 A  illustrates a first cross section of the screen element  616  of  FIG.  73    defined by the first cross section direction A to A of  FIG.  73   . The view of  FIG.  73 A  is drawn with a 2:1 scale. Cross section A to A of  FIG.  73 A  illustrates a plurality of reinforcement members  132  (e.g., see the discussion related to  FIG.  70 A ) that are parallel to side edges  122  of screen element  616 .  FIG.  73 B  illustrates an enlarged view of a portion “B” of the first cross section illustrated in  FIG.  73 A .  FIG.  73 B  also shows reinforcement members  132 . 
       FIG.  73 C  illustrates a second cross section of the screen element  616  of  FIG.  73    defined by the second cross section direction C to C of  FIG.  73   . The view of  FIG.  73 C  is drawn with a 2:1 scale and illustrates reinforcement members  34  and  134  (e.g., see the discussion related to  FIGS.  70 A,  71 F, and  72 C ) that are parallel to end portions  120  of screen element  616 .  FIG.  73 D  illustrates an enlarged view of the second cross section of screen element  616  illustrated in  FIG.  73 C .  FIG.  73 D  illustrates a plurality of screening openings  86  and surface elements  84 , in addition to the reinforcement members  34  and  134  shown in  FIG.  73 C . Details of the screening openings  86  and surface elements  84  are described in greater detail below with reference to  FIGS.  74 C and  74 D . 
       FIG.  74    illustrates a top-down view of the center screen subassembly formed by attaching screen element  616  to an end subgrid unit  818 , similar to screen subassembly  960  shown in  FIG.  68 A .  FIG.  74    defines a cross sectional direction A to A, which is used to define views in  FIGS.  74 B,  74 C, and  74 D .  FIG.  74 A  illustrates a side view of center screen subassembly  960  of  FIG.  74    showing screen element  616  and end subgrid unit  818 . For the purpose of illustration, screen element  616  is shown positioned slightly above end subgrid unit  818 . 
       FIG.  74 B  illustrates a cross section of the center screen subassembly of  FIG.  74    defined by the cross section direction A to A of  FIG.  74   .  FIG.  74 B  also illustrates a region of detail “B” that is enlarged in  FIGS.  74 C and  74 D . Elements of support frameworks  488  and  558  are also shown. As described above, elements of support frameworks  488  and  588  spatially align and provide support for reinforcement members  34  and  134  of screen element  516 , respectively. 
       FIG.  74 C  illustrates an enlarged view of the portion “B” of the cross section of center screen subassembly of  FIG.  74 B .  FIG.  74 C  shows detail similar to that shown in  FIG.  10 C . In this regard,  FIG.  74 C  illustrates a subgrid end member  36 , a secondary subgrid support member  488 , and a tertiary subgrid support framework  588  (e.g., see  FIGS.  71 ,  71 A,  71 B,  71 C,  71 D and  71 F ).  FIG.  74 C  also illustrates reinforcement members  34  and  134 , shown above in  FIG.  73 D . The detail region labeled “C” in  FIG.  74 C  shown in an enlarged view in  FIG.  74 D . 
       FIG.  74 D  illustrates a cross sectional view of a plurality of surface elements  84  separated by a series of screening openings  86 . As described above with reference to  FIG.  2 D , surface elements  84  have a thickness T, which may vary depending on the screening application and configuration of the screening openings  86 . T may be chosen depending on the open screening area desired and the width W of screening openings  86 . The screening openings  86  are elongated slots having a length L and a width W (e.g., see  FIG.  2 D ), which may be varied for a chosen configuration. The slots, having length L (e.g., see  FIG.  2 D  for definition of L, not shown in  FIG.  74 D ), extend substantially into the plane of  FIG.  74 D  and are shown horizontally in  FIG.  2 D . 
     Table 1. (below) illustrates the percent open area of example embodiments of screen assemblies including screen element  616 , as a function of parameters W, T, and L, describing the width of screen openings  86 , the width of surface elements  84 , and the length of screen openings  86 , respectively. As described above, the percent open area shown below is achieved by generating example screen assemblies that include elements  616  and example subgrid structures (e.g., subgrids  818  and  918 ) having corresponding structural elements to support screen elements  616 . In this way, appropriately designed screen elements  616  and subgrid structures (e.g., subgrids  818  and  918 ) work together to maximize open screening area. 
     In this example, surface elements  84  have a fixed thickness T=0.014 in. Screening openings  86  have a fixed length L=0.076 in and variable width W. As may be expected, for a fixed number of screen openings  86 , the percent open area decreases with the width W of each screen opening  86 . In this example, the percent open area varies from a minimum of 6.2% open area, for the smallest width W=0.0017 in, to a maximum of 23.3% open area for the largest width W=0.0071. 
     
       
         
           
               
               
               
               
               
             
               
                 TABLE 1 
               
               
                   
               
               
                 mesh 
                 W (in) 
                 T (in) 
                 L (in) 
                 % open area 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 80 
                 0.0071 
                 0.014 
                 0.076 
                 23.3 
               
               
                 100 
                 0.0059 
                 0.014 
                 0.076 
                 20.3 
               
               
                 120 
                 0.0049 
                 0.014 
                 0.076 
                 17.6 
               
               
                 140 
                 0.0041 
                 0.014 
                 0.076 
                 13.4 
               
               
                 170 
                 0.0035 
                 0.014 
                 0.076 
                 12.2 
               
               
                 200 
                 0.0029 
                 0.014 
                 0.076 
                 10.3 
               
               
                 230 
                 0.0025 
                 0.014 
                 0.076 
                 9.1 
               
               
                 270 
                 0.0021 
                 0.014 
                 0.076 
                 7.9 
               
               
                 325 
                 0.0017 
                 0.014 
                 0.076 
                 6.2 
               
               
                   
               
            
           
         
       
     
     Table 2. (below) illustrates the percent open area of further example embodiments of screen assemblies including screen element  616 , as a function of parameters W, T, and L. As described above, the percent open area shown below is achieved by generating example screen assemblies that include elements  616  and example subgrid structures (e.g., subgrids  818  and  918 ) having corresponding structural elements to support screen elements  616 . 
     Table 2 illustrates the effect of reducing the length L of screening openings  86  and reducing the width T of surface elements  84  so that screen element  616  may include more screen elements. In this example, surface elements  84  have a fixed thickness T=0.007 in. Screening openings  86  have a fixed length L=0.046 in and variable width W. The resulting percent open area varies from a minimum of 10.1% open area, for the smallest width W=0.0017 in, to a maximum of 27.3% open area for the largest width W=0.0071. Thus, the maximum percent open area is increased from 23.3% to 27.3% by reducing T from 0.014 in to 0.007 in, and by reducing L from 0.076 in to 0.046 in, as seen by comparing the results of Table 2 with those of Table 1. As mentioned above, the increase in maximum percent open area occurs because when the screening openings  86  and surface features are reduced in size, more screening openings may be included on screen element  516 . 
     
       
         
           
               
               
               
               
               
             
               
                 TABLE 2 
               
               
                   
               
               
                 mesh 
                 W (in) 
                 T (in) 
                 L (in) 
                 % open area 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 80 
                 0.0071 
                 0.007 
                 0.046 
                 27.3 
               
               
                 100 
                 0.0059 
                 0.007 
                 0.046 
                 25.2 
               
               
                 120 
                 0.0049 
                 0.007 
                 0.046 
                 23.1 
               
               
                 140 
                 0.0041 
                 0.007 
                 0.046 
                 20.5 
               
               
                 170 
                 0.0035 
                 0.007 
                 0.046 
                 18.5 
               
               
                 200 
                 0.0029 
                 0.007 
                 0.046 
                 16.5 
               
               
                 230 
                 0.0025 
                 0.007 
                 0.046 
                 14.9 
               
               
                 270 
                 0.0021 
                 0.007 
                 0.046 
                 12.8 
               
               
                 325 
                 0.0017 
                 0.007 
                 0.046 
                 10.1 
               
               
                   
               
            
           
         
       
     
     Table 3. (below) illustrates the percent open area of further example embodiments of screen assemblies including screen element  616 , as a function of parameters W, T, and L. As described above, the percent open area shown below is achieved by generating example screen assemblies that include elements  616  and example subgrid structures (e.g., subgrids  818  and  918 ) having corresponding structural elements to support screen elements  616 . 
     Table 3 shows that the trend may be continued. In this example, surface elements  84  have a fixed thickness T=0.005 in. Screening openings  86  have a fixed length L=0.032 in and variable width W. The resulting percent open area varies from a minimum of 12.1% open area, for the smallest width W=0.0017 in, to a maximum of 31.4% open area for the largest width W=0.0071. Thus, by reducing T from 0.007 in to 0.005 in, and by reducing L from 0.046 in to 0.032 in, the maximum percent open area is increased from 27.3% to 31.4%, as seen by comparing the results of Table 3 with those of Table 2. 
     
       
         
           
               
               
               
               
               
             
               
                 TABLE 3 
               
               
                   
               
               
                 mesh 
                 W (in) 
                 T (in) 
                 L (in) 
                 % open area 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 80 
                 0.0071 
                 0.005 
                 0.032 
                 31.4 
               
               
                 100 
                 0.0059 
                 0.005 
                 0.032 
                 29.3 
               
               
                 120 
                 0.0049 
                 0.005 
                 0.032 
                 27.0 
               
               
                 140 
                 0.0041 
                 0.005 
                 0.032 
                 24.1 
               
               
                 170 
                 0.0035 
                 0.005 
                 0.032 
                 22.0 
               
               
                 200 
                 0.0029 
                 0.005 
                 0.032 
                 19.7 
               
               
                 230 
                 0.0025 
                 0.005 
                 0.032 
                 16.4 
               
               
                 270 
                 0.0021 
                 0.005 
                 0.032 
                 14.7 
               
               
                 325 
                 0.0017 
                 0.005 
                 0.032 
                 12.1 
               
               
                   
               
            
           
         
       
     
     Table 4. (below) illustrates the percent open area of further example embodiments of screen assemblies including screen element  616 , as a function of parameters W, T, and L. As described above, the percent open area shown below is achieved by generating example screen assemblies that include elements  616  and example subgrid structures (e.g., subgrids  818  and  918 ) having corresponding structural elements to support screen elements  616 . 
     Table 4 shows further increase in percent open area as T and L are reduced. In this example, surface elements  84  have a fixed thickness T=0.003 in. Screening openings  86  have a fixed length L=0.028 in and variable width W. The resulting percent open area varies from a minimum of 13.2% open area, for the smallest width W=0.0017 in, to a maximum of 32.2% open area for the largest width W=0.0071. Thus, by reducing T from 0.005 in to 0.003 in, and by reducing L from 0.032 in to 0.028 in, the maximum percent open area is increased from 31.4% to 32.2%, as seen by comparing the results of Table 4 with those of Table 3. 
     
       
         
           
               
               
               
               
               
             
               
                 TABLE 4 
               
               
                   
               
               
                 mesh 
                 W (in) 
                 T (in) 
                 L (in) 
                 % open area 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 80 
                 0.0071 
                 0.003 
                 0.028 
                 32.2 
               
               
                 100 
                 0.0059 
                 0.003 
                 0.028 
                 30.1 
               
               
                 120 
                 0.0049 
                 0.003 
                 0.028 
                 27.8 
               
               
                 140 
                 0.0041 
                 0.003 
                 0.028 
                 25.2 
               
               
                 170 
                 0.0035 
                 0.003 
                 0.028 
                 23.1 
               
               
                 200 
                 0.0029 
                 0.003 
                 0.028 
                 20.1 
               
               
                 230 
                 0.0025 
                 0.003 
                 0.028 
                 17.2 
               
               
                 270 
                 0.0021 
                 0.003 
                 0.028 
                 15.3 
               
               
                 325 
                 0.0017 
                 0.003 
                 0.028 
                 13.2 
               
               
                   
               
            
           
         
       
     
     According to embodiments, multiple subassemblies may be secured together to form screen assemblies having a desired total screening area. For example, multiple subgrids secured together to form the screen assembly having a screening surface that has a total screening area in a range of approximately 0.4 m 2  to 6.0 m 2 . In various embodiments, screen assemblies may be constructed having total screening areas of: 0.41 m 2 , 0.68 m 2 , 0.94 m 2 , 3.75 m 2 , 4.08 m 2 , 4.89 m 2 , and 5.44 m 2 . In further example embodiments, screen assemblies may be constructed having virtually any total screening area by appropriate choice of a size of screening subassemblies and a total number of screening subassemblies. 
       FIGS.  75 A to  76 C  illustrate different embodiments in which alternate strategies may be employed for combining screen elements to form screening assemblies.  FIG.  75 A , for example, illustrates a system including a first  702  and a second  704  plurality of rails. The first plurality  702  of rails may be configured to be substantially parallel to one another. Likewise, the second  704  plurality of rails may be configured to be substantially parallel to one another. Further, the first plurality  702  of rails may be configured to be substantially perpendicular to the second plurality  704  of rails. In this way, the first  702  and second  704  plurality of rails forms a rectangular grid framework. 
     Rather than binding screen subassemblies (e.g., subassembly  760  of  FIG.  62 A , subassembly  860  of  FIG.  67 A , etc.) together using clips (e.g., clips  42  of  FIG.  3   , clips  142  of  FIG.  60   , clips  242  of  FIG.  63   , etc.), to form screen assemblies (e.g., screen assembly  10  of  FIG.  1   , screen assembly  410  of  FIG.  47   , screen assembly  510  of  FIG.  58   , etc.), screen assemblies may be formed by attaching screen elements  416  to rails  702  and  704 , as shown in  FIG.  75 A . 
       FIG.  75 B  illustrates a top perspective view of a grid framework  7500  to which screen elements may be attached to form a screen assembly, according to an embodiment. As shown, screen elements  516   a ,  516   b  (e.g., see screen element  516  of  FIGS.  66 - 66 C ), may be attached to grid framework  7500 . Openings in grid framework  7500  may be configured to allow undersized particles that fall through screen elements  516   a ,  516   b , etc., to likewise fall through grid framework  7500 . Grid framework  7500  may be configured as a replaceable panel that may be installed in a vibratory screening machine. In this example, grid framework  7500  has a rectangular shape with a handle  7502  that may facilitate installation. Other embodiments may include grid frameworks having other shapes such as circles, ovals, squares, triangles, hexagons, etc. Other embodiments may include grid frameworks having a shape of a closed polygon or smooth closed curve having any shape. Grid framework  7500  may include a frame  7504  that is configured to engage with a corresponding support structure of a vibratory screening machine (not shown). Grid framework  7500  may be constructed of metal, plastic, nylon, etc., or any suitable structural material. 
       FIG.  75 C  illustrates a bottom perspective view of the grid framework  7500  of  FIG.  75 B , according to an embodiment. The view of  FIG.  75 C  illustrates an extended structure  7506  separating frame  7504  from an inner grid support area  7508 . Frame  7504  and extended structure  7506  may be configured to allow grid framework  7500  to be securely installed in a vibratory screening machine. For example, the shape of extended structure  7506  may be configured to engage with a corresponding rectangular-shaped hole (not shown) in a support structure of a vibratory screening machine. Further, frame  7504  may be configured to extend beyond the rectangular-shaped hole of the vibratory screening machine to thereby engage with a corresponding support structure of the vibratory screening machine. In this way, grid framework  7500  may be installed and may be securely held in the vibratory screening machine. Once installed, grid framework  7500  may be secured to the support structure of the vibratory screening machine using various fasteners (e.g., bolts, screws, rivets, clamps, etc.) or may be welded to the support structure of the vibratory screening machine. 
       FIG.  76    illustrates a further embodiment in which screen elements may be attached directly to a plate structure  752  without the need to first attach the screen elements to subgrids. In this example, a plate  752  may be provided that has a plurality of window apertures  753   a ,  753   b ,  753   c , and  753   d . The window apertures  753   a  to  753   d  may be formed into the plate structure  752  by removing portions of the plate  752  material so that window apertures  753   a  to  753   d  include respective grid frameworks  754   a ,  754   b ,  754   c , and  754   d . The grid frameworks  754   a ,  754   b ,  754   c , and  754   d  may serve as structures that may provide support for screen elements that may be attached thereto. In this way, the grid frameworks  754   a ,  754   b ,  754   c , and  754   d  may act in the same way as the above-described subgrids of other embodiments. The window apertures  753   a  to  753   d  are shown as an exemplary embodiment of the concept. In other embodiments, plate structure  752  may have many more window apertures that may be closely spaced so that a screen assembly may be formed having large open area as described above with reference to other embodiments. 
       FIG.  76 A  illustrates screen elements  786  configured to be directly attached to a punched plate  780 , according to an embodiment. In this embodiment, plate  780  may be a metal plate that has been mechanically punched to remove material to create apertures  782   a ,  782   b ,  782   c , etc. In this example, apertures  782   a ,  782   b , and  782   c , etc., are rectangular apertures. In other embodiments, different shaped apertures may be provided. Plate  780  may be configured to be attached to a support structure  783 . Support structure  783  may be a metal or plastic frame having a plurality of openings  784   a ,  784   b ,  784   c , etc. Apertures  782   a ,  782   b , and  782   c , may be configured to accommodate a plurality of similarly sized screen elements  786 . 
     In this example, screen element  786  may be a 1×6 screen element that may be similar to screen elements  516  and  616 . A screen assembly may be generated by attaching a plurality of screen elements  786  to plate  780 . In this regard, a plurality of screen elements  786  may be attached to apertures  782   a ,  782   b , and  782   c , as indicated by arrows  788   a ,  788   b , and  788   c . Screen elements  786  may be attached to plate  780  by gluing edges of screen elements  786  to corresponding edges of apertures  782   a ,  782   b , and  782   c . Alternatively, screen elements  786  may molded into plate  780  by placing them into apertures  782   a ,  782   b ,  782   c , etc., and pouring a thermoset material around their perimeters. In an alternative embodiment, screen elements  786  may have a size specifically designed so that screen elements  786  may be snapped into place into apertures  782   a ,  782   b , and  782   c  and held in place by compressive forces exerted by edges of apertures  782   a ,  782   b ,  782   c , etc. 
       FIG.  76 B  illustrates screen elements configured to be directly attached to a corrugated punched plate, according to an embodiment. In this example, plate  880  may have a corrugated shape. Plate  880  may be configured to be attached to a support structure  783  (e.g., see  FIG.  76 A ). In this regard, plate  880  may have a plurality of flat surfaces  882   a ,  882   b ,  882   c , etc. Flat surfaces  882   a ,  882   b ,  882   c , etc., may be separated by raised features  884   a ,  884   b , etc. Raised features  884   a ,  884   b , etc., may include respective flat surfaces  886   a ,  886   b , etc., as well as respective angled surfaces  888   a ,  888   b ,  888   c ,  888   d , etc. Each of the flat surfaces  882   a ,  882   b ,  882   c , etc., may include punched apertures, as described above with reference to  FIG.  76 A . Similarly, raised features  884   a ,  884   b , etc., may include punched apertures on respective flat surfaces  886   a ,  886   b , etc. Likewise, raised features  884   a ,  884   b , etc., may include punched apertures on respective angled surfaces  888   a ,  888   b ,  888   c ,  888   d , etc. 
     Each of the apertures on flat surfaces  882   a ,  882   b ,  882   c , etc., on flat surfaces  886   a ,  886   b , etc., and on angled surfaces  888   a ,  888   b ,  888   c ,  888   d , etc., may be configured to accommodate screen elements, such as screen element  786  illustrated, for example, in  FIG.  76 A . As described above, screen elements  786  may be attached to apertures of corrugated plate  880  by gluing. Similarly, screen elements  786  may be molded into corrugated plate  880  by placing them into apertures and pouring a thermoset material around their perimeters. Similarly, screen elements  786  may be snapped into apertures and held in place by compressive forces. 
       FIG.  76 C  illustrates a frame  980  having pockets to accommodate screen elements, according to an embodiment. In this example, support structure  980  may be a thermoplastic molded frame. Support structure may be a single injection molded piece having a thickness  981  and may be configured to contain a plurality of apertures or pockets  982 . In other embodiments, support structure  980  may be a metal frame. Thickness  981  may be about 0.125 inches to about 2 inches thick. In this example, pockets  982  are rectangular openings. In other embodiments, other shaped pockets may be provided. Pockets  982  may include edges  984  that may be configured to accommodate edges of a screen element  786 . As shown in  FIG.  76 C , screen element may be placed over pockets  982  and may be attached to edges  984  by gluing. Similarly, as described above with reference to  FIGS.  76 A and  76 B , screen element  786  may be molded into support structure  980  by placing screen elements  786  into pockets  982  and pouring a thermoset material around a perimeter of screen element  786  to thereby form a bond between edges of screen element  786  and edges  984  of pockets  982 . Similarly, screen elements  786  may be snapped into apertures and held in place by compressive forces. 
     The embodiments of  FIGS.  75 A to  76 C  demonstrate that many different support structures may be provided for screen elements, in addition to the subgrid structures described above with reference to  FIGS.  3  to  4 A,  10 ,  10 A,  11 ,  11 A,  22 ,  22 A,  23  to  24 D,  34 ,  35 ,  49  to  57 A,  59  to  63 A,  64  to  65 A,  67  to  68 A, and  71    to  72 C. A support structure need only provide sufficient mechanical and thermal stability to screen elements. The embodiments of  FIGS.  75 A to  76 C  may also allow a wider selection of materials to be used in generating screening members. In some embodiments, it may be advantageous to attach screen elements to subgrid structures using laser welding, as described in greater detail above. In this regard, certain subgrid structures (e.g., some of embodiments illustrated in  FIGS.  3  to  4 A,  10 ,  10 A,  11 ,  11 A,  22 ,  22 A,  23  to  24 D,  34 ,  35 ,  49  to  57 A,  59  to  63 A,  64  to  65 A,  67  to  68 A, and  71    to  72 C) may have material properties that are complementary to the material properties of a screen element. 
     For embodiments in which screen elements are to be joined to subgrid structures using laser welding, screen elements should be optically transparent while subgrid structures should have optical properties that absorb electromagnetic radiation. In this way, laser light may pass through a screen element and may be absorbed by the optically absorbing material of the subgrid structure. Electromagnetic radiation absorbed by the subgrid structure generates heat that locally melts material of the subgrid structure. Upon cooling, a bond is formed between the screen element and the subgrid structure. The need to have an optically transparent screen element places constraints on material compositions used to generate screen elements. In this regard, glass fibers that are transparent may be used as reinforcing filler material. However, other filler materials such as carbon fibers should not be used as they are not transparent. 
     The embodiments of  FIGS.  75 A to  76 C  may use joining methods other than laser welding, such as gluing, as described above. Thus, using joining techniques that do not rely on laser welding removes the restriction that the screen elements should be optically transparent. In this regard, a wider selection of materials may be used to generate screen elements, such as carbon fibers mentioned above. Filler materials are generally used to strengthen material properties of screen elements; however, the presence of filler materials and other additives tends to degrade cut, abrasion, and tear resistance, properties of the material. Thus, depending on the support structure, the screen element may need more or less filler material. Therefore, certain material properties, such as cut, abrasion, and tear resistance, may be improved in situations requiring less filler material. For example, higher temperatures (e.g., &gt;54° C. for mining operations, &gt;90° C. for oil and gas operations) generally require more filler material to improve material strength. For situations involving lower temperatures and stronger support structures, however, less filler material may needed. For such situations, material properties such as cut, abrasion, and tear resistance, may be improved. 
     There are many ways to generate screening assemblies using support structures in embodiments illustrated in  FIGS.  75 A to  76 C . For example, screen elements  786  may be attached to support structures illustrated in  FIGS.  75 A to  76 C  using automated processes, such as using robotic devices to generate screening assemblies. Further, although screening assemblies generated using subgrid structures (e.g., such as illustrated in  FIGS.  3  to  4 A,  10 ,  10 A,  11 ,  11 A,  22 ,  22 A,  23  to  24 D,  34 ,  35 ,  49  to  57 A,  59  to  63 A,  64  to  65 A,  67  to  68 A, and  71    to  72 C) may be replaceable and removable, some screening assemblies may be permanently or semi-permanently attached to screening machines. For example, screening assemblies constructed using support structures illustrated, for example, in  FIGS.  75 A to  76 C  may be bolted or welded into a screening machine as a semi-permanent or permanent structure. Alternatively, embodiments illustrated in  FIGS.  75 A to  76 C  may also be configured to be removable and replaceable components of screening machines. 
     Many of the above-described embodiment subgrids have location members  444  and fusion bars  476  and  478  (e.g., see  FIGS.  49 ,  59 ,  51 ,  52 - 55 ,  57 ,  59 - 65 ,  68 , and  71 - 71 B ). Similarly, many of the above-described screen elements have location apertures,  424  and  524 , and cavity pockets  472  (e.g., see  FIGS.  45 A- 45 E,  46 ,  48 B,  48 C,  66 B,  66 C, and  70 A ). According to the above-described embodiments, screen elements are aligned with subgrids by inserting location members  444  (of subgrids) into location apertures,  424  and  524  (of screen elements), so that fusion bars,  476  and  478  (of subgrids) reside within cavity pockets  472  (of screen elements). Screen elements may then attached to subgrids by melting (e.g., using laser welding, heat staking, etc.) fusion bars,  476  and  478 , to fuse with cavity pockets  472  to form a bond. 
     The presence of location apertures,  424  and  525 , in screen elements, however, may present problems when manufacturing screen elements using techniques involving thermoplastic injection molding. In this regard, the presence of location apertures,  424  and  524 , may reduce the flow of thermoplastic material during the injection molding process. 
       FIGS.  77 A,  77 B, and  77 C  illustrate new embodiments in which location apertures (e.g.,  424  and  525  of  FIGS.  45 A- 45 E,  46 ,  48 B,  48 C,  66 B,  66 C, and  70 A ) are eliminated from screen elements. According to new embodiments illustrated, for example, in  FIGS.  77 A,  77 B , and  77 C, cavity pockets and fusion bars may be re-designed to play a role formerly played by location apertures and location members, respectively, thus eliminating the need for separate location apertures in screen elements and location members in subgrids.  FIG.  77 A  illustrates an embodiment fusion bar  544  having sharp corners  546   a  and  546   b .  FIG.  77 B  illustrates an embodiment cavity pocket having first  574   a  and second  574   b  approximately flat internal surfaces. Cavity pocket  572  is designed to be slightly larger than fusion bar  544  so that fusion bar  544  may fit within the shape of cavity pocket  572  when a screen element having cavity pocket  572  is place over a subgrid having fusion bar  544 , as illustrated in  FIG.  77 C . 
       FIG.  77 C  illustrates an embodiment in which cavity pocket  572  acts as a location aperture and fusion bar  544  acts as a location member. In this regard, sharp points,  546   a  and  546   b , of fusion bar  572  make contact with respective approximately flat internal surfaces  574   a  and  574   b  of cavity pocket  572 . The size and shape of fusion bar  544  allows fusion bar  544  to make close contact with internal surfaces,  546   a  and  546   b , of cavity pocket  572 . According to this design, there is little freedom for relative motion between cavity pocket  572  and fusion bar  544 . Thus, as shown in  FIG.  77 C , screen element may be properly aligned on a subgrid through the close tolerance of the alignment between fusion bar  544  and cavity pocket  572 . In this regard, the need for separate location members and location apertures is eliminated. 
     The various screening assemblies described above are configured to be self-supporting, stand-alone structures that may be installed in a vibratory screening machine. In the embodiments of  FIGS.  75 A to  76 C , screen elements are supported by rail structures (e.g., see  FIG.  75 A ), plate structures (e.g., see  FIGS.  75 B,  76 , and  76 A ), corrugated punched plates (e.g., see  FIG.  76 B ), and frame structures (e.g., see  FIG.  76 C ). Screening assemblies involving subgrid structures (e.g., see  FIGS.  3  to  4 A,  10 ,  10 A,  11 ,  11 A,  22 ,  22 A,  23  to  24 D,  34 ,  35 ,  49  to  57 A,  59  to  63 A,  64  to  65 A,  67  to  68 A, and  71    to  72 C) are self-supporting due to the mechanical properties of the interconnected array of subgrids. Subgrids are configured to have sufficient stiffness to be self-supporting under compression in open areas between support structures (e.g., see support structures in FIGS. 17 and 33 of U.S. Pat. No. 9,027,760) of vibrational screening machines, while having stiffness that is not so great as to prevent deformation to allow the screen assembly to conform with shaker machine bed, as described in greater detail below. 
     As described above, subgrids may be held together via clips (e.g., clips  42  of  FIGS.  11 ,  11 A,  63 B,  63 C, and  63 D ; clips  142  of  FIG.  60   ; clips  242  of  FIG.  63   ; etc.) and clip apertures  40  (e.g., see  FIGS.  11 ,  11 A,  63 B,  63 C, and  63 D ). The clips illustrated in  FIGS.  63 C and  63 D , are configured to reduce relative rotation of subgrids and to thereby make a tight assembly that is self-supporting. Such self-supporting, stand-alone structures may be removably installed in a vibratory screening machine.  FIGS.  1  to  1 B,  7 ,  7 A,  8 ,  19  to  21 ,  25 ,  47 ,  58  and  69    illustrate such self-supporting, stand-alone structures that may be installed in various vibratory screening machines such as screening machines illustrated in  FIGS.  12  to  12 B,  13 ,  13 A,  14 ,  15 ,  27 ,  30  to  32 , and  39   , and described in greater detail above. 
     In various embodiments, self-supporting, stand-alone, screening assemblies may be installed in a vibratory screening machine and held in place under compression. As such, screening assemblies such as those shown in  FIGS.  1  to  1 B,  7 ,  8 ,  19  to  21 ,  25 ,  47 ,  58  and  69    include binder bars  12 . Binder bars  12  may be configured to receive compression forces from a compression assembly (e.g., see  FIG.  12 B ) as described, for example, in U.S. Pat. No. 7,578,394. In various embodiments, binder bars  12  may be fabricated using various materials. For example, binder bars  12  may be made of: aluminum, carbon steel, 70% glass fiber in nylon, etc. Generating binder bars  12  using injection molding of glass-in-nylon materials may avoid manufacturing problems that would otherwise arise with casting complicated shapes from aluminum or other metals. A compression force may be applied to a binder bar  12  or a side member of the screen assembly such that the screen assembly deflects downward into a concave shape as shown, for example, in  FIGS.  12  to  12 B,  13 ,  13 A, and  14   . A bottom side of the screen assembly may mate with a screen assembly mating surface of the vibratory screening machine as described in U.S. Pat. Nos. 7,578,394 and 8,443,984. 
       FIG.  78 A  illustrates a side view of a compression assembly  7800  configured to apply a compressive force to a screen assembly  7806  via a binder bar  7808 , according to an embodiment. In this example, compression assembly  7800  includes a spring  7802  that applies a compressive force to a pin  7804 . In turn, pin  7804  transfers the compressive force to screen assembly  7806  via binder bar  7808 . In this example, pin  7804  engages binder bar  7808  at a downward angle of approximately 12 degrees. In other embodiments, pin  7804  may engage binder bar  7808  at different angles. As shown, pin  7804  contacts an edge of binder bar  7808  and binder bar  7808  distributes the compressive load across screen assembly  7806 . A compression assembly  7800  may have a plurality of pins  7804  that transfer a compressive force to screen assembly  7806 . 
     A screening machine such as shown in  FIGS.  12 ,  12 A, and  12 B , and described in U.S. Pat. No. 7,578,394, for example, may have three pins  7804  per side, while a screening machine such as shown in  FIGS.  13 ,  13 A, and  15   , and described in U.S. Pat. No. 9,027,760, for example, may have four pins  7804  per side. Other embodiments may have different numbers of pins  7804  per side. For example, vibratory screening machines may be configured to have 5, 6, etc., pins  7804  per side. Pins  7804  may be configured to engage with a binder bar (e.g., binder bar  12  of  FIGS.  1 ,  5 A, and  8   ; binder bar  7808  of  FIGS.  78 A, and  78 B to  78 D ; etc.) via a groove or undercut edge (e.g., see  FIGS.  78 B to  78 D  below) to form a secure mechanical coupling between pins  7804  and a binder bar. 
       FIG.  78 B  illustrates a first perspective view of binder bar  7808  of  FIG.  78 A , according to an embodiment. As shown, binder bar  7808  may include clip apertures  40  and clips  42  such that binder bar  7808  may be clipped to a side of an assembly of screen panels (e.g., see  FIG.  9   ). Other types of clips (e.g., clips  142  of  FIG.  60   , clips  242  of  FIG.  63   , etc.) may be used in other embodiments. As with subgrids, fasteners on the binder bar  7808  are shown as clips (e.g., clips  42 ,  142 ,  242 , etc.) and clip apertures  40  but other fasteners may be utilized to engage fasteners of the subgrids in further embodiments. 
     Binder bar  7808  may be fabricated using various materials. For example, binder bar  7808  may be made of: aluminum, carbon steel, 70% glass fiber in nylon, etc. Generating binder bars  7808  using injection molding of glass-in-nylon materials may avoid manufacturing problems that would otherwise arise with casting complicated shapes from aluminum or other metals. A compression force may be applied to a binder bar  7808  such that screen assembly  7806  (e.g., see  FIG.  78 A ) deflects downward into a concave shape as shown, for example, in  FIGS.  12  to  12 B,  13 ,  13 A,  14 , and  78 A , and described in greater detail below with reference to  FIG.  78 E . Binder bar  7808  further includes an undercut edge  7810  that may be configured to engage with pin  7804  (e.g., see  FIG.  78 A ), as described in greater detail below with reference to  FIGS.  78 C and  78 D . 
       FIG.  78 C  illustrates a second perspective view of binder bar  7808  of  FIGS.  78 A and  78 B , according to an embodiment. In this view, undercut edge  7810  forms a concave wedge-shaped region running along a length of binder bar  7808 . Under a compressive force, pin  7804  (e.g., see  FIG.  78 A ) is configured to mechanically engage with undercut edge  7810  to thereby transmit the compressive force to screen assembly  7806 . As described above, compression assembly  7800  may include a plurality of pins  7804  that may be configured to engage binder bar  7808  by making mechanical contact with undercut edge  7810  of binder bar  7808  at various points along undercut edge  7810 . 
       FIG.  78 D  illustrates an end view of binder bar  7808  of  FIGS.  78 A to  78 C , according to an embodiment. This view illustrates a cross-sectional shape of binder bar  7808  in which clip  42  and undercut edge  7810  are shown. Other embodiments may include binder bars having other shapes. The shape of binder bar  7808  may be configured based on a size and shape of screen assembly  7806  (e.g., see  FIGS.  78 A and  78 E ) and based on a compressive force that is designed to be imposed on screen assembly  7806  via compression assembly  7800  (e.g., see  FIG.  78 A ). For a given compressive force, binder bar  7808  may be designed to have a shape and size to mechanically support imposed forces. Further, a position of undercut edge  7808  may be chosen such that a predetermined force imposed by pins  7804  generates appropriately designed forces and torques on binder bar  7808 . For example, as described above, the force imposed by pins  7804  forces screen assembly to bend into a concave shape which requires forces and torques to be properly balanced. 
       FIG.  78 E  illustrates a screen assembly  7806  installed in a vibratory screening machine, according to an embodiment. As described above with reference to  FIG.  78 A , the vibratory screening machine of  FIG.  78 E  includes a compression assembly  7800  that applies a compressive force to binder bar  7808  that is attached to a first end  7812   a  of screen assembly  7806 . In this example, screen assembly  7806  is mechanically constrained at a second end  7812   b . Because screen assembly  7806  is constrained at the second end  7812   b , a force applied by compression assembly  7800  to first end  7812   a  causes screen assembly  7806  to deform. Compression assemblies may generate compression forces on the order of 2,000 lb to 5,000 lb per pin  7804 . Such compression forces act to deform a shape of screen assembly  7806  from a starting shape to a deformed shape that conforms to a shape of a mating surface  7906  of the vibratory screening machine. 
     Self-supporting, stand-alone, screening assemblies may be configured to have a starting shape that includes a slight arc as shown, for example, in  FIGS.  1 ,  1 B,  7 A, and  8   . As shown in  FIG.  7 A , for example, the subgrids may have subgrid support members  48  configured such that screen assembly has a slightly concave shape when the subgrid support members  48  are fastened to each other via clips  42  and clip apertures  40  (e.g., see  FIGS.  11 ,  11 A,  63 B,  63 C , and  63 D). Other types of clips (e.g., clips  142  of  FIG.  60   , clips  242  of  FIG.  63   , etc.) may be used in other embodiments. Because screen assembly  7806  (e.g., see  FIGS.  78 A and  78 E ) is constructed with a slightly concave shape it may be configured to deform to a desired concavity upon application of a compression load without a need to guide the screen assembly into a concave shape (e.g., see  FIG.  78 E ). Alternatively, in other embodiments, subgrids may be configured to create a slightly convex screen assembly (e.g., see  FIG.  20   ) or a substantially flat screen assembly (e.g., see  FIG.  19   ). 
       FIG.  79    illustrates an edge view  7900  of a surface of an uncompressed screen assembly  7806 , having a first radius of curvature  7904 , positioned over a mating surface  7906 , of a vibratory screening machine, the mating surface  7906  having a second radius of curvature  7908 , according to an embodiment. In this example, first radius of curvature  7904  is larger than the second radius of curvature  7908 . During installation, assembly  7806  may be placed over mating surface  7906  of a screening bed of a vibratory screening machine, as shown in  FIGS.  78 E and  79   . In this configuration, a small separation  7910  exists between the screen assembly  7806  and the mating surface  7906  due to the difference in radius of curvature of screen assembly  7806  relative to that of the mating surface  7906 . In some embodiments, separation  7910  may be as large as a half inch. Other separations may be generated in other embodiments. Compressive forces generated by compression assembly  7800  (e.g., see  FIGS.  78 A and  78 E ) may then cause screen assembly  7806  to deform into a deformed shape in which the radius of curvature  7904  of the deformed shape is approximately equal to the radius of curvature  7908  of the mating surface  7906  (e.g., see  FIG.  78 E ). In this way, the compression assembly  7800  forces screen assembly  7806  to conform to the shape of the mating surface  7906 . 
     Various embodiments may employ screening assemblies  7806  and mating surfaces  7906  with various shapes. For example, a screening machine such as shown in  FIGS.  12 ,  12 A , and  12 B, and described in U.S. Pat. No. 7,578,394, for example, may have a mating surface  7906  that has a radius of curvature  7908  of approximately 50 inches. Alternatively, a screening machine such as shown in  FIGS.  13 ,  13 A, and  15   , and described in U.S. Pat. No. 9,027,760, for example, may have a radius of curvature  7908  of approximately 75 inches. Embodiments having a smaller radius of curvature and shorter width screening assemblies (e.g., as shown in  FIGS.  12 ,  12 A, and  12 B , and described in U.S. Pat. No. 7,578,394) are generally are easier to secure (i.e., require lower compressive forces) relative to embodiments having larger radius of curvature and longer width screening assemblies (e.g., as shown in  FIGS.  13 ,  13 A, and  15   , and described in U.S. Pat. No. 9,027,760). 
     As described above, subgrids may be held together via clips (e.g., clips  42  of  FIGS.  11 ,  11 A,  63 B,  63 C, and  63 D ; clips  142  of  FIG.  60   ; clips  242  of  FIG.  63   ; etc.) and clip apertures  40  (e.g., see  FIGS.  11 ,  11 A,  63 B,  63 C, and  63 D ). In certain embodiments, clips  142  and  242  (e.g., see  FIGS.  60 ,  63 C, and  63 D ) may be configured to reduce relative rotation of subgrids and to thereby make a tight assembly that is self-supporting. Further, clips  42 ,  142 ,  242  and clip apertures  40  may be configured to give a screen assembly a pre-determined radius of curvature of the resulting self-supporting, stand-alone structures. Clip apertures  40  and clips  142  and  242 , described above with reference to  FIGS.  60 ,  63 C, and  63 D  may be further configured to allow deformation of the screen assembly under compression that is needed to force an initial shape of the screen assembly into the deformed screen assembly that conforms to the shape of the mating surface (e.g., see  FIGS.  78 A and  78 E ), as described above. In embodiments in which screening assemblies are secured with compressive forces, a screen assembly may have either a nominally flat surface (albeit with a slight curvature) as shown, for example, in  FIGS.  1 ,  1 B,  7 A, and  8   , or screening assemblies may have a pyramidal shape as shown, for example, in  FIGS.  21 ,  25 B,  27 , and  30  to  32   . In contrast, conventional metal screens may only support pyramidal screens under compression. 
     Screening assemblies that include subgrids may suffer additional deformation under compression. For example, subgrids that are made of thermoplastic or nylon may suffer creep deformation under compression and may thereby shrink in size over time. Further, deformation may be enhanced in high temperature environments, for example, with temperatures up to approximately 190° F. Under such conditions, subgrids become more malleable and may more-readily deform under compression. In the presence of creep deformation, a constant compressive force may be maintained through the use of compression assemblies  7800  (e.g., see  FIG.  78 A ) that impose adjustable spring-loaded forces. In this regard, springs (e.g., spring  7802  of  FIG.  78 A ) generally impose a force that is a linear function of the degree of deformation of the spring. Thus, as screening assemblies shrink under creep, an applied compressive force may be adjusted by adjusting the degree of deformation of the spring, as described in greater detail below. Alternatively, when a screen assembly is installed, the compression assembly  7800  (e.g., see  FIG.  78 A ) may be adjusted to pre-compensate for creep, as described in greater detail below. 
     Spring rate (also called “spring constant”) is the proportion of a spring&#39;s force (pounds or Newtons) to one unit of deformation (inch or millimeter). It is a constant value that determines a force needed to compress the spring (e.g., spring  7802  of  FIG.  78 A ) by a certain distance and, equivalently, determines a compressive deformation that is required to generate a specified force. In this regard, when a screen assembly deforms under creep, the applied compressive force decreases due to the corresponding deformation (i.e., relaxation) of the spring. A pre-determined applied compressive force may be restored, however, by imposing a corresponding additional deformation (i.e., compression) of the spring by adjusting a position the compression assembly. Alternatively, when a screen assembly is installed, the compression assembly  7800  (e.g., see  FIG.  78 A ) may be adjusted to pre-compensate for creep. In this regard, the springs may be initially deformed to an extent greater than that needed to generate a minimum pre-determined force. In this way, although the compressive force decreases over time as the screen assembly shrinks under creep, the imposed force may be maintained above the pre-determined minimum force. 
     Spring rate is a value measured in either pounds per inch (in the royal system) or Newtons per millimeter (in the metric system). As such, an un-stretched spring measuring 0.250″, having a spring rate of 15 lb/in, may be deformed by an amount 0.050 inches by applying a force of 0.75 lbs. Similarly, a creep deformation of 0.050 inches would lead to a reduction in compressive force by 0.75 lbs. As described above, the force may then be restored by adjusting the compression assembly to impose a further 0.050 inch compression of the spring to restore the force. Alternatively, the compression assembly  7800  (e.g., see  FIG.  78 A ) may be adjusted to pre-compensate for creep, as described above. 
     In certain applications, screening assemblies may suffer additional deformations that may offset creep deformation. In this regard, in wet screening applications, subgrid materials such as nylon may absorb liquid and expand. The expansion due to swelling may offset the effects of creep. In certain embodiments, the effect of swelling may dominate the tendency for subgrids to shrink under creep. In this case, as subgrids swell, compression forces may increase due to the corresponding increased deformation of springs of the compression assembly. In such cases, the compression force may thereby be reduced by adjusting the compression assembly to reduce compression of the springs. In this way, the compression force may be restored to a pre-determined value. In situations in which swelling is expected to dominate creep deformation, screening assemblies may be installed by imposing compressive forces that are less than a desired pre-determined value, with the knowledge that the compressive forces will increase over time to the desired pre-determined value due to swelling. 
     Screening assemblies have been described above as generally having a rectangular shape. However, the shape of screening assemblies need not be so limited. For example, other embodiments may include screening assemblies having a perimeter that is any closed smooth or piecewise-smooth curve. For example, a screen assembly may have a perimeter that is a circle, square, rectangle, triangle, pentagon, hexagon, or other multi-sided pentagon. In other embodiments, the perimeter need not have any specific symmetry and may be an asymmetric smooth or piecewise smooth curve. In this regard, a frame of any shape (e.g., circular, triangular, square, rectangular, pentagonal, hexagonal, etc.) may be used as a substrate on which a screen assembly may be attached. According to an embodiment, a screen assembly may be a TPU based screen assembly that is supported by a subgrid structure. The screen assembly may include individual screen and sub grid assemblies that are snapped together to form a multi-piece assembly to cover or encompass an inside area of the frame. The frame may be any metallic or non-metallic material that provides suitable mechanical support for the screen assembly. The outside shape of the screen assembly may then be cut to generate a shape that matches a shape of a perimeter of the frame. The resulting screen assembly, having a shape similar to the frame, may then be bonded to the frame, clamped to the frame, or otherwise secured by the frame. 
       FIG.  80 A  illustrates a circular screen assembly  8000 , according to an embodiment. In this example, a self-supporting, stand-alone screen assembly such as shown in  FIG.  1    may be cut into a circle. Cutting of a stand-alone screen assembly (e.g., such as shown in  FIG.  1   ) may be accomplished using various cutting techniques. For example, a mechanical saw may be used. The resulting circular screen assembly  8000  may then be mounted to a circular frame  8002  for use in various screening applications. As shown in  FIG.  80 A , circular screen assembly  8000  includes a plurality of subgrids  8004  that are attached to one another. For example, subgrids  8004  may be attached to one another via clips (e.g., clips  42  of  FIGS.  11 ,  11 A,  63 B,  63 C, and  63 D ; clips  142  of  FIG.  60   ; clips  242  of  FIG.  63   ; etc.) and clip apertures  40  (e.g., see  FIGS.  11 ,  11 A,  63 B,  63 C, and  63 D ). 
     Subgrids may be attached to one another in a staggered configuration as shown, for example, by the sets  8006   a  and  8006   b  of connected subgrids in  FIG.  80 A , and described in greater detail below with reference to  FIGS.  80 E and  80 F . In this example, the stand-alone screen assembly includes first  8008   a  and second  8008   b  portions that are separated by a support structure  8010 . First  8008   a  and second  8008   b  portions may be generated as semi-circular screening assemblies cut from a stand-alone screen assembly such as shown in  FIG.  1   , as described in greater detail below. 
       FIG.  80 B  illustrates a perspective top view of circular screen assembly  8000  of  FIG.  80 A , according to an embodiment. As described above, circular screen assembly  8000  includes circular frame  8002  and support structure  8010 . Screen assembly  8000  includes first  8008   a  and second  8008   b  semi-circular portions that are separated by a support structure  8010 , as described above with reference to  FIG.  80 A . Circular frame  8002  and support structure  8010  provide mechanical support for first  8008   a  and second  8008   b  semi-circular portions. 
       FIG.  80 C  illustrates a perspective bottom view of circular screen assembly  8000  of  FIGS.  80 A and  80 B , according to an embodiment. As shown, circular frame  8002  may be configured to have an extended overhang or lip  8012  that may be configured to engage a support structure of a vibratory screening machine. For example, circular screen assembly  8000  may be removably installed in a corresponding circular hole (not shown) of a support structure of a vibratory screening machine. Upon installation, overhang  8012  may engage with a corresponding circular support portion of the vibratory screening machine to thereby support circular screen assembly  8000  in the vibratory screening machine. Circular screen assembly  8000  may then be secured to the vibratory screening machine using clamps, fasteners, etc. Circular frame  8002  may include a plurality of circular arc segments that may be assembled to form frame  8002 , as described in greater detail below with reference to  FIG.  80 D . Circular frame  8002  and support structure  8010  (also see  FIGS.  80 A and  80 B ) may be made of aluminum, carbon steel, 70% glass fiber in nylon, etc., or any other suitable structural material. 
       FIG.  80 D  illustrates a top view of structural support components  8014  for circular screen assembly  8000  of  FIGS.  80 A,  80 B, and  80 C , according to an embodiment. Structural support components  8014  include a circular arc  8016 , two components  8016   a  and  8016   b  of support structure  8010  (e.g., see  FIGS.  80 A to  80 C ), and a weld on rib  8018 . In this example, circular arc  8016  may be combined with three similar additional circular arcs (not shown) to form circular frame  8002  (e.g., see  FIGS.  80 A to  80 C ). In this regard, circular arcs  8016  may be configured to be attached to one another to form circular frame  8002 . Circular arcs  8016  may be configured to be snapped together or may be held together with various fasteners, clamps, etc. In some embodiments, circular arcs  8016  may be combined and attached together via welding. For example, weld on rib  8018  may be used to fasten circular arcs  8016  together. Further, components  8016   a  and  8016   b  may form top and bottom components of support structure  8010 . Components  8016   a  and  8016   b  may be configured to be snapped together, or to be clamped, fastened, etc., to form support structure  8010 . 
     Subgrids  8004  (e.g., see  FIG.  80 A ) may support a corresponding plurality of screening structures (e.g., screen element  416  of  FIG.  75 A , screen elements  516   a  and  516   b  of  FIG.  75 B , etc.) that may be injection molded structures including TPU. Such screen elements may include surface elements  84  separated by a series of screening openings  86 , as described above with reference to  FIG.  2 D . According to an embodiment, circular screen assembly  8000  (e.g., see  FIGS.  80 A to  80 C ) may have a diameter of up to 18 inches. Other sizes of screening assemblies may be provided in other embodiments. For example, circular screen assembly  8000  may have a diameter: in a range from approximately 18 inches to approximately 72 inches; in a range from approximately 24 inches to approximately 66 inches; in a range from approximately 30 inches to approximately 60 inches; in a range from approximately 36 inches to approximately 54 inches; in a range from approximately 42 inches to approximately 48 inches; etc. The disclosure is not limited by the disclosed diameters of screen assembly  8000 , and other embodiments have additional diameters or ranges of diameters as needed for specific applications. 
     As with other screening assemblies, circular screen assembly  8000  of  FIGS.  80 A to  80 C  (having TPU screen elements) may exhibit increased life due to the inherent abrasion and cut resistant properties of TPU relative to screens made of non-TPU materials. Circular screen assembly  8000  may further exhibit anti-blinding properties due to the high relief angle design of TPU screening openings, as described above in the context of other embodiments (e.g., see  FIG.  74 D  and related description). Further, circular screen assembly  8000  is configured to be self-supporting and has an advantage in that it does not need to be stretched in any direction in order to be used in screening applications. It may simply be attached or otherwise secured to an appropriately shaped frame. As such, circular screen assembly  8000  would thereby be configured for various screening applications without further support structures. 
       FIG.  80 E  illustrates a top view of an example subgrid  8020  that may be combined with other similar subgrids to form a screen assembly, according to an embodiment. Subgrid  8020  is similar to subgrids  718 , described above with reference to  FIGS.  64  and  64 A , subgrids  818 , described above with reference to  FIGS.  65  and  65 A , and subgrids  8004 , described above with reference to  FIG.  80 A . In this example, subgrid  8020  is shown without clips (e.g., clips  42  of  FIGS.  11 ,  11 A,  63 B,  63 C, and  63 D ; clips  142  of  FIG.  60   ; clips  242  of  FIG.  63   ; etc.) for simplicity. Subgrid  8020  may have a width of 2 and ⅛ th  inches, and a length of 5 and 9/16 th  inches. Other embodiments may have other dimensions for similar features. As mentioned above, with reference to  FIG.  80 A , subgrids  8020  may be combined with other subgrids  8020  to form a self-supporting, stand-alone screen assembly such as shown in  FIG.  1   , which may be cut into a circle (or into semi-circles  8008   a  and  8008   b  of  FIG.  80 A ) to generate circular screen assembly  8000 . Subgrids may be combined in a staggered orientation, as shown by sets  8006   a  and  8006   b  of connected subgrids in  FIG.  80 A , and described in greater detail below with reference to  FIG.  80 F . 
       FIG.  80 F  illustrates a top view of three subgrids  8020   a ,  8020   b , and  8020   c  that are combined in a staggered arrangement  8022 , according to an embodiment. In this arrangement  8022 , subgrid  8020   b  is displaced along a longitudinal axis relative to subgrid  8020   a . Similarly, subgrid  8020   c  is displaced relative to subgrid  8020   b . The displacement of subgrid  8020   c  relative to subgrid  8020   b  is opposite to the displacement of subgrid  8020   b  relative to subgrid  8020   a . In this way, subgrids  8020   a  and  8020   c  are aligned with one another but are each displaced relative to subgrid  8020   b . Displacing subgrids  8020   a  to  8020   c  in this way may lead to an arrangement  8022  having greater mechanical strength relative other arrangements. 
     This disclosure is not limited to arrangement  8022 , however, and many other arrangements are possible in other embodiments. Arrangement  8022  may have an overall length of 13 and 31/32 inches and a width of 6 and ⅜ inches. These example dimensions are based on the dimensions of subgrid  8020  of  FIG.  80 E . Other embodiments may have other dimensions for similar features. Subgrids  8020   a  to  8020   c  may be attached to one another using various types of mechanical fasteners. For example,  8020   a  to  8020   c  may be attached to one another using clips (e.g., clips  42  of  FIGS.  11 ,  11 A,  63 B,  63 C, and  63 D ; clips  142  of  FIG.  60   ; clips  242  of  FIG.  63   ; etc.) and clip apertures  40  (e.g., see  FIGS.  11 ,  11 A,  63 B,  63 C, and  63 D ). In further embodiments, subgrids  8020   a  to  8020   c  may be attached to one another via gluing, welding, etc. 
       FIG.  80 G  illustrates a cross-sectional view of the staggered arrangement  8022  of subgrids shown in  FIG.  80 F , according to an embodiment. The cross sectional view of  FIG.  80 G  is based on the cross section  80 G- 80 G defined in  FIG.  80 F . As shown in  FIG.  80 G , subgrid  8020   b  is displaced relative to subgrids  8020   a  and  8020   b . In the view of  FIG.  80 G , subgrid  8020   b  is shown closer to the foreground while subgrids  8020   a  and  8020   c  are shown closer to the background of  FIG.  80 G . This view is consistent with the displacement of subgrid  8020   b  relative to subgrids  8020   a  and  8020   c  described above with reference to  FIG.  80 F . As mentioned above, other arrangements of subgrids are possible in other embodiments. 
     The circular screen assembly  8000  of  FIGS.  80 A to  80 C  is only one possible shape provided by disclosed embodiments. In further embodiments, other shaped screening assemblies may be constructed in a similar manner. For example, oval, triangular, square, pentagonal, hexagonal, etc., screening assemblies may be generated by starting with a self-supporting, stand-alone screen assembly, such as shown in  FIG.  1   . For example, a triangular shaped screen assembly may be generated by cutting the screen assembly of  FIG.  1    into a triangular shape as described in greater detail below with reference to  FIG.  80 H . 
       FIG.  80 H  illustrates a triangular arrangement  8024  of subgrids used to generate a triangular screen assembly, according to an embodiment. Arrangement  8024  may be generated by attaching a plurality of subgrids (e.g., subgrids  8020  of  FIGS.  80 E and  80 F , subgrids  8004  of  FIG.  80 A , etc.) together to form arrangement  8024 , as shown. Triangular arrangement  8024  may then be cut along cut lines  8026   a  and  8026   b  to remove jagged edges formed by edges of individual subgrids. Cutting along cut lines  8026   a  and  8026   b  generates a triangular screen assembly having smooth edges. As mentioned above, cutting may be performed using various cutting techniques including cutting with a mechanical saw, cutting using a laser cutting process, etc. Screen elements  416  (e.g., see  FIGS.  48  to  48 C ),  516  (e.g., see  FIGS.  66  to  66 C ), etc., may be attached to subgrids (e.g., subgrids  8020  of  FIGS.  80 E and  80 F , subgrids  8004  of  FIG.  80 A , etc.) prior to cutting arrangement  8024  along cut lines  8026   a  and  8026   b . The resulting triangular screen assembly may be supported by a frame, as described in greater detail below with reference to  FIGS.  80 I and  80 J . 
       FIG.  80 I  illustrates a triangular screen assembly  8028  including a triangular support frame  8030 , according to an embodiment. Screen assembly  8028  includes the triangular arrangement  8024  of subgrids (optionally having screen elements attached) that has been cut as described above with reference to  FIG.  80 H . Triangular arrangement  8024  of subgrids is supported by a triangular support frame  8030 . As with the circular frame  8002 , described above with reference to  FIGS.  80 A to  80 D , triangular support frame  8030  may include several components that may be coupled together to form triangular support frame  8030 . For example, triangular support frame  8030  may have a first frame piece  8032   a , a second frame piece  8032   b , and a third frame piece  8032   c . Frame pieces  8032   a  to  8032   c  may be configured to be snapped together or may be coupled together using various fasteners, clamps, etc. In further embodiments, frame pieces  8032   a  to  8032   c  may be bonded together using glue or adhesive, may be welded together, etc. 
       FIG.  80 J  illustrates an enlarged view of the triangular screen assembly  8028  of  FIG.  80 I , according to an embodiment. Frame pieces  8032   b  and  8032   c  are shown coupled together along a joining line  8034 . As shown, frame pieces  8032   b  and  8032   c  may include coupling features  8036  that may allow frame pieces  8032   b  and  8032   c  to be snapped together to form a mechanical connection between frame pieces  8032   b  and  8032   c . Flat edges of frame pieces  8032   a  to  8032   c  may be configured to engage with a support structure (not shown) of a vibratory screening machine, as described above with reference to  FIG.  80 C  in the context of the circular screen assembly  8000 . As such, flat portions of frame pieces  8032   c  to  8032   c  may be configured as an extended overhang or lip that is configured to make contact with a corresponding flat surface (not shown) of a support structure. For example, a support structure (not shown) of a vibratory screening machine may have a triangularly-shaped hole that is smaller than an outer perimeter of triangular frame pieces  8032   a  to  8032   c  such that triangular screen assembly  8028  is secured by mechanical contact between flat edges of frame pieces  8032   a  to  8032   c  that come in contact with a corresponding flat surface (not shown) of a support structure. Frame pieces  8032   a  to  8032   c  may be made of aluminum, carbon steel, 70% glass fiber in nylon, etc., or any other suitable structural material. A similar process may be used to generate screening assemblies having other shapes. 
     In certain screening applications, it may be advantageous to adapt or alter an amount of, and location of, attachment of screen elements to subgrids. As described above with reference to  FIGS.  67  and  67 A , a screen element  516  may be attached to a subgrid  718 . For example, screen element  516  may be attached to subgrid  718  via laser welding. In this regard, fusion bars  476  may engage with corresponding cavity pockets  472  (e.g., see  FIGS.  66 B  and  66 C) of screen element  516 . Application of laser radiation may then be used to melt fusion bars  476  to thereby form a bond between screen element  516  and subgrid  718 . In some embodiments, it may be advantageous to melt all of the fusion bars  476  to thereby form a tight connection between screen element  516  and subgrid  718 . In other embodiments, it may be advantageous to laser weld only a sub-set of fusion bars  476  to thereby form a less-tight connection between screen element  516  and subgrid  718 . Points at which fusion bars  476  are not laser welded to subgrid  718  allow motion of screen element  516  relative to subgrid  718 , as described in greater detail below. 
       FIG.  81    illustrates a top view of a screen element and frame assembly  8100  with various regions  8101  to  8120  that may be laser welded to an underlying subgrid, according to an embodiment. As described above, laser welding all of regions  8101  to  8120  leads to a strong binding between screen element  8100  and subgrid. Such a fully-welded configuration allows little relative motion between screen element  8100  and the underlying subgrid. In further configurations, some of the potential laser weld locations (i.e., some of regions  8101  to  8120 ) may be left un-welded to allow relative motion between screen element  8100  and the underlying subgrid. 
     In a first example application, a screen element fully bonded to a subgrid would be desirable for a situation in which a screening operation is needed to be performed for dewatering of a high-solids slurry. In such an application, it would be desirable to assure that the screen is completely and securely attached to the support subgrid. In this regard, screen element  8100  may be laser welded to the underlying subgrid around a perimeter and across the middle of the screen element including laser welding all regions  8101  to  8120 . Such a configuration would allow the assembly (screen and subgrid) to move as a rigid unit in unison with vibrating motion of the vibrating screening machine. This is especially useful when dewatering heavy solids at high flow rates and at high accelerations (i.e., high G forces). Such solids must be moved quickly along a screening surface. This sometimes occurs at high G forces or large amplitudes of motion at the screen surface. In such a situation, any relative movement of the subgrid and screen surface that is not in sync with the vibrating screening machine may cause a reduction in conveyance of solids and, in turn, a reduction in a flow of material through the screen. 
     In other situations, it may be desirable to have a screen element that is not fully laser-welded to the underlying subgrid. As such, during operation, relative motion (i.e., 2 nd  order movement) between the screen element and the subgrid may be beneficial. For example, in a dry screening or sifting application (i.e., attrition screening) a 2 nd  order movement or vibration of the screen element or surface relative to the subgrid may aid in de-blinding of the screen (i.e., removing particles that may in certain situations become stuck in screen openings). A slight vertical impact or force could be applied in order to dislodge particles that are transitionally retained in the tapered screen openings. Such a situation may occur, for example, in square or slotted screen openings. 
     For this type of application, it may be beneficial to generate a partially bonded screen element in screen element and frame assembly  8100  (e.g., see  FIG.  81   ) by bonding (e.g., via laser welding) regions  8105 ,  8106 ,  8107 ,  8101 ,  8109 ,  8110 ,  8112 ,  8113 ,  8115 ,  8116 ,  8117 , and  8120 , while leaving regions  8102 ,  8103 ,  8104 ,  8108 ,  8111 ,  8114 ,  8118 , and  8119  un-bonded. Such a configuration would allow vertical movement of the screen element surface and would aid in dislodging transitionally retained particles form screen element openings due to impacts between screen element  8100  and a surface of the subgrid. 
       FIG.  82    illustrates a vibrational amplitude profile of a screen element  8100  that is partially bonded to a subgrid  8200 , according to an embodiment. In this example, screen element  8100  is bonded to subgrid  8200  to allow movement in only one direction perpendicular to a surface of subgrid  8200 . In this configuration, vibrational motion of screen element  8100  relative to subgrid  8200  occurs in a direction perpendicular to the surface of subgrid  8200  such that the amplitude has maxima at first  8202   a  and second locations  8202   b , as shown in  FIG.  82   . Further, screen element  8100  is bonded to have zero amplitude of relative motion at first  8204   a , second  8204   b , and third  8204   c  locations such that screen element  8100  moves rigidly with subgrid  8200  at these locations. In this example, vertical motion causes screen element  8100  to pull away from subgrid  8200  on an up stoke and to impact subgrid  8200  on a down stroke. As described above, such motion may be useful in dry screening application to aid in de-blinding. 
     In addition to a bonding configuration of screen element  8100  to subgrid  8200  (e.g., see  FIGS.  81  and  82   ), material properties of subgrid  8200  may influence relative motion of screen  8100  and subgrid. For example, subgrids  8200  may be configured to be more or less rigid based on thickness and the types of materials used to construct subgrid  8200 . As such, it may be desirable to have a subgrid  8200  that is more rigid for applications in which screen element  8100  is tightly bonded to subgrid  8200 . Alternatively, in other applications, it may be advantageous to have subgrids  8200  that are less rigid to allow more relative motion between subgrid  8200  and partially bonded screen element  8100 . Further, toughness of subgrid materials may influence relative motion of screen element  8100  and subgrid  8200  due to the relative tendency of subgrid materials to absorb more/less vibrational energy for materials having greater/lesser toughness. 
       FIG.  83    illustrates an example attrition screening machine  8300 , according to an embodiment. Attrition screening machine  8300  may be used to separate dry materials of various sizes. In this example, attrition screening machine  8300  includes two circular screens  8302   a  and  8302   b . A first material  8304  may be introduced into attrition screening machine  8300  through an inlet  8306  of attrition screening machine  8300 . First material  8304  may be separated by first screen  8302   a  into a first oversized component and a first undersized component. The first oversized component that does not fall through first screen  8302   a  may be removed from attrition screening machine  8300  as a first separated material  8308   a  through a first outlet  8310   a  of attrition screening machine  8300 . The first undersized component that falls through first screen  8302   a  may be further separated into a second oversized component and a second undersized component. The second oversized component that does not fall through screen  8302   b  may be removed from attrition screening machine  8300  as a second separated material  8308   b  through a second outlet  8310   b . Lastly, the second undersized component that falls through second screen  8302   b  may be removed from attrition screening machine  8300  as a third separated material  8308   c  through a third outlet  8310   c  of attrition screening machine  8300 . Separation of first material  8304  in to first  8308   a , second  8308   b , and  8308   c  separated materials may be assisted by vibrations of screens  8302   a  and  8302   b  that may be provided by a vibratory motor  8312 . Other embodiment attrition screening machines may include greater or fewer screens to respectively separate greater or fewer components of an input material. 
     Attrition screening machine  8300  may use circular screens  8302   a  and  8302   b  as described above. For example, circular screens  8302   a  and  8302   b  may be constructed as described above with references to  FIGS.  80 A to  80 F . Further, circular screens  8302   a  and  8302   b  may include screen elements that are configured to be loosely attached to subgrids, as described above with reference to  FIGS.  81  and  82   . Such loose binding of screen elements to subgrids allows relative motion of screen elements with respect to motion of subgrids. Such motion may aid de-blinding of screen elements. In this regard, particulate matter may become lodged in screen openings  86  (e.g., see  FIG.  2 D ) causing blockage of screen openings  86 . Such blockage of screen element openings  86  is called screen blinding. Screen blinding reduces a screen&#39;s ability to separate particulate materials into an oversized component and an undersized component because a blocked opening  86  fails to allow undersized materials to fall through the screen element. Further embodiments, described below, provide additional systems and methods for screen de-blinding. 
     As described above, deblinding may refer to the removal of one or more occlusions present in one or more openings of a screen, screen assembly, or material separation apparatus. Particulate matter may lodge in a sifting screen, for example, blocking one or more openings of the sifting screen. The blockage of one or more openings may be referred to as blinding, and the removal of blocking particulate matter may be referred to as deblinding. According disclosed embodiments, deblinding of a sifting screen may rely on collisions of objects with the sifting screen. 
     A deblinding apparatus may include a support frame, having a rectangular array of support members, and a grid structure (e.g., a metal or plastic grid structure) attached to a first side of the support frame. A plurality of rectangular compartments may be formed when the grid structure is attached to the support frame. In this regard, support members of the support frame forms side-walls of the plurality of rectangular compartments, while portions of the grid structure form bottom surfaces of the rectangular compartments. The deblinding apparatus may further include scattering members disposed within a plurality of the compartments. Such scattering members may be removably affixed to portions of the grid structure that forms bottom surfaces of the rectangular compartments. The scattering members may include rigid objects having elongated shapes (e.g., a strip or a bar) or more symmetric shapes (e.g., a disc or a dome). The deblinding apparatus may further include or more unsecured objects that may be disposed within various compartments. 
     A screen assembly may be attached to a second side of the support frame to thereby form a screening system having a deblinding apparatus. Attaching the screen assembly to the second side of the support frame causes the rectangular compartments to form three-dimensional closed volumes with portions of the screen assembly forming top surfaces of the closed rectangular compartments. In response to movement of the screening system having the deblinding apparatus, the unsecured objects may collide with scattering members which cause the unsecured scattering members to collide with the screen assembly. Collisions of the unsecured objects with the screen assembly may cause deblinding of the screen assembly, according to embodiments of the present disclosure. Sizes, shapes, masses, and morphologies of unsecured objects may be designed to optimize collision rates of unsecured objects with scattering members and with the screen assembly, as described in greater detail below. 
     The screening system having a deblinding apparatus may be used to separate solid particulate materials from a slurry (i.e., a material having solid particulates dispersed/suspended in a liquid medium), as follows. During operation of the screening system, the slurry may be introduced onto an external side of the screen assembly. Sizes of screen openings may be chosen to separate and remove particles that are larger than screen openings, while allowing smaller particles to pass through the screen along with the liquid medium. A vibratory/oscillatory motion may be imparted to the screening system to cause the liquid material of the slurry and smaller particles to flow through the screen assembly while leaving larger solid particulate materials on the external surface of the screen assembly, thereby separating the larger dispersed solids from the smaller particles and the liquid medium. After flowing through the screen assembly, the liquid medium and smaller particles may further flow out of the screening system through the grid structure. 
     While screening slurry materials in this way, various occlusions of screen openings may form as larger solid particles become lodged in screen openings. In other words, the screen assembly may become blinded. The presence of the deblinding apparatus, however, tends to deblind the screen during operation of the screening system. In this regard, the vibratory/oscillatory motion imparted to the screening system, to separate the larger particles from the liquid and smaller particles, also causes the unsecured objects to collide with scattering members, and in turn, to collide with the screen assembly. The collisions with the screen assembly tend to remove occluded particles to thereby deblind the screen assembly. Thus, any occlusions that form during operation are quickly removed by the deblinding system to leave the screen assembly effectively deblinded on average. 
     Disclosed embodiments are not limited to particular placements of scattering members and unsecured objects within the compartments of the deblinding apparatus. Various configurations of scattering members and unsecured objects may be assembled among the compartments of the deblinding apparatus to adjust collision rates of unsecured objects with the screen assembly. 
     Disclosed deblinding apparatuses may be used for deblinding of screens/screen assemblies such as those described in U.S. Pat. Nos. 8,584,866; 9,010,539; 9,375,756; 9,403,192 and 9,908,150; each of which is incorporated herein by reference. The disclosed deblinding apparatuses are not limited to use only with screens and screen assemblies of the above-referenced patent documents. Rather, disclosed deblinding apparatuses may be used with other, more conventional, screens and screening systems. In this regard, deblinding apparatuses may be retrofitted for use with existing separation equipment, in accordance with embodiments of the disclosure. Similar screening assemblies that are configured to de-blind screen elements are disclosed in U.S. patent application Ser. No. 16/117,798 (published as U.S. Patent Application Publication No. 2019/0070638 A1), the disclosure of which is hereby incorporated by reference in its entirety. 
       FIG.  84 A  illustrates a perspective exploded view of a screen assembly  8400  that is configured to facilitate screen de-blinding, according to an embodiment. As shown, screen assembly  8400  has a first screen element  8402   a , a second screen element  8402   b , a support frame  8404 , and one or more unsecured objects  8406 . In this example, support frame  8404  has four walls and a single internal support structure  8408 . First  8402   a  and second  8402   b  screens may be mounted to respective first and second sides of support frame  8402  to generate an enclosed structure having first  8410   a  and second  8410   b  compartments. As such, unsecured objects  8406  may be enclosed in one or both compartments  8410   a  and  8410   b . When assembled (e.g., see  FIG.  84 B  below), screen assembly  8400  may be used as one component in a screen assembly, such as circular screen assembly  8000  of  FIGS.  80 A to  80 C , triangular screen assembly  8028  of  FIGS.  80 I and  80 J , etc. 
     During operation, vibrations received from a vibratory screening machine may cause unsecured objects  8406  to move within compartments  8410   a  and  8410   b . In this way, unsecured objects  8406  may make collisions with screen elements  8402   a  and  8402   b . Such collisions may act to dislodge and thereby remove any particles that may stick to openings  86  (e.g., see  FIG.  2 D ) of screen elements  8402   a  and  8402   b . In this way, motion of unsecured objects  8406  may act to de-blind screen elements  8402   a  and  8402   b.    
       FIG.  84 B  illustrates an assembled view of screen assembly  8400  of  FIG.  84 A , according to an embodiment. In this view, screen element  8402   a  is attached to a top surface of support frame  8404  and screen element  8402   b  is attached to a bottom surface of support frame  8404 . Screen elements  8402   a  and  8402   b  may be attached to support frame using many attachment techniques, such as gluing, heat steaking, laser welding, etc., as described in greater detail above. Support frame  8404  may be made of aluminum, carbon steel, 70% glass fiber in nylon, etc., or any other suitable structural material. 
       FIGS.  85 A to  85 D  show various support frames that may be used to generate screening assemblies that are configured to facilitate screen de-blinding, according to an embodiment.  FIG.  85 A  provides an isolated view of support frame  8404 , described above with reference to  FIG.  84 A . As mentioned above, support frame  8404  includes a single internal support structure  8408 . Screen elements  8402   a  and  8402   b  may be mounted to support frame  8402  (e.g., see  FIGS.  84 A and  84 B ) to generate an enclosed structure having first  8410   a  and second  8410   b  compartments. Unsecured objects (e.g., see objects  8406  of  FIG.  84 A ) may be enclosed in first  8410   a  and second  8410   b  compartments. 
       FIG.  85 B  shows a support frame  8502  having three internal support structures  8503   a ,  8503   b , and  8503   c  forming four internal compartments  8504   a ,  8504   b ,  8504   c , and  8504   d .  FIG.  85 C  shows a support frame  8506  having two crossed internal support structures  8508   a  and  8508   b  forming four internal compartments  8510   a ,  8510   b ,  8510   c , and  8510   d .  FIG.  85 D  shows a support frame  8512  having four crossed internal support structures  8514   a  to  8514   d  forming eight internal compartments  8516   a  to  8516   h . The various support frames of FIGS.  85 A to  85 D provide varying degrees of support to screen elements (e.g., screen elements  8402   a  and  8402   b  of  FIG.  84 A ). Further, the degree to which screen elements  8402   a  and  8402   b  are bonded to the various support structures of support frames of  FIGS.  85 A to  85 D  may be varied to control motion of screen elements  8402   a  and  8402   b  relative to support frames, as described above with reference to  FIGS.  81  and  82   . The choice of support frame may be dictated by the screening application and the degree to which screen elements are designed to allow motion of the screen element relative to the support frame, as described above with reference to  FIGS.  81  and  82   . 
       FIG.  85 E  illustrates a top view of a screen assembly having support frames and unsecured objects, according to an embodiment. In this example, a plurality of different types of support frames have been combined with screen elements and unsecured objects. The view of  FIG.  85 E  is transparent to allow internal structures (e.g., frame support structures and unsecured objects) to be seen. As shown, a first frame  8518   a  has only four walls (i.e., no internal support structures) supporting screen elements. Frame  8518   a  provides little support for mounted screen elements and thereby allows considerable movement of screen elements relative to frame  8518   a . As shown, frame  8518   a  encloses a single unsecured object  8520   a . A second frame  8518   b  includes a single horizontal support structure  8522   a . Frame  8518   b  encloses three unsecured objects  8520   b ,  8520   c , and  8520   d  in two internal compartments. Frame  8518   b  is similar to frame  8404  described above with reference to  FIGS.  84 A,  84 B, and  85 A . 
     Frame  8518   c  has a single internal support structure  8522   b  and differs from frame  8518   b  only in the orientation of internal support structure  8522   b . Internal support structure  8522   b  defines two internal compartments that house four unsecured objects  8520   e  to  8520   h  with two unsecured objects per compartment. Frame  8518   d  includes two crossed internal support structures  8522   c  and  8522   d  forming four internal compartments. Frame  8518   d  is similar to frame  8506 , described above with reference to  FIG.  85 C . As shown, frame  8518   d  encloses four unsecured objects  8520   i ,  8520   j ,  8520   k , and  85201 , with one unsecured object per compartment. As shown in  FIG.  85 E , various frame structures may be combined in various ways to generate a screen assembly that is configured to de-blind screen elements. 
     According to an embodiment, an unsecured object (e.g., unsecured objects  8520   a  to  85201  of  FIG.  85 E ) may be a substantially cylindrically-symmetric solid having an opening or a through hole (not shown), as described in greater detail in U.S. patent application Ser. No. 16/117,798 (published as U.S. Patent Application Publication No. 2019/0070638 A1), the disclosure of which is hereby incorporated by reference in its entirety. As such, in some embodiments, an unsecured object may be a solid having a substantially annular cross-section, for example, a substantially circular annulus or a substantially elliptical annulus. As an example, the substantially annular cross-section may have an outer diameter of about 41.3 mm and an inner diameter having a value in a range from about 10.3 mm to about 25.4 mm. 
     In other embodiments, an unsecured object may be a substantially spherical solid or a substantially ellipsoidal solid. A substantially circular cross-section of such an unsecured object may have a diameter of about 41.3 mm. Regardless a specific shape, the unsecured object may be made of a polymer and may have a mass in a range from about 23 g to about 46 g. The polymer may be or may include, for example, a rubber or a plastic. In some embodiments, the rubber may be silicone rubber, natural rubber, butyl rubber, nitrile rubber, neoprene rubber, a combination of the foregoing, etc. 
     According to various embodiments, a size, shape, mass, and morphology (e.g., with or without a through-hole) of unsecured impact members may be designed to optimize a collision rate of unsecured objects with screen elements. In this regard, for a given vibrational motion of the screening system, a collision rate of an unsecured object depends on its mass as well as its size relative to a size of a screen assembly. Further, the mass of an unsecured object, for a given size and shape, may be reduced with the introduction of an opening or through hole, and thus the mass may be tuned as needed. The choice of material (e.g., rubber rather than metal, plastic, etc.) may also be optimized to provide de-blinding while reducing a tendency for the unsecured objects to cause damage to the screen assembly through collisions with the screen assembly. 
     The disclosure is not limited to embodiments having a single unsecured impact member per compartment (e.g., compartments  8410   a  and  8410   b  of screen assembly  8400  shown in  FIG.  84 A ). Other embodiments may include more than one unsecured impact member per compartment. As mentioned above, compartments of a screen assembly may contain different respective numbers of unsecured impact members. Further, some compartments may have no unsecured objects. 
       FIG.  86    is a flowchart illustrating a method  8600  of manufacturing a screening apparatus, according to an embodiment. Method  8600  may be used to generate a screening apparatus such as those illustrated in  FIGS.  80 A to  80 J  and described in greater detail above. In a first stage  8602 , the method includes generating a plurality of screen elements. Screen elements may be generated using various methods. For example, screen elements may be generated by injection molding using a TPU material as described in greater detail above. In stage  8604 , the method includes generating a plurality of subgrids. Subgrids may be generated according to methods described above. For example, subgrids may be injection molded using a nylon based material. In stage  8606 , the method includes attaching the plurality of screen elements respectively to the plurality of subgrids. In stage  8608 , the method includes attaching the plurality of subgrids to one another to form a screening pre-assembly such as the screening pre-assembly illustrated in  FIG.  1   . Lastly, in stage  8610 , the method includes cutting edges of the screening pre-assembly to form the screen assembly having a perimeter that is a pre-determined shape. The pre-determined shape may be any shape defined by a smooth or piecewise-smooth closed curve. For example, the pre-assembly may be cut into a circle (e.g., see  FIGS.  80 A to  80 C ), a triangle (e.g., see  FIGS.  80 H to  80 J ), an oval, a square, a hexagon, a polygon, etc. As described above, the pre-assembly may be cut using various techniques, for example, using a mechanical saw, using a laser-cut process, etc. 
       FIG.  87 A  illustrates a top perspective view of a screening assembly  8700  and a plug  8702  that may be installed in a damaged area  8704  of the screening assembly, according to an embodiment. As with other embodiments, screening assembly  8700  includes a screening element  8708  attached to a subgrid  8710 . Over time, areas of the screening element  8708  may become damaged. For example, area  8704  may be a damaged area having holes or tears in the screening surface. The presence of damaged areas, such as area  8704 , may be detrimental to the performance of screening assembly  8700 . In this regard, holes or other imperfections of screening area  8704  may allow particulate matter having particulate sizes larger than screening openings to flow through screening assembly  8700 . Plug  8702  may be used to block damaged areas  8704  to prevent flow of material through the screen having particulate sizes larger than screening openings. 
     Plug  8702  may have hook structures  8706  that may be configured to be inserted through a surface of screening element  8708 . Hook structures  8706  may be configured to mechanically engage with locking structures in subgrid  8710 , as described in greater detail below with reference to  FIGS.  90 A and  90 B . For example, to repair a damaged screen section, a user may insert plug  8702  through damaged screen section  8704  by applying a force by hand to move plug  8702  into an installed configuration as shown, for example, in  FIG.  87 B . To assist in insertion, the user may cut out screening bars in the area  8704  if such screening bars interfere with the hooks  8706  passing through the screening surface. 
       FIG.  87 B  illustrates plug  8702  in an installed configuration in screen assembly  8700 , according to an embodiment. In this example, a single plug  8702  may be used to repair one quarter of screen assembly  8700 . Multiple plugs  8702  may be inserted into a single screen assembly  8700  to repair multiple damaged areas, and in this example, up to four plugs  8702  may be inserted into a single screen assembly  8700 . As shown in  FIG.  87 B , plug  8702  is configured to be inserted through the top of the screening element  8708  so that if plug  8702  were to fall out, it would not fall into the product (i.e., screened fluid containing undersized materials). As such, if plug  8702  were to fall out, it would be collected with the oversized screened materials that are disposed of as waste materials of the screening process. In an installed configuration, such as shown in  FIG.  87 B , plug  8702  may be configured to make close mechanical contact with the screening surface of screening element  8708 . As such, in this example, plug  8702  is flush with the screening surface to thereby prevent fluid buildup. 
       FIGS.  88 A and  88 B  illustrate respective top and bottom perspective views of plug  8702  of  FIGS.  87 A and  87 B , according to an embodiment. A top surface  8800  of plug  8702  may have a flat, rectangular structure as shown. In further embodiments, however, surface  8800  of plug  8702  need not be flat and may have a pyramid structure, a dome structure, etc. In certain embodiments, a tapered surface may be more suitable than a flat surface. For example, in some situations, a flat surface may cause fluid to settle on the surface. Such settled fluid may create conveyance issues. Plug  8702  may further be configured to have a thickness that is relatively small compared with a thickness of screening element  8708  of  FIG.  87 A . A relatively small thickness of plug  8702  may avoid buildup of fluid and particles around outside edges of plug  8702  in an installed configuration (e.g., see  FIG.  87 B ). A bottom surface  8802  (e.g., see  FIG.  88 B ) may have a flat structure that may be configured to make close contact with the surface of the screening element  8708  (e.g., see  FIG.  87 B ). In further embodiments, bottom surface  8802  may be slightly tapered. 
     Plug  8702  (e.g., see  FIGS.  87 A to  88 B ) may be made of plastic, nylon, thermoplastic polyurethane or any suitable material such as nylon having 50% glass fiber filler. For example, plug  8702  may include nylon containing 0-70% glass filler fiber. In further embodiments, plug  8702  may include a high-durometer thermoplastic polyurethane having enhanced abrasion resistance, or plug  8702  may include a mixture of glass fibers in a thermoplastic polyurethane material. As mentioned above, plug  8702  may include hooks  8706  (e.g., see  FIGS.  87 A,  88 A, and  88 B ) that may be configured to latch onto a latching structure of the subgrid  8710  (e.g.,  87 A and  87 B), as described in greater detail below with reference to  FIGS.  90 A and  90 B . 
       FIG.  89    illustrates an exploded view  8900  of screening assembly  8700  and plug  8702  of  FIGS.  87 A and  87 B , according to an embodiment. As shown, screening assembly  8700  includes screening element  8708  and subgrid  8710 . As described above, plug  8702  may be installed in screening assembly  8700  by forcing hooks  8706  through screening element  8708  so that hooks  8706  may be passed through grid framework  8902  of subgrid  8710 . Upon passing hooks  8706  through grid framework  8902  of subgrid  8710 , hooks  8706  may be caused to engage with latching structures of subgrid  8710 , as described in greater detail below with reference to  FIGS.  90 A and  90 B .  FIG.  89    further shows a cutout  8904  that may be used to improve injection molding of subgrid  8710 . This inclusion of cutout  8904 , however, is optional and further embodiments may be provided without cutout  8904 . 
       FIG.  90 A  illustrates a bottom perspective view  9000 , and  FIG.  90 B  illustrates a bottom view  9004  of plug  8702  and screen assembly  8700  of  FIGS.  87 A,  87 B, and  89    with the plug  8702  in an installed configuration (e.g., see  FIG.  90 B ), according to an embodiment. As shown, hooks  8706  have been passed through grid framework  8902  of subgrid  8710 . Further, hooks  8706  have been caused to engage with latching structures  9002 . In this example, latching structure  9002  are rails built into grid framework  8902  of subgrid  8710 . Coupling structures, such as hooks  8706  and latching structure  9002  allow plug  8702  to be easily installed by hand. As such, hooks  8706  snap into place and are prevented from falling out of the screening assembly  8700  (e.g., see  FIG.  87 B ) during use. In further embodiments, hooks may be configured to engage with any portion of the grid framework  8902  or other portions of the subgrid  8710 . 
     Other latching structures may be provided in further embodiments. Similarly, in other embodiments, plug  8702  may have coupling structures other than hooks  8706 . As such, plug  8702  may be provided with any other coupling structures that are configured to establish a secure structure with complementary coupling structures of subgrid  8710 . For example, alternative coupling structures may include glue/adhesives, plastic welding, clips, clamps, alternative hook geometries, mechanical fasteners, etc. 
     As described above, it may be advantageous to have plug  8702  installed on a top surface of screening assembly  8700 , as shown in  FIG.  87 B . As such, should plug  8702  fall out of the screening assembly  8700 , it would not enter the screened fluid containing undersized particulates. In this way, a plug  8702  that accidentally falls out of screening assembly  8700  may be removed along with oversized particulates, which are intended to be removed as waste materials that have been screened by screening assembly  8700 . Plug  8702  need not be installed in a top surface of screening assembly  8700 , however. In further embodiments, plug  8702  may be installed from the bottom of screening assembly  8700  (not shown). In further embodiments, plug  8702  may be configured to be larger to thereby span a larger section of screening element  8707 . For example, plug  8702  may be configured to span multiple sections of screening assembly  8700  or may be configured to cover an entire screen assembly  8700 . In further embodiments, a damaged area  8704  of screening assembly  8700  may be filled (e.g., with glue or an adhesive) rather than being plugged. 
       FIGS.  91 A and  91 B  illustrate a screening assembly  9100  having a subgrid  9102  and a replaceable screening element  9104 , according to an embodiment.  FIG.  91 A  illustrates an exploded top perspective view of screening assembly  9100  and  FIG.  91 B  shows a top perspective view of screening assembly  9100  with replaceable screening element  9104  and subgrid  9102  in an installed configuration, according to an embodiment. As with other embodiments described above, subgrid  9102  may include fusion bars  9106  that may be used to attach an initial screening element. For example, laser welding may be used to attach an initial screening element, as described in greater detail herein. During the course of use, the initial screening element may become damaged and may need to be replaced or plugged (e.g., as described above with reference to  FIGS.  87 A to  90 B ). According to an embodiment, such a damaged initial screening element may be removed and replaced with a replaceable screening element such as screening element  9104  shown in  FIGS.  91 A and  91 B . The initial screening element may be removed by tearing away (i.e. breaking laser welds of) the initial screening element. The initial screening element may be configured to be easily torn away from subgrid  9102  using hand tools. 
     Replaceable screening element  9104  may include attachment arrangements  9108 . For example, attachment arrangements  9108  may be hooks that are configured to engage with corresponding hook apertures (also referred to as “eye holes”) of subgrid  9102 , as described in greater detail below with reference to  FIGS.  92 A to  95 B . Replaceable screening element  9104  may be attached to subgrid  9102  (e.g., as shown in  FIG.  91 B ) by engaging the attachment arrangements  9108  with corresponding attachment structures of subgrid  9104 . Subgrid  9102  of screening assembly  9100  is configured to remain connected to other subgrids during replacement of screening element  9104 . Thus, any damaged screening elements may easily and quickly be replaced without disassembling subgrids. 
     In an alternative embodiment, replaceable screen element  9104  may have hooks or alternative coupling structures that secure directly to complementary coupling structures of the subgrid structure. For example, screen element  9104  may include hooks  8706  similar to those described herein in the context of plug  8702 . 
       FIG.  92 A  illustrates a perspective bottom view of screening element  9104  having attachment arrangements configured as hooks  9108  and  FIG.  92 B  is a close-up bottom perspective view of screening element  9104  of  FIG.  92 A  showing details of hooks  9108 , according to an embodiment. Each hook  9108  may be configured to have a shape that may be compressed when it is forced through a corresponding hook aperture (e.g., described in greater detail below with reference to  FIGS.  93 A,  93 B,  95 A, and  95 B ). In this regard, upon being forced through an eyehole, hook  9108  may be configured to expand on an opposite side of a hook aperture to thereby mechanically engage with the hook aperture to secure screening element  9104  to subgrid  9102 , as shown in  FIG.  91 B . 
     As shown in  FIG.  92 B , for example, hook  9108  may have a dome shape and may have slots  9202  that allow the dome shape to be compressed so that hook  9108  may be forced through an eyehole in subgrid  9102 , as described in greater detail below with reference to  FIGS.  93 A,  95 A, and  95 B . In this example, screening element  9104  is provided with eight hooks  9108 , as shown in  FIG.  92 A . In further embodiments, greater or fewer hooks  9108  may be provided depending on the intended application. For example, a greater number of hooks  9108  may be provided to give a tighter connection between screening element  9104  and subgrid  9102  (e.g., see  FIG.  91 B ) relative to embodiments with fewer hooks  9108 . 
     Although hooks  9108  with dome shapes having slots are described herein, attachment arrangements need not be so limited. In further embodiments, many other types of attachment arrangements having different shapes may be provided. Placement of hooks  9108  may also be provided in many different configurations. In  FIGS.  91 A and  92 A , for example, hooks  9108  are placed around edges of screening element  9104 . In further embodiments, hooks  9108  may be placed in different configurations, including in configurations that cover various portions of the screening surface of screening element  9104 . Further, hooks  9108  may be injection molded as an integral parts of screening element  9104  or may be configured as separate elements that may be attached to screening element  9104  using adhesive, etc. 
       FIG.  93 A  illustrates a top perspective view of subgrid  9102  having hook apertures  9302 , according to an embodiment. A hook aperture  9302  may be a hole (also referred to as an “eyehole”) that may be configured to accept a hook  9108  from a screening element  9104  (e.g., see  FIGS.  92 A and  92 B ). In addition to hook apertures  9302 , subgrid may include one or more relatively larger openings  9304  in the grid structure (e.g., also see  FIG.  93 B ). In this example, opening  9304  is a space in subgrid  9102  that may allow easy removal of subgrid  9102  from a mold at the completion of the injection molding process. The presence of opening  9304  is not essential and further embodiments may be provided without opening  9304 . Openings  9304  may reduce or eliminate an undercut that may otherwise form in the injection molding process. As described in greater detail below (e.g., see  FIG.  93 B ) subgrid  9102  may further include a shelf  9308  that may provide additional mechanical support to subgrid  9102  in the presence of openings  9304 . The presence or absence of openings  9304  in subgrid  9102  is not expected to affect screening performance of screening assembly  9100  (e.g., see  FIGS.  91 A and  91 B ). In certain embodiments, subgrid  9102  may include one or more raised bars  9306  that may be configured to support screening element  9108 . Alternative embodiments may be provided without raised bars  9306 . 
     Placement of hook apertures  9302  in  FIG.  93 A  corresponds to the placement of hooks  9108  in screening element  9104  (e.g., see  FIG.  92 A ). As described above, many different configurations of hooks  9108  and corresponding hook apertures  9302  may be provided. As shown in  FIG.  93 A , hook apertures  9302  are placed around outside edges of subgrid  9102  to correspond with similarly placed hooks  9108  in screening element  9104  of  FIG.  92 A . In the embodiment of  FIG.  93 A , hook apertures  9302  are shown adjacent to opening  9304 . In further embodiments, it may be advantageous to omit the hook apertures  9302  that are adjacent to opening  9304  to avoid complications that may arise with injection molding of subgrid  9102  due to overhanging support structures for hook apertures  9302  in certain embodiments. 
       FIG.  93 B  illustrates a bottom view of subgrid  9102  of  FIG.  93 A , according to an embodiment. Hook apertures  9302  are shown along with opening  9304 . In this embodiment, subgrid  9102  further includes a shelf  9308  that is provided below opening  9304 . The presence of shelf  9308  may provide additional mechanical support that may strengthen subgrid  9102 . 
       FIG.  94    illustrates close-up exploded view of screening assembly  9100  of  FIG.  91 A  having subgrid  9102  and replaceable screening element  9104 , according to an embodiment. As shown, hooks  9108  are positioned above corresponding hook apertures  9302 . As described above, replaceable screening element  9104  may be installed by forcing hooks  9108  into hook apertures  9302 . In this regard, hooks  9108  are configured to deform under compressive force so that hooks  9108  may be forced into hook apertures, as described above with reference to  FIGS.  92 A and  92 B . 
       FIGS.  95 A and  95 B  illustrate bottom views of screening assembly  9100  of  FIG.  91 B  having subgrid  9102  and replaceable screen element  9104  in an installed configuration, according to an embodiment.  FIG.  95 A  illustrates a bottom perspective view of screening assembly  9100  and  FIG.  95 B  shows a close-up bottom view of screening assembly  9100 . As shown, the dome-shaped end of hook  9108  has been forced through hook aperture  9302  and is thereby engaged with a shelf region  9502  (e.g., see  FIG.  95 B ) associated with hook aperture  9302  (e.g., see hook apertures  9302  in  FIGS.  93 A,  93 B, and  94   ). In this regard, the dome shaped end of hook  9108  has a profile that is larger than hook aperture  9302 . During installation of hook  9108 , slots  9202  (e.g., see  FIGS.  92 B and  95 B ) allow the dome shaped end of hook  9108  to compress to allow the dome shaped end of hook  9108  to pass through hook aperture  9302  (e.g., see  FIGS.  92 B and  93 A to  94   ). Upon passing hook  9108  through hook aperture  9108  (e.g., see  FIG.  94   ), the dome shaped end of hook  9108  is configured to expand and to thereby mechanically engage with shelf  9502  (e.g., see  FIG.  95 B ) associated with hook aperture  9302 . 
     In further embodiments, screening element  9104  may be secured to subgrid  9102  (e.g., see  FIGS.  91 A and  91 B ) in different ways. Although embodiments of  FIGS.  91 A to  95 B  have been described in which hooks  9108  engage with hook apertures  9302 , the disclosure is not so limited. For example, hooks  9108  and hook apertures  9302  having many different sizes and shapes may be provided. Further, the placement of hooks  9108  and hook apertures  9302  may be varied in many different ways. In alternative embodiments, screen element  9104  and be secured to subgrid  9102  using glue, adhesive, or various fasteners. For example, screening element  9104  may be secured to subgrid  9102  using clips, clamps, plastic welding, rivets, or other mechanical fasteners. 
       FIG.  96 A  illustrates a top perspective exploded view of a three-piece screening assembly  9600 , according to an embodiment. Screening assembly  9600  includes a screening element  9602 , a top subgrid  9604 , and a bottom subgrid  9606 . Screening element  9602  is configured to be permanently attached to top subgrid  9604 . For example, screening element  9602  may be secured to top subgrid  9604  using laser welding, as described in greater detail herein with respect to other embodiments. Top subgrid  9604  may be configured to be removably attached to bottom subgrid  9605 . As such, a plurality of bottom subgrids  9606  may be assembled and connected to one another via clips  9608  and clip apertures  9610  to form a framework of bottom subgrids  9606 . Then screening surfaces, provided by screening elements  9602  attached to top subgrids  9604 , may be removably attached to the framework of bottom subgrids  9602  to form a continuous screening surface containing a plurality of screening elements  9602 . When a screening element  9602  becomes damaged during use, a new screening element  9602  that is coupled to a new top subgrid  9604  may be replaced without removing bottom subgrid  9602  from the framework of coupled bottom subgrids  9606 . 
       FIG.  96 B  illustrates a top perspective exploded view of three-piece screening assembly  9600  of  FIG.  96 A  in which screening element  9602  has been attached to top subgrid  9604 , according to an embodiment. As such, screening element  9602  and top subgrid  9604  may be configured as a replaceable screening sub-assembly  9612 . As described above, replaceable screening sub-assembly  9612  may be removably secured to bottom subgrid  9606 . As with other embodiments, screening element  9602  may be permanently secured to top subgrid  9604  to form screening sub-assembly  9612 . For example, screening element  9602  may be laser welded to top subgrid  9604 . In other embodiments, screening element  9602  may be secured to top subgrid  9604  using glue, adhesive, or various fasteners. For example, screening element  9602  may be secured to top subgrid  9604  using clips, clamps, plastic welding, rivets, or other mechanical fasteners. As described in greater detail below, screening sub-assembly  9612  may then be secured to bottom subgrid  9606  using various removable mechanical coupling mechanisms. 
       FIG.  96 C  illustrates a top perspective view of screening assembly  9600  of  FIGS.  96 A and  96 B  in an installed configuration, according to an embodiment. In this regard, screening sub-assembly  9612  has been removably secured to bottom subgrid  9606 . As described above, screening sub-assembly  9612  may include screening element  9602  permanently secured to top subgrid  9604 . In this way, screening sub-assembly  9612  may be removed from bottom subgrid  9606  and replaced without the need to remove bottom subgrid  9606  from a plurality of neighboring bottom subgrids (not shown) that may be coupled to form a framework of bottom subgrids  9606 . Screening sub-assembly  9612  may be secured to bottom subgrid  9606  using various non-permanent fastening structures, as described in greater detail below with reference to  FIGS.  97 B to  99 B . 
       FIG.  97 A  illustrates a top perspective view of top subgrid  9604  of  FIGS.  96 A to  96 C , according to an embodiment. Top subgrid  9604  may be similar to other subgrids described above. For example, top subgrid  9604  may include fusion bars  9702  to may be configured to couple with corresponding cavity pockets (not shown) of screening element  9602  (e.g., see  FIGS.  96 A to  96 C ). Laser welding may then be used to melt fusion bars  9702  to thereby generate a permanent mechanical coupling between screening element  9602  (e.g., see  FIGS.  96 A to  96 C ) and top subgrid  9604 , as described above in the context of other embodiments. Subgrid  9604  may further include one or more elongated rectangular structures  9704  protruding from a top surface subgrid  9604 . Such elongated rectangular structures  9704  may provide additional support for screening element  9602  (e.g., see  FIG.  96 A ) during loading so that screening element  9602  is braced from moving downward. In this example, screen element  9602  is configured to be not attached (e.g., by laser welding or other fastening methods) in areas having elongated rectangular structures  9704 . As such, screening element  9602  may be configured to move/vibrate relative to top subgrid  9604  during use. The presence of elongated rectangular structures  9704  is not unique to this embodiment and may be provided in various other subgrids in other embodiments. 
     Top subgrid  9604  may further include openings  9706  at ends of subgrid  9606 . Openings  9706  are similar to openings  9304  described above with reference to  FIGS.  93 A and  93 B . In this regard, openings  9706  may serve a similar purpose as openings  9304  to aid in removal of subgrid  9604  from a mold at the completion of an injection molding process. As such, openings  9706  are not unique to the currently-described embodiment and may similarly be provided as features of various other subgrids in other embodiments. In other embodiments, top subgrid  9604  may be provided without openings  9706 . As with other subgrids, top subgrid  9604  further includes a plurality of spanning support bars  9708  that provide mechanical support for screening element  9602 . Further, screening element  9602  may be configured to be not attached in the area that includes spanning support bars  9708 . As such, screening element  9602  may exhibit motion/vibration relative to top subgrid  9604  during use. 
       FIG.  97 B  illustrates a bottom perspective view of top subgrid  9604  of  FIGS.  96 A to  97 A , according to an embodiment. This view shows openings  9706  at ends of subgrid  9604 , as described above with reference to  FIG.  97 A .  FIG.  97 B  further shows spanning support bars  9708 . Top subgrid  9604  may further include a plurality of hooks  9610  that may be configured to interface with bottom subgrid  9606  (e.g., see  FIGS.  96 A to  96 C ). As mentioned above, hooks  9610  are only one type of non-permanent fastening structure, and many different types of fastening structures may be provided in other embodiments. Hooks  9610  may be provided in many different shapes. Further, the number and placement of hooks  9610  may be varied based on a given application. For example, embodiments having a greater number of hooks  9610  may provide a stronger coupling between top subgrid  9604  and bottom subgrid  9606  relative to embodiments having fewer hooks. Hooks  9610  may be configured to engage with hook apertures (not shown) or may have elongated structures configured to interface with support structures of bottom subgrid  9606 , as described in greater detail below. 
       FIG.  97 C  illustrates screening sub-assembly  9612  of  FIG.  96 B  including screening element  9602  attached to top subgrid  9604 , according to an embodiment. This view shows screening sub-assembly  9612  in isolation, emphasizing that screening sub-assembly  9612  may be configured to be removably coupled to many different types of bottom subgrids in addition to bottom subgrid  9606  shown in  FIG.  96 B . As described above, screening element  9602  may be attached to top subgrid  9604  via laser welding to generate screening sub-assembly  9612 . In other embodiments, screening element  9602  may be secured to top subgrid  9604  using glue/adhesives, plastic welding, rivets, clips, clamps, or clips/hooks with alternative geometries. 
     A plurality of screening sub-assemblies  9612  may be provided as part of an initial installation to be installed on a respectively plurality of bottom subgrids  9606  (e.g., see  FIGS.  96 A to  96 C ). Screening sub-assemblies  9612  may be removably attached to respective bottom subgrids  9606  that have previously been assembled into a framework of bottom subgrids  9606 . Alternatively, screening sub-assemblies  9612  may be removably attached to respective bottom subgrids  9606  before such bottom subgrids  9606  are assembled into a connected framework of screening assemblies (e.g., see  FIGS.  96 A to  96 C ). Further, a single screening sub-assembly  9612  may be removed and replaced when a screening surface of screening element  9602  becomes damaged during use, as described above. For example, a screening sub-assembly  9612  may be forcibly removed using a screwdriver or similar tool. Such removal, however, may cause components of screening sub-assembly  9612  (e.g., hooks  9610 ) to become broken. Thus, in further embodiments, a special tool may be provided that may be used to remove sub-assembly  9612  without breakage. For example, such a tool may be configured to push down on latching structures to release hooks  9610  to thereby release hooks  9610  without breakage. 
       FIG.  98 A  illustrates a top perspective view of bottom subgrid  9606  of  FIGS.  96 A to  96 C , according to an embodiment. In this example, bottom subgrid  9606  is provided with a plurality of hook apertures  9802 . Hook apertures  9802  may be configured to form a non-permanent, removable, mechanical connection with respective hooks  9610  of top subgrid  9604  (e.g., see  FIG.  97 B ), as described in greater detail below with reference to  FIGS.  99 A and  99 B . As shown, hook apertures  9802  may be located on an interior surface of bottom subgrid  9606 . The number and placement of hook apertures  9802  may be varied according to a given application to correspond to a number and placement of respective hooks  9610  of top subgrid  9604 . For example, embodiments having a greater number of hook apertures  9802  that correspond to a greater number of hooks  9610  of top subgrid  9604  may form a stronger connection between top subgrid  9604  and bottom subgrid  9606  relative to embodiments having fewer hook apertures  9802  and hooks  9610 . 
     As shown in  FIG.  98 A , bottom subgrid  9606  may be provided with void regions  9804 . Such void regions  9804  do not have spanning support bars in contrast to the spanning support bars  9708  of top subgrid  9604  (e.g., see  FIG.  97 B ). Indeed, such spanning support bars are not needed because bottom subgrid  9606  is not used to support screening element  9602  (e.g., see  FIGS.  96 A to  96 C and  97 C ). In further embodiments, however, spanning support bars, similar to support bars  9708  of top subgrid  9604  (e.g., see  FIG.  97 A ), may be provided to strengthen bottom subgrid  9606 , depending on the intended application, if needed. 
       FIG.  98 B  illustrates a bottom perspective view of bottom subgrid  9606  of  FIG.  98 A , according to an embodiment. This view shows hook apertures  9802  located near an upper edge of bottom subgrid  9606 . Other embodiments may include hook apertures  9802  located in different positions of bottom subgrid  9606 . As described above, the number and placement of hook apertures  9802  may be varied depending on the intended application. Void regions  9804  are also shown in the view of  FIG.  98 B . As mentioned above, void regions  9804  may be present or absent depending on the application. For example, void regions  9804  may allow bottom subgrid  9606  to be more lightweight and more easily manufactured via injection molding relative to an embodiment without void regions  9802 . However, as described above, additional support structures, similar to spanning support bars  9708  of top subgrid  9604  (e.g., see  FIG.  97 B ), may be provided to strengthen bottom subgrid  9606 , as needed. 
       FIG.  99 A  illustrates a bottom perspective exploded view of three-piece screening assembly  9600  of  FIG.  96 B  in which screening element  9602  has been attached to top subgrid  9604  to form screening sub-assembly  9612 , according to an embodiment. In this view, screening sub-assembly  9612  is positioned over bottom subgrid  9606  such that hooks  9610  of top subgrid  9604  are spatially aligned with hook apertures  9802  of bottom subgrid  9606 . In this way, screening sub-assembly  9612  may be removably installed on bottom subgrid  9606  by forcing screening sub-assembly  9612  toward bottom subgrid  9606  such that hooks  9610  of top subgrid  9604  mechanically engage with hook apertures  9802  of bottom subgrid  9606 . In this regard, hooks  9610  of top subgrid  9604  may snap into hook apertures  9802  of bottom subgrid  9606  to form a non-permanent, removable connection between screening sub-assembly  9612  and bottom subgrid  9606 . The strength of the mechanical connection may be determined by the size, shape, and placement of hooks  9610  of top subgrid  9604  and respective hook apertures  9802  of bottom subgrid  9606 , as described above. 
       FIG.  99 B  illustrates a bottom perspective view of screening assembly  9600  of  FIGS.  96 A to  96 C and  99 A  in an installed configuration, according to an embodiment. This view shows a configuration in which screening sub-assembly  9612 , including screening element  9602  attached to top subgrid  9604 , is installed on bottom subgrid  9606 . As described above, screening sub-assembly  9612  is installed on bottom subgrid  9606  via a mechanical connection  9902  between hooks  9610  and hook apertures  9802 . 
     As described above, the embodiment of  FIG.  99 B  is only one example of an embodiment in which a non-permanent, replaceable connection may be formed between screening sub-assembly  9612  and bottom subgrid  9606 . For example, in other embodiments, hooks  9610  of top subgrid  9604  may engage with various other support structures in bottom subgrid  9604 . For example, connections between hooks  9610  and bottom subgrid  9606  may be configured as described above with reference to  FIGS.  90 A and  90 B  in relation to the plug  8702  of  FIGS.  87 A to  89   . In further embodiments, permanent or semi-permanent connections between screening sub-assembly  9612  and bottom subgrid  9606  may be formed using other mechanical structures. For example, screening sub-assembly  9612  and bottom subgrid  9606  may be attached using alternative coupling structures such as glue/adhesives, rivets, nails, screws, metallic inserts, etc. 
     In further embodiments, bottom subgrid  9606  may include one or more dissimilar materials that may facilitate alternative attachment structures. Further embodiments may include hooks with dome shaped ends that pass through hook apertures, as described above with reference to  FIGS.  92 A to  95 B . In still further embodiments, hooks and hook apertures, or other mechanical fastening structures may be configured on an external surface or region of top  9604  and bottom  9606  subgrids. Further, bottom subgrid  9606  may include pins or other locating structures to assist in alignment with screening sub-assembly  9612 . In such an embodiment, top subgrid  9604  may include pins/apertures configured to engage with apertures/pins or other locating structures of bottom subgrid  9606  to assist in alignment during attachment of screening sub-assembly  9612  to bottom subgrid  9606 . 
     Top  9604  and bottom  9606  subgrids may include various materials. Further, top  9604  and bottom  9606  subgrids may be made of the same materials or include dissimilar materials. For example, bottom subgrid  9606  may be made of nylon with 50% glass filler or other thermoplastic material, while top subgrid  9604  may be made from nylon containing 0-50% glass filler. The use of dissimilar materials may help to facilitate attachment and removal of top subgrid  9604  from bottom subgrid  9606 . In one embodiment top subgrid  9604  may be include nylon with 20% glass filler to allow the hooks to be disengaged using pliers. In this example, use of pliers may apply a force that is approximately 125 lb. In another example, top subgrid  9604  may include nylon with 10% glass filler to allow the hooks to be disengaged by hand. In this regard, the force required to remove top subgrid  9604  may be approximately 50 lb. Such material have mechanical properties allow easy attachment and removal of top subgrid  9604  from bottom subgrid  9606 . 
     In further embodiments, top subgrid  9604  may be made from another type of thermoplastic material such as a high durometer polyurethane. Using this type of material allows top subgrid  9604  to be removed from bottom subgrid  9606  by hand. For example, a user may start at one end of the subgrid assembly and place their thumb against a hook  9610  (e.g., see  FIG.  99 B ). By applying a force to hook  9610  by hand, a user may push hook  9610  away from hook aperture  9802  until hook  9610  is disengaged from hook aperture  9802 . The user may then repeat the process from one end of screening sub-assembly  9612  to an opposite end of screening sub-assembly  9612  until all hooks  9610  are disengaged from hook apertures  9802 . In certain instances, it may be difficult or impossible to disengage one or more hooks  9610  from corresponding hook apertures  9802  by hand. In such situations, a user may break hooks  9610 , for example, by bending them with hand tools (e.g., with pliers or a screwdriver). 
       FIGS.  100 A to  100 C  illustrate various views of a screening element  10000  that includes screening openings having rounded corners, according to an embodiment.  FIG.  100 A  illustrates a top view of screening element  10000  and  FIG.  100 B  illustrates a side view  10004  of screening element  10000  of  FIG.  100 A , according to an embodiment. A small portion  10002  of screening element  10000  of  FIG.  100 A  is shown in an exploded view  10006  in  FIG.  100 C , according to an embodiment. As shown in  FIG.  100 C , each of the screening openings  10008  includes rounded corners. The rounded corners of screening openings  10008  act to reduce local stress concentrations that typically form near sharp corners, such as corners of screening openings in other embodiments. 
     For example, in certain other embodiments, sharp corners may create an increased stress concentration factor near intersection points of the screen surface elements and walls of the screen element. These stress concentration factors may cause premature panel failure. A common point of failure occurs when a surface element breaks away from a wall of the screen element. To extend the screen life, a fillet has been added to each of the sharp edges in the embodiments of  FIGS.  100 A to  100 C . The presence of this added fillet reduces geometric discontinuities and leads to a decrease in the intensity of the local stress field where the bars connect to the walls. Additional advantages include improved ease of injection molding by allowing a wider path for material to travel down during filling. The reduction in sharp corners also promises to reduce material shear during injection molding which may otherwise be a cause of premature material degradation. The advantages of embodiments having rounded corners may possibly be offset by disadvantages including slightly reduced open area caused by the fillets. There may also be a potential for increased blinding due to the decreased slot width due to the presence of the fillets. 
       FIGS.  101 A to  101 D  illustrate embodiments in which screening apertures may have different orientations, according to an embodiment.  FIG.  101 A  illustrates a top view of a screening element  10100  that includes transversely aligned screening openings, and  FIG.  101 B  illustrates an exploded top view of a portion of the screening element  10100  of  FIG.  101 A  showing details of transversely aligned screening openings, according to an embodiment. FIG.  101 C illustrates a top view of a screening element  10102  that includes longitudinally aligned screening openings, and  FIG.  101 D  illustrates an exploded top view of a portion of the screening element  10102  of  FIG.  101 C  showing details of longitudinally aligned screening openings, according to an embodiment. 
     The orientation of screening openings relative to flow direction may have an effect on screening characteristics. For example, slots perpendicular to the flow may create an indirect path for fluid to transfer through the screen. As such, flow through the screen may be impeded since the direction of flow is towards the smaller open slot dimension (width). By rotating the slots, the flow may be directed along the longer dimension (length) increasing the length of time the fluid makes contact with the screening openings. Such longer contact time may increase screening efficiency by allowing gravity and vibrational motion imposed by the vibratory screening machine additional time to act on the fluid as it passes over the screening surface. 
     Having slots aligned with the flow direction may provide certain advantages. One advantage may be an increase in capacity caused by an increased affinity for fluid to pass through the screen when the slots are directed along the direction of flow. In a similar way efficiency may also be increased by improved sizing capabilities (caused by more undersize material traveling through the screen along with the fluid leading to a dryer oversize screened component). Disadvantages may include increased blinding. In this regard, having the flow direction aligned with the slots may give solid near-size particles more time to jam themselves in-between surface elements. In any case, having the freedom to orient the slots in various ways (e.g., see  FIGS.  101 A to  101 D ) allows flexibility in design of screen elements to improve screening characteristics based on fluid properties and flow characteristics. 
     The disclosed embodiments, including screening members and screening assemblies, may be configured for use with various different vibratory screening machines and parts thereof, including machines designed for wet and dry applications, machines having multi-tiered decks and/or multiple screening baskets, and machines having various screen attachment arrangements such as tensioning mechanisms (under and overmount), compression mechanisms, clamping mechanisms, magnetic mechanisms, etc. For example, the screen assemblies described in the present disclosure may be configured to be mounted on the vibratory screening machines described in U.S. Pat. Nos. 7,578,394; 5,332,101; 6,669,027; 6,431,366; and 6,820,748. 
     Indeed, the screen assemblies described herein may include: side portions or binder bars including U-shaped members configured to receive overmount type tensioning members, e.g., as described in U.S. Pat. No. 5,332,101; side portions or binder bars including finger receiving apertures configured to receive undermount type tensioning, e.g., as described in U.S. Pat. No. 6,669,027; side members or binder bars for compression loading, e.g., as described in U.S. Pat. No. 7,578,394; or may be configured for attachment and loading on multi-tiered machines, e.g., such as the machines described in U.S. Pat. No. 6,431,366. The screen assemblies and/or screen elements may also be configured to include features described in U.S. Pat. No. 8,443,984, including the guide assembly technologies described therein and preformed panel technologies described therein. 
     Still further, the screen assemblies and screen elements may be configured to be incorporated into the prescreening technologies (e.g., compatible with the mounting structures and screen configurations) described in U.S. Pat. Nos. 8,439,203; 7,578,394; 5,332,101; 4,882,054; 4,857,176; 6,669,027; 7,228,971; 6,431,366; and 6,820,748; 8,443,984; and 8,439,203; which, along with their related patent families and applications, and the patents and patent applications referenced in these documents, are expressly incorporated herein by reference hereto. In the foregoing, example embodiments are described. It will, however, be evident that various modifications and changes may be made thereunto without departing from the broader spirit and scope hereof. The specification and drawings are accordingly to be regarded in an illustrative rather than in a restrictive sense.