Patent Publication Number: US-2023153484-A1

Title: Internal Generation of Contact Entities to Model Contact Behavior in Simulations Involving Non-Circular Beam Elements

Description:
BACKGROUND 
     Computer-aided design (CAD) software offers many benefits in enabling a user to model structural and behavioral aspects of complex real-world objects through the use of three-dimensional (3D) CAD models, e.g., finite element models and solid models, amongst others. CAD software users often seek to model not only individual static real-world objects, but also interactions between multiple real-world objects and components thereof, in order to gather information pertaining to real-world use cases of various real-world objects. Such interactions between objects often include physical contact between the objects in various states of motion. 
     Beam elements are a common type of component used in many industries. Therefore, beam elements are oftentimes the subject of CAD models created by CAD software users working in those industries. Contact events involving modeled beam elements are often simulated in CAD environments to evaluate the effects of components resembling beams touching, bumping, striking, or otherwise physically interacting with components, e.g. other beams or non-beam components. 
     SUMMARY 
     In existing methods, for computational simplicity, circular cross sections are often assumed in beam element modeling and behavior, e.g., contact, simulation. However, cross-sectional geometry of a beam element has a significant effect on the physical behavior of the beam element, particularly on the behavior of the beam element in a contact event. Therefore, functionality is needed to improve upon these existing methods and more accurately model and simulate physical behavior of beam elements. Embodiments provide such functionality. 
     One such embodiment provides these improvements by automatically generating contact entities (of a CAD model) based upon an indication of a beam element’s cross-sectional geometry. An embodiment automatically creates contact entities within a CAD model to provide reference points from which to define extremities of a surface of a given modeled component, such that physical effects of a contact event between the given modeled component and another modeled component may be determined through simulation. That is, the automatically generated contact entities define or otherwise logically serve as potential points of contact on the model for purposes of simulation of modeled object behavior. The defined potential points of contact increase accuracy of simulations addressing the need in the art. 
     Another embodiment is directed to a computer implemented method of determining contact behavior of a real-world object that begins by creating, in memory, a beam element model representing a component of a real-world object. In such an embodiment, the beam element model includes beam nodes. To continue, the method automatically generates contact entities of the beam element model based on a cross sectional geometry of the component of the real-world object and the created beam element model. Next, such an embodiment establishes, based on the generated contact entities, a mesh representing a surface geometry of the component of the real-world object. In turn, contact behavior of the real-world object is determined by performing a computer-based simulation using the beam element model and the established mesh, where motion of the mesh is constrained to correspond to motion of the beam nodes. 
     In another embodiment of the method, the generated contact entities include contact nodes of the beam element model. In such an embodiment, the method includes connecting the contact nodes to establish the mesh. An embodiment connects the contact nodes in a tessellated pattern. In another embodiment, the method includes setting locations of the contact nodes based on the cross-sectional geometry. According to an embodiment, establishing the mesh includes connecting contact entities generated based on a first cross-sectional geometry with corresponding contact entities generated based on a second cross-sectional geometry. 
     In some embodiments, the method includes receiving a user indication of the cross-sectional geometry in the form of a keyword. In some such embodiments, the method includes providing a drop-down menu, pop-up menu, other user-selectable listing, or the like. The drop-down menu may display a plurality of keywords, or representations thereof. The user indication of the cross-sectional geometry may be received via a user selection from the drop-down menu of the keyword from among the plurality of keywords. 
     In some embodiments of the method, the beam will include a pair of beam nodes. In such embodiments, creating the beam element model includes (i) defining an edge between the pair of beam nodes and (ii) defining a material comprised by the beam. In some embodiments of the method, the component of the real-world object is a first component, and determining the contact behavior of the real-world object includes receiving a finite element model of a second component. In such embodiments, the method includes performing the simulation using the beam element model, the established mesh, and the received finite element model of the second component to determine the contact behavior of the first component in response to contacting the second component. 
     Another embodiment is directed to a system that includes a processor and a memory with computer code instructions stored thereon. In such an embodiment, the processor and the memory, with the computer code instructions, are configured to cause the system to implement any embodiments or combination of embodiments described herein. 
     In another embodiment, a computer program product includes a non-transitory computer-readable medium having computer-readable program instructions stored thereon. In such an embodiment, the instructions, when executed by a processor, cause the processor to implement any embodiments or combination of embodiments described herein. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The foregoing will be apparent from the following more particular description of example embodiments, as illustrated in the accompanying drawings in which like reference characters refer to the same parts throughout the different views. The drawings are not necessarily to scale, emphasis instead being placed upon illustrating embodiments. 
         FIG.  1    illustrates a beam element model representing a component of a real-world object bending. 
         FIGS.  2 A-B  illustrate beam element models representing an example component of a real-world object. 
         FIGS.  3 A-C  illustrate beam element models representing an example component of a real-world object at various stages of modeling according to an embodiment. 
         FIGS.  4 A-C  illustrate beam element models representing an example component of a real-world object at various stages of responding to contacting a modeled point mass according to an embodiment. 
         FIG.  5    is a flow diagram of various example methods of automatically determining contact behavior of a real-world object according to embodiments. 
         FIGS.  6 A-C  illustrate example beam element model cross-sectional geometries with various optional corner radii according to an embodiment. 
         FIGS.  7  and  8 A  illustrate beam element models with example cross-sectional geometries according to embodiments. 
         FIG.  8 B  illustrates a beam element model with the example cross-sectional geometry of  FIG.  8 A , representing a component of a real-world object twisting according to an embodiment. 
         FIG.  9    illustrates example CAD models to be used in embodiments to automatically determine contact behavior. 
         FIGS.  10 A-B  illustrate beam element models, representing components of a pair of example real-world objects, that can be used in an embodiment to automatically determine mutual contact behavior of the objects. 
         FIG.  11    depicts a computer network or similar digital processing environment in which embodiments of the present invention may be implemented. 
         FIG.  12    is a block diagram of an example internal structure of a computer in the environment of  FIG.  11   . 
     
    
    
     DETAILED DESCRIPTION 
     A description of example embodiments follows. 
     As described above, embodiments provide improved methods for determining physical behavior of real-word objects, in particular, beams. In computer-based simulation and modeling, e.g., finite element simulation, beam elements are modeled to demonstrate, or determine by simulation, bending or other physical responses of structures, e.g., slender structures.  FIG.  1    shows a representation, i.e., model,  100  of a slender part modeled with five beam elements  105   a ,  105   b ,  105   c ,  105   d ,  105   e , involving six beam nodes  110   a ,  110   b ,  110   c ,  110   d ,  110   e , and  110   f . Beam nodes  110   a - f  can be seen in  FIG.  1    with line segments  108   a ,  108   b ,  108   c ,  108   d , and  108   e  between adjacent beam nodes thereof. Such line segments represent beam edges  108   a - e . Beam edges are described further hereinbelow, at least with respect to  FIGS.  3 B and  4 A . Each beam element  105   a - e  is composed of a beam edge and two beam nodes. In the example model  100 , the beam element  105   a  is composed of the nodes  110   a  and  110   b  connected by the edge  108   a . The beam element  105   b  is composed of the nodes  110   b  and  110   c  connected by the edge  108   b . The beam element  105   c  is composed of the nodes  110   c  and  110   d  connected by the edge  108   c . The beam element  105   d  is composed of the nodes  110   d  and  110   e  connected by the edge  108   d , and the beam element  105   e  is composed of the nodes  110   e  and  110   f  connected by the edge  108   e . 
     The model  100  also depicts the cross-sectional geometries  120   a ,  120   b ,  120   c ,  120   d ,  120   e , and  120   f  that are perpendicular to beam edges  108   a - e , respectively. Slight variations in the depiction of cross-sectional geometries  120   a - f  can be seen in  FIG.  1    as corresponding to changes in orientation of the beam element models  105   a - e , as centered around the beam edges  108   a - e . The cross-sectional geometries  120   a - f  are rectangular in this example, although embodiments are not limited to rectangular cross-sectional geometries and any desired cross-section shapes may be utilized. For instance, embodiments can employ cross sections for beams such as I-beams, L-beams, and U-beams, amongst other examples. 
     The representation  100  of  FIG.  1    incorporates, as an example, three translational degrees of freedom and three rotational degrees of freedom at each node  110   a - e , but other amounts of translational and rotational freedom may be incorporated. Beam element models  105   a - e  of the type of  FIG.  1    may be used to determine contact behavior between individual beam element components of a real-world object. Such beam element models  105   a - e  may also be used to demonstrate bending properties or other responses of at least a single beam element or similar slender structure. The behaviors and properties determined using beam element components, e.g., components  105   a - e , can be used to design, manufacture, and improve the real-world objects that the beam element components represent. Design modifications, for instance, to strengthen a beam by changing the thickness thereof, can be determined through use of the simulation methods and systems described herein. 
     A continuous curve characteristic of a beam subject to bending may be approximated to increasing degrees of accuracy by increasing the number of beam elements in the model, and accordingly decreasing the respective sizes of the beam elements. For example, in simulating a car crash event, a slender part like a strut can be represented with the strategy described herein such that stiffness and inertia aspects of the part (strut) are accurately and efficiently represented by beam elements. In such an example, surfaces based on membrane or surface elements may provide accurate geometric representations for contact computations. 
     Historically, regardless of the actual cross-sectional area of the beam, existing simulation methods model the beam with a circular cross section. This is shown in  FIG.  2 A , where a representation  200   a  of a beam element model  205   a  with a circular cross-sectional geometry  220   a  is depicted. However, treating all beams as circular is problematic. For instance, representing an I-beam using a circular cross section beam can lead to inaccurate simulation results. 
     As such, realistic representations for beams with rectangular and other cross sections are needed.  FIG.  2 B  depicts one such example representation  200   b  of a beam element model  205   b  with a rectangular cross-sectional geometry  220   b  that can be accurately and realistically simulated using the embodiments described herein. By using the embodiments described herein, behavior, e.g., physical behavior of the beam element model  205   b  in a contact event, can be accurately determined. 
       FIG.  3 A  shows a representation  300   a  of a beam element model  305   a . The beam element model  305   a  is shown to have a circular cross-sectional geometry  320   a . The circular cross-sectional geometry  320   a  provides for efficient computation with regards to movement or other aspects of the beam element model  305   a . However, the circular cross-sectional geometry  320   a  does not provide for accurate simulation of the effects of a contact event when the real-world object represented by the model  305   a  does not have a circular cross-sectional geometry in the real-world. For example, the beam element model  305   a , or an object contacting the beam element represented by the beam element model  305   a , may exhibit differences in deflection of motion as a result of a contact event therebetween. 
     For a beam element having a circular cross-sectional geometry, such that the beam element is represented as a cylinder as illustrated in  FIG.  3 A , the contact force to resist penetration is aligned with the radial direction from a beam edge to the point mass. Such a beam edge is defined along a longitudinal axis of the beam element, and runs internally to the cylindrical representation of the beam element. Further description of beam edges is provided hereinbelow. Simulating contact requires efficiently and accurately determining when and where impacts and/or penetrations occur, as well as determining magnitudes and directions of contact forces that resist penetrations and model frictional behavior. 
     However, the radial direction is not relevant for non-circular cross sections, as are commonly simulated within the CAD software environment by industry users, since the contact force to resist penetration should typically be normal to the beam exterior.  FIG.  3 B  shows a representation  300   b  of a beam element model  305   b  with a rectangular cross-sectional geometry  320   b . Such a beam element model  305   b , by its rectangular cross-sectional geometry  320   b , may more accurately model a given beam element, and thus more accurately simulate contact events involving the given beam element. 
     One improvement to the historic method of modeling all beams as having a circular cross-sectional area requires a user to perform a tedious manual procedure. This manual procedure requires the following strategy to attempt to more realistically treat the beam cross section shape in contact calculations. First, beam elements are used to represent physical stiffness behavior of a part or component. Next, a mesh of membrane elements with negligible stiffness (or “surface elements” with no stiffness) are built in memory around the beam elements to represent a surface geometry of the part. The user manually specifies a nodal position of every membrane or surface element. Specifying a greater number of membrane or surface elements may enable the surface geometry of the part to be represented with more accuracy. Typical applications may require the user to manually specify, for example, over one hundred, over one thousand, or more membrane or surface elements for a single beam element. Finally, nodal positions of the membrane or surface elements are constrained to move according to motion of beam nodes. The user establishes such constraints for every membrane or surface element of the beam, forcing coordinates of the membranes or surface elements to be dependent upon coordinates of the beam nodes. 
     Fundamental entities involved in contact calculations within a finite element simulation include nodes (representing points), edges (one-dimensional segments connecting nodes), and faces (two-dimensional polygons, usually representing exposed sides of finite elements with nodes at vertices of the faces). Beam nodes, such as beam nodes  110   a - f  of  FIG.  1   , are located along a beam reference line, or the longitudinal axis of a beam. Beam edges, such as beam edges  108   a - e  of  FIG.  1   , connect beam nodes. A beam edge can be used to determine a radial direction from the beam edge to another point. A beam edge can be used to determine an axial position where another point projects to the beam edge along the radial direction. Beam edges may not always be disposed along the surface of a modeled beam, but rather, may be disposed internally to the modeled beam. Faces connecting beam nodes do not naturally exist, as beam edges usually run internally to their respective beams. 
     In addition to beam nodes and beam edges, other types of entities that may be involved in contact calculations within a finite element simulation include contact entities such as contact nodes, contact edges, and contact faces. Data pertaining to contact nodes, for example, may be used in such contact calculations, while data pertaining to contact edges and faces may be generated by such contact calculations. 
       FIG.  3 C  shows a mesh representation  300   c  of a beam element model  305   c  using a rectangular cross-sectional geometry  320   c , wherein contact nodes  314 , contact edges  318 , and contact faces  321  embody contact entities  315  that are connected to form the mesh  300   c . The mesh  300   c  represents surface geometry of the beam element model  305   c  and may be constrained to correspond to motion of the beam element model  305   c  or aspects thereof. The mesh  300   c  illustrated in  FIG.  3 C  has a tessellated pattern formed by the contact nodes  314 , and the contact edges  318  and contact faces  321 . Is it noted that embodiments are not limited to tessellated mesh representations and any mesh representation may be utilized. 
       FIG.  4 A  shows a front view  400   a  of a beam element model  405   a  wherein a beam node  410   a  is centrally located within a cross-section  420   a  of the beam element model  405   a , and wherein a modeled point mass  412   a  is, according to a simulation, travelling from right to left and presently impacting the beam element model  405   a . Beam nodes may herein be referred to interchangeably as beam element nodes. The beam element model  405   a  is shown in  FIG.  4 A  as having an oblong rectangular cross-sectional geometry  420   a . The beam element model  405   a  is shown in  FIG.  4 A  as being viewed directly from an end of the beam exhibiting the oblong rectangular cross-sectional geometry  420   a , such that the longitudinal axis of the beam element model  405   a  is perpendicular to the plane of the page, screen, or other means of display upon which  FIG.  4 A  is viewed. Beam node  410   a  may be a proximal beam node connected to at least one distal beam node located apart from the proximal beam node such that a beam edge connecting said proximal and distal beam node is oriented in a parallel direction to a lengthwise direction of the beam  405   a . The proximal and distal beam node, along with the beam edge situated therebetween, together influence determination of contact entities related to a surface geometry of the beam. Surfaces representing contact faces  421   a - 1 ,  421   a - 2 , with constituent edges disposed along the length of the beam, are not visible in  FIG.  4 A  beyond a single respective edge thereof, due to the aforementioned perpendicular orientation of the beam element model  405   a  of  FIG.  4 A . 
       FIG.  4 B  shows an isometric view  400   b  of a beam element model  405   b  having beam node  410   b . Beam element model  405   b  of  FIG.  4 B  illustrates an altered orientation of the beam element model  405   a  of  FIG.  4 A  at a time shortly after undergoing a contact event. In the contact event, the beam element model  405   b  reacts as if the beam element has been impacted by a moving point mass modeled by point mass  412   b . As can be seen in  FIG.  4 B , contact with the point mass  412   b  has caused the beam element model  405   b  to begin to rotate, thus beginning to reveal a pair of surfaces representing contact faces  421   b - 1 ,  421   b - 2  with constituent edges disposed along the length of the beam  405   a . Oblong rectangular cross-sectional geometry  420   b  is easily visible in  FIG.  4 B  despite the rotated orientation. More difficult to discern from  FIG.  4 B , but helpful to understand, is that at the depicted time shortly after the contact event, the modeled point mass  412   b  has bounced off the beam element model  405   b  and is travelling in a direction different from its initial direction of travel before impact (the contact event). 
       FIG.  4 C  shows a representation  400   c  of a beam element model  405   c  having beam node  410   c . Beam element model  405   c  of  FIG.  4 C  illustrates a further altered orientation of the beam element model  405   b  of  FIG.  4 B  after additional time has passed since the aforementioned contact event than had passed in the representation  400   b  of  FIG.  4 B . In  FIG.  4 C , the beam element model  405   c  can be seen to have assumed a further rotated orientation versus the orientation depicted by the view of representation  400   b  in  FIG.  4 B  and described hereinabove. Modeled point mass  412   c , surfaces representing contact faces  421   c - 1 ,  421   c - 2 , and cross-sectional geometry  420   c  are visible in  FIG.  4 C  as are their respective counterparts  412   b ,  421   b - 1 ,  421   b - 2 ,  420   b  in  FIG.  4 B . 
       FIG.  5    illustrates a computer implemented method  500  of determining contact behavior of a real-world object according to an example embodiment. The method  500  begins by creating  505  a beam element model in computer memory. In the embodiment, the beam element model created  505  represents a component of a real-world object and includes one or more beam nodes  510 . The one or more beam nodes  510  are located along a beam reference line, or longitudinal axis of a beam model  505 , as illustrated by beam nodes  110   a - f  of  FIG.  1   . The one or more beam nodes may be centrally located within a cross-section of the beam element model  505 , as illustrated by beam nodes  410   a - c  of  FIGS.  4 A-C . Typically, the beam element model created  505  includes multiple beam nodes  510 . Multiple beam nodes  510  may include a proximal beam node and a distal beam node, disposed at opposing longitudinal ends of a beam element model  505 . The beam element model created  505  includes a beam edge, such as any of beam edges  108   a - e  of  FIG.  1   , represented by a line segment that (i) connects a pair of adjacent beam nodes and (ii) defines the length and orientation of a corresponding segment of the beam element model  505 . 
     The method  500  continues and contact entities (of or for the beam element model) are automatically generated  515  based on both a cross sectional geometry  520  of the real-world component and the beam element model created  505 . In the embodiment, a mesh is established  525  based on the generated contact entities  515 . The established mesh  525  represents surface geometry  530  of the component of the real-world object. To continue, contact behavior of the real-world object is determined  535  by performing a computer-based simulation using the created beam element model  505  and the established mesh  525 . In the simulation, motion of the mesh is constrained to correspond to motion of the beam nodes  510 . Accordingly, the automatically generated contact entities define or otherwise logically serve as potential points of contact on the model for purposes of simulation of modeled object behavior. Such defined points of contact increase accuracy of simulations heretofore unachieved. 
     In embodiments, e.g., the method  500 , the automatically generated contact nodes, contact edges, and contact faces (surface portions or sub-surface portions of the established mesh) can mostly participate as equals with other contact nodes, contact edges, and contact faces in a contact simulation performed at step  535  to detect, for example, penetrations, and compute contact forces acting on contact nodes. 
     In performing the simulation at step  535  contact forces acting on automatically-generated contact nodes of the present disclosure may be redirected to nodal forces and moments of the same beam nodes that control their motion, such that subsequent motion and rotation of beam nodes is properly influenced by contact forces. This may be accomplished with force redistribution equations common or known in the art. 
     In an alternative embodiment based on the aforementioned example embodiment  500 , automatically generated contact entities  515  include contact nodes such as the contact nodes  314  of the mesh representation  300   c  shown in  FIG.  3 C . In such an embodiment, establishing a mesh  525  includes connecting the contact nodes  314 . The contact nodes  314  may be connected in a tessellated pattern as shown and described hereinabove with reference to  FIG.  3 C . 
     In yet another alternative embodiment based upon the aforementioned example embodiment  500 , a method establishes a mesh  525  based on contact entities  515  that are automatically generated based on multiple cross-sectional geometries  520 . In such an embodiment, the multiple cross-sectional geometries  520  include at least a first cross-sectional geometry and a second cross-sectional geometry. To continue, the method includes connecting the contact entities generated based on the first cross-sectional geometry with the contact entities generated based on the second cross-sectional geometry. 
     Another embodiment of the method  500  includes obtaining an indication of a cross-sectional geometry  520  of a component of a real-world object from a user. In the non-limiting example embodiment, a drop-down menu is provided. The provided drop-down menu may display a plurality of keywords, or representations thereof. In such an implementation, a user indication of the cross-sectional geometry  520  is received in the form of a keyword selected by the user from among the plurality of keywords displayed by the provided drop-down menu. Pop-up menus, other user interactive listings of keywords or representations thereof, other graphical user interface widgets, and the like are suitable. 
     In yet another example embodiment based upon the aforementioned example embodiment  500 , beam nodes  510  include a pair of beam nodes defined respectively at proximal and distal ends of a beam element model  505 , such as, for example, beam nodes  110   a  and  110   b  of  FIG.  1   . In this non-limiting example embodiment, a beam edge, like beam edge  108   a  of  FIG.  1   , is defined within the beam element model  505 , between the subject pair of beam nodes. To continue, a material, comprised by the component represented by the beam element model  505 , is defined. A beam element model is thus created  505 , according to the present example embodiment, based on information including length, orientation, and material of a beam element. 
     In yet another alternative embodiment based on the aforementioned example embodiment  500 , a beam element model  505 , representing a first component of the real-world object, is created. In the example embodiment, a finite element model of a second component of the real-world object is received. To continue, contact behavior of a real-world object is determined  535  by performing a computer-based simulation using the created beam element model  505  of the first component, the corresponding established mesh  525 , and the received finite element model of the second component. This simulation determines contact behavior of the first component in response to contacting the second component. In the simulation, motion of the mesh  525  is constrained to correspond to the motion of the beam nodes  510 . 
       FIGS.  6 A-C  respectively show representations  600   a ,  600   b ,  600   c  of example beam element models  605   a ,  605   b ,  605   c  having various example cross-sectional geometries  620   a ,  620   b ,  620   c . The beam element models  605   a ,  605   b ,  605   c  may be created at step  505  of the method  500  and used to determine contact behavior at step  535  of the method  500 . The example cross-sectional geometries  620   a ,  620   b ,  620   c  show different amounts of rounding of corners. Further context will be provided by  FIG.  7   , to be described hereinbelow, using a cross-sectional geometry resembling that of  620   b  of  FIG.  6 B . 
       FIG.  6 A  shows contact nodes  614   a - 1 ,  614   a - 2 ,  614   a - 3 , and  614   a - 4 . The contact nodes  614   a - 1  through  614   a - 4  are connected by contact edges  617   a - 1 ,  617   a - 2 ,  617   a - 3 , and  617   a - 4  where the contact edge  617   a - 1  connects the contact nodes  614   a - 1  and  614   a - 2 , the contact edge  617   a - 2  connects the contact nodes  614   a - 2  and  614   a - 3 , the contact edge  617   a - 3  connects the contact nodes  614   a - 3  and  614   a - 4 , and the contact edge  617   a - 4  connects the contact nodes  614   a - 4  and  614   a - 1 . More context regarding contact edges  617   a - 1  through  617   a - 4  is provided hereinbelow, in reference to proximal contact edges  717 - 1  through  717 - 4  and distal contact edges  716 - 1  through  716 - 4  illustrated by  FIG.  7   . The contact nodes  614   a - 1  through  614   a - 4 , interconnected by the contact edges  617   a - 1  through  617   a - 4 , define a rectangular area that corresponds directly to the rectangular cross-sectional geometry  620   a , centered around beam node  610   a . 
       FIG.  6 B  shows contact nodes  614   b - 1 ,  614   b - 2 ,  614   b - 3 ,  614   b - 4 . The contact nodes  614   b - 1  through  614   b - 4  are connected by contact edges  617   b - 1 ,  617   b - 2 ,  617   b - 3 , and  617   b - 4  where the contact edge  617   b - 1  connects the contact nodes  614   b - 1  and  614   b - 2 , the contact edge  617   b - 2  connects the contact nodes  614   b - 2  and  614   b - 3 , the contact edge  617   b - 3  connects the contact nodes  614   b - 3  and  614   b - 4 , and the contact edge  617   b - 4  connects the contact nodes  614   b - 4  and  614   b - 1 . More context regarding contact edges  617   b - 1  through  617   b - 4  is provided hereinbelow, in reference to proximal contact edges  717 - 1  through  717 - 4  and distal contact edges  716 - 1  through  716 - 4  illustrated by  FIG.  7   . The contact nodes  614   b - 1  through  614   b - 4 , interconnected by the contact edges  617   b - 1  through  617   b - 4 , define a rectangular area, shown to exist within the dotted lines in  FIG.  6 B . Also included is a corner radius parameter applied circularly around contact nodes  614   b - 1  through  614   b - 4 . The rectangular area shown within the dotted lines, when combined with the corner radius parameter applied as described, results in the rectangular cross-sectional geometry with rounded corners  620   b , centered around beam node  610   b . The corner radius parameter may be used as described to impart a dimension of surface thickness to the beam element model  605   b . 
       FIG.  6 C  shows contact nodes  614   c - 1 ,  614   c - 2 ,  614   c - 3 ,  614   c - 4 . The contact nodes  614   c - 1  through  614   c - 4  are connected by contact edges  617   c - 1 ,  617   c - 2 ,  617   c - 3 , and  617   c - 4  where the contact edge  617   c - 1  connects the contact nodes  614   c - 1  and  614   c - 2 , the contact edge  617   c - 2  connects the contact nodes  614   c - 2  and  614   c - 3 , the contact edge  617   c - 3  connects the contact nodes  614   c - 3  and  614   c - 4 , and the contact edge  617   c - 4  connects the contact nodes  614   c - 4  and  614   c - 1 . More context regarding contact edges  617   c - 1  through  617   c - 4  is provided hereinbelow, in reference to proximal contact edges  717 - 1  through  717 - 4  and distal contact edges  716 - 1  through  716 - 4  illustrated by  FIG.  7   . The contact nodes  614   c - 1  through  614   c - 4 , interconnected by the contact edges  617   c - 1  through  617   c - 4 , define a rectangular area, shown to exist within the dotted lines in  FIG.  6 C . Also included is a corner radius parameter applied circularly around contact nodes  614   c - 1 ,  614   c - 2 ,  614   c - 3 ,  614   c - 4 , which is larger than the corner radius parameter of  FIG.  6 B . The rectangular area shown within the dotted lines, when combined with the corner radius parameter applied as described, results in the rectangular cross-sectional geometry with rounded corners  620   c , centered around beam node  610   c , wherein the rounded corners are larger than those of  FIG.  6 B . The corner radius parameter may be used as described to impart a dimension of surface thickness to the beam element model  605   c . The larger corner radius parameter of  FIG.  6 C , in comparison to that of  FIG.  6 B , thus imparts a larger surface thickness dimension to  FIG.  6 C  than the surface thickness dimension of  FIG.  6 B . 
       FIG.  7    shows a representation  700  of an example beam element model  705  exhibiting the moderately rounded corners of  FIG.  6 B . In  FIG.  7   , the rounded corners incorporate an element of surface thickness to the beam element model  705 . The beam element model  705  is constructed based on proximal beam node  711  and distal beam node  709  located apart from proximal beam node  711 . At corresponding longitudinal ends, proximal contact nodes  714 - 1 ,  714 - 2 ,  714 - 3 ,  714 - 4  and distal contact nodes  713 - 1 ,  713 - 2 ,  713 - 3 ,  713 - 4  are shown. 
     Contact edges, specifically longitudinal contact edges  718 - 1 ,  718 - 2 ,  718 - 3 ,  718 - 4 , can be seen in  FIG.  7    respectively connecting corresponding proximal  714 - 1 ,  714 - 2 ,  714 - 3 ,  714 - 4  and distal  713 - 1 ,  713 - 2 ,  713 - 3 ,  713 - 4  contact nodes. Further, the representation  700  includes additional contact edges, particularly, proximal contact edges  717 - 1 ,  717 - 2 ,  717 - 3 , and  717 - 4  connecting the proximal contact nodes  714 - 1 ,  714 - 2 ,  714 - 3 , and  714 - 4 . In particular, contact edge  717 - 1  connects contact nodes  714 - 1  and  714 - 2 , contact edge  717 - 2  connects contact nodes  714 - 2  and  714 - 3 , contact edge  717 - 3  connects contact nodes  714 - 3  and  714 - 4 , and contact edge  717 - 4  connects contact nodes  714 - 4  and  714 - 1 . Likewise, the representation  700  includes additional contact edges, particularly distal contact edges  716 - 1 ,  716 - 2 ,  716 - 3 , and  716 - 4 , connecting distal contact nodes  713 - 1 ,  713 - 2 ,  713 - 3 , and  713 - 4 . Contact edge  716 - 1  connects contact nodes  713 - 1  and  713 - 2 , contact edge  716 - 2  connects contact nodes  713 - 2  and  713 - 3 , contact edge  716 - 3  connects contact nodes  713 - 3  and  713 - 4 , and contact edge  716 - 4  connects contact nodes  713 - 4  and  713 - 1 . 
     Contact faces, specifically longitudinal contact faces  722 - 1 ,  722 - 2 ,  722 - 3 ,  722 - 4  are shown in  FIG.  7    to be formed between sets of contact nodes and edges as follows: {face  722 - 1  formed by nodes  714 - 1 ,  714 - 2 ,  713 - 2 ,  713 - 1  connected by edges  717 - 1 ,  718 - 2 ,  716 - 1 , 718-1}, {face  722 - 2  formed by nodes  714 - 2 ,  714 - 3 ,  713 - 3 ,  713 - 2  connected by edges  717 - 2 ,  718 - 3 ,  716 - 2 ,  718 - 2 }, {face  722 - 3  formed by nodes  714 - 3 ,  714 - 4 ,  713 - 4 ,  713 - 3  connected by edges  717 - 3 ,  718 - 4 ,  716 - 3 ,  718 - 3 }, and {face  722 - 4  formed by nodes  714 - 4 ,  714 - 1 ,  713 - 1 ,  713 - 4  connected by edges  717 - 4 ,  718 - 1 ,  716 - 4 ,  718 - 4 }. 
     Also shown in the representation  700  of  FIG.  7   , coplanar to the respective beam nodes  711  and  709 , are additional contact faces, specifically a proximal contact face  724  and a distal contact face  723 , drawn respectively according to user-specified rectangular proximal cross-sectional geometry  720  and distal cross-sectional geometry  719 . Proximal contact face  724  is formed by nodes  714 - 1 ,  714 - 2 ,  714 - 3 ,  714 - 4  connected by edges  717 - 1 ,  717 - 2 ,  717 - 3 ,  717 - 4 . Distal contact face  723  is formed by nodes  713 - 1 ,  713 - 2 ,  713 - 3 ,  713 - 4  connected by edges  716 - 1 ,  716 - 2 ,  716 - 3 ,  716 - 4 . 
     Contact entities, which may be generated according to step  515  of the method  500 , are shown in the representation  700  to include proximal contact nodes  714 - 1 ,  714 - 2 ,  714 - 3 ,  714 - 4 , and distal contact nodes  713 - 1 ,  713 - 2 ,  713 - 3 ,  713 - 4 ; longitudinal contact edges  718 - 1 ,  718 - 2 ,  718 - 3 ,  718 - 4 , proximal contact edges  717 - 1 ,  717 - 2 ,  717 - 3 ,  717 - 4 , and distal contact edges  716 - 1 ,  716 - 2 ,  716 - 3 ,  716 - 4 ; and longitudinal contact faces  722 - 1 ,  722 - 2 ,  722 - 3 ,  722 - 4 , proximal contact face  724 , and distal contact face  723 , all as detailed hereinabove. 
     Additionally, rounded corners have been incorporated into the cross-sectional geometries  720 ,  719  through inclusion of a corner radius parameter as introduced hereinabove with reference to  FIG.  6 B . The corner radius parameter dictates surface thickness of the beam element model  705 . As such, contact edges  718 - 1 ,  718 - 2 ,  718 - 3 ,  718 - 4  may not represent locations along the surface of the beam element model  705 , but rather a central axis of a cylinder defined by the corner radius applied to the cross-sectional geometries  719 ,  720  and centered about the contact nodes  714 - 1 ,  714 - 2 ,  714 - 3 ,  714 - 4 ,  713 - 1 ,  713 - 2 ,  713 - 3 ,  713 - 4 . A portion of the surface of the cylinder may thus actually represent at least a portion of the surface of the beam element model  705 . According to the present disclosure, a mesh, such as mesh  300   c  of  FIG.  3 C , may be generated surrounding a beam element model, e.g., model  705 , based on the automatically generated contact entities  515 , e.g., contact entities  714 - 1 ,  714 - 2 ,  714 - 3 ,  714 - 4 ,  713 - 1 ,  713 - 2 ,  713 - 3 ,  713 - 4 ,  718 - 1 ,  718 - 2 ,  718 - 3 ,  718 - 4 ,  717 - 1 ,  717 - 2 ,  717 - 3 ,  717 - 4 ,  716 - 1 ,  716 - 2 ,  716 - 3 ,  716 - 4 ,  722 - 1 ,  722 - 2 ,  722 - 3 ,  722 - 4 ,  724 ,  723 . Motion of the mesh may then be constrained to follow motion of the beam element model  705 , e.g., according to step  535  of the method  500  of  FIG.  5   , based on the automatically generated contact entities  515 . 
       FIG.  8 A  shows a representation  800   a  of an example beam element model  805   a  for a type of beam commonly known as an L-beam, wherein an L-shaped cross-sectional geometry  820   a ,  819   a  has been specified. The representation  800   a  is but one example of beam models that may be created and modeled using embodiments and other example beam types may be similarly represented, including, but not limited to, I-beams and U-beams. The beam element model  805   a  is constructed based on proximal beam node  811   a  and distal beam node  809   a , shown at opposing longitudinal ends of the beam  805   a . At corresponding longitudinal ends, proximal contact nodes  814   a - 1 ,  814   a - 2 ,  814   a - 3 ,  814   a - 4 ,  814   a - 5 ,  814   a - 6  and distal contact nodes  813   a - 1 ,  813   a - 2 ,  813   a - 3 ,  813   a - 4 ,  813   a - 5 ,  813   a - 6  are shown. 
     Contact edges, specifically longitudinal contact edges  818 - 1 ,  818 - 2 ,  818 - 3 ,  818 - 4 ,  818 - 5 ,  818 - 6  can be seen in  FIG.  8 A  respectively connecting corresponding proximal  814   a - 1 ,  814   a - 2 ,  814   a - 3 ,  814   a - 4 ,  814   a - 5 ,  814   a - 6  and distal  813   a - 1 ,  813   a - 2 ,  813   a - 3 ,  813   a - 4 ,  813   a - 5 ,  813   a - 6  contact nodes. Further, the representation  800   a  includes additional contact edges, particularly, proximal contact edges  817   a - 1 ,  817   a - 2 ,  817   a - 3 ,  817   a - 4 ,  817   a - 5 , and  817   a - 6  connecting the proximal contact nodes  814   a - 1 ,  814   a - 2 ,  814   a - 3 ,  814   a - 4 ,  814   a - 5 , and  814   a - 6 . In particular, contact edge  817   a - 1  connects contact nodes  814   a - 1  and  814   a - 2 , contact edge  817   a - 2  connects contact nodes  814   a - 2  and  814   a - 3 , contact edge  817   a - 3  connects contact nodes  814   a - 3  and  814   a - 4 , contact edge  817   a - 4  connects contact nodes  814   a - 4  and  814   a - 5 , contact edge  817   a - 5  connects contact nodes  814   a - 5  and  814   a - 6 , and contact edge  817   a - 6  connects contact nodes  814   a - 6  and  814   a - 1 . Likewise, the representation  800   a  includes additional contact edges, particularly distal contact edges  816   a - 1 ,  816   a - 2 ,  816   a - 3 ,  816   a - 4 ,  816   a - 5 , and  816   a - 6 , connecting distal contact nodes  813   a - 1 ,  813   a - 2 ,  813   a - 3 ,  813   a - 4 ,  813   a - 5 , and  813   a - 6 . Contact edge  816   a - 1  connects contact nodes  813   a - 1  and  813   a - 2 , contact edge  816   a - 2  connects contact nodes  813   a - 2  and  813   a - 3 , contact edge  816   a - 3  connects contact nodes  813   a - 3  and  813   a - 4 , contact edge  816   a - 4  connects contact nodes  813   a - 4  and  813   a - 5 , contact edge  816   a - 5  connects contact nodes  813   a - 5  and  813   a - 6 , and contact edge  816   a - 6  connects contact nodes  813   a - 6  and  813   a - 1 . 
     Contact faces, specifically longitudinal contact faces  822 - 1 ,  822 - 2 ,  822 - 3 ,  822 - 4 ,  822 - 5 ,  822 - 6  are shown in  FIG.  8 A  to be formed between sets of contact nodes as follows: {face  822 - 1  formed by nodes  814   a - 1 ,  814   a - 2 ,  813   a - 2 ,  813   a - 1  connected by edges  817   a - 1 ,  818 - 2 ,  816   a - 1 ,  818 - 1 }, {face  822 - 2  formed by nodes  814   a - 2 ,  814   a - 3 ,  813   a - 3 ,  813   a - 2  connected by edges  817   a - 2 ,  818 - 3 ,  816   a - 2 ,  818 - 2 }, {face  822 - 3  formed by nodes  814   a - 3 ,  814   a - 4 ,  813   a - 4 ,  813   a - 3  connected by edges  817   a - 3 ,  818 - 4 ,  816   a - 3 ,  818 - 3 }, {face  822 - 4  formed by nodes  814   a - 4 ,  814   a - 5 ,  813   a - 5 ,  813   a - 4  connected by edges  817   a - 4 ,  818 - 5 ,  816   a - 4 ,  818 - 4 }, {face  822 - 5  formed by nodes  814   a - 5 ,  814   a - 6 ,  813   a - 6 ,  813   a - 5  connected by edges  817   a - 5 ,  818 - 6 ,  816   a - 5 ,  818 - 5 }, and {face  822 - 6  formed by nodes  814   a - 6 ,  814   a - 1 ,  813   a - 1 ,  813   a - 6  connected by edges  817   a - 6 ,  818 - 1 ,  816   a - 6 ,  818 - 6 }. 
     Also shown in the representation  800   a  of  FIG.  8 A , coplanar to the respective beam nodes  811   a ,  809   a , are additional contact faces, specifically a proximal contact face  824   a  and a distal contact face  823   a , drawn respectively according to the user-specified L-beam proximal cross-sectional geometry  820   a  and distal cross-sectional geometry  819   a . Proximal contact face  824   a  is formed by nodes  814   a - 1 ,  814   a - 2 ,  814   a - 3 ,  814   a - 4 ,  814   a - 5 ,  814   a - 6  connected by edges  817   a - 1 ,  817   a - 2 ,  817   a - 3 ,  817   a - 4 ,  817   a - 5 ,  817   a - 6 . Distal contact face  823   a  is formed by nodes  813   a - 1 ,  813   a - 2 ,  813   a - 3 ,  813   a - 4 ,  813   a - 5 ,  813   a - 6  connected by edges  816   a - 1 ,  816   a - 2 ,  816   a - 3 ,  816   a - 4 ,  816   a - 5 ,  816   a - 6 . 
       FIG.  8 A  illustrates example contact entities which may be generated according to step  515  of the method  500 , in particular, proximal contact nodes  814   a - 1 ,  814   a - 2 ,  814   a - 3 ,  814   a - 4 ,  814   a - 5 ,  814   a - 6  and distal contact nodes  813   a - 1 ,  813   a - 2 ,  813   a - 3 ,  813   a - 4 ,  813   a - 5 ,  813   a - 6 ; longitudinal contact edges  818 - 1 ,  818 - 2 ,  818 - 3 ,  818 - 4 ,  818 - 5 ,  818 - 6 , proximal contact edges  817   a - 1 ,  817   a - 2 ,  817   a - 3 ,  817   a - 4 ,  817   a - 5 ,  817   a - 6 , and distal contact edges  816   a - 1 ,  816   a - 2 ,  816   a - 3 ,  816   a - 4 ,  816   a - 5 ,  816   a - 6 ; and longitudinal contact faces  822 - 1 ,  822 - 2 ,  822 - 3 ,  822 - 4 ,  822 - 5 ,  822 - 6 , proximal contact face  824   a , and distal contact face  823   a , all as detailed hereinabove. 
     Additionally, rounded corners have been incorporated into the cross-sectional geometries  820   a ,  819   a  through inclusion of a corner radius parameter as described hereinabove with reference to  FIGS.  6 B and  7   . The corner radius parameter dictates surface thickness of the beam element model  805   a . As such, contact edges  818 - 1 ,  818 - 2 ,  818 - 3 ,  818 - 4 ,  818 - 5 ,  818 - 6  may not represent the outermost extremities of the beam element model  805   a , but rather a central axis of a cylinder defined by the corner radius applied to the cross-sectional geometries  820   a ,  819   a  centered about the contact nodes  814   a - 1 ,  814   a - 2 ,  814   a - 3 ,  814   a - 4 ,  814   a - 5 ,  814   a - 6 ,  813   a - 1 ,  813   a - 2 ,  813   a - 3 ,  813   a - 4   813   a - 5 ,  813   a - 6 . A portion of the surface of the cylinder may thus actually represent at least a portion of the surface of the beam element model  805   a . According to the present disclosure, a mesh, such as mesh  300   c  of  FIG.  3 C , may be generated surrounding a beam element model, e.g., model  805   a , based on the automatically generated contact entities  515 , e.g., contact entities  814   a - 1 ,  814   a - 2 ,  814   a - 3 ,  814   a - 4 ,  814   a - 5 ,  814   a - 6 ,  813   a - 1 ,  813   a - 2 ,  813   a - 3 ,  813   a - 4 ,  813   a - 5 ,  813   a - 6 ,  818 - 1 ,  818 - 2 ,  818 - 3 ,  818 - 4 ,  818 - 5 ,  818 - 6 ,  817   a - 1 ,  817   a - 2 ,  817   a - 3 ,  817   a - 4 ,  817   a - 5 ,  817   a - 6 ,  816   a - 1 ,  816   a - 2 ,  816   a - 3 ,  816   a - 4 ,  816   a - 5 ,  816   a - 6 ,  822 - 1 ,  822 - 2 ,  822 - 3 ,  822 - 4 ,  822 - 5 , 822 - 6 ,  824   a ,  823   a . Motion of the mesh may then be constrained to follow motion of the beam element model  805   a , e.g., according to step  535  of the method  500  of  FIG.  5   , based on the automatically generated contact entities  515 . 
       FIG.  8 B  shows a manipulated representation  800   b  of an example beam element model  805   b , representing the beam element model  805   a  of  FIG.  8 A  after undergoing a twisting event. Motion of automatically generated contact entities  814   b - 1 ,  814   b - 2 ,  814   b - 3 ,  814   b - 4 ,  814   b - 5 ,  814   b - 6 ,  813   b - 1 ,  813   b - 2 ,  813   b - 3 ,  813   b - 4 ,  813   b - 5 ,  813   b - 6 ,  817   b - 1 ,  817   b - 2 ,  817   b - 3 ,  817   b - 4 ,  817   b - 5 ,  817   b - 6 ,  816   b - 1 ,  816   b - 2 ,  816   b - 3 ,  816   b - 4 ,  816   b - 5 ,  816   b - 6 ,  824   b ,  823   b , during a simulation, is dictated by translations and rotations of beam nodes, such as beam node  811   b , which has at least been rotated by an amount relative to beam node  811   a  of the view of representation  800   a  in  FIG.  8 A . A proximal contact face  824   b , comprising beam node  811   b , is shown in  FIG.  8 B  as having been rotated, by an amount, about said beam node  811   b . Longitudinal contact edges are not shown in  FIG.  8 B  so as to preserve visibility of the other elements of the figure, and, as such, longitudinal contact edges are not expressly illustrated in  FIG.  8 B . The beam element model  805   b  is constructed based on proximal beam node  811   b  and distal beam node  809   b , shown at opposing longitudinal ends of the beam  805   b . At corresponding longitudinal ends, proximal contact nodes  814   b - 1 ,  814   b - 2 ,  814   b - 3 ,  814   b - 4 ,  814   b - 5 ,  814   b - 6  and distal contact nodes  813   b - 1 ,  813   b - 2 ,  813   b - 3 ,  813   b - 4 ,  813   b - 5 ,  813   b - 6  are shown. 
     The representation  800   b  includes contact edges, particularly, proximal contact edges  817   b - 1 ,  817   b - 2 ,  817   b - 3 ,  817   b - 4 ,  817   b - 5 , and  817   b - 6  connecting the proximal contact nodes  814   b - 1 ,  814   b - 2 ,  814   b - 3 ,  814   b - 4 ,  814   b - 5 , and  814   b - 6 . In particular, contact edge  817   b - 1  connects contact nodes  814   b - 1  and  814   b - 2 , contact edge  817   b - 2  connects contact nodes  814   b - 2  and  814   b - 3 , contact edge  817   b - 3  connects contact nodes  814   b - 3  and  814   b - 4 , contact edge  817   b - 4  connects contact nodes  814   b - 4  and  814   b - 5 , contact edge  817   b - 5  connects contact nodes  814   b - 5  and  814   b - 6 , and contact edge  817   b - 6  connects contact nodes  814   b - 6  and  814   b - 1 . Likewise, the representation  800   b  includes additional contact edges, particularly distal contact edges  816   b - 1 ,  816   b - 2 ,  816   b - 3 ,  816   b - 4 ,  816   b - 5 , and  816   b - 6 , connecting distal contact nodes  813   b - 1 ,  813   b - 2 ,  813   b - 3 ,  813   b - 4 ,  813   b - 5 , and  813   b - 6 . Contact edge  816   b - 1  connects contact nodes  813   b - 1  and  813   b - 2 , contact edge  816   b - 2  connects contact nodes  813   b - 2  and  813   b - 3 , contact edge  816   b - 3  connects contact nodes  813   b - 3  and  813   b - 4 , contact edge  816   b - 4  connects contact nodes  813   b - 4  and  813   b - 5 , contact edge  816   b - 5  connects contact nodes  813   b - 5  and  813   b - 6 , and contact edge  816   b - 6  connects contact nodes  813   b - 6  and  813   b - 1 . 
     Contact faces, specifically a proximal contact face  824   b  and a distal contact face  823   b , are drawn in  FIG.  8 B  respectively according to the user-specified L-beam proximal cross-sectional geometry  820   b  and distal cross-sectional geometry  819   b . Proximal contact face  824   b  is formed by nodes  814   b - 1 ,  814   b - 2 ,  814   b - 3 ,  814   b - 4 ,  814   b - 5 ,  815   b - 6  connected by edges  817   b - 1 ,  817   b - 2 ,  817   b - 3 ,  817   b - 4 ,  817   b - 5 ,  817   b - 6 . Distal contact face  823   b  is formed by nodes  813   b - 1 ,  813   b - 2 ,  813   b - 3 ,  813   b - 4 ,  813   b - 5 ,  813   b - 6  connected by edges  816   b - 1 ,  816   b - 2 ,  816   b - 3 ,  816   b - 4 ,  816   b - 5 ,  816   b - 6 . 
     Contact entities, which may be generated according to step  515  of the method  500 , are shown in the representation  800   b . In particular, the contact entities in  FIG.  8 B  include proximal contact nodes  814   b - 1 ,  814   b - 2 ,  814   b - 3 ,  814   b - 4 ,  814   b - 5 ,  814   b - 6  and distal contact nodes  813   b - 1 ,  813   b - 2 ,  813   b - 3 ,  813   b - 4 ,  813   b - 5 ,  813   b - 6 ; proximal contact edges  817   b - 1 ,  817   b - 2 ,  817   b - 3 ,  817   b - 4 ,  817   b - 5 ,  817   b - 6 , and distal contact edges  816   b - 1 ,  816   b - 2 ,  816   b - 3 ,  816   b - 4 ,  816   b - 5 ,  816   b - 6 ; proximal contact face  824   b , and distal contact face  823   b , all as referenced hereinabove. Not shown in  FIG.  8 B  are longitudinal contact edges  818 - 1 ,  818 - 2 ,  818 - 3 ,  818 - 4 ,  818 - 5 ,  818 - 6 ; and longitudinal contact faces  822 - 1 ,  822 - 2 ,  822 - 3 ,  822 - 4 ,  822 - 5 ,  822 - 6 . 
       FIG.  9    shows an example CAD model  900  including a separate first and second beam element model  905  and  906 . Each beam element model  905 ,  906  is shown in  FIG.  9    to have multiple connected parts (portions) as defined by the apparent multiple disparate beam element orientations depicted within each beam element model  905 ,  906 . Also shown in  FIG.  9    is an example modeled rectangular solid  907 . Any solid characterized by any shape that one of skill in the art would not think of as a beam element may be so modeled for simulations of contact events with beam elements. Also depicted in  FIG.  9    are a point of contact  956  between the first and second beam element models  905 ,  906 , two points of contact  957 - 1 ,  957 - 2  between the first beam element model  905  and the rectangular solid  907 , and a point of contact  967  between the second beam element model  906  and the rectangular solid  907 . 
     Embodiments described herein may be utilized to model and simulate behavior of the beams  905  and  906 . In an embodiment, contact entities are automatically generated using the embodiments described herein for portions of the beams  905  and  906  that may interact with each other or with other objects or bodies. In other words, embodiments may be used to model and simulate portions of the beams  905  and  906  involved in the contacts  956 ,  957 - 1 ,  957 - 2 , and  967 . Further, an implementation may utilize the methods described herein, e.g., the method  500 , to model and simulate portions of the beams  905  and  906  involved in the contacts  956 ,  957 - 1 ,  957 - 2 , and  967  while using existing methods for portions of the beams  905  and  906  not involved in the contact. 
     For example, the beam elements  902  of beam element model  905  in the upper-left of  FIG.  9    are not close to being in contact with other objects or beam element models. An example implementation identifies such regions (which often evolve during a simulation) and can implement a simulation where the portion  902  of beam element model  905  is modeled with an existing method where contact entities are not automatically generated and other portions of the beam element model  905  are modeled using the methods described herein. In this way, embodiments can enhance computational performance and implement simulations to determine contact behavior that bypass computations involving more detailed surface representations in regions not involved in the contact (contact points  956 ,  957 - 1 ,  957 - 2 , and  967 ). 
     As illustrated by the forgoing various non-limiting examples, the automatically generated contact entities of embodiments define or otherwise logically serve as potential points of contact on the model for purposes of simulation of modeled object behavior. Such defined points of contact increase accuracy of simulations heretofore unachieved in the art. 
       FIG.  10 A  shows an example CAD model  1000   a  including a model of a pair of tweezers  1007  comprising beam segments such as tweezer tip segments respectively modeled by beam element models  1005   a - 1  and  1005   a - 2 . The example model  1000   a  also includes a separate singular beam represented by a beam element model  1006   a . Embodiments of the present invention may be utilized to simulate contact between the tweezer  1007  tips represented by the models  1005   a - 1  and  1005   a - 2  and the beam element model  1006   a . 
       FIG.  10 B  shows another view  1000   b  of the example CAD model  1000   a  of  FIG.  10 A  wherein the display showing the model has been configured through a zoom setting to show regions of interface  1056 - 1 ,  1056 - 2  between the respective beam element models  1005   b - 1 ,  1005   b - 2  of the tweezer tips and the beam element model  1006   b  of the singular beam. In  FIG.  10 B , it can be seen that the beam element model of the singular beam  1006   b  incorporates a hexagonal cross-sectional geometry  1020 . The beam element models  1005   b - 1 ,  1005   b - 2  of the tweezer tips are assumed to have rectangular cross-sectional geometries. Such cross-sectional geometries are not explicitly and completely shown in the figure, but can be inferred from the apparent right angles between adjacent surfaces of the beam element models  1005   b - 1 ,  1005   b - 2  of the tweezer tips, given the perspective of view  1000   b . 
     The models  1000   a  and  1000   b  illustrate advantages and benefits of embodiments. To illustrate, imagine the singular beam element model  1006   b  being configured to rotate about an axis central to its cross-sectional area and perpendicular to its cross-sectional plane, while the beam element models  1005   b - 1 ,  1005   b - 2  of the tweezer tips are configured to mutually compress towards, and ultimately make contact with, the singular beam element model  1006   b . In such a state, the tweezer tips may be understood to be pinching the end of the singular beam element. One would expect deflection of motion of the beam element models  1005   b - 1 ,  1005   b - 2  of the tweezer tips as at least the first vertex of the hexagonal cross-sectional geometry  1020  of the singular beam element comes in contact with the beam element models  1005   b - 1 ,  1005   b - 2  of the tweezer tips during rotation of the singular beam element model  1006   b . Assuming that sufficient spring resistance is built into the tweezers  1007  of the example model so as to maintain the pinching of the singular beam element between the tweezer tips, one would expect a bouncing effect to be exhibited by the beam element models  1005   b - 1 ,  1005   b - 2  of the tweezer tips as the singular beam element model  1006   b  continues to rotate and vertices of the hexagonal cross-sectional geometry  1020  pass between the beam element models  1005   b - 1 ,  1005   b - 2  of the tweezer tips. 
     It is made readily apparent by  FIG.  10 B  that if contact events involving the hexagonal cross-sectional geometry  1020  of the singular beam element model  1006   b  were simulated using existing methods where all beams are treated as having circular cross-sectional areas, such a simulation would fail to predict any significant amount of deflection of motion or bouncing in the beam element models  1005   b - 1 ,  1005   b - 2  of the tweezer tips as the singular beam element model  1006   b  rotates between the beam element models  1005   b - 1 ,  1005   b - 2  of the tweezer tips. 
     In addition, if the cross-sectional geometries of the beam element models  1005   b - 1 ,  1005   b - 2  of the tweezer tips are rectangular as assumed above, the beam element models  1005   b - 1 ,  1005   b - 2  of the tweezer tips would likewise be treated as having circular cross-sectional areas in contact simulations implemented using existing methods. Existing methods would establish circular cross-sections for contact calculations by circumscribing a circular area about a rectangular cross-section of each beam element model  1005   b - 1 ,  1005   b - 2 , thus enlarging the respective cross-sectional areas under consideration. As a result, using existing methods, contact simulations involving beam element models  1005   b - 1 ,  1005   b - 2  would identify contact events that physically do not occur. In other words, using existing methods, regions of interface  1056 - 1 ,  1056 - 2  would appear artificially large, rendering the simulation inaccurate. As such, the methods and systems described herein support contact simulations with increased accuracy over contact simulations implemented using existing methods by considering true cross-sectional geometries of the beam element models involved. 
     Structural simulations of dynamic events with central difference time integration require very small time increment or step sizes, thus often requiring, for example, at least 100,000 increments or steps. A simulation will often involve, for example, a number on the order of ten million contact nodes, edges, and faces. The claimed methods, systems, and products provide for reasonable simulation run-times by enabling efficient determination of which combinations of contact entities are actively in contact and what contact forces should be generated at each increment or step. The claimed methods, systems, and products impart, to each contact entity, characteristics that promote efficient and parallelizable processes. For example, the claimed methods, systems, and products keep the total number of types of contact entities small to enable code development and maintenance to focus on a few types of combinations of entities. 
       FIG.  11    illustrates a computer network or similar digital processing environment in which embodiments of the present disclosure may be implemented. 
     Client computer(s)/devices  50  and server computer(s)  60  provide processing, storage, and input/output devices executing application programs and the like. The client computer(s)/devices  50  can also be linked through communications network  70  to other computing devices, including other client devices/processes  50  and server computer(s)  60 . The communications network  70  can be part of a remote access network, a global network (e.g., the Internet), a worldwide collection of computers, local area or wide area networks, and gateways that currently use respective protocols (TCP/IP, Bluetooth®, etc.) to communicate with one another. Other electronic device/computer network architectures are suitable. 
       FIG.  12    is a diagram of an example internal structure of a computer (e.g., client processor/device  50  or server computers  60 ) in the computer system of  FIG.  11   . Each computer  50 ,  60  contains a system bus  79 , where a bus is a set of hardware lines used for data transfer among the components of a computer or processing system. The system bus  79  is essentially a shared conduit that connects different elements of a computer system (e.g., processor, disk storage, memory, input/output ports, network ports, etc.) that enables the transfer of information between the elements. Attached to the system bus  79  is an I/O device interface  82  for connecting various input and output devices (e.g., keyboard, mouse, displays, printers, speakers, etc.) to the computer  50 ,  60 . A network interface  86  allows the computer to connect to various other devices attached to a network (e.g., network  70  of  FIG.  11   ). Memory  90  provides volatile storage for computer software instructions  92  (shown in  FIG.  12    as computer software instructions  92 A and  92 B) and data  94  used to implement an embodiment of the present disclosure, e.g., the method  500  and supporting graphical user interface discussed above. Disk storage  95  provides nonvolatile storage for computer software instructions  92  and data  94  used to implement an embodiment of the present disclosure. A central processor unit  84  is also attached to the system bus  79  and provides for the execution of computer instructions. 
     In one embodiment, the processor routines  92  and data  94  are a computer program product (generally referenced  92 ), including a non-transitory computer-readable medium (e.g., a removable storage medium such as one or more DVD-ROM’s, CD-ROM’s, diskettes, tapes, etc.) that provides at least a portion of the software instructions for an embodiment. The computer program product  92  can be installed by any suitable software installation procedure, as is well known in the art. In another embodiment, at least a portion of the software instructions may also be downloaded over a cable communication and/or wireless connection. In other embodiments, the processor routines  92  and data  94  are a computer program propagated signal product embodied on a propagated signal on a propagation medium (e.g., a radio wave, an infrared wave, a laser wave, a sound wave, or an electrical wave propagated over a global network such as the Internet, or other network(s)). Such carrier medium or signals may be employed to provide at least a portion of the software instructions for the present processor routines/program  92  and data  94 . 
     Advantages provided by the claimed methods, systems, and products include more accurate modeling of contact events involving beam elements, at least in part due to computer implemented determination of contact entities of CAD beam element models. Having the outer surface representation of beam geometry generated by the software specifically to model effects of contact events helps ensure that the resulting surface representation is well suited for contact simulations with regard to performance, robustness, accuracy, and maintainability. A user would normally be disincentivized to manually construct a similar outer surface representation within the CAD software, due to common constraints such as time and cost to implement, as well as a significant potential for human error, given the complexities inherent to many real-world objects modeled by the software. The claimed methods, systems, and products effectively eliminate such disincentives and potential for human error, allowing users to realize and build upon benefits that were heretofore impractical or impossible to attain within a real product design setting. 
     Moreover, association between the original beam representation and the automatically-generated, detailed outer surface representation can be helpful in optimizing performance. The automatically generated contact entities in a particular region only need to be considered while parent beam elements are judged to be potentially involved in contact, based on crude screening methods. 
     While example embodiments have been particularly shown and described, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the scope of the embodiments encompassed by the appended claims. For example, implementations may change the order in which operations are performed. Further, depending on the needs of an implementation, particular operations described herein may be implemented as a combined operation, eliminated, added to, or otherwise rearranged. Further, particular user interface operations relative to a mouse (e.g., click, drag, drop, etc.) are by way of illustration and not limitation. Other user interface operations for selecting, moving, placing, etc., model or design data are suitable.