Abstract:
Systems and methods for modeling stress intensity solutions of integrally stiffened panels are disclosed. In one embodiment, a method includes serving a process over the internet. The process includes taking a problem definition, automatically forming a finite element model at least partially based on the problem definition, automatically verifying a suitability condition of the finite element model, automatically solving a computational solution using the finite element model and automatically validating the computational solution. In one aspect, providing a problem definition includes at least one of providing a geometry definition, providing a crack definition, and providing load and constraint definition.

Description:
FIELD OF THE INVENTION 
   This invention relates to structural analysis, and, more specifically, to methods and systems for modeling stress intensity solutions for integrally stiffened panels. 
   BACKGROUND OF THE INVENTION 
   The calculation of stress intensity solutions can be one of the most difficult problems in engineering. With the ever-increasing pressure to reduce manufacturing and maintenance costs, the use of unitized structures to decrease part count is increasing. One of the most effective unitized structural designs is an integrally stiffened panel. The damage tolerance requirements for these integrally stiffened panels are the same as those for the built-up structure being replaced. These requirements may necessitate the calculation of crack growth rates and residual strength, both of which require accurate stress intensity solutions. 
   Previously, stress intensity determinations in integrally stiffened structures were performed by engineering specialists who were typically experts in finite element analysis. Currently, there are very few such engineering specialists available to perform such stress intensity calculations. Furthermore, solving a single problem typically takes such a specialist engineer weeks or months of effort, making design trade studies of integral panels expensive and time-consuming. Therefore, methods and systems for calculating stress intensities in a more cost effective manner would be useful. 
   SUMMARY OF THE INVENTION 
   The present invention is directed to methods and systems for modeling stress intensity solutions of integrally stiffened panels with cracks. Methods and systems in accordance with the present invention may advantageously allow stress intensity calculations to be performed by persons not having expertise in the field of finite element analysis, substantially reducing the time and expense associated with stress intensity determinations in comparison with the prior art. Structural design trade studies can be performed relatively cheaply and quickly, and may result in more robust, lighter weight, and more affordable structural components. 
   In one embodiment, a method of performing stress intensity computations includes providing a problem definition, and automatically forming a finite element model at least partially based on the problem definition. The method further includes automatically verifying a suitability condition of the finite element model, and automatically solving a computational solution using the finite element model. Finally, the method includes automatically validating the computational solution. In one aspect, providing a problem definition includes at least one of providing a geometry definition, providing a crack definition, and providing a load and constraint definition. 
   In another aspect, a method includes automatically forming a finite element model at least partially based on the problem definition wherein the problem definition includes at least one crack. Alternately, automatically forming a finite element model may include building a panel cross-section, adding at least one crack to the panel cross-section, extruding a first cross-section to build a full panel model, building a computational mesh, and applying at least one of a load and a constraint. 
   In yet another embodiment, a method of performing stress intensity computations includes providing a plurality of servers, each server being operatively coupled to at least one other server and having an application service. A plurality of client computers is provided, each client computer being operatively coupled to at least one of the servers. A problem definition is provided from a respective one of the client computers to a corresponding one of the servers. Using the application service of the corresponding one of the servers, a resource availability of the corresponding one of the servers is determined and if the resource availability is sufficient, an application corresponding to the problem definition is performed on the corresponding one of the servers. If the resource availability of the corresponding one of the servers is not sufficient, the application service of the corresponding one of the servers determines a second resource availability of at least one other server and if the second resource availability is sufficient, the application corresponding to the problem definition is performed on the other server. The performance of the application includes automatically forming a finite element model at least partially based on the problem definition, automatically verifying a suitability condition of the finite element model, automatically solving a computational solution using the finite element model, and automatically validating the computational solution. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     Preferred and alternate embodiments of the present invention are described in detail below with reference to the following drawings. 
       FIG. 1  is a flowchart of a method for calculating stress intensity solutions for integrally stiffened panels in accordance with an embodiment of the present invention; 
       FIG. 2  is an end view of a stiffener geometry in accordance with an embodiment of the present invention; 
       FIG. 3  is an end view of a plurality of common stiffener geometries that may be modeled in accordance with embodiments of the present invention; 
       FIG. 4  is a representative crack front model in accordance with an embodiment of present invention; 
       FIG. 5  is a schematic view of a set of loading and boundary constraints that may be applied in accordance with the method of  FIG. 1 ; 
       FIG. 6  is a representative menu of a menu-based input program for performing a panel definition input of the problem definition portion of  FIG. 1 ; 
       FIG. 7  is a representative menu of the menu-based input program for performing a stiffener definition input of the problem definition portion of  FIG. 1 ; 
       FIG. 8  is a flowchart of a process of building a finite element model including cracks in accordance with an embodiment of present invention; 
       FIGS. 9 and 10  show representative locations along crack front geometries that are defined by the user for extraction of stress intensity data in accordance with alternate embodiments of the present invention; 
       FIG. 11  is representative output menu of a stress intensity solutions as viewed by a user in graphical form in accordance with an embodiment of the invention; 
       FIG. 12  is a schematic view of a web-based system for calculating stress intensity solutions for integrally stiffened panels in accordance with another embodiment of the present invention; 
       FIG. 13  is a representative menu of the menu-based input program for providing stiffener locations in accordance with an embodiment of the invention; 
       FIG. 14  is a representative menu of the menu-based input program for providing crack geometry in accordance with an embodiment of the invention; 
       FIG. 15  is a representative menu of the menu-based input program for defining load and constraints applied to the structure to be analyzed in accordance with an embodiment of the invention.; 
       FIG. 16  is a representative menu of the menu-based input program for presenting plots of results in accordance with an embodiment of the invention; and 
       FIG. 17  is a representative menu of the menu-based input program for presenting results of previously computed analyses in accordance with another embodiment of the invention. 
   

   DETAILED DESCRIPTION 
   The present invention relates to methods and systems for modeling stress intensity solutions of integrally stiffened panels, including panels with cracks. Many specific details of certain embodiments of the invention are set forth in the following description and in  FIGS. 1-17  to provide a thorough understanding of such embodiments. One skilled in the art, however, will understand that the present invention may have additional embodiments, or that the present invention may be practiced without several of the details described in the following description. 
   In general, embodiments of methods and systems in accordance with the present invention advantageously automate the process of building a finite element model, extracting a stress intensity solution, and validating the results. A user does not need to be a finite element expert to perform stress intensity computations using the methods and systems in accordance with the present invention. Building a relatively sophisticated finite element model requires only that a user enter a cross-sectional geometry of a structural member to be analyzed (e.g., panel) and to input the desired cracked lengths for which stress intensities are desired. Embodiments of the present invention enable the user to access a single computational tool that will generate stress intensity solutions for structures, including integrally stiffened panels, for use in calculating the crack growth rate and residual strength with virtually any damage tolerance analysis software. 
     FIG. 1  is a flowchart of a method  100  for calculating stress intensity solutions for integrally stiffened panels in accordance with an embodiment of the present invention. The method  100  has a problem definition portion  102  that includes a geometry definition at a block  104 , a crack definition at a block  106 , and a load and constraint definition at a block  108 . In the geometry definition (block  104 ), a user provides inputs to the method  100  defining the structure to be analyzed. In one embodiment, the structure to be analyzed may include a stiffener.  FIG. 2  is an end view of a stiffener geometry  200 , and the associated parameters that may be input by the user to define the stiffener geometry  200  for subsequent analysis by the method  100 . More specifically, as shown in  FIGS. 2 ,  6 , and  13 , the user may define the stiffener geometry  200  based on the following variables: 
   h—overall stiffener height, 
   W FL —width of upper stiffener flange on left side, 
   W FR —width of upper stiffener flange on right side, 
   W PL —width of lower stiffener pad on left side, 
   W PR —width of lower stiffener pad on right side, 
   t W —thickness of the stiffener web, 
   t f —thickness of the upper stiffener flange, 
   t PL —thickness of the lower stiffener pad on the left side, 
   t PR —thickness of the lower stiffener pad on the right side, 
   R a —radius of the lower stiffener pad-to-skin transition on the left side, 
   R b —radius of the lower stiffener pad-to-stiffener web transition on the left side, 
   R c —radius of the lower stiffener pad-to-stiffener web transition on the right side, 
   R d —radius of the lower stiffener pad-to-skin transition on the right side, 
   W—panel width, 
   L—panel length, 
   t s —skin thickness, 
   Label—descriptive label of each stiffener type for identification purposes, 
   x—distance of the centerline of each individual stiffeners from the origin, 
   Using the above-referenced representative parameters, the user may model a wide variety of stiffener geometries  200  for analysis using the method  100 . For example,  FIG. 3  is an end view of a plurality of common stiffener geometries  300  that may be modeled using the above-referenced representative parameters. As shown in  FIG. 3 , the above referenced representative parameters may be used to define a variety of different symmetric stiffener geometries  302  and asymmetric stiffener geometries  304 . It will be appreciated that alternate embodiments of stiffener geometries may be modeled using the above-referenced representative parameters, and that the method  100  is not limited to the particular stiffener geometries  302 ,  304  shown in  FIG. 3 . 
   As described above, the user may define one or more crack definitions (block  106 ) to apply to the stiffener geometry  200 .  FIGS. 4 and 14  is a representative crack front model  400  in accordance with an embodiment of present invention. In this embodiment, the crack front model  400  may be defined by the user using the following crack front definition parameters: 
   crack configuration—center crack or edge crack, 
   c 1 —crack front vertical axis for corner cracks 
   a 1 —crack front horizontal axis for corner cracks 
   a—overall crack length, 
   w cr —stiffener web crack length (input for each stiffener) 
   Using the crack front definition parameters shown in  FIG. 4 , the user may model a variety of crack fronts, including straight-through and elliptical crack fronts. Furthermore, in alternate embodiments, multiple crack fronts can be modeled using the method  100 . This may be useful, for example, to account for the interaction of a skin crack with a partially-failed stiffener. Also during the problem definition portion  102  of the method  100 , the user defines the loading and boundary constraints (block  108 ) that are to be applied to the geometry definition (block  104 ). More specifically,  FIG. 5  is a schematic view of a set of loading and boundary constraints  500  that may be applied by the user in accordance with the method  100  of  FIG. 1 . Following the definition of the geometry (block  104 ), in this case an integrally-stiffened panel  502 , the user defines the loading and boundary constraint parameters  504  to be applied to the geometry, including the following representative variables (see  FIG. 5 ): Grip length, Intermediate Rib position, Intermediate Rib width, Intermediate Rib spring constant, Buckling bar height, Buckling bar gap, Buckling bar material elastic modulus (E), Buckling bar material Poisson&#39;s ratio, Gap material elastic modulus (E), Gap material shear modulus (G), Applied tension stress, Applied displacement, and Axis of symmetry. 
   In some embodiments, either a uniform stress or a uniform displacement may be defined using the loading and boundary constraint parameters  504 . Additionally, the out-of-plane restraint scheme may have the capability to utilize a user-input stiffness to simulate the effect of ribs. More specifically, a spring constant applied over the whole skin surface in a direction normal to the xy-plane of the panel  502  ( FIG. 5 ) may be defined to simulate the effect of ribs. In one particular embodiment, the spring coefficient may be defined by a formula that evaluates to zero everywhere except in a narrow band parallel to the x-axis where the rib is located. The user only inputs the position and width of the rib (spring) and the stiffness (spring constant in kips/in/in 2 ). 
   In addition, buckling bars  506  may be added by the user in the region of the model where buckling constraints are required. The buckling bars may increase the local stiffness of a panel  508  of the geometry definition  502  but do not include any external constraints. A thin layer of elements  510  may be inserted between the panel  508  and the buckling bars  506 , wherein the elements  510  may have orthotropic material properties selected in such a way that the stiffness in the in-plane direction is much less than the stiffness normal to the skin. In such embodiments, the buckling bars  506  may be prevented from taking any significant amount of the externally applied load the user inputs a height of the buckling bar  506 , a gap (i.e., thickness of elements  510  between the panel  508  and bar  506 ), and the material is defined by entering Young&#39;s modulus (ksi) and Poisson&#39;s ratio v. 
   Referring again to  FIG. 1 , following the input of the user&#39;s problem definition (blocks  104 ,  106 ,  108 ), the user&#39;s inputs (or suitable default inputs) are passed to a job queue at a block  110 . In one embodiment, the problem definition portion  102  of the method  100  may be performed on a user&#39;s personal computer (PC) and may be transmitted to a remote server via a communication network  112  (e.g., wireless link, Internet, world wide web, intranet, etc.) for further processing. 
   More specifically, in one particular embodiment, the problem definition portion  102  may utilize a menu-based input program that receives the user&#39;s problem definition inputs (blocks  104 ,  106 ,  108 ) and formulates suitable outputs to the job queue  110 .  FIG. 6  is a representative menu  600  of a menu-based input program for performing a panel definition input of the problem definition portion  102  of  FIG. 1 . In this embodiment, the representative menu  600  includes a first window portion  602  including a plurality of section options  604 . The section options  604  approximately correspond to various portions of the method  100  that may be accessed by the user. For example, the section options  604  include problem definition options  610  devoted to the problem definition portion  102  of the method  100 , a job status option  612  (not shown) for checking the status of a particular job that has been submitted to the job queue  110 , a submitted analysis option  614  (not shown) for submitting a particular job to the job queue  110 , and options for viewing the computational results  616  in tabular form and in graphical form are provided. 
   As depicted in  FIG. 6 , the user may highlight the “PANEL DEFINITION” option to provide the inputs associated with the panel portion of the structure being analyzed. A second window portion  606  includes a set of input areas  608 . In the representative example shown in  FIG. 6 , the set of input areas  608  correspond to the inputs defined by the user for defining the panel of the structure being analyzed. A visual representation  609  of the structure being analyzed is also provided in the second window portion  606 . 
   It will be appreciated that the menu-based software program may further provide additional menus having alternate sets of input areas corresponding to the other problem definition section options  604  (i.e., stiffener types, stiffener location, crack definition, constraints, applied loading). For example,  FIG. 7  is a representative menu  700  of the menu-based input program for performing a stiffener definition input. In this embodiment, the user has highlighted the “STIFFENER TYPES” option in the first window portion  602  to provide the inputs associated with the stiffeners of the structure being analyzed. A second window portion  706  includes a set of input areas  708  corresponding to the stiffener parameters that will be defined by the user for defining the stiffeners of the structure being analyzed. Again, a visual representation  709  of the stiffener being defined by the user is also provided in the second window portion  706 . Furthermore,  FIG. 13  is a representative menu  1300  of the menu-based input program for performing stiffener location functions. In this embodiment, the user has highlighted the “STIFFENER LOCATION” option in the first window portion  602  to provide the inputs associated with the locations of the stiffeners of the structure being analyzed, and a visual representation  1309  of the stiffener locations is provided in a second window portion  1306 . Thus, the menu-based software program may allow the user to define the problem quickly and efficiently in comparison with prior art methods and systems. 
   As further shown in  FIG. 1 , a finite element model is built based on the problem definition portion  102  at a block  114 . The finite element model may include cracks as defined by the user (block  106 ).  FIG. 8  is a flowchart of a process  800  of building a finite element model including cracks in accordance with an embodiment of present invention. In this embodiment, the structure under analysis is an integrally-stiffened panel member. A panel cross-section is built at a block  802 , which involves the construction of a complete finite element model from the geometric definition provided by the invention, including defining the stiffeners as described above. Cracks are then added to the panel at a block  804 .  FIG. 14  is a representative menu  1400  of the menu-based input program for performing crack definition functions. In this embodiment, the user has highlighted the “CRACK DEFINITION” option in the first window portion  602  to provide the inputs associated with the definitions of the cracks of the structure being analyzed. A plurality of crack definition parameters  1408 , and a visual representation  1409  of the crack being defined, are provided in a second window portion  1406 . 
   As further shown in  FIG. 8 , the process  800  further includes extruding a cross-section to build a full panel model at a block  806 . This includes defining a 2D panel cross-section, and then extruding the 2D cross-section to form a 3D panel. A computational mesh is built to perform the finite element stress computations at a block  808 . In one particular embodiment, an automated mesh-generating software program known as StressCheck, commercially-available from Engineering Software Research and Development, Inc. of St. Louis, Mo., may be employed. At a block  810 , loads and constraints defined by the user during the loads and constraints definition (block  108 ) are applied.  FIG. 15  is a representative menu  1500  of the menu-based input program for defining load and constraints applied to the structure to be analyzed. In this embodiment, the user has highlighted the “CONSTRAINTS/LOADING” option in the first window portion  602  to provide the inputs associated with the applied loads and constraints. A plurality of loads and constraints parameters  1508  are provided in a second window portion  1506 . 
   Referring again to  FIG. 1 , following the definition of the finite element model (block  114 ), a verification is performed to determine if the finite element model is valid and solvable at block  116 . Various methods of determining whether a finite element model is valid and solvable are known in the art. Following this verification (block  116 ), the finite element model is transmitted to a finite element solver for computational solution at a block  118 . Typically, the number of p-levels that will be computed by the finite element solver is controllable by the user. In some embodiments, a minimum of three p-levels are desirable to insure solution convergence. It will be appreciated that the finite element solver used for the computational solution at block  118  may be any suitable finite element analysis program. Again, in one particular embodiment, the finite element analysis program known as StressCheck, commercially-available from Engineering Software Research and Development, Inc. of St. Louis, Mo., may be employed. Other suitable finite element analysis programs that may be used for this purpose include, for example, the ABAQUS program commercially available from ABAQUS, Inc. of Pawtucket, R.I., and the Pro/Mechanica program commercially available from Parametric Technology Corporation of Needham, Mass. 
   At block  118 , the entire (global) finite element model is solved and at that time, stresses and displacements in the model are available. As this point, however, the stress intensities are still unknown. At a block  120 , the global energy norm error is computed by determining how it is converging as a function of the overall model fidelity (e.g., either increasing p-level or number of elements in the model). This typically gives an indication as to whether or not the overall finite element model ran successfully but may not provide an accurate indication as to whether there are localized problems in certain regions of the overall model. At a block  122 , the stress intensities are computed from the model results (that are available from block  118 ) in the region near the crack tip(s). At a block  124 , the stress intensities from block  122  are validated by checking the convergence of the stress intensities as a function of the finite element model fidelity (the same as in block  120 ). This provides an indication as to whether the model provided good results in the local area near the crack tip(s). The stress intensity solution may be stored in database at a block  126 , and a report on the stress intensity solution may be provided at a block  128 . 
   The extraction of selected results from the stress intensity solution performed at block  122  may be performed in a variety of ways according to the user&#39;s preferences. Generally, the stress intensities may be extracted from the finite element model results at a user-defined number of locations along each crack front. For example,  FIGS. 9 and 10  show representative locations  900 ,  902 ,  1000  along the crack front geometries that are defined by the user for extraction of stress intensity data. More specifically,  FIG. 9  shows five locations  900  along a first straight crack and five locations  902  along a second straight crack, while  FIG. 10  shows five locations  1000  along an elliptical crack. Of course, an alternate embodiment, a greater or fewer number of locations for data extraction along each crack may be used. 
   Typically, one more portions of the method  100  (e.g., block  122 , block  124 , block  128 , etc.) will involve viewing the results of the stress intensity solution by the user. For example,  FIG. 11  is a representative output menu  1100  of a stress intensity solution as viewed by a user in graphical form. In this embodiment, the output menu  1100  includes the first window portion  602  described above, and a second window portion  1106  that includes a table of stress intensities  1108 . More specifically, the table of stress intensities  1108  provides the stress intensity values at each user defined location for each individual crack ( FIGS. 9 and 10 ). Alternately, the user may elect to view the stress intensity solution in graphical form by clicking on the appropriate graph options  1110  provided in the second window portion  1106 .  FIG. 16  is a representative menu  1600  of the menu-based input program for presenting plots of results. In this embodiment, the user has highlighted the “PLOT RESULTS” option in the first window portion  602 . A plurality of plotting options  1608 , and a visual plot  1609  of the results, are provided in a second window portion  1606 . 
     FIG. 17  is a representative menu  1700  of the menu-based input program for presenting resulting of previously computed analyses. In this embodiment, the user has highlighted the “EXISTING ANALYSES” option in the first window portion  602 . A plurality of previously determined analysis results  1708  are provided in a second window portion  1706 . The menu  1700  allows the user to easily and efficiently review previously determined results. 
     FIG. 12  is a schematic view of a web-based system  1200  for calculating stress intensity solutions for integrally stiffened panels in accordance with another embodiment of the present invention. The web-based system  1200  includes a plurality of servers  1202 , each server  1202  adapted to run Windows-based software programs. An application service  1204  is operating on each server  1202  and is adapted to monitor a queue  1206  of each server  1202  and to communicate with other application services  1204  of other servers  1202  via a communication link  1208 , such as a web, a global computer communication system (i.e., Internet), a wireless link, or any other suitable communication device. A plurality of clients  1212  communicate with one or more of the servers  1202  via another communication link  1214  (e.g., a web, a global computer communication system, a wireless link, etc.) to provide suitable inputs to initiate a job on one or more of the servers  1202 . In some embodiments, the communications links  1210 ,  1214  are portions of a single communication network. 
   In operation, one of the clients  1212  may provide the necessary inputs for the problem definition  102  of the method  100  ( FIG. 1 ), and communicate this information to one of the application services  124 . The application service  1204  may check the status of the queue  1206  associated with its particular server  1202 , and if adequate resources exist to perform the requested computation, an application  1216  is generated on the server  1202  to compute a stress intensity solution. Depending upon the size of the applications  1216  and the capacity of the server  1202 , one or more applications  1216  may run on any given server  1202 . If the application service  1204  determines, however, that there are insufficient resources to perform the requested computation on a particular server  1202 , then the application service  1204  may perform a load balancing function by checking the resource availability on other servers  1202 . If another server  1202  has capacity to handle a particular application  1216 , the application service  1204  may pass the application  1216  to that server  1202 . Alternately, if none of the servers  1202  have the capacity to handle that particular application  1216 , then the application service  1204  may store the application  1216  in a queue  1206  to await the availability of adequate resources needed to perform the computation. The applications services  1204  may be further adapted to provide status information back to the clients  1212  indicating the location, status, and progress of each application  1216  of the system  1200 . The application services  1204  may be adapted to perform the above-referenced tasks without input from the clients  1212 , or alternately, may solicit and receive instructions from the clients  1212  regarding the load balancing or other functions. 
   Embodiments of methods and systems in accordance with the present invention may provide significant advantage over the prior art. For example, the entire process may be processed over the world wide web or a company intranet. No local software installation is required beyond a standard web interface (e.g., MS Internet Explorer or Netscape). Additionally, since the process of building a finite element model, extracting a stress intensity solution, and validating the results is highly automated, a user does not need to be a finite element expert or damage tolerance expert to perform the desired stress intensity computations. Building a relatively sophisticated finite element model requires only that a user enter a cross-sectional geometry of a structural member to be analyzed (e.g., panel) and to input the desired cracked lengths for which stress intensities are desired. Thus, embodiments of the present invention enable the user to access a single computational tool that will generate stress intensity solutions for structures, including integrally stiffened panels, for use in calculating the crack growth rate and residual strength using any suitable damage tolerance analysis software without requiring the user to become proficient in the operation of any finite element modeling tools. 
   While preferred and alternate embodiments of the invention have been illustrated and described, as noted above, many changes can be made without departing from the spirit and scope of the invention. Accordingly, the scope of the invention is not limited by the disclosure of these preferred and alternate embodiments. Instead, the invention should be determined entirely by reference to the claims that follow.