CN110837707A - Finite element analysis system, finite element analysis method, computer equipment and storage medium - Google Patents
Finite element analysis system, finite element analysis method, computer equipment and storage medium Download PDFInfo
- Publication number
- CN110837707A CN110837707A CN201911067815.0A CN201911067815A CN110837707A CN 110837707 A CN110837707 A CN 110837707A CN 201911067815 A CN201911067815 A CN 201911067815A CN 110837707 A CN110837707 A CN 110837707A
- Authority
- CN
- China
- Prior art keywords
- module
- finite element
- grid
- target
- element analysis
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
Images
Landscapes
- Management, Administration, Business Operations System, And Electronic Commerce (AREA)
Abstract
The embodiment of the invention discloses a finite element analysis system, a finite element analysis method, computer equipment and a storage medium, wherein the system comprises a module combination module, a module grid processing module, a simulation condition setting module, a physical solving module and a post-processing module which are connected through communication; the module combination module is used for defining and combining modules; the module grid processing module is used for carrying out subdivision processing on the module according to at least two sets of grid control parameters to obtain at least two sets of grids to be processed; the simulation condition setting module is used for setting simulation environment parameters; the physical solving module is used for combining the at least two sets of meshes to be processed into a set of target meshes and solving according to the simulation environment parameters by using a finite element analysis method; and the post-processing module is used for processing the solving result of the physical solving module to obtain the target engineering parameters. The technical scheme of the embodiment of the invention can improve the efficiency and the performance of finite element analysis.
Description
Technical Field
The embodiment of the invention relates to the technical field of finite elements, in particular to a finite element analysis system, a finite element analysis method, computer equipment and a storage medium.
Background
Finite element analysis techniques are used extensively in engineering design and product performance analysis. Wherein, the model, the grid and the solver are necessary conditions in the finite element analysis technology.
In the prior art, no matter how many modules a model contains, only one set of meshes can be used in a finite element analysis application. By a set of grids is meant nodes, cells and boundaries that are consistently described by a grid file, which together may completely fill all modules in the model. For example, the mesh file generated by the mesh generation software Gmsh contains: head, nodes, elements and boundary elements described by the four files can be combined together to fill all modules in the model.
In the process of implementing the invention, the inventor finds that the prior art has the following defects: in the finite element analysis technology, if only one set of mesh can be adopted for a model, the operation of setting and modifying simulation conditions (including controlling the density of the mesh, setting material parameters, boundary conditions and the like) is complex, the mesh generation time is long, the number of units generated in the mesh generation process is difficult to estimate, and in sum, the efficiency and the performance of finite element analysis on the model by adopting one set of mesh are low.
Disclosure of Invention
The embodiment of the invention provides a finite element analysis system, a finite element analysis method, computer equipment and a storage medium, which are used for improving the efficiency and the performance of finite element analysis.
In a first aspect, an embodiment of the present invention provides a finite element analysis system, including a module combination module, a module grid processing module, a simulation condition setting module, a physical solving module, and a post-processing module; the module combination module, the module grid processing module, the simulation condition setting module, the physical solving module and the post-processing module are in communication connection through an interface program;
the module combination module is used for defining and combining modules;
the module grid processing module is used for carrying out subdivision processing on the module according to at least two sets of grid control parameters to obtain at least two sets of grids to be processed;
the simulation condition setting module is used for setting simulation environment parameters;
the physical solving module is used for combining the at least two sets of grids to be processed into a set of target grids and solving the target grids according to the simulation environment parameters by using a preset finite element analysis method;
and the post-processing module is used for processing the solving result of the physical solving module to obtain the target engineering parameters.
In a second aspect, an embodiment of the present invention further provides a finite element analysis method, including:
defining and combining modules;
carrying out subdivision processing on the module according to at least two sets of grid control parameters to obtain at least two sets of grids to be processed;
combining the at least two sets of meshes to be processed into a set of target meshes, and solving the target meshes according to the set simulation environment parameters by using a preset finite element analysis method;
and processing the solving result to obtain the target engineering parameters.
In a third aspect, an embodiment of the present invention further provides a computer device, where the computer device includes:
one or more processors;
storage means for storing one or more programs;
when executed by the one or more processors, cause the one or more processors to implement a finite element analysis method as provided by any of the embodiments of the present invention.
In a fourth aspect, an embodiment of the present invention further provides a computer storage medium, on which a computer program is stored, where the computer program, when executed by a processor, implements the finite element analysis method provided in any embodiment of the present invention.
The embodiment of the invention defines and combines modules through the provided finite element analysis system, subdivides the combined modules according to at least two sets of grid control parameters to obtain at least two sets of grids to be processed, then combines the at least two sets of grids to be processed into a set of target grid, solves the target grid according to the set simulation environment parameters by using a preset finite element analysis method, and finally processes the solved result to obtain target engineering parameters.
Drawings
FIG. 1 is a schematic structural diagram of a finite element analysis system according to an embodiment of the present invention;
FIG. 2 is a flow chart of a finite element analysis method according to a second embodiment of the present invention;
fig. 3 is a schematic structural diagram of a computer device according to a third embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and examples. It is to be understood that the specific embodiments described herein are merely illustrative of the invention and are not limiting of the invention.
It should be further noted that, for the convenience of description, only some but not all of the relevant aspects of the present invention are shown in the drawings. Before discussing exemplary embodiments in more detail, it should be noted that some exemplary embodiments are described as processes or methods depicted as flowcharts. Although a flowchart may describe the operations (or steps) as a sequential process, many of the operations can be performed in parallel, concurrently or simultaneously. In addition, the order of the operations may be re-arranged. The process may be terminated when its operations are completed, but may have additional steps not included in the figure. The processes may correspond to methods, functions, procedures, subroutines, and the like.
It should be noted that there are many types of finite element analysis systems in the prior art, such as CAE (computer aided Engineering), ANSYS, or hypertorks, for example. The finite element analysis system provided by the embodiment of the invention can be functionally expanded on the basis of the existing finite element analysis system, and a user can use the finite element analysis system provided by the embodiment of the invention to analyze in combination with actual engineering problems. Because the finite element analysis system provided by the embodiment of the invention no longer limits the model to only provide one set of grids for analysis, the operation of setting and modifying simulation conditions is simplified. For example, setting a certain boundary Condition (Condition type) for a certain boundary surface (Face), the existing finite element analysis system must click the Face with a mouse or by other methods. If the module is before being synthesized into the model through Boolean operation, any Face can be pointed by a mouse without any effort; but this click operation is very complex to perform if the modules are synthesized into a model. The finite element analysis system provided by the embodiment of the invention can effectively solve the defects, so that the finite element analysis system has good user operation experience. In addition, in the existing finite element analysis system, the problem that the mesh generation time is too long and the number of units generated in the mesh generation process is difficult to estimate only by using one set of meshes is caused by a model. The finite element analysis system provided by the embodiment of the invention is not limited to adopt one set of mesh generation module any more, so that the mesh number in the finite element analysis process and the time consumption in the mesh generation process can be accurately estimated. For the solution of the problem of determining the engineering type, the time consumption of the solution process can be estimated on the premise of determining the grid number, so that the time consumption of the whole simulation process can be estimated. Therefore, the finite element analysis system provided by the embodiment of the invention has higher analysis efficiency and performance.
Example one
Fig. 1 is a schematic structural diagram of a finite element analysis system according to an embodiment of the present invention, and as shown in fig. 1, the finite element analysis system structurally includes: the simulation system comprises a module combination module 10, a module grid processing module 20, a simulation condition setting module 30, a physical solving module 40 and a post-processing module 50; the module combination module 10, the module grid processing module 20, the simulation condition setting module 30, the physical solving module 40 and the post-processing module 50 are in communication connection through an interface program; the module combination module 10 is used to define and combine modules; the module grid processing module 20 is used for performing subdivision processing on the module according to at least two sets of grid control parameters to obtain at least two sets of grids to be processed; the simulation condition setting module 30 is used for setting simulation environment parameters; the physical solving module 40 is configured to combine the at least two sets of meshes to be processed into a set of target meshes, and solve the target meshes according to the simulation environment parameters by using a preset finite element analysis method; the post-processing module 50 is configured to process the solving result of the physical solving module 40 to obtain the target engineering parameter.
In an embodiment of the present invention, the finite element analysis system may include a module combination module 10, a module grid processing module 20, a simulation condition setting module 30, a physical solving module 40, and a post-processing module 50, which are connected to each other by an interface program, wherein:
the module combination module 10 can be used for combining and assembling geometric primitives in a finite element analysis system to form a module meeting requirements. It should be noted that a geometric primitive can be used alone as an independent module. Considering that the number of modules directly affects the memory usage of the system, the frequent use of memory across sectors can be reduced by redefining and assembling multiple geometric primitives into modules. In embodiments of the invention, a module may be a "small model" formed from a combination of multiple geometric primitives.
In an alternative embodiment of the present invention, the module combination module 10 is specifically configured to: redefining and combining the modules by utilizing at least one parameterized geometric primitive and a preset module operation method; the preset module operation method comprises a Boolean operation method.
Specifically, in the embodiment of the present invention, at least one parameterized geometric primitive may be subjected to boolean operations to form a module. It should be noted that, in the finite element system, various boolean operations can be used in the process of combining geometric primitives into modules, but only boolean additions can be used in the process of combining modules into models. The model is formed by the module through Boolean addition to determine the structural characteristics of the finite element system algorithm and also determine the structural characteristics related to grid control, material parameters and boundary condition setting in the finite element analysis system.
The module grid processing module 20 can be used for subdividing the module formed by recombining and assembling according to a plurality of sets of grid control parameters on the premise of keeping the grid unit not to cross the module interface, thereby obtaining a plurality of sets of different grids to be processed.
In an alternative embodiment of the invention, the mesh control parameters may include a reference mesh size, a coarsest mesh size, a finest mesh size, and a minimum number of nodes per edge. The modular grid processing module 20 is specifically configured to: and subdividing the module and the associated interface of the module according to the grid control parameters.
The grid control parameters may be related parameters for performing grid generation on the module, and may be defined according to actual requirements. The associated interfaces may be all interfaces between the module and other modules.
In the embodiment of the present invention, when the module mesh processing module 20 performs mesh subdivision on the module, mesh subdivision can be performed on each module according to different mesh control parameters. Specifically, the modules and their associated interfaces may be subdivided. For example, assuming that Module _ i represents the ith Module, when segmenting Module _ i, the segmentation may be performed according to Fragment (Module _ i, BFace _ ij, BFace _ ik, …). And BFace _ ij represents the interface between the ith module and the jth module, and BFace _ ik represents the interface between the ith module and the kth module. Fragment () is a geometric function embedded in a mesh generation software. After the module is subdivided by using mesh subdividers such as Gmsh and Hypermesh, a plurality of sets of different meshes to be processed can be obtained.
The simulation condition setting module 30 may be configured to set simulation environment parameters according to the engineering problem to be processed. For example, the simulation environment parameters may include, but are not limited to, temperature, humidity, hardness, and the like, and may be specifically set according to actual requirements of engineering issues, and the specific type and content of the simulation environment parameters are not limited in the embodiments of the present invention.
The physical solving module 40 may be configured to combine the at least two sets of meshes to be processed into a set of target meshes, and solve the target meshes according to the simulation environment parameters by using a preset finite element analysis method.
The target grid is a set of grid formed by combining and assembling at least two sets of grids to be processed. The preset finite element analysis method is various available finite element analysis methods in the prior art, and the specific content of the preset finite element analysis method is not limited in the embodiment of the present invention. The physical solving module 40 may be an algorithm engine.
It should be noted that the finite element analysis system provided in the embodiment of the present invention performs subdivision processing on a module to obtain at least two sets of meshes to be processed, and combines the at least two sets of meshes to be processed into a set of target meshes, which is invisible to a user and is automatically completed inside a system background. That is, when the user performs data analysis using the finite element analysis system provided in the embodiment of the present invention, the module mesh generation result presented to the user by the system is only one set of target mesh. Therefore, the finite element analysis system provided by the embodiment of the invention can independently carry out a set of mesh subdivision on each module of the complex model, and can realize independent setting of material properties and boundary conditions, thereby effectively improving the user experience of the finite element analysis system.
In addition, it should be noted that, if the model is simple, the module can be further subdivided according to a set of grid control parameters to obtain a set of grids to be processed. At this time, the physical solving module 40 in the finite element analysis system does not need to combine the obtained set of to-be-processed grids, and can directly perform subsequent processing and analysis by using the obtained to-be-processed grids as target grids.
In an alternative embodiment of the present invention, the physical solving module 40 includes a system variable definition unit 410, the system variable definition module unit 410 is configured to: and deleting the sparse grid variable on the correlation interface of the module, and reserving the dense grid variable.
In an embodiment of the present invention, the finite element variables in the finite element analysis system are defined at the edges of each element. Specifically, the physical solving module 40 may delete the sparse grid variables on the association interface of the module and retain the dense grid variables by using the system variable defining unit 410. The benefits of this arrangement are: the accuracy of module data analysis processing can be improved.
In an optional embodiment of the present invention, the physical solving module 40 is specifically configured to: sorting the parameterized geometric primitives and the association interface of the module according to the appearance sequence of the parameterized geometric primitives in the process of combining the parameterized geometric primitives into the module; sequencing the nodes and the units according to the sequence of the association interface; sorting the edges according to the sorting result of the units; and combining the at least two sets of grids to be processed into a set of target grids according to the sequencing result.
In the embodiment of the present invention, when the physical solving module 40 combines at least two sets of grids to be processed into a set of target grids, the parameterized geometric primitives and the associated interfaces of the modules may be sorted according to the occurrence sequence of the parameterized geometric primitives in the process of combining into the modules, then the nodes and the units are sorted according to the sequence of the associated interfaces, then the edges are sorted according to the sorting result of the units, and finally at least two sets of grids to be processed are combined into a set of target grids according to the sorting result.
Specifically, the parameterized geometric primitives are sequenced and numbered according to the sequence of the parameterized geometric primitives appearing in Boolean operation when the parameterized geometric primitives are combined into modules. And then, sequencing and numbering the association interfaces of the modules according to the serial numbers of the modules. Then, the nodes may be ordered and numbered, and specifically, the interface BFace _ ij may be used as a reference: in a Module Module _ i, increasing the number of nodes in the sequence from far to near; in the Module _ j, the node numbers are incremented in the order from far to near. The arrangement principle can enable the serial number of the node number to be generally increased along the interface, thereby avoiding reading and writing the memory across the sector to the maximum extent. After the nodes are sorted, the units can be sorted and numbered according to the same principle as the node sorting. Note that the cell-to-interface distance is defined as the average distance from all the nodes of the cell to the interface. And finally, sequencing the edges in a unit number accumulation mode. After the sorting of the elements is completed, the finite element analysis system can combine at least two sets of grids to be processed into a set of target grids according to the sorting results.
For example, after the sequencing of each element is completed, assuming that one set of to-be-processed grids of the module 1 includes the node 1, the node 2, and the node 3, and the other set of to-be-processed grids includes the node 4 and the node 5, after the to-be-processed grids of the module 1 are combined, the nodes in the target grid corresponding to the module 1 are: node 1, node 2, node 3, node 4, and node 5. It should be noted that if the module has an associated interface, the dense grid can be retained and the sparse grid can be omitted.
In an optional embodiment of the present invention, the physical solving module 40 may further include a system matrix assembling unit 420, where the system matrix assembling unit 420 is configured to: transforming the control equation set of the finite element unit according to a matrix marking method to obtain a target transformation equation set; and if the first unknown number included in the target conversion equation set on the coarse grid side of the interface of the finite element unit is determined to be from the element object on the interface, interpolating the first unknown number according to a set interpolation mode by adopting a second unknown number included in the target conversion equation set on the fine grid side of the interface of the finite element unit.
The target conversion equation set may be an equation set obtained by transforming a control equation set of the finite element unit according to a matrix labeling method. The first unknowns may be unknowns included in the set of target conversion equations on the coarse mesh side of the interface of the finite element, and the second unknowns may be unknowns included in the set of target conversion equations on the fine mesh side of the interface of the finite element. The element object may be an element of a finite element, including but not limited to a node or an edge, etc. The interpolation setting mode can be an interpolation mode adopted according to the type of the finite element unit, and includes but is not limited to plane interpolation and three-dimensional interpolation.
In the embodiment of the present invention, after the physical solving module 40 is used to combine the grids to be processed into a set of target grids, the control equation sets of the units are required to be assembled into the whole system equation set. The physics solving module 40 can assemble the control equation set through the system matrix assembling unit 420. Specifically, the system matrix assembling unit 420 may transform the control equation set of the finite element unit according to a matrix labeling method, so as to obtain a target conversion equation set. And if the first unknown number included in the target conversion equation set on the coarse grid side of the interface of the finite element unit is determined to be from the element object on the interface, determining an interpolation mode according to the type of the finite element unit by adopting the second unknown number included in the target conversion equation set on the fine grid side of the interface of the finite element unit, and interpolating the first unknown number according to the determined interpolation mode.
In an optional embodiment of the invention, the finite element elements are node finite element elements; the set interpolation mode is a plane interpolation mode; the system matrix assembling unit 420 is specifically configured to: taking the unknown number of the node to be interpolated on one side of the coarse grid as the first unknown number, and taking the unknown number of the target interpolation node on one side of the fine grid as the second unknown number; and interpolating the unknown number of the node to be interpolated in a plane interpolation mode by adopting the unknown number of the target interpolation node included in the target conversion equation set on the fine grid side of the interface of the finite element unit.
Correspondingly, if the type of the finite element is a node finite element, the interpolation mode can be a planar interpolation mode. The system matrix assembling unit 420 may use the unknown number of the node to be interpolated on one side of the coarse grid as a first unknown number, and use the unknown number of the target interpolation node on one side of the fine grid as a second unknown number; and interpolating the unknown number of the node to be interpolated in a plane interpolation mode by adopting the unknown number of the target interpolation node included in the target conversion equation set on the fine grid side of the interface of the finite element unit.
In an optional embodiment of the invention, the finite element is a vector finite element; the set interpolation mode is a three-dimensional interpolation mode; the system matrix assembling unit 420 is specifically configured to: taking the unknown number of the edge to be interpolated on one side of the coarse grid as the first unknown number, and taking the unknown number of the target interpolation edge on one side of the fine grid as the second unknown number; and interpolating the unknown number of the edge to be interpolated in a plane interpolation mode by adopting the unknown number of the target interpolation edge included in the target conversion equation set on the fine grid side of the interface of the finite element unit.
Correspondingly, if the type of the finite element is a vector finite element, the interpolation mode can be a three-dimensional interpolation mode. The system matrix assembling unit 420 may use the unknown number of the edge to be interpolated on one side of the coarse grid as a first unknown number, and use the unknown number of the target interpolation edge on one side of the fine grid as a second unknown number; and interpolating the unknown number of the edge to be interpolated according to a plane interpolation mode by adopting the unknown number of the target interpolation edge included in the target conversion equation set on one side of the fine grid of the interface of the finite element unit.
In a specific example, let f (V) be 0, and V be a vector. For the electromagnetic field microwave equation, f is the Maxwell equation and V represents the electric field vector. Assuming that the unknown vector at any point in the finite element e is V _ e, the interpolation expression of the i component can be written as:
v_e(i)＝sum(n,v_e(n)*fai(n,i))
where sum (n,) represents the sum over all edges of the cell, fai (n, i) represents the vector interpolation function, v _ e (n) represents the unknown vector, and i represents the coordinate component.
Thus, the system of control equations for finite element e can be written as:
Integrating(fai(m,1)*f(sum(n,v_e(n)*fai(n,1)))+fai(m,2)*f(sum(n,v_e(n)*fai(n,2)))+fai(m,3)*f(sum(n,v_e(n)*fai(n,3))))＝0
where m represents an edge in the finite element e, and fai (m,) represents the interpolation function. Expanding the control equation set of the finite element unit e in detail, and introducing a matrix marking method to transform the control equation set of the finite element unit e to obtain a target conversion equation set:
AeXe＝Be
where Ae represents the coefficient matrix of the finite element e, Xe represents the vector of unknowns for the finite element e, and Be represents the sum of other terms of the finite element e that do not contain unknowns.
After the target conversion equation set is obtained, the target conversion equation set can be assembled to the whole system equation set. In the system matrix assembling process, the most critical step is how to assemble the cell equation on one side of the interface coarse grid.
Specifically, if the finite element unit is a node finite element unit and the unknown number of the target transformation equation set on the interface coarse grid side comes from a node on the interface, the unknown number on the interface fine grid side is used for interpolation. The interpolation mode can be plane interpolation, that is, the unknown number on the node of the plane unit on which the point to be interpolated falls is used for interpolation. Unlike conventional nodal finite element elements, vector finite element elements must be interpolated with all edges of the three-dimensional element. That is, if the finite element unit is a node finite element unit, a three-dimensional interpolation mode is adopted to replace a two-dimensional interpolation mode, and an edge is adopted to replace a node for interpolation.
The post-processing module 50 may be configured to process the solution result of the physical solution module 40 to obtain the target engineering parameter.
The target engineering parameter may be an engineering parameter obtained by processing a solution result obtained by a mathematical method.
In the embodiment of the present invention, the physical solving module 40 in the finite element analysis system solves the target mesh according to the simulation environment parameters by using the preset finite element analysis method, and the obtained solving result is only one numerical value. Therefore, the post-processing module 50 is further required to process the solving result of the physical solving module 40 according to the simulation environment parameter information, so as to obtain the final target engineering parameters.
It should be noted that, in addition to the functional modules described above, the finite element analysis system provided in the embodiment of the present invention may further include a visualization module. The main function of the visualization module is to provide visualization functions for users, such as an interactive interface for providing visualization control.
In the embodiment of the invention, the finite element analysis system can be quickly realized by utilizing the existing open source resources. In particular, the finite element analysis system may employ, but is not limited to, partial open source resources based on the LGPL protocol: the method comprises the steps of a development platform FreeCAD based on parametric geometric modeling, a multi-physics solver Elmer, a mesh dissector Gmsh, a visualization toolkit VTK and the like. In developing the finite element analysis system, the interactive interface and corresponding daemon supporting the module assembly 10 can be developed on the basis of FreeCAD. A mesh control interactive interface supporting the module mesh processing module 20 and an interface program connecting the mesh control file and the mesh dissector Gmsh may be developed on the basis of FreeCAD. The marking method of system grids and variables of Elmer may be modified to implement the function of combining at least two sets of grids to be processed into one set of target grids and system variable definition unit 410. In addition, the assembly process from the unit matrix to the system matrix in the Elmer can be modified, and a system equation set is formed through interface interpolation, so that the function of the system matrix assembly unit 420 is realized. Further, an interactive interface for setting simulation conditions and an interface program for connecting the simulation condition file and the solver elmersover may be developed to implement the function of the simulation condition setting module 30. And an interactive interface for performing visual control, an interface program for connecting the view operation control file with the graphic display tool kit VTK and the like can be developed.
The embodiment of the invention defines and combines modules through the provided finite element analysis system, subdivides the combined modules according to at least two sets of grid control parameters to obtain at least two sets of grids to be processed, then combines the at least two sets of grids to be processed into a set of target grid, solves the target grid according to the set simulation environment parameters by using a preset finite element analysis method, and finally processes the solved result to obtain target engineering parameters.
Example two
Fig. 2 is a flowchart of a finite element analysis method according to a second embodiment of the present invention, where the present embodiment is applicable to a finite element analysis system that uses multiple sets of mesh partitioning modules and performs finite element analysis, the method may be performed by the finite element analysis system, and the system may be implemented by software and/or hardware, and may be generally integrated in a computer device. Accordingly, as shown in fig. 2, the method includes the following operations:
and S110, defining and combining the modules.
In the embodiment of the invention, the geometric primitives can be combined and assembled through a finite element analysis system to form a module meeting the requirement. It should be noted that a geometric primitive can be used alone as an independent module. Considering that the number of modules directly affects the memory footprint, the frequent use of memory across sectors can be reduced by redefining and assembling multiple geometric primitives into modules. In embodiments of the invention, a module may be a "small model" formed from a combination of multiple geometric primitives.
In an alternative embodiment of the invention, the finite element analysis system may redefine and combine the modules using at least one parameterized geometric primitive and a predetermined modular algorithm; the preset module operation method comprises a Boolean operation method.
Specifically, in the embodiment of the present invention, the finite element analysis system may perform boolean operations on at least one parameterized geometric primitive to form a module. It should be noted that, in the finite element system, various boolean operations can be used in the process of combining geometric primitives into modules, but only boolean additions can be used in the process of combining modules into models. The model is formed by the module through Boolean addition to determine the structural characteristics of the finite element system algorithm and also determine the structural characteristics related to grid control, material parameters and boundary condition setting in the finite element analysis system.
And S120, performing subdivision processing on the module according to at least two sets of grid control parameters to obtain at least two sets of grids to be processed.
Correspondingly, after the module combination is completed, the finite element analysis system can divide the module formed by the recombination and assembly according to a plurality of sets of grid control parameters on the premise of keeping the grid unit not to cross over the module interface, thereby obtaining a plurality of sets of different grids to be processed.
In an alternative embodiment of the invention, the mesh control parameters may include a reference mesh size, a coarsest mesh size, a finest mesh size, and a minimum number of nodes per edge. The finite element analysis system can divide the module and the associated interface of the module according to the grid control parameters.
The grid control parameters may be related parameters for performing grid generation on the module, and may be defined according to actual requirements. The associated interfaces may be all interfaces between the module and other modules.
In the embodiment of the invention, when the finite element analysis system carries out mesh subdivision on the modules, the mesh subdivision can be carried out on each module according to different mesh control parameters. Specifically, the modules and the associated interfaces of the modules can be subdivided according to the method. For example, assuming that Module _ i represents the ith Module, when segmenting Module _ i, the segmentation may be performed according to Fragment (Module _ i, BFace _ ij, BFace _ ik, …). And BFace _ ij represents the interface between the ith module and the jth module, and BFace _ ik represents the interface between the ith module and the kth module. Fragment () is a geometric function embedded in a mesh generation software. And after the segmentation of the module is completed by utilizing Fragment (), a plurality of sets of different grids to be processed can be obtained.
S130, combining the at least two sets of grids to be processed into a set of target grids, and solving the target grids according to the set simulation environment parameters by using a preset finite element analysis method.
Specifically, the finite element analysis system may combine the at least two sets of meshes to be processed into a set of target meshes, and solve the target meshes according to the simulation environment parameters by using a preset finite element analysis method.
The target grid is a set of grid formed by combining and assembling at least two sets of grids to be processed. The preset finite element analysis method is various available finite element analysis methods in the prior art, and the specific content of the preset finite element analysis method is not limited in the embodiment of the present invention.
It should be noted that the finite element analysis system provided in the embodiment of the present invention performs subdivision processing on a module to obtain at least two sets of meshes to be processed, and combines the at least two sets of meshes to be processed into a set of target meshes, which is invisible to a user and is automatically completed inside a system background. That is, when the user performs data analysis using the finite element analysis system provided in the embodiment of the present invention, the module mesh generation result presented to the user by the system is only one set of target mesh. Therefore, the finite element analysis system provided by the embodiment of the invention can independently carry out a set of mesh subdivision on each module of the complex model, and can realize independent setting of material properties and boundary conditions, thereby effectively improving the user experience of the finite element analysis system.
In an optional embodiment of the present invention, when defining the system variable, the finite element analysis system may delete the sparse grid variable on the association interface of the module, and retain the dense grid variable.
In an embodiment of the present invention, the finite element variables in the finite element analysis system are defined at the edges of each element. Specifically, the sparse grid variables on the association interface of the module can be deleted, and the dense grid variables are reserved. The benefits of this arrangement are: the accuracy of module data analysis processing can be improved.
In an optional embodiment of the present invention, the finite element analysis system may sort the parameterized geometric primitives and the association interfaces of the modules according to the appearance order of the parameterized geometric primitives in the process of combining the parameterized geometric primitives into the modules; sequencing the nodes and the units according to the sequence of the association interface; sorting the edges according to the sorting result of the units; and combining the at least two sets of grids to be processed into a set of target grids according to the sequencing result.
In the embodiment of the invention, when the finite element analysis system combines at least two sets of grids to be processed into a set of target grids, the parameterized geometric primitives and the associated interfaces of the modules can be firstly sequenced according to the occurrence sequence of the parameterized geometric primitives in the process of combining the parameterized geometric primitives into the modules, then the nodes and the units are sequenced according to the sequence of the associated interfaces, then the edges are sequenced according to the sequencing result of the units, and finally at least two sets of grids to be processed are combined into a set of target grids according to the sequencing result.
Specifically, the parameterized geometric primitives are sequenced and numbered according to the sequence of the parameterized geometric primitives appearing in Boolean operation when the parameterized geometric primitives are combined into modules. And then, sequencing and numbering the association interfaces of the modules according to the serial numbers of the modules. Then, the nodes may be ordered and numbered, and specifically, the interface BFace _ ij may be used as a reference: in a Module Module _ i, increasing the number of nodes in the sequence from far to near; in the Module _ j, the node numbers are incremented in the order from far to near. The arrangement principle can enable the serial number of the node number to be generally increased along the interface, thereby avoiding reading and writing the memory across the sector to the maximum extent. After the nodes are sorted, the units can be sorted and numbered according to the same principle as the node sorting. Note that the cell-to-interface distance is defined as the average distance from all the nodes of the cell to the interface. And finally, sequencing the edges in a unit number accumulation mode. After the sorting of the elements is completed, the finite element analysis system can combine at least two sets of grids to be processed into a set of target grids according to the sorting results.
For example, after the sequencing of each element is completed, assuming that one set of to-be-processed grids of the module 1 includes the node 1, the node 2, and the node 3, and the other set of to-be-processed grids includes the node 4 and the node 5, after the to-be-processed grids of the module 1 are combined, the nodes in the target grid corresponding to the module 1 are: node 1, node 2, node 3, node 4, and node 5. It should be noted that if the module has an associated interface, the dense grid can be retained and the sparse grid can be omitted.
In an optional embodiment of the present invention, the finite element analysis system may further transform the control equation set of the finite element unit according to a matrix labeling method to obtain a target transformation equation set; and if the first unknown number included in the target conversion equation set on the coarse grid side of the interface of the finite element unit is determined to be from the element object on the interface, interpolating the first unknown number according to a set interpolation mode by adopting a second unknown number included in the target conversion equation set on the fine grid side of the interface of the finite element unit.
The target conversion equation set may be an equation set obtained by transforming a control equation set of the finite element unit according to a matrix labeling method. The first unknowns may be unknowns included in the set of target conversion equations on the coarse mesh side of the interface of the finite element, and the second unknowns may be unknowns included in the set of target conversion equations on the fine mesh side of the interface of the finite element. The element object may be an element of a finite element, including but not limited to a node or an edge, etc. The interpolation setting mode can be an interpolation mode adopted according to the type of the finite element unit, and includes but is not limited to plane interpolation and three-dimensional interpolation.
In the embodiment of the invention, after the finite element analysis system combines the meshes to be processed into a set of target meshes, the control equation sets of the units are required to be assembled into the whole system equation set. Specifically, the control equation set of the finite element unit may be transformed according to a matrix labeling method, so as to obtain a target transformation equation set. And if the first unknown number included in the target conversion equation set on the coarse grid side of the interface of the finite element unit is determined to be from the element object on the interface, determining an interpolation mode according to the type of the finite element unit by adopting the second unknown number included in the target conversion equation set on the fine grid side of the interface of the finite element unit, and interpolating the first unknown number according to the determined interpolation mode.
In an optional embodiment of the invention, the finite element elements are node finite element elements; the set interpolation mode is a plane interpolation mode; the finite element analysis system can take the unknown number of the node to be interpolated on one side of the coarse grid as the first unknown number and take the unknown number of the target interpolation node on one side of the fine grid as the second unknown number; and interpolating the unknown number of the node to be interpolated in a plane interpolation mode by adopting the unknown number of the target interpolation node included in the target conversion equation set on the fine grid side of the interface of the finite element unit.
Correspondingly, if the type of the finite element is a node finite element, the interpolation mode can be a planar interpolation mode. The finite element analysis system can take the unknown number of the node to be interpolated on one side of the coarse grid as a first unknown number and take the unknown number of the target interpolation node on one side of the fine grid as a second unknown number; and interpolating the unknown number of the node to be interpolated in a plane interpolation mode by adopting the unknown number of the target interpolation node included in the target conversion equation set on the fine grid side of the interface of the finite element unit.
In an optional embodiment of the invention, the finite element is a vector finite element; the set interpolation mode is a three-dimensional interpolation mode; the finite element analysis system can take the unknown number of the edge to be interpolated on one side of the coarse mesh as the first unknown number and take the unknown number of the target interpolation edge on one side of the fine mesh as the second unknown number; and interpolating the unknown number of the edge to be interpolated in a plane interpolation mode by adopting the unknown number of the target interpolation edge included in the target conversion equation set on the fine grid side of the interface of the finite element unit.
Correspondingly, if the type of the finite element is a vector finite element, the interpolation mode can be a three-dimensional interpolation mode. The finite element analysis system can take the unknown number of the edge to be interpolated on one side of the coarse grid as a first unknown number and take the unknown number of the target interpolation edge on one side of the fine grid as a second unknown number; and interpolating the unknown number of the edge to be interpolated according to a plane interpolation mode by adopting the unknown number of the target interpolation edge included in the target conversion equation set on one side of the fine grid of the interface of the finite element unit.
In a specific example, let f (V) be 0, and V be a vector. For the electromagnetic field microwave equation, f is the Maxwell equation and V represents the electric field vector. Assuming that the unknown vector at any point in the finite element e is V _ e, the interpolation expression of the i component can be written as:
v_e(i)＝sum(n,v_e(n)*fai(n,i))
where sum (n,) represents the sum over all edges of the cell, fai (n, i) represents the vector interpolation function, v _ e (n) represents the unknown vector, and i represents the coordinate component.
Thus, the system of control equations for finite element e can be written as:
Integrating(fai(m,1)*f(sum(n,v_e(n)*fai(n,1)))+fai(m,2)*f(sum(n,v_e(n)*fai(n,2)))+fai(m,3)*f(sum(n,v_e(n)*fai(n,3))))＝0
where m represents an edge in the finite element e, and fai (m,) represents the interpolation function. Expanding the control equation set of the finite element unit e in detail, and introducing a matrix marking method to transform the control equation set of the finite element unit e to obtain a target conversion equation set:
AeXe＝Be
where Ae represents the coefficient matrix of the finite element e, Xe represents the vector of unknowns for the finite element e, and Be represents the sum of other terms of the finite element e that do not contain unknowns.
After the target conversion equation set is obtained, the target conversion equation set can be assembled to the whole system equation set. In the system matrix assembling process, the most critical step is how to assemble the cell equation on one side of the interface coarse grid.
Specifically, if the finite element unit is a node finite element unit and the unknown number of the target transformation equation set on the interface coarse grid side comes from a node on the interface, the unknown number on the interface fine grid side is used for interpolation. The interpolation mode can be plane interpolation, that is, the unknown number on the node of the plane unit on which the point to be interpolated falls is used for interpolation. Unlike conventional nodal finite element elements, vector finite element elements must be interpolated with all edges of the three-dimensional element. That is, if the finite element unit is a node finite element unit, a three-dimensional interpolation mode is adopted to replace a two-dimensional interpolation mode, and an edge is adopted to replace a node for interpolation.
The finite element analysis system can also set simulation environment parameters according to the engineering problem to be processed. For example, the simulation environment parameters may include, but are not limited to, temperature, humidity, hardness, and the like, and may be specifically set according to actual requirements of engineering issues, and the specific type and content of the simulation environment parameters are not limited in the embodiments of the present invention. Correspondingly, the finite element analysis system can utilize a preset finite element analysis method to solve the target grid according to the set simulation environment parameters.
And S140, processing the solving result to obtain the target engineering parameters.
The target engineering parameter may be an engineering parameter obtained by processing a solution result obtained by a mathematical method.
In the embodiment of the invention, the finite element analysis system utilizes the preset finite element analysis method to solve the target grid according to the simulation environment parameters, and the obtained solution result is only one numerical value. Therefore, the solution result needs to be processed according to the simulation environment parameter information, so as to obtain the final target engineering parameters.
It should be noted that, in addition to the above functions, the finite element analysis system provided by the embodiment of the present invention may also provide a visualization function for a user, such as an interactive interface providing visualization control.
The method comprises the steps of defining and combining modules, carrying out subdivision processing on the modules obtained by combination according to at least two sets of grid control parameters to obtain at least two sets of grids to be processed, combining the at least two sets of grids to be processed into a set of target grid, solving the target grid according to set simulation environment parameters by using a preset finite element analysis method, and processing a solving result to obtain target engineering parameters.
EXAMPLE III
Fig. 3 is a schematic structural diagram of a computer device according to a third embodiment of the present invention. FIG. 3 illustrates a block diagram of a computer device 312 suitable for use in implementing embodiments of the present invention. The computer device 312 shown in FIG. 3 is only an example and should not bring any limitations to the functionality or scope of use of embodiments of the present invention.
As shown in FIG. 3, computer device 312 is in the form of a general purpose computing device. The components of computer device 312 may include, but are not limited to: one or more processors 316, a storage device 328, and a bus 318 that couples the various system components including the storage device 328 and the processors 316.
The computer device 312 may also communicate with one or more external devices 314 (e.g., keyboard, pointing device, camera, display 324, etc.), with one or more devices that enable a user to interact with the computer device 312, and/or with any devices (e.g., network card, modem, etc.) that enable the computer device 312 to communicate with one or more other computing devices. Such communication may be through an Input/Output (I/O) interface 322. Also, computer device 312 may communicate with one or more networks (e.g., a Local Area Network (LAN), Wide Area Network (WAN), etc.) and/or a public Network, such as the internet, via Network adapter 320. As shown, network adapter 320 communicates with the other modules of computer device 312 via bus 318. It should be appreciated that although not shown in the figures, other hardware and/or software modules may be used in conjunction with the computer device 312, including but not limited to: microcode, device drivers, Redundant processing units, external disk drive arrays, disk array (RAID) systems, tape drives, and data backup storage systems, to name a few.
That is, the processing unit implements, when executing the program: defining and combining modules; carrying out subdivision processing on the module according to at least two sets of grid control parameters to obtain at least two sets of grids to be processed; combining the at least two sets of meshes to be processed into a set of target meshes, and solving the target meshes according to the set simulation environment parameters by using a preset finite element analysis method; and processing the solving result to obtain the target engineering parameters.
Example four
A fourth embodiment of the present invention further provides a computer storage medium storing a computer program, which when executed by a computer processor is configured to perform the finite element analysis method according to any one of the above embodiments of the present invention: defining and combining modules; carrying out subdivision processing on the module according to at least two sets of grid control parameters to obtain at least two sets of grids to be processed; combining the at least two sets of meshes to be processed into a set of target meshes, and solving the target meshes according to the set simulation environment parameters by using a preset finite element analysis method; and processing the solving result to obtain the target engineering parameters.
Computer storage media for embodiments of the invention may employ any combination of one or more computer-readable media. The computer readable medium may be a computer readable signal medium or a computer readable storage medium. A computer readable storage medium may be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination of the foregoing. More specific examples (a non-exhaustive list) of the computer readable storage medium would include the following: an electrical connection having one or more wires, a portable computer diskette, a hard disk, a Random Access Memory (RAM), a Read Only Memory (ROM), an Erasable Programmable Read Only Memory (EPROM) or flash Memory), an optical fiber, a portable compact disc Read Only Memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In the context of this document, a computer readable storage medium may be any tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device.
A computer readable signal medium may include a propagated data signal with computer readable program code embodied therein, for example, in baseband or as part of a carrier wave. Such a propagated data signal may take many forms, including, but not limited to, electro-magnetic, optical, or any suitable combination thereof. A computer readable signal medium may also be any computer readable medium that is not a computer readable storage medium and that can communicate, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device.
Program code embodied on a computer readable medium may be transmitted using any appropriate medium, including but not limited to wireless, wireline, optical fiber cable, Radio Frequency (RF), etc., or any suitable combination of the foregoing.
Computer program code for carrying out operations for aspects of the present invention may be written in any combination of one or more programming languages, including an object oriented programming language such as Java, Smalltalk, C + + or the like and conventional procedural programming languages, such as the "C" programming language or similar programming languages. The program code may execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the case of a remote computer, the remote computer may be connected to the user's computer through any type of network, including a Local Area Network (LAN) or a Wide Area Network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet service provider).
It is to be noted that the foregoing is only illustrative of the preferred embodiments of the present invention and the technical principles employed. It will be understood by those skilled in the art that the present invention is not limited to the particular embodiments described herein, but is capable of various obvious changes, rearrangements and substitutions as will now become apparent to those skilled in the art without departing from the scope of the invention. Therefore, although the present invention has been described in greater detail by the above embodiments, the present invention is not limited to the above embodiments, and may include other equivalent embodiments without departing from the spirit of the present invention, and the scope of the present invention is determined by the scope of the appended claims.
Claims (11)
1. A finite element analysis system is characterized by comprising a module combination module, a module grid processing module, a simulation condition setting module, a physical solving module and a post-processing module; the module combination module, the module grid processing module, the simulation condition setting module, the physical solving module and the post-processing module are in communication connection through an interface program;
the module combination module is used for defining and combining modules;
the module grid processing module is used for carrying out subdivision processing on the module according to at least two sets of grid control parameters to obtain at least two sets of grids to be processed;
the simulation condition setting module is used for setting simulation environment parameters;
the physical solving module is used for combining the at least two sets of grids to be processed into a set of target grids and solving the target grids according to the simulation environment parameters by using a preset finite element analysis method;
and the post-processing module is used for processing the solving result of the physical solving module to obtain the target engineering parameters.
2. The system of claim 1, wherein the module combination module is specifically configured to:
redefining and combining the modules by utilizing at least one parameterized geometric primitive and a preset module operation method;
the preset module operation method comprises a Boolean operation method.
3. The system of claim 1, wherein the grid control parameters include a reference grid size, a coarsest grid size, a finest grid size, and a minimum number of nodes per edge;
the module grid processing module is specifically configured to: and subdividing the module and the associated interface of the module according to the grid control parameters.
4. The system of claim 1, wherein the physical solving module comprises a system variable definition module unit to:
and deleting the sparse grid variable on the correlation interface of the module, and reserving the dense grid variable.
5. The system of claim 1, wherein the physical solving module is specifically configured to:
sorting the parameterized geometric primitives and the association interface of the module according to the appearance sequence of the parameterized geometric primitives in the process of combining the parameterized geometric primitives into the module;
sequencing the nodes and the units according to the sequence of the association interface;
sorting the edges according to the sorting result of the units;
and combining the at least two sets of grids to be processed into a set of target grids according to the sequencing result.
6. The system of claim 1, wherein the physical solution module comprises a system matrix assembly unit to:
transforming the control equation set of the finite element unit according to a matrix marking method to obtain a target transformation equation set;
and if the first unknown number included in the target conversion equation set on the coarse grid side of the interface of the finite element unit is determined to be from the element object on the interface, interpolating the first unknown number according to a set interpolation mode by adopting a second unknown number included in the target conversion equation set on the fine grid side of the interface of the finite element unit.
7. The system of claim 6, wherein the finite element elements are nodal finite element elements; the set interpolation mode is a plane interpolation mode;
the system matrix assembly unit is specifically configured to:
taking the unknown number of the node to be interpolated on one side of the coarse grid as the first unknown number, and taking the unknown number of the target interpolation node on one side of the fine grid as the second unknown number;
and interpolating the unknown number of the node to be interpolated in a plane interpolation mode by adopting the unknown number of the target interpolation node included in the target conversion equation set on the fine grid side of the interface of the finite element unit.
8. The system of claim 6, wherein the finite element is a vector finite element; the set interpolation mode is a three-dimensional interpolation mode;
the system matrix assembly unit is specifically configured to:
taking the unknown number of the edge to be interpolated on one side of the coarse grid as the first unknown number, and taking the unknown number of the target interpolation edge on one side of the fine grid as the second unknown number;
and interpolating the unknown number of the edge to be interpolated in a plane interpolation mode by adopting the unknown number of the target interpolation edge included in the target conversion equation set on the fine grid side of the interface of the finite element unit.
9. A finite element analysis method, comprising:
defining and combining modules;
carrying out subdivision processing on the module according to at least two sets of grid control parameters to obtain at least two sets of grids to be processed;
combining the at least two sets of meshes to be processed into a set of target meshes, and solving the target meshes according to the set simulation environment parameters by using a preset finite element analysis method;
and processing the solving result to obtain the target engineering parameters.
10. A computer device, characterized in that the computer device comprises:
one or more processors;
storage means for storing one or more programs;
when executed by the one or more processors, cause the one or more processors to implement the finite element analysis method of claim 9.
11. A computer storage medium having stored thereon a computer program, characterized in that the program, when being executed by a processor, implements a finite element analysis method according to claim 9.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201911067815.0A CN110837707B (en) | 2019-11-04 | 2019-11-04 | Finite element analysis system, method, computer equipment and storage medium |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201911067815.0A CN110837707B (en) | 2019-11-04 | 2019-11-04 | Finite element analysis system, method, computer equipment and storage medium |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN110837707A true CN110837707A (en) | 2020-02-25 |
| CN110837707B CN110837707B (en) | 2023-06-06 |
Family
ID=69576079
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201911067815.0A Active CN110837707B (en) | 2019-11-04 | 2019-11-04 | Finite element analysis system, method, computer equipment and storage medium |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN110837707B (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116205009A (en) * | 2023-05-05 | 2023-06-02 | 陕西空天信息技术有限公司 | Impeller model structure analysis method and device, electronic equipment and storage medium |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106557612A (en) * | 2016-10-18 | 2017-04-05 | 华南理工大学 | A kind of aeroperformance emulated computation method of process of truck wind-shielding |
| CN106980742A (en) * | 2017-05-09 | 2017-07-25 | 湖南天汽模汽车模具技术股份有限公司 | A kind of load projection mapping method that punch forming information is introduced to limit element artificial module |
| CN108229085A (en) * | 2018-04-12 | 2018-06-29 | 上海索辰信息科技有限公司 | computer simulation analysis system and method |
| CN109033501A (en) * | 2018-06-08 | 2018-12-18 | 昆明理工大学 | A kind of geometrical model modeling method of the solution domain dynamic evolution comprising rigid motion |
-
2019
- 2019-11-04 CN CN201911067815.0A patent/CN110837707B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106557612A (en) * | 2016-10-18 | 2017-04-05 | 华南理工大学 | A kind of aeroperformance emulated computation method of process of truck wind-shielding |
| CN106980742A (en) * | 2017-05-09 | 2017-07-25 | 湖南天汽模汽车模具技术股份有限公司 | A kind of load projection mapping method that punch forming information is introduced to limit element artificial module |
| CN108229085A (en) * | 2018-04-12 | 2018-06-29 | 上海索辰信息科技有限公司 | computer simulation analysis system and method |
| CN109033501A (en) * | 2018-06-08 | 2018-12-18 | 昆明理工大学 | A kind of geometrical model modeling method of the solution domain dynamic evolution comprising rigid motion |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116205009A (en) * | 2023-05-05 | 2023-06-02 | 陕西空天信息技术有限公司 | Impeller model structure analysis method and device, electronic equipment and storage medium |
Also Published As
| Publication number | Publication date |
|---|---|
| CN110837707B (en) | 2023-06-06 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| JP6787661B2 (en) | Simulation of machining of workpieces | |
| Kim et al. | Feature-based simplification of boundary representation models using sequential iterative volume decomposition | |
| Kiss et al. | Adaptive CAD model (re-) construction with THB-splines | |
| CN112669463B (en) | Method for reconstructing curved surface of three-dimensional point cloud, computer device and computer-readable storage medium | |
| CN107464286B (en) | Method, device, equipment and readable medium for repairing holes in three-dimensional city model | |
| JP2010518458A (en) | Case / partial differential expression based blanking technique and related accuracy evaluation | |
| US20150379769A1 (en) | Method and apparatus for mesh simplification | |
| Chen et al. | Triangulated manifold meshing method preserving molecular surface topology | |
| US20160239597A1 (en) | Apparatus and method for performing finite element computation | |
| CN113724401B (en) | Three-dimensional model cutting method and device, computer equipment and storage medium | |
| CA2868755A1 (en) | Updating a cad model to reflect global or local shape changes | |
| CN109388843B (en) | Visualization system and method of truss antenna based on VTK (virtual terminal K), and terminal | |
| US10943037B2 (en) | Generating a CAD model from a finite element mesh | |
| WO2021246931A1 (en) | Node for providing a simulation model, system for illustrating estimated fluid movements around a structure, methods therefore and a computer program product | |
| JP2018067124A (en) | Simulation program, simulation method and information processing apparatus | |
| Burczyński et al. | Intelligent optimal design of spatial structures | |
| CN110837707B (en) | Finite element analysis system, method, computer equipment and storage medium | |
| CN111583268A (en) | Point cloud virtual selection and cutting method, device and equipment | |
| CN110532670B (en) | Method and system for constructing spline entity model suitable for analysis | |
| Vincent et al. | Graph morphology in image analysis | |
| CN117975031A (en) | Feature line extraction method, device, electronic equipment and computer readable storage medium | |
| Fries | Higher-order accurate integration for cut elements with Chen-Babuška nodes | |
| EP2926244B1 (en) | Method and apparatus for creating 3d model | |
| JP4520822B2 (en) | Electromagnetic wave analysis apparatus, electromagnetic wave analysis method, and electromagnetic wave analysis program | |
| CN113987652A (en) | Wall model generation method and device |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |