Finite element analysis device and method considering mesh deformation, equipment and medium
By taking mesh deformation into consideration, the finite element analysis method solves the problem of insufficient calculation accuracy of small deformation theory in nuclear reactors, and achieves high-precision and stable fuel rod performance analysis, which is suitable for complex engineering design.
Patent Information
- Application Number
- CN202510993280.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-07-18
- Publication Date
- 2025-09-19
AI Technical Summary
The existing numerical analysis framework based on small deformation theory cannot accurately simulate the significant deformation and stress changes of fuel rods in nuclear reactors under high temperature, high pressure and high radiation environment, resulting in insufficient accuracy and reliability of the calculation results.
The finite element analysis method considering mesh deformation is adopted. By storing the undeformed and deformed meshes separately, using two sets of calculation systems for displacement problems and non-displacement problems, the displacement of mesh nodes is updated in real time, and the finite element data is recalculated in each time step to adapt to large deformation and nonlinear deformation conditions.
It improves the calculation accuracy and stability of fuel rod performance analysis, reduces repeated calculations, supports parallel computing, significantly shortens calculation time, and is suitable for complex engineering design.
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Figure CN120671474A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of finite element numerical analysis, and in particular to a finite element analysis device, method, equipment and medium taking mesh deformation into consideration. Background Art
[0002] Fuel rods are the core components of nuclear reactors. In-depth analysis and optimization of their performance is crucial for improving nuclear power generation efficiency and ensuring the long-term stable operation of nuclear power plants. In practical applications, fuel rods not only release chemical energy but also undergo complex structural responses, including thermal and mechanical stresses, material creep, and fatigue, which significantly impact their performance and lifespan. Therefore, accurate numerical simulation of the structural response of fuel rods is a crucial issue in nuclear power engineering.
[0003] The current reactor numerical development framework has developed a thermomechanical coupling module based on small deformation theory. However, this theory has certain limitations. During nuclear reactor operation, fuel rods experience high temperatures, high pressures, and high radiation. These extreme conditions can cause significant deformation and stress changes in the fuel rods. Small deformation theory cannot accurately capture the stress-strain characteristics under these large deformation conditions, thus affecting the accuracy and reliability of fuel performance analysis. Furthermore, large deformation problems are often accompanied by nonlinear material behavior, further increasing the complexity and difficulty of the calculations.
[0004] The above problems not only significantly increase the complexity of nuclear reactor calculations, but may also introduce additional errors, seriously affecting the accuracy and reliability of the calculation results.
[0005] To accurately simulate large deformation problems, mesh deformation must be considered. Mesh deformation refers to the changes in the positions of mesh nodes and the shapes of mesh elements as the physical system's state changes during finite element analysis. Accounting for these changes in the calculations allows for a more realistic reflection of the geometric and mechanical behavior of the physical system, improving the accuracy of the results. Summary of the Invention
[0006] The present invention provides a finite element analysis device, method, equipment and medium that considers grid deformation, so as to solve the problem that the existing numerical analysis framework based on small deformation theory cannot cope with the high-precision solution of complex working conditions of nuclear reactors.
[0007] The present invention is achieved through the following technical solutions: A first aspect of the present invention provides a finite element analysis device that takes mesh deformation into consideration, comprising: A deformation calculation module is used to create a deformation grid and a displacement problem object; the displacement problem object is used to record the geometric shape of the deformed grid at each calculation time step and the mechanical response data after deformation; An undeformed calculation module is used to create an original mesh and a non-displacement problem object; the non-displacement problem object is used to record the mechanical response data of the original mesh at each calculation time step, and the geometric shape of the original mesh does not deform during the calculation process; A finite element updating module, configured to calculate finite element data based on the mechanical response data of the deformed mesh or the mechanical response data of the original mesh at each calculation time step; A solver module is used for assembling and solving nonlinear mechanical equations based on the finite element data at each calculation time step; The deformation judgment module is used to select and transfer the mechanical response data of the deformed mesh or the mechanical response data of the original mesh to the finite element updating module.
[0008] In the above-mentioned solution of the present invention, two calculation systems, one for displacement problems and the other for non-displacement problems, are used by storing the undeformed and deformed meshes separately. The undeformed mesh serves as the reference mesh for the initial state, while the deformed mesh reflects the current geometric state of the structure in real time. When mesh deformation needs to be considered, the algorithm updates the displacements of the mesh nodes in real time at each time step based on the results of the solved mechanical equations, while simultaneously recalculating the finite element data in the displacement problem. When assembling discrete interfaces, the algorithm calls upon the updated finite element data to calculate the large deformation mechanical equations. When the problem is undeformed, the discrete interface assembly calls upon the undeformed mesh data. This solution takes into account the high-precision analysis requirements for fuel rods under extreme operating conditions, improves the accuracy and stability of the calculation results, avoids reduced calculation accuracy and failures due to mesh distortion, and expands solutions for similar problems.
[0009] In some embodiments, the deformation determination module is configured to: determine whether there is a deformation problem based on the geometric shape of the deformed mesh at each calculation time step; If it is a deformation problem, the mechanical response data of the deformed mesh is passed into the finite element update module; if it is a non-deformation problem, the mechanical response data of the original mesh is passed into the finite element update module.
[0010] In some embodiments, the deformation judgment module is configured to: determine whether it is a deformation problem based on specified parameters; if the specified parameters indicate a deformation problem, then pass the mechanical response parameters of the deformed mesh into the finite element update module; if the specified parameters indicate a non-deformation problem, then pass the mechanical response parameters of the original mesh into the finite element update module, and the specified parameters are passed in by the input card.
[0011] In some embodiments, the geometry of the deformed mesh at each computational time step is the node coordinates of the deformed mesh at the previous computational time step plus the node displacements; the node displacements are obtained by solving the nonlinear mechanical equations by the solver module.
[0012] In some embodiments, the finite element data includes a residual vector and a Jacobian matrix for assembling the nonlinear mechanical equations.
[0013] In some embodiments, the deformation calculation module is configured to: upon detecting a displacement variable name, copy an original mesh as a deformed mesh, and create a displacement problem object based on the deformed mesh; the displacement variable name is passed in via an input card.
[0014] In some embodiments, the solver module includes N parallel solver modules, the deformed grid is divided into N sub-regions, each parallel solver module solves one sub-region, and N≥2; The finite element analysis device further includes a memory module, which is used to allocate a storage area to each parallel solver; n The first part of the storage area will be n The displacement solutions of the parallel solvers are stored as entity data, and the latter part will be n The displacement solutions of parallel solvers other than the first parallel solver are stored as ghost data. .
[0015] A second aspect of the present invention provides a finite element analysis method considering mesh deformation, comprising: Copying the original mesh as the initial deformed mesh; wherein the geometry of the original mesh does not deform during the finite element analysis process, and the geometry of the deformed mesh is updated according to the node displacement at each calculation time step; The following steps are performed at each computational time step during the finite element analysis process: (1) updating the geometry of the deformed mesh based on the node displacements solved in the previous time step; (2) respectively calculating the mechanical response data of the original grid and the deformed grid at the current calculation time step; (3) Calculating finite element data based on the mechanical response data of the original mesh or the mechanical response data of the deformed mesh according to the problem type; the finite element data includes a residual vector and a Jacobian matrix for assembling nonlinear mechanical equations; (4) Assembling nonlinear mechanical equations based on the updated finite element data and solving the node displacements.
[0016] In some embodiments, the problem type includes a deformation problem type and a non-deformation problem type; and selecting, according to the problem type, to calculate finite element data based on the mechanical response data of the original mesh or the mechanical response data of the deformed mesh includes: Determining whether the problem is a deformation problem based on the geometric shape of the deformed mesh; If it is a deformation problem, the finite element data is calculated based on the mechanical response data of the deformed mesh; if it is a non-deformation problem, the finite element data is calculated based on the mechanical response data of the original mesh.
[0017] In some embodiments, the method further includes: when a displacement variable is detected to be input, creating a displacement problem object and a non-displacement problem object; the displacement problem object is used to record the geometric shape of the deformed mesh at each calculation time step and the mechanical response data after deformation, and the non-displacement problem object is used to record the mechanical response data of the original mesh at each calculation time step.
[0018] According to a third aspect of the present invention, an electronic device is provided, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the finite element analysis method considering mesh deformation as described in any one of the second aspects of the present invention is implemented.
[0019] According to a fourth aspect of the present invention, a computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the finite element analysis method considering mesh deformation as described in any one of the second aspects of the present invention is implemented.
[0020] Compared with the prior art, the present invention has the following advantages and beneficial effects: The system stores undeformed and deformed meshes separately, and runs two sets of finite element calculations, displacement and non-displacement, simultaneously. The two sets of calculation results are selectively called according to the problem type, adapting to various complex deformation modes, including nonlinear deformation, large displacement and large strain, ensuring stable operation under different deformation conditions. In displacement problems, the deformed mesh is updated in real time, and relevant data such as finite element shape functions and integration rules are recalculated based on the deformed mesh data. The Jacobian matrix and residual vector are assembled according to the deformed formula to improve the calculation accuracy and stability in large deformation problems.
[0021] By storing and processing the unshifted problem and the shifted problem separately, the algorithm reduces unnecessary repeated calculations and improves the overall calculation speed; It supports parallel computing and can run efficiently on multi-core processors or multiple computers, significantly shortening the calculation time of complex engineering problems. BRIEF DESCRIPTION OF THE DRAWINGS
[0022] In order to more clearly illustrate the technical solutions of the exemplary embodiments of the present invention, the following briefly introduces the drawings required for use in the examples. It should be understood that the following drawings only illustrate certain embodiments of the present invention and should not be considered as limiting the scope. A person of ordinary skill in the art can also derive other relevant drawings based on these drawings without inventive effort. In the drawings: Figure 1 is a block diagram of a finite element analysis device considering mesh deformation according to an embodiment of the present invention; Figure 2 is a schematic diagram of a global grid structure according to an embodiment of the present invention; Figure 3 is a flow chart of a finite element analysis method considering mesh deformation according to an embodiment of the present invention; Figure 4 Schematic diagram of a finite element mesh deformation algorithm process according to an embodiment of the present invention. DETAILED DESCRIPTION
[0023] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with examples and drawings. The exemplary embodiments of the present invention and their descriptions are only used to explain the present invention and are not intended to limit the present invention.
[0024] It should be noted that the terms "including" and "having" and any variations thereof in the specification and claims of the present invention and the above-mentioned drawings are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to or inherent to other steps or units of the device.
[0025] The terms used in the various embodiments of the present invention are only used for the purpose of describing specific embodiments and are not intended to limit the various embodiments of the present invention. As used herein, the singular form is intended to also include the plural form, unless the context clearly indicates otherwise. Unless otherwise specified, all terms used herein (including technical terms and scientific terms) have the same meaning as those commonly understood by those skilled in the art to which the various embodiments of the present invention belong. The terms (such as those defined in generally used dictionaries) will be interpreted as having the same meaning as the contextual meaning in the relevant technical field and will not be interpreted as having an idealized meaning or an overly formal meaning unless clearly defined in the various embodiments of the present invention.
[0026] Embodiments of the present invention provide a finite element analysis device, method, equipment, and medium that take mesh deformation into account. These devices are suitable for complex engineering designs in the field of mechanics, facilitate accurate simulation of the geometric changes and mechanical behavior of structures or materials during large deformation processes, and improve computational accuracy. They adapt to various complex deformation modes, including nonlinear deformation, large displacement, and large strain, ensuring stable operation under different deformation conditions.
[0027] To accurately simulate large deformation problems, this paper considers mesh deformation within the finite element numerical framework, storing and calculating displacement and non-displacement problems separately. Mesh deformation refers to the changes in the positions of mesh nodes and the shapes of mesh elements as the state of the physical system changes during finite element analysis. Incorporating these changes in the calculations allows for a more realistic reflection of the geometric and mechanical behavior of the physical system, improving the accuracy of the results.
[0028] See also Figure 1 , Figure 1 This is a block diagram of a finite element analysis device that considers mesh deformation, as proposed in an embodiment of the present invention. By storing and calculating the original and deformed meshes separately, this device can solve mechanical analysis problems in complex working conditions. The device is divided into a deformed calculation module 101, an undeformed calculation module 102, a finite element update module 103, a solver module 104, and a deformation determination module 105, based on computational functions.
[0029] Among them, the undeformed calculation module 102 is used to create the original mesh and non-displacement problem objects, and the deformed calculation module 101 is used to create the deformed mesh and displacement problem objects. The original mesh is also an undeformed mesh. The mesh does not deform during the calculation process. The mesh is used as a reference to describe the geometric and mechanical behavior of the structure or material in the initial state. The generation of the undeformed mesh can adopt existing mesh generation technologies, such as tetrahedral mesh, hexahedral mesh, etc. The mechanical behavior includes the initial geometric shape, material properties, boundary conditions and load conditions of the structure. The deformed mesh in the initial state is the same as the original mesh. A copy of the original mesh is stored in the deformation calculation module 101. As the solver iterates the calculation, the deformed mesh is updated according to the deformation of the structure in each calculation time step, that is, the deformation of the mesh in the calculation condition is taken into account. The mesh nodes and other information of the deformed mesh in the initial state inherit the original mesh, and describe the geometric and mechanical behavior of the structure or material after displacement in subsequent calculations.
[0030] A non-displacement problem object is created based on the original mesh. Users can define the non-displacement problem in the undeformed calculation module 102 according to analysis needs. The non-displacement problem object is used to record the mechanical response data based on the original mesh at each calculation time step. A displacement problem object is created based on the deformed mesh. Users can define the displacement problem in the deformed calculation module 101 according to analysis needs. The displacement problem object records the mechanical response of the structure or material after displacement at each calculation time step. Initially, the displacement problem is identical to the non-displacement problem, but it is continuously updated during subsequent calculations.
[0031] The program implementation logic for creating a displacement problem object is to create a process object DisplacedProblem that carries the deformation simulation problem after completing the initial work of the deformed mesh object in the finite element framework MeshCompletePluginLoader. This object includes the degree of freedom information of the deformed mesh unit, the finite element shape function information, the Gaussian integral data of the deformed unit, the value of the shape function and field variables at the unit integration point, etc.
[0032] In the framework, two sets of meshes and finite element problems are run, one undeformed and one deformed. Which one is used for subsequent calculations depends on whether the current working condition is a displacement problem.
[0033] The finite element update module 103 is used to calculate finite element data based on the mechanical response data of the deformed mesh or the mechanical response data of the original mesh at each calculation time step. The solver module 104 is used to assemble nonlinear mechanical equations and solve the displacement field based on the finite element data from the finite element update module 103 at each calculation time step.
[0034] In some embodiments, the finite element data includes residual vectors and Jacobian matrices for assembling nonlinear mechanical equations.
[0035] The deformation judgment module 105 is used to determine whether it is a displacement problem or a non-displacement problem, select whether to pass the mechanical response data of the deformed grid or the mechanical response data of the original grid into the finite element update module for calculation, and call which set of calculation data to assemble the nonlinear mechanical equations.
[0036] During the entire finite element analysis process, the entire analysis process is divided into multiple time steps for calculation. Within each calculation time step, the deformation and mechanical behavior of the structure or material are gradually solved. In the first calculation time step (at this time, the displacement is zero and the deformed mesh is the same as the original mesh), the assembly equations based on the undeformed mechanical response are solved, and a determination is made as to whether the deformed data will be used in subsequent time steps. In each subsequent calculation time step, the mechanical equations are solved based on the undisplaced problem and the current displaced problem. The displacement of each mesh node is calculated, and the node coordinates, finite element data, and material properties are updated in real time. By calling the updated finite element data, the discrete interface is reassembled and the large deformation mechanical equations are calculated. The solver terminates the calculation when the solution iteration stopping condition is met.
[0037] Specifically, the real-time updated data includes the following data: (1) Finite element data update: According to the deformed state, the finite element data is updated in real time, such as the finite element shape function derivatives of the volume element and the surface element shape function derivatives; (2) Integration rule update: According to the deformed state, the integration rules are updated in real time, such as the Jacobian matrix of the mapping of volume elements and surface elements to isoparametric elements; (3) Element data update: According to the deformed state, the element data is updated in real time. In addition to the node data updated in step 4, the normal vector, tangent vector, etc. are also updated; (4) Material property update: Material properties such as elastic modulus and Poisson’s ratio are updated in real time according to the deformed state.
[0038] Finally, based on the updated finite element data, the discrete interface is reassembled to perform calculations of large deformation mechanics equations.
[0039] In some embodiments, the deformation determination module is configured to determine whether a deformation problem exists based on specified parameters; if the specified parameters indicate a deformation problem, the mechanical response parameters of the deformed mesh are transmitted to the finite element update module; if the specified parameters indicate no deformation problem, the mechanical response parameters of the original mesh are transmitted to the finite element update module. The specified parameters may be transmitted via an input card.
[0040] The program's implementation logic involves adding finite element equation objects and boundary condition objects to discretize and assemble nonlinear equations. If a finite element equation object is detected with the "use_displaced_mesh" parameter, it is assumed to use deformed mesh cell data to assemble the nonlinear equations. When constructing the finite element equation object, the DisplacedProblem parameter is passed as a parameter via the input card. Whether the deformed mesh cell data or the original mesh data is used during the actual assembly of the equations depends on whether the "use_displaced_mesh" parameter is enabled.
[0041] In some embodiments, the deformation judgment module 105 is configured to: at each calculation time step, determine whether it is a deformation problem based on the geometric shape of the deformed mesh; if it is a deformation problem, pass the mechanical response data of the deformed mesh to the finite element update module; if it is not a deformation problem, pass the mechanical response data of the original mesh to the finite element update module.
[0042] In the above implementation, the original mesh serves as the reference mesh. The degree of deformation of the updated deformed mesh compared to the reference mesh determines whether to ignore mesh deformation or use the deformed mesh data for the solution. The degree of mesh deformation can be measured by comparing local or global mesh shapes, or by quantifying the displacement of mesh nodes. The algorithm automatically determines whether to use the deformed mesh cell data or the original mesh data based on the quantified degree of deformation.
[0043] In some embodiments, the deformation calculation module 101 receives the node displacements calculated by the solver module in the previous calculation time step, and updates and records the geometry of the deformed mesh based on the node positions in the current calculation time step. Specifically, the deformation calculation module 101 adds a displacement vector to the coordinates of each node based on the deformed mesh recorded in the previous calculation time step. The displacement vector in the first calculation time step is a zero vector, and the deformed mesh is the same as the original mesh.
[0044] In some embodiments, the solver module 104 includes N parallel solver modules, the deformed grid is divided into N sub-regions, and the parallel solver module solves one sub-region correspondingly, wherein N is an integer greater than or equal to 2. The finite element analysis device also includes a memory module, and the memory module allocates a storage area to each parallel solver, such as n The storage area corresponds to the storage n displacement solutions of parallel solvers, In each storage area n Storage area n The first part will be the corresponding parallel solution module according to the entity data n The displacement solution of the local process is stored in the storage area nThe latter part will be based on the ghost data to other processes (except the parallel solution module n The displacement solutions of processes other than those in the original process are stored.
[0045] Deformation calculation module 101 obtains displacement solution vectors from multiple processes in solver module 104 and updates the deformed mesh. The program's implementation logic involves calling the UpdateMesh function in DisplacedProblem to perform the actual mesh transformation. The mesh deformation operation essentially iterates over all mesh points in each process, adding the displacement field data set in [Mesh] to the original coordinates of each mesh point to produce the new deformed mesh.
[0046] In parallel computing, the displacement solution vector is stored in segments according to the process. When a process updates the grid, it is impossible to obtain the full-field data of the grid. Only the data on the area stored by this process can be obtained. Therefore, communication is required to obtain the displacement data of other processes on the entire grid.
[0047] UpdateMesh is the key interface for implementing deformed meshes. Its process is as follows: (1) Based on the displacement variable parameter name, the corresponding equation number and variable number are obtained to obtain the displacement data. That is, the displacement solution is stored in which variable of which equation. By traversing all displacement variables, a map structure is constructed as shown in Table 1 for the subsequent displacement solution acquisition.
[0048] Table 1 Map structure
[0049] (2) Traverse the above map structure and obtain the displacement variable data owned by this process in turn. Since the displacement variable data is distributed among all processes in parallel, only the data of this process can be obtained at present. In order to obtain the full-field grid data, it is necessary to reconstruct a displacement variable solution vector. This solution vector uses the ghost vector mechanism of Petsc to store the displacement data owned by this process as normal entity data and the data on other processes as ghost storage.
[0050] As for Figure 2 The global grid structure shown in the figure, the yellow part is the grid sub-region data owned by a process, then 7, 8, 9, 13, 14, 15, 19, 20, 21 are the data of this process, and the rest of the data are on other processes. They need to be used as ghost values to construct an entire vector, such as [7, 8, 9, 13, 14, 15, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 10, 11, 12, 16, 17, 18, …].
[0051] The first half of the storage area is the data of this process, and the second half is the ghost data. The ghost data is actually stored in other processes.
[0052] (3) After obtaining the global displacement solution, mesh deformation only requires traversing all nodes of the original mesh and adding the displacement data to the coordinates of each direction (x, y, z) of the node. The deformed mesh is stored in the displaced_mesh structure.
[0053] The finite element analysis device considering mesh deformation of the present invention supports parallel operation on multi-core processors or multiple computers, and can significantly shorten the calculation time of complex engineering problems through task allocation and data synchronization.
[0054] In some embodiments, the deformation calculation module 101 is configured to: upon detecting a displacement variable name, copy the original mesh as a deformed mesh, and create a displacement problem object based on the deformed mesh; the displacement variable name is passed in via an input card.
[0055] The program implementation logic is as follows: enter the displacement variable name displacements in the [Mesh] module of the input card, set the displacement field variable data of each direction of the mesh (x, y, z) to identify the deformation displacement data of the mesh node in each direction. The program detects that displacements is entered in the input card [Mesh], and completely copies the original mesh in the MeshPluginLoader as the deformed mesh object displace_mesh, and installs it into the framework. At the same time, it relies on the deformed mesh to construct the displacement problem object DisplacedProblem, which manages the deformed mesh unit degree of freedom information, finite element shape function data, deformed Gaussian integral data, etc.
[0056] The embodiment of the present invention also provides a finite element analysis method considering mesh deformation, such as Figure 3 As shown, the following steps are included.
[0057] S1, copy the original mesh as the initial deformed mesh.
[0058] The geometry of the original mesh does not deform during the finite element analysis process, and the geometry of the deformed mesh is updated according to the node displacement at each calculation time step. Step S2 is executed at each calculation time step of the finite element analysis process: S2-1, updates the geometry of the deformed mesh based on the node displacements solved in the previous time step; S2-2, calculate the mechanical response data of the original grid and the deformed grid at the current calculation time step respectively; S2-3, calculating finite element data based on the mechanical response data of the original mesh or the mechanical response data of the deformed mesh according to the problem type; wherein the finite element data includes a residual vector and a Jacobian matrix for assembling the nonlinear mechanical equations; S2-4, assemble the nonlinear mechanical equations based on the updated finite element data and solve the nodal displacements.
[0059] Furthermore, the problem type includes deformation problem type and non-deformation problem type. According to the problem type, the finite element data is calculated based on the mechanical response data of the original mesh or the mechanical response data of the deformed mesh, specifically including: Determine whether it is a deformation problem based on the geometry of the deformed mesh; If the problem is deformation, the finite element data is calculated based on the mechanical response data of the deformed mesh. If the problem is non-deformation, the finite element data is calculated based on the mechanical response data of the original mesh.
[0060] Furthermore, the method further includes: when a displacement variable is detected, creating a displacement problem object and a non-displacement problem object. The displacement problem object is used to record the geometric shape of the deformed mesh at each calculation time step and the mechanical response data after deformation, and the non-displacement problem object is used to record the mechanical response data of the original mesh at each calculation time step.
[0061] Specifically, the overall process of the mesh deformation algorithm for finite element analysis is as follows: Figure 4 As shown, the execution steps are as follows.
[0062] Step 1: Detect the displacement variable name displacements in the [mesh] module of the input card and start the displacement problem calculation.
[0063] When the program detects a displacement variable, it copies the original mesh as the deformed mesh object displaced_mesh, and at the same time relies on the deformed mesh to construct the displacement problem object DisplacedProblem, which manages the deformed mesh unit degree of freedom information, finite element shape function data, deformed Gaussian integral data, etc.
[0064] Step 2: The displacement problem object DisplacedProblem is passed to the problem solving object Problem. The Problem object manages various data assembled by shape functions, as well as residual and Jacobian matrix calculations of nonlinear solutions.
[0065] In this step, the "use_displaced_mesh" parameter is used to determine whether the undeformed problem or the deformed problem needs to be solved. If it is an undeformed problem, the Problem object will not call DisplacedProblem (the data interface of the displacement problem object). At this time, the undeformed related data will be used to complete the Jacobian matrix and residual vector calculations of the numerical discrete interface; if it is a deformed problem, Problem will call the related interfaces of DisplacedProblem, which will recalculate the related data including the deformed one. At this time, the Jacobian matrix and residual vector calculations of the numerical discrete interface are completed for the deformed related data.
[0066] Step 3: Assemble the Jacobian matrix and residual vector, and use the nonlinear solver to solve the nonlinear mechanical equations.
[0067] This article discusses the relevant processes for solving deformation problems, so the "use_displaced_mesh" parameter is used to introduce the deformation calculation process. As explained in Step 2, specifying the "use_displaced_mesh" parameter will call DisplacedProblem to recalculate the relevant data after deformation. The main steps of mesh deformation are to traverse all mesh points in each process, add the original mesh point coordinates to the displacement field data, and obtain the deformed mesh displaced_mesh. The DisplacedProblem object relies on the deformed mesh data in displaced_mesh to recalculate the finite element shape functions, integration rules, and other related data. It then assembles the Jacobian matrix and residual vector according to the deformed formula and solves it.
[0068] This algorithm supports parallel computing and can run efficiently on multi-core processors or multiple computers, significantly reducing the computation time for complex engineering problems. This invention not only improves the accuracy and stability of large deformation calculations, but also enhances computational efficiency. It is applicable to complex engineering designs in the field of mechanics, optimizes structural performance and safety, and provides a foundation for the development of fuel performance analysis software.
[0069] An embodiment of the present invention further provides an electronic device comprising a processor and a memory, wherein the number of processors may be one or more. The memory, as a computer-readable storage medium, can be used to store software programs, computer-executable programs, and modules. The processor executes the software programs, instructions, and modules stored in the memory to perform various functional applications and data processing of the electronic device, thereby implementing the finite element analysis method with consideration of mesh deformation according to any of the above-mentioned embodiments of the present invention.
[0070] The memory may primarily include a program storage area and a data storage area. The program storage area may store an operating system and at least one application required for a function; the data storage area may store data generated based on the use of the terminal, etc. Furthermore, the memory may include high-speed random access memory and may also include non-volatile memory, such as at least one disk storage device, flash memory device, or other non-volatile solid-state memory device. In some instances, the memory may further include memory remotely located relative to the processor, and these remote memories may be connected to the electronic device via a network. Examples of the aforementioned networks include, but are not limited to, the Internet, an intranet, a local area network, a mobile communication network, and combinations thereof.
[0071] An embodiment of the present invention further provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the finite element analysis method considering mesh deformation according to any embodiment of the present invention is implemented.
[0072] The computer storage media of the embodiments of the present 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. The computer-readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device, or component, or any combination thereof. More specific examples (a non-exhaustive list) of computer-readable storage media include: an electrical connection having one or more wires, a portable computer disk, 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 disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination thereof. In the present invention, a computer-readable storage medium may be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, device, or component.
[0073] A computer-readable signal medium may include a data signal propagated in baseband or as part of a carrier wave, which carries computer-readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A computer-readable signal medium may also be any computer-readable medium other than a computer-readable storage medium that can transmit, propagate, or transport a program for use by or in conjunction with an instruction execution system, apparatus, or device.
[0074] An embodiment of the present invention further provides a computer program product. When the computer program product is run on a computer, the computer is enabled to execute the finite element analysis method considering mesh deformation according to any of the above embodiments of the present invention.
[0075] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.
Claims
1. A finite element analysis device considering mesh deformation, characterized in that: include: Deformation calculation module, used to create deformed meshes and displacement problem objects; The displacement problem object is used to record the geometric shape of the deformed grid at each calculation time step and the mechanical response data after deformation; Undeformed calculation module, used to create the original mesh and non-displaced problem objects; The non-displacement problem object is used to record the mechanical response data of the original grid at each calculation time step, and the geometric shape of the original grid does not deform during the calculation process; A finite element updating module, configured to calculate finite element data based on the mechanical response data of the deformed mesh or the mechanical response data of the original mesh at each calculation time step; A solver module is used for assembling and solving nonlinear mechanical equations based on the finite element data at each calculation time step; The deformation judgment module is used to select and transfer the mechanical response data of the deformed mesh or the mechanical response data of the original mesh to the finite element updating module.
2. The finite element analysis device considering mesh deformation according to claim 1, characterized in that: The deformation judgment module is configured to: determine whether there is a deformation problem based on the geometric shape of the deformed mesh at each calculation time step; If it is a deformation problem, the mechanical response data of the deformed mesh is passed into the finite element update module; if it is a non-deformation problem, the mechanical response data of the original mesh is passed into the finite element update module.
3. The finite element analysis device considering mesh deformation according to claim 1, characterized in that: The deformation judgment module is configured to: determine whether it is a deformation problem based on specified parameters; if the specified parameters indicate a deformation problem, then pass the mechanical response parameters of the deformed mesh into the finite element update module; if the specified parameters indicate a non-deformation problem, then pass the mechanical response parameters of the original mesh into the finite element update module, and the specified parameters are passed in by the input card.
4. The finite element analysis device considering mesh deformation according to any one of claims 1 to 3, characterized in that: The geometric shape of the deformed grid at each calculation time step is the node coordinates of the deformed grid at the previous calculation time step plus the node displacement; the node displacement is obtained by solving the nonlinear mechanical equations through the solver module.
5. The finite element analysis device considering mesh deformation according to any one of claims 1 to 3, characterized in that: The finite element data includes a residual vector and a Jacobian matrix for assembling the nonlinear mechanical equations.
6. The finite element analysis device considering mesh deformation according to claim 1, characterized in that: The deformation calculation module is configured to: when a displacement variable name is detected, copy an original grid as a deformed grid, and create a displacement problem object based on the deformed grid; the displacement variable name is input from an input card.
7. The finite element analysis device considering mesh deformation according to claim 1, characterized in that: The solver module includes N parallel solver modules, the deformed grid is divided into N sub-regions, each parallel solver module solves one sub-region, and N≥2; The finite element analysis device further includes a memory module, wherein the memory module is used to allocate a storage area to each parallel solver; No. n The first part of the storage area will be n The displacement solutions of the parallel solvers are stored as entity data, and the latter part will be n The displacement solutions of parallel solvers other than the first parallel solver are stored as ghost data. .
8. A finite element analysis method considering mesh deformation, characterized in that: include: Copying the original mesh as the initial deformed mesh; wherein the geometry of the original mesh does not deform during the finite element analysis process, and the geometry of the deformed mesh is updated according to the node displacement at each calculation time step; The following steps are performed at each computational time step during the finite element analysis process: (1) updating the geometry of the deformed mesh based on the node displacements solved in the previous time step; (2) respectively calculating the mechanical response data of the original grid and the deformed grid at the current calculation time step; (3) Calculating finite element data based on the mechanical response data of the original mesh or the mechanical response data of the deformed mesh according to the problem type; the finite element data includes a residual vector and a Jacobian matrix for assembling nonlinear mechanical equations; (4) Assembling nonlinear mechanical equations based on the updated finite element data and solving the node displacements.
9. The finite element analysis method considering mesh deformation according to claim 8, characterized in that: The problem types include deformation problem types and non-deformation problem types; The step of selecting, according to the problem type, the mechanical response data of the original mesh or the mechanical response data of the deformed mesh to calculate the finite element data includes: Determining whether the problem is a deformation problem based on the geometric shape of the deformed mesh; If it is a deformation problem, the finite element data is calculated based on the mechanical response data of the deformed mesh; if it is a non-deformation problem, the finite element data is calculated based on the mechanical response data of the original mesh.
10. The finite element analysis method considering mesh deformation according to claim 8, characterized in that: The method further includes: when a displacement variable is detected to be input, creating a displacement problem object and a non-displacement problem object; the displacement problem object is used to record the geometric shape of the deformed grid at each calculation time step and the mechanical response data after deformation, and the non-displacement problem object is used to record the mechanical response data of the original grid at each calculation time step.
11. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the computer program, the finite element analysis method considering mesh deformation according to any one of claims 8 to 10 is implemented.
12. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the finite element analysis method considering mesh deformation according to any one of claims 8 to 10 is implemented.