Configuration self-adaptive determination method and device based on arbitrary configuration lagrange finite element, equipment and medium

Abstract

The application provides a configuration self-adaptive determination method and device based on an arbitrary configuration Lagrange finite element, equipment and a medium, comprising: obtaining an initial configuration of a problem to be analyzed; based on the mechanical state parameters of the cells and nodes of the current time step and the previous time step, a continuously changing configuration interpolation parameter and a target function are constructed; based on an optimization algorithm, the optimal configuration parameter that makes the target function reach the optimal value is searched in the configuration interpolation parameter, and the intermediate reference configuration corresponding to the optimal configuration parameter is taken as the target reference configuration of the current time step; the target reference configuration is subjected to global nonlinear finite element analysis, so that the state variable of the current time step is updated based on the target reference configuration. Numerical abnormalities such as negative volume and mesh flipping caused by serious distortion of the current configuration are effectively avoided, and the simulation efficiency and numerical stability of the nonlinear finite element analysis are improved.

Description

Technical Field

[0001] This application relates to the field of computational mechanics technology, and in particular to a method, apparatus, device and medium for adaptive determination of configuration based on arbitrary configuration Lagrange finite element method. Background Technology

[0002] In finite element analysis of nonlinear continuum mechanics, especially in problems involving large deformations and strains (such as high-speed impacts, explosive forming, and metal plastic processing), the kinematics and constitutive behavior of materials must be defined and numerically integrated under a well-defined reference configuration. Since objects undergo significant geometric deformation during loading, and their initial and current configurations differ markedly, selecting a suitable reference configuration to ensure accurate stress updates and computational stability becomes a crucial issue in nonlinear finite element analysis.

[0003] Existing technologies typically employ two fixed reference configuration strategies: (1) using the initial configuration as a reference, employing the second type of Piola-Kirchhoff stress and Green-Lagrange strain tensor, suitable for path-independent materials (such as hyperelastic rubber), but difficult to accurately describe elastoplastic materials undergoing complex deformation histories; (2) using the current time step configuration as a reference, constructing constitutive relations based on Cauchy stress and Almansi strain, widely used in commercial finite element software (such as LS-DYNA, Abaqus) to handle path-dependent materials (such as elastoplastic metals). Although this method can reflect the local deformation state well, under large deformation conditions, as the elements undergo severe distortion (such as twisting, flipping, or overstretching), the Jacobian determinant becomes negative, the mesh quality drops sharply, leading to numerical instability or even solution interruption. In summary, the main drawback of existing technologies is that the selection of reference configuration is fixed and rigid, unable to adaptively adjust according to the actual deformation state, resulting in problems such as increased mesh distortion, numerical oscillation, solution failure, and forced reduction of time step under large deformation conditions. Therefore, there is an urgent need for a new method that can improve computational robustness and efficiency by dynamically selecting the optimal reference configuration while keeping the finite element topology unchanged. Summary of the Invention

[0004] In view of this, the purpose of this application is to provide a method, apparatus, device, and medium for adaptive configuration determination based on arbitrary configuration Lagrange finite element method. By introducing continuously adjustable configuration interpolation parameters, it realizes that any intermediate configuration from the initial configuration to the current configuration can be used as a reference frame for constitutive integration. On this basis, combined with the objective function, the optimal configuration parameters are automatically searched, effectively avoiding numerical anomalies such as negative volume and mesh flipping caused by severe distortion of the current configuration, thereby improving the simulation efficiency and numerical stability of nonlinear finite element analysis.

[0005] This application provides a configuration adaptive determination method based on arbitrary configuration Lagrange finite element method, the configuration adaptive determination method includes:

[0006] Obtain the initial configuration of the problem to be analyzed;

[0007] Based on the mechanical state parameters of the elements and nodes at the current time step and the previous time step, a continuously changing configuration interpolation parameter and objective function are constructed; wherein, the configuration interpolation parameter is used to define any intermediate reference configuration between the initial configuration and the current configuration, and the objective function is an index reflecting the mesh geometric quality or the numerical stability of the constitutive integral.

[0008] Based on the optimization algorithm, the optimal configuration parameters that make the objective function reach the optimal value are searched within the configuration interpolation parameters, and the intermediate reference configuration corresponding to the optimal configuration parameters is used as the target reference configuration for the current time step.

[0009] A global nonlinear finite element analysis is performed on the target reference configuration to update the state variables at the current time step based on the target reference configuration.

[0010] In one possible implementation, the objective function includes the following:

[0011] The objective function aims to maximize the value of the minimum Jacobian determinant among all cells at the current time step.

[0012] The objective function aims to maximize the minimum cell length among all cells at the current time step.

[0013] The objective function aims to minimize the numerical oscillation amplitude generated after performing a trial constitutive integral based on the candidate configuration.

[0014] In one possible implementation, the determination of the optimal configuration parameters further includes using an AI algorithm to provide the optimal configuration parameters within the configuration interpolation parameters, and using the intermediate reference configuration corresponding to the optimal configuration parameters as the target reference configuration for the current time step.

[0015] The optimal configuration parameters are given within the configuration interpolation parameters based on empirical formulas, and the intermediate reference configuration corresponding to the optimal configuration parameters is used as the target reference configuration for the current time step.

[0016] In one possible implementation, for the Jacobian determinant, the search for the optimal configuration parameters within the configuration interpolation parameters based on the optimization algorithm to achieve the optimal value of the objective function includes:

[0017] Based on the optimization algorithm, a first candidate parameter is searched within the range of values ​​of the configuration interpolation parameter, and a first reference configuration is generated based on the first candidate parameter;

[0018] Based on the objective function, Jacobian determinant analysis is performed on the first reference configuration to determine the minimum value of the Jacobian determinant of the first reference configuration.

[0019] Continue iterative processing until the minimum value of the Jacobi determinant is determined to be the maximum value. Then, the candidate parameter corresponding to the Jacobi determinant is taken as the optimal configuration parameter.

[0020] In one possible implementation, performing a global nonlinear finite element analysis on the target reference configuration to update the state variables at the current time step based on the target reference configuration includes:

[0021] Calculate the deformation gradient and velocity gradient under the target reference configuration;

[0022] The strain tensor and strain rate tensor based on the target reference configuration are calculated according to the deformation gradient and the velocity gradient.

[0023] Constitutive integration is performed based on the deformation gradient, the velocity gradient, the strain tensor, and the strain rate tensor to update the state variables at the current time step based on the target reference configuration.

[0024] In one possible implementation, the deformation gradient and the velocity gradient under the target reference configuration are determined by the following formula:

[0025] ;

[0026]

[0027] in, for The target reference configuration at time steps relative to Deformation gradient of the configuration at time step, for The node coordinates of the configuration at each time step. for The node coordinates of the configuration at each time step. for The velocity gradient of the target reference configuration at each time step. for Target reference configuration at time step relative to time step The derivative of the deformation gradient of the lower configuration with respect to time. For the current time step, For the previous time step tWith the current time step The intermediate time step between them.

[0028] In one possible implementation, the strain tensor and the strain rate tensor are determined by the following formula:

[0029] ;

[0030] ;

[0031] in, for The target reference configuration at time steps relative to Strain tensor of configuration at time step, I It is the identity matrix. for The target reference configuration at time steps relative to Deformation gradient of the configuration at time step, for The target reference configuration at time steps relative to The strain rate tensor of the configuration at the time step. D The deformation rate.

[0032] This application embodiment also provides a configuration adaptive selection and adaptive determination device for arbitrary configuration Lagrange finite element methods, the configuration adaptive selection and adaptive determination device comprising:

[0033] The acquisition module is used to acquire the initial configuration of the problem to be analyzed.

[0034] The function construction module is used to construct a continuously changing configuration interpolation parameter and objective function based on the mechanical state parameters of the elements and nodes at the current time step and the previous time step; wherein, the configuration interpolation parameter is used to define any intermediate reference configuration between the initial configuration and the current configuration, and the objective function is an index reflecting the mesh geometric quality or the numerical stability of the constitutive integral;

[0035] The configuration optimization module is used to search for the optimal configuration parameters that make the objective function reach the optimal value within the configuration interpolation parameters based on the optimization algorithm, and to use the intermediate reference configuration corresponding to the optimal configuration parameters as the target reference configuration for the current time step.

[0036] The analysis module is used to perform global nonlinear finite element analysis on the target reference configuration in order to update the state variables at the current time step based on the target reference configuration.

[0037] This application embodiment also provides an electronic device, including: a processor, a memory, and a bus. The memory stores machine-readable instructions executable by the processor. When the electronic device is running, the processor communicates with the memory via the bus. When the machine-readable instructions are executed by the processor, the steps of the configuration adaptive determination method based on arbitrary configuration Lagrange finite element are performed as described above.

[0038] This application also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, performs the steps of the above-described configuration adaptive determination method based on arbitrary configuration Lagrange finite element.

[0039] This application provides a method, apparatus, device, and medium for adaptive configuration determination based on arbitrary configuration Lagrange finite element method. The adaptive configuration determination method includes: obtaining the initial configuration of the problem to be analyzed; constructing a continuously changing configuration interpolation parameter and an objective function based on the mechanical state parameters of elements and nodes at the current and previous time steps; wherein the configuration interpolation parameter is used to define any intermediate reference configuration between the initial configuration and the current configuration, and the objective function is an index reflecting the mesh geometric quality or the numerical stability of the constitutive integral; searching for the optimal configuration parameter within the configuration interpolation parameter based on an optimization algorithm to achieve the optimal value of the objective function, and using the intermediate reference configuration corresponding to the optimal configuration parameter as the target reference configuration for the current time step; performing global nonlinear finite element analysis on the target reference configuration to update the state variables of the current time step based on the target reference configuration. By introducing a continuously adjustable configuration interpolation parameter, any intermediate configuration between the initial configuration and the current configuration can be used as a reference frame for the constitutive integral. Based on this, the optimal configuration parameters are automatically searched by combining the objective function, which effectively avoids numerical anomalies such as negative volume and mesh flipping caused by severe distortion of the current configuration, and improves the simulation efficiency and numerical stability of nonlinear finite element analysis.

[0040] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0041] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of this application and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0042] Figure 1A flowchart illustrating an adaptive configuration determination method based on arbitrary configuration Lagrange finite element method provided in this application embodiment;

[0043] Figure 2 A schematic diagram illustrating an adaptive configuration determination method based on arbitrary configuration Lagrange finite element method provided in this application embodiment;

[0044] Figure 3 A schematic diagram of a configuration adaptive determination device based on arbitrary configuration Lagrange finite element method provided in this application embodiment;

[0045] Figure 4 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. Detailed Implementation

[0046] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. The components of the embodiments of this application described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely represents selected embodiments of this application. Based on the embodiments of this application, every other embodiment obtained by those skilled in the art without inventive effort falls within the scope of protection of this application.

[0047] First, the applicable scenarios for this application will be introduced. This application can be applied to the field of computational mechanics technology.

[0048] Research has found that existing technologies typically employ two fixed reference configuration strategies: (1) using the initial configuration as a reference, employing the second type of Piola-Kirchhoff stress and Green-Lagrange strain tensor, which is suitable for path-independent materials (such as hyperelastic rubber), but is difficult to accurately describe elastoplastic materials that have undergone complex deformation histories; (2) using the current time step configuration as a reference, constructing constitutive relations based on Cauchy stress and Almansi strain, which is widely used in commercial finite element software (such as LS-DYNA, Abaqus) to handle path-dependent materials (such as elastoplastic metals). Although this method can reflect the local deformation state well, under large deformation conditions, as the elements undergo severe distortion (such as twisting, flipping, or overstretching), the Jacobian determinant becomes negative, the mesh quality drops sharply, and numerical instability or even solution interruption occurs. In summary, the main defects in existing technologies are: the selection of reference configuration is fixed and rigid, and cannot be adaptively adjusted according to the actual deformation state, which leads to problems such as increased mesh distortion, numerical oscillation, solution failure, and forced reduction of time step under large deformation conditions. Therefore, there is an urgent need for a new method that can improve computational robustness and efficiency by dynamically selecting the optimal reference configuration while keeping the finite element topology unchanged.

[0049] Based on this, embodiments of this application provide a method, apparatus, and device for adaptive configuration determination based on arbitrary configuration Lagrange finite element method. By introducing continuously adjustable configuration interpolation parameters, any intermediate configuration from the initial configuration to the current configuration can be used as a reference frame for constitutive integration. Furthermore, by automatically searching for optimal configuration parameters using the objective function, numerical anomalies such as negative volume and mesh flipping caused by severe distortion of the current configuration are effectively avoided, thus improving the simulation efficiency and numerical stability of nonlinear finite element analysis.

[0050] Please see Figure 1 , Figure 1 This is a flowchart illustrating an adaptive configuration determination method based on arbitrary configuration Lagrange finite element method, provided as an embodiment of this application. Figure 1 As shown in the embodiments of this application, the configuration adaptive determination method includes:

[0051] S101: Obtain the initial configuration of the problem to be analyzed.

[0052] Here, the problem to be analyzed refers to a specific physical and mechanical process or engineering scenario that needs to be numerically simulated using the Lagrange finite element method. Its core components include geometry and network, material behavior, loads and boundary conditions, and the solution objective. For example, the problem to be analyzed could be simulating the large deformation dynamics of a metal Taylor bar during a high-speed impact with a rigid plate.

[0053] S102: Based on the mechanical state parameters of the elements and nodes at the current time step and the previous time step, construct a continuously changing configuration interpolation parameter and objective function.

[0054] In this step, based on the mechanical state parameters of the elements and nodes in the current time step and the previous time step, a continuously changing configuration interpolation parameter and objective function are constructed.

[0055] The configuration interpolation parameters are used to define any intermediate reference configuration between the initial configuration and the current configuration, and the objective function is an index that reflects the mesh geometric quality or the numerical stability of the constitutive integral.

[0056] It should be noted that the mechanical state parameters include other parameters such as incremental displacement, deformation gradient, stress tensor, and equivalent plastic strain.

[0057] Here, at each incremental time step In the middle, the system knows the previous time step. The complete mechanical state includes state variables such as the coordinates of each node, incremental displacement, deformation gradient, stress tensor, and equivalent plastic strain. Based on this information, this application introduces a dimensionless configuration interpolation parameter. Its value range is [0,1], and it is used to parameterize any intermediate reference configuration between the initial configuration and the current configuration. =0 indicates that the arbitrary reference configuration is the initial configuration. =1 indicates that the arbitrary reference configuration is the current configuration, 0< β A value less than 1 indicates an intermediate reference configuration defined by interpolation.

[0058] To automatically select the "optimal" reference configuration from an infinite number of possible configuration interpolation parameter values, a quantitative evaluation criterion, namely an objective function, must be established. The design of this function depends on the element and nodal mechanical states extracted from the previous time step, and aims to improve numerical stability, mesh quality, and result accuracy. The objective function should satisfy the following characteristics: continuous or piecewise continuous; its value can be obtained through rapid evaluation of trial configurations; it has a definite maximum or minimum value corresponding to the optimal configuration parameters; and it is sensitive to adverse phenomena such as mesh distortion, contact penetration, and stress oscillations.

[0059] In one possible implementation, the objective function includes the following:

[0060] (1): The smallest Jacobian determinant among all units at the current time step, and the objective function aims to maximize the value of the smallest Jacobian determinant.

[0061] Here, it is defined as maximizing the minimum Jacobian determinant among all cells, when the cells are flipped. Maximizing the minimum Jacobian determinant effectively prevents the negative volume problem.

[0062] (2): The minimum unit length among all units at the current time step, and the objective function aims to maximize the minimum unit length.

[0063] Here, the optimization function is defined as the minimum cell length. The goal is to maximize this value so that the minimum cell length is as large as possible, thereby improving the computation time step.

[0064] (3): The numerical oscillation amplitude generated after performing a trial constitutive integral based on the candidate configuration, and the objective function aims to minimize the numerical oscillation amplitude.

[0065] Here, after performing a tentative constitutive integral, an index value is used to evaluate the magnitude of numerical oscillations.

[0066] It should be noted that the objective function includes other components besides those mentioned above, but this part does not specify any limitations.

[0067] S103: Based on the optimization algorithm, search for the optimal configuration parameters within the configuration interpolation parameters to make the objective function reach the optimal value, and use the intermediate reference configuration corresponding to the optimal configuration parameters as the target reference configuration for the current time step.

[0068] In this step, the optimal configuration parameters that make the objective function reach its optimal value are searched within the configuration interpolation parameters according to the optimization algorithm, and the intermediate reference configuration corresponding to the optimal configuration parameters is used as the target reference configuration for the current time step.

[0069] Here, optimization algorithms include golden section search, gradient ascent, genetic algorithm, particle swarm optimization algorithm, machine learning prediction model, or rule-based judgment method based on empirical formulas.

[0070] In one possible implementation, the determination of the optimal configuration parameters further includes:

[0071] The AI ​​algorithm provides the optimal configuration parameters within the configuration interpolation parameters, and the intermediate reference configuration corresponding to the optimal configuration parameters is used as the target reference configuration for the current time step; or, the empirical formula provides the optimal configuration parameters within the configuration interpolation parameters, and the intermediate reference configuration corresponding to the optimal configuration parameters is used as the target reference configuration for the current time step.

[0072] In addition to the methods mentioned above, other methods may be used to determine the optimal configuration parameters, which are not specifically limited here.

[0073] In one possible implementation, for the Jacobian determinant, the search for the optimal configuration parameters within the configuration interpolation parameters based on the optimization algorithm to achieve the optimal value of the objective function includes:

[0074] Based on the optimization algorithm, a first candidate parameter is searched within the range of values ​​of the configuration interpolation parameter, and a first reference configuration is generated based on the first candidate parameter. Based on the objective function, Jacobi determinant analysis is performed on the first reference configuration to determine the minimum value of the Jacobi determinant of the first reference configuration. Iterative processing continues until the minimum value of the Jacobi determinant is determined to be the maximum value, and the candidate parameter corresponding to the Jacobi determinant is taken as the optimal configuration parameter.

[0075] Here, the first candidate parameter is searched within the range of configuration interpolation parameters according to the optimization algorithm, and the first reference configuration is generated based on the first candidate parameter; the Jacobian determinant analysis is performed on the first reference configuration according to the objective function to determine the minimum value of the Jacobian determinant of the first reference configuration; the above steps are repeated until the minimum value of the Jacobian determinant is determined to be the maximum value, and the candidate parameter corresponding to the Jacobian determinant is taken as the optimal configuration parameter.

[0076] In a specific implementation, the optimizer is started, and it is assumed that in the first iteration, the optimizer proposes the first candidate parameter. Based on this tentative configuration, a nonlinear finite element analysis is run at the current time step to evaluate the intrinsic quality of the mesh under deformation and to examine the Jacobian determinant of all elements in the analysis based on the tentative configuration. Assuming a minimum Jacobian value of 0.55 is found, it is recorded. 0.55. The optimizer proposes based on existing data. =0.6, thus obtaining Repeating the above steps for 8 iterations, it was found that when When = 0.20, F The maximum value of 0.82 was reached, and no better solution could be obtained in three consecutive iterations. The optimization process was declared convergent, and the optimal configuration parameters were output as follows. = 0.20.

[0077] This application, for the first time, transforms the reference configuration selection problem into an optimizable mathematical decision-making process: by defining an objective function (such as maximizing the minimum Jacobian determinant, minimizing strain gradient oscillations, etc.) and combining it with numerical optimization algorithms to automatically search for optimal configuration parameters, a shift from "passive bearing" to "active control" is achieved. This mechanism can intelligently adjust the reference frame according to the local deformation characteristics at each step, making the strain measurement closer to the physical reality, especially exhibiting higher stress update accuracy and energy conservation capabilities in strongly nonlinear regions such as shear band formation, local necking, and contact slip. Simultaneously, by setting a multi-condition joint triggering mechanism (such as mesh quality degradation, sudden increase in plastic strain, drastic contact changes, etc.), the optimization process is initiated only when necessary, avoiding the additional overhead caused by frequent calls and significantly improving computational efficiency while ensuring high accuracy.

[0078] S104: Perform global nonlinear finite element analysis on the target reference configuration to update the state variables at the current time step based on the target reference configuration.

[0079] In this step, a global nonlinear finite element analysis is performed on the target reference configuration to update the state variables of the current time step based on the selected target reference configuration.

[0080] In one possible implementation, performing a global nonlinear finite element analysis on the target reference configuration to update the state variables at the current time step based on the target reference configuration includes:

[0081] A: Calculate the deformation gradient and velocity gradient under the target reference configuration.

[0082] Here, the deformation gradient and the velocity gradient under the target reference configuration are determined by the following formulas:

[0083] ;

[0084]

[0085] in, for The target reference configuration at time steps relative to Deformation gradient of the configuration at time step, for The node coordinates of the configuration at each time step. for The node coordinates of the configuration at each time step. for The velocity gradient of the target reference configuration at each time step. for Target reference configuration at time step relative to time step The derivative of the deformation gradient of the lower configuration with respect to time. For the current time step, For the previous time step t With the current time step The intermediate time step between them.

[0086] B: Calculate the strain tensor and strain rate tensor based on the target reference configuration according to the deformation gradient and the velocity gradient.

[0087] Here, the strain tensor and the strain rate tensor are determined using the following formulas:

[0088] ;

[0089] ;

[0090] in, for The target reference configuration at time steps relative to Strain tensor of configuration at time step, I It is the identity matrix. for The target reference configuration at time steps relative to Deformation gradient of the configuration at time step, for The target reference configuration at time steps relative to The strain rate tensor of the configuration at the time step. D The deformation rate is denoted as .

[0091] C: Perform constitutive integration based on the deformation gradient, the velocity gradient, the strain tensor, and the strain rate tensor to update the state variables of the current time step based on the target reference configuration.

[0092] Here, the linear elasticity of ARC is determined using the following formula:

[0093]

[0094] in, for Cauchy stress of the target reference configuration at time step. for Cauchy stress of the configuration at time step, for Configuration at time step relative to The Jacobian determinant of the deformation gradient of the target reference configuration at time step. C It is a fourth-order tangent modulus tensor.

[0095] Here, when the constitutive model is hyperelastic, the stress is updated using the following formula:

[0096]

[0097] in, for The fourth-order tangent modulus tensor of the configuration at the time step. It is a unit The deformation gradient of the configuration relative to the initial configuration at any given time. For the initial configuration relative to Jacobian determinant of the deformation gradient of the configuration at time step.

[0098] In a specific implementation, the problem is described as: simulating the impact process of a Taylor bar. The Taylor bar moves downward with an initial velocity and impacts a rigid plate, causing large deformation. This process involves geometric nonlinearity, material nonlinearity, and contact nonlinearity, which can easily lead to severe distortion of the elements on the Taylor bar, forcing explicit analysis to use extremely small step sizes, or even resulting in negative Jacobian values ​​and halting the calculation. The implementation goal is to automatically find the optimal configuration parameters in each analysis step (or every N steps, or under certain conditions) to maximize mesh quality, thereby stabilizing the calculation and increasing the critical time step.

[0099] For further details, please refer to Figure 2 , Figure 2 This is a schematic diagram illustrating an adaptive configuration determination method based on arbitrary configuration Lagrange finite element method, provided as an embodiment of this application. Figure 2 As shown, the steps are as follows: Step 1: Problem initialization; Step 2: Define the configuration interpolation parameters and the objective function for element quality; Step 3: Start the optimization algorithm; Step 4: The optimizer determines the candidate configuration parameters; Step 5: Generate intermediate configurations of elements based on the candidate configuration parameters; Step 6: Perform explicit dynamics analysis; Step 7: Check if the value of the objective function satisfies the maximization of the minimum Jacobian determinant; Step 8: If not, continue the optimization process; Step 9: If yes, output the optimal configuration parameters and apply them to the global explicit dynamics analysis.

[0100] This application provides an adaptive configuration determination method based on arbitrary configuration Lagrange finite element method. The method includes: obtaining the initial configuration of the problem to be analyzed; constructing a continuously changing configuration interpolation parameter and an objective function based on the mechanical state parameters of elements and nodes at the current and previous time steps; wherein the configuration interpolation parameter is used to define any intermediate reference configuration between the initial and current configurations, and the objective function is an index reflecting the mesh geometric quality or the numerical stability of the constitutive integral; searching for the optimal configuration parameter within the configuration interpolation parameter based on an optimization algorithm to achieve the optimal value of the objective function, and using the intermediate reference configuration corresponding to the optimal configuration parameter as the target reference configuration for the current time step; performing global nonlinear finite element analysis on the target reference configuration to update the state variables of the current time step based on the target reference configuration. By introducing a continuously adjustable configuration interpolation parameter, any intermediate configuration between the initial and current configurations can be used as a reference frame for the constitutive integral. Based on this, the optimal configuration parameters are automatically searched by combining the objective function, which effectively avoids numerical anomalies such as negative volume and mesh flipping caused by severe distortion of the current configuration, and improves the simulation efficiency and numerical stability of nonlinear finite element analysis.

[0101] Please see Figure 3 , Figure 3 This is a schematic diagram of a configuration adaptive determination device based on arbitrary configuration Lagrange finite element method, provided as an embodiment of this application. Figure 3 As shown, the configuration adaptive determination device 300 based on arbitrary configuration Lagrange finite element method includes:

[0102] Module 310 is used to acquire the initial configuration of the problem to be analyzed.

[0103] The function construction module 320 is used to construct a continuously changing configuration interpolation parameter and objective function based on the mechanical state parameters of the elements and nodes at the current time step and the previous time step; wherein, the configuration interpolation parameter is used to define any intermediate reference configuration between the initial configuration and the current configuration, and the objective function is an index reflecting the mesh geometric quality or the numerical stability of the constitutive integral;

[0104] The configuration optimization module 330 is used to search for the optimal configuration parameters that make the objective function reach the optimal value within the configuration interpolation parameters based on the optimization algorithm, and to use the intermediate reference configuration corresponding to the optimal configuration parameters as the target reference configuration of the current time step.

[0105] The analysis module 340 is used to perform global nonlinear finite element analysis on the target reference configuration in order to update the state variables of the current time step based on the target reference configuration.

[0106] Furthermore, the configuration optimization module 330 is used to search for the optimal configuration parameters that make the objective function reach its optimal value within the configuration interpolation parameters, based on the optimization algorithm, for the Jacobian determinant:

[0107] Based on the optimization algorithm, a first candidate parameter is searched within the range of values ​​of the configuration interpolation parameter, and a first reference configuration is generated based on the first candidate parameter;

[0108] Based on the objective function, Jacobian determinant analysis is performed on the first reference configuration to determine the minimum value of the Jacobian determinant of the first reference configuration.

[0109] Continue iterative processing until the minimum value of the Jacobi determinant is determined to be the maximum value. Then, the candidate parameter corresponding to the Jacobi determinant is taken as the optimal configuration parameter.

[0110] Furthermore, the analysis module 340 is used to perform global nonlinear finite element analysis on the target reference configuration, so as to update the state variables at the current time step based on the target reference configuration:

[0111] Calculate the deformation gradient and velocity gradient under the target reference configuration;

[0112] The strain tensor and strain rate tensor based on the target reference configuration are calculated according to the deformation gradient and the velocity gradient.

[0113] Constitutive integration is performed based on the deformation gradient, the velocity gradient, the strain tensor, and the strain rate tensor to update the state variables at the current time step based on the target reference configuration.

[0114] Furthermore, the analysis module 340 determines the deformation gradient and the velocity gradient under the target reference configuration using the following formulas:

[0115] ;

[0116]

[0117] in, for The target reference configuration at time steps relative to Deformation gradient of the configuration at time step, for The node coordinates of the configuration at each time step. for The node coordinates of the configuration at each time step. for The velocity gradient of the target reference configuration at each time step. for Target reference configuration at time step relative to time step The derivative of the deformation gradient of the lower configuration with respect to time. For the current time step, For the previous time step t With the current time step The intermediate time step between them.

[0118] Furthermore, the analysis module 340 determines the strain tensor and the strain rate tensor using the following formulas:

[0119] ;

[0120] ;

[0121] in, for The target reference configuration at time steps relative to Strain tensor of configuration at time step, I It is the identity matrix. for The target reference configuration at time steps relative to Deformation gradient of the configuration at time step, for The target reference configuration at time steps relative to The strain rate tensor of the configuration at the time step. D The deformation rate is denoted as .

[0122] This application provides a configuration adaptive determination device based on arbitrary configuration Lagrange finite element method. The configuration adaptive determination device includes: an acquisition module for acquiring the initial configuration of the problem to be analyzed; a function construction module for constructing a continuously changing configuration interpolation parameter and an objective function based on the mechanical state parameters of elements and nodes at the current time step and the previous time step; wherein the configuration interpolation parameter is used to define an arbitrary intermediate reference configuration between the initial configuration and the current configuration, and the objective function is an index reflecting the mesh geometric quality or the numerical stability of the constitutive integral; a configuration optimization module for searching for the optimal configuration parameter within the configuration interpolation parameter based on an optimization algorithm to achieve the optimal value of the objective function, and using the intermediate reference configuration corresponding to the optimal configuration parameter as the target reference configuration for the current time step; and an analysis module for performing global nonlinear finite element analysis on the target reference configuration to update the state variables of the current time step based on the target reference configuration. By introducing a continuously adjustable configuration interpolation parameter, any intermediate configuration between the initial configuration and the current configuration can be used as a reference frame for the constitutive integral. Based on this, the optimal configuration parameters are automatically searched by combining the objective function, which effectively avoids numerical anomalies such as negative volume and mesh flipping caused by severe distortion of the current configuration, and improves the simulation efficiency and numerical stability of nonlinear finite element analysis.

[0123] Please see Figure 4 , Figure 4 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. Figure 4 As shown, the electronic device 400 includes a processor 410, a memory 420, and a bus 430.

[0124] The memory 420 stores machine-readable instructions executable by the processor 410. When the electronic device 400 is running, the processor 410 communicates with the memory 420 via the bus 430. When the machine-readable instructions are executed by the processor 410, they can perform the operations described above. Figure 1 as well as Figure 2 The steps of the configuration adaptive determination method based on arbitrary configuration Lagrange finite element in the method embodiment shown are specifically implemented in the method embodiment and will not be repeated here.

[0125] This application also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, can perform the above-described actions. Figure 1 as well as Figure 2 The steps of the configuration adaptive determination method based on arbitrary configuration Lagrange finite element in the method embodiment shown are specifically implemented in the method embodiment and will not be repeated here.

[0126] Those skilled in the art will understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0127] In the several embodiments provided in this application, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. The apparatus embodiments described above are merely illustrative. For example, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. Furthermore, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Additionally, the shown or discussed mutual couplings, direct couplings, or communication connections may be through some communication interfaces; indirect couplings or communication connections between devices or units may be electrical, mechanical, or other forms.

[0128] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0129] In addition, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.

[0130] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a processor-executable, non-volatile, computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0131] Finally, it should be noted that the above-described embodiments are merely specific implementations of this application, used to illustrate the technical solutions of this application, and not to limit them. The scope of protection of this application is not limited thereto. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments, or make equivalent substitutions for some of the technical features, within the scope of the technology disclosed in this application. Such modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be covered within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A configuration adaptive determination method based on arbitrary configuration Lagrangian finite element method, characterized in that, The configuration adaptive determination method includes: Obtain the initial configuration of the problem to be analyzed; Based on the mechanical state parameters of the elements and nodes at the current time step and the previous time step, a continuously changing configuration interpolation parameter and objective function are constructed; wherein, the configuration interpolation parameter is used to define any intermediate reference configuration between the initial configuration and the current configuration, and the objective function is an index reflecting the mesh geometric quality or the numerical stability of the constitutive integral. Based on the optimization algorithm, the optimal configuration parameters that make the objective function reach the optimal value are searched within the configuration interpolation parameters, and the intermediate reference configuration corresponding to the optimal configuration parameters is used as the target reference configuration for the current time step. A global nonlinear finite element analysis is performed on the target reference configuration to update the state variables at the current time step based on the target reference configuration; A global nonlinear finite element analysis is performed on the target reference configuration to update the state variables at the current time step based on the target reference configuration, including: Calculate the deformation gradient and velocity gradient under the target reference configuration; The strain tensor and strain rate tensor based on the target reference configuration are calculated according to the deformation gradient and the velocity gradient. Constitutive integration is performed based on the deformation gradient, the velocity gradient, the strain tensor, and the strain rate tensor to update the state variables at the current time step based on the target reference configuration.

2. The configuration adaptive determination method according to claim 1, characterized in that, The objective function includes the following items: The objective function aims to maximize the value of the minimum Jacobian determinant among all cells at the current time step. The objective function aims to maximize the minimum cell length among all cells at the current time step. The objective function aims to minimize the numerical oscillation amplitude generated after performing a trial constitutive integral based on the candidate configuration.

3. The configuration adaptive determination method according to claim 1, characterized in that, The method for determining the optimal configuration parameters also includes: Based on the AI ​​algorithm, the optimal configuration parameters are given within the configuration interpolation parameters, and the intermediate reference configuration corresponding to the optimal configuration parameters is used as the target reference configuration for the current time step. Alternatively, based on empirical formulas, the optimal configuration parameters can be given within the configuration interpolation parameters, and the intermediate reference configuration corresponding to the optimal configuration parameters can be used as the target reference configuration for the current time step.

4. The configuration adaptive determination method according to claim 2, characterized in that, For the Jacobian determinant, the optimization algorithm searches for the optimal configuration parameters within the configuration interpolation parameters to achieve the optimal value of the objective function, including: Based on the optimization algorithm, a first candidate parameter is searched within the range of values ​​of the configuration interpolation parameter, and a first reference configuration is generated based on the first candidate parameter; Based on the objective function, a Jacobian determinant analysis is performed on the first reference configuration to determine the minimum value of the Jacobian determinant of the first reference configuration. Continue iterative processing until the minimum value of the Jacobian determinant is determined to be the maximum value. Then, the candidate parameter corresponding to the Jacobian determinant is taken as the optimal configuration parameter.

5. The configuration adaptive determination method according to claim 1, characterized in that, The deformation gradient and the velocity gradient under the target reference configuration are determined by the following formulas: ； in, for The target reference configuration at time steps relative to Deformation gradient of the configuration at time step, for The node coordinates of the configuration at each time step. for The node coordinates of the configuration at each time step. for The velocity gradient of the target reference configuration at each time step. for Target reference configuration at time step relative to time step The derivative of the deformation gradient of the lower configuration with respect to time. For the current time step, For the previous time step t With the current time step The intermediate time step between them.

6. The configuration adaptive determination method according to claim 1, characterized in that, The strain tensor and the strain rate tensor are determined by the following formulas: ； ； in, for The target reference configuration at time steps relative to Strain tensor of configuration at time step, I It is the identity matrix. for The target reference configuration at time steps relative to Deformation gradient of the configuration at time step, for The target reference configuration at time steps relative to The strain rate tensor of the configuration at the time step. D The deformation rate.

7. A configuration adaptive determination device based on arbitrary configuration Lagrange finite element method, characterized in that, The configuration adaptive determination device includes: The acquisition module is used to acquire the initial configuration of the problem to be analyzed. The function construction module is used to construct a continuously changing configuration interpolation parameter and objective function based on the mechanical state parameters of the elements and nodes at the current time step and the previous time step; wherein, the configuration interpolation parameter is used to define any intermediate reference configuration between the initial configuration and the current configuration, and the objective function is an index reflecting the mesh geometric quality or the numerical stability of the constitutive integral; The configuration optimization module is used to search for the optimal configuration parameters that make the objective function reach the optimal value within the configuration interpolation parameters based on the optimization algorithm, and to use the intermediate reference configuration corresponding to the optimal configuration parameters as the target reference configuration for the current time step. The analysis module is used to perform global nonlinear finite element analysis on the target reference configuration to update the state variables at the current time step based on the target reference configuration, including: Calculate the deformation gradient and velocity gradient under the target reference configuration; The strain tensor and strain rate tensor based on the target reference configuration are calculated according to the deformation gradient and the velocity gradient. Constitutive integration is performed based on the deformation gradient, the velocity gradient, the strain tensor, and the strain rate tensor to update the state variables at the current time step based on the target reference configuration.

8. An electronic device, characterized in that, include: The device includes a processor, a memory, and a bus. The memory stores machine-readable instructions executable by the processor. When the electronic device is running, the processor communicates with the memory via the bus. The machine-readable instructions are executed by the processor to perform the steps of the configuration adaptive determination method based on arbitrary configuration Lagrange finite element as described in any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, performs the steps of the configuration adaptive determination method based on arbitrary configuration Lagrange finite element as described in any one of claims 1 to 6.

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