CN-121145573-B - Configuration self-adaptive determination method, device, equipment and medium based on Lagrange finite element with arbitrary configuration

CN121145573BCN 121145573 BCN121145573 BCN 121145573BCN-121145573-B

Abstract

The application provides a configuration self-adaptive determination method, device, equipment and medium based on Lagrangian finite elements of any configuration, which comprises the steps of obtaining an initial configuration of a problem to be analyzed, constructing a continuously-changing configuration interpolation parameter and an objective function based on mechanical state parameters of units and nodes of a current time step and a previous time step, searching an optimal configuration parameter which enables the objective function to reach an optimal value in the configuration interpolation parameter based on an optimization algorithm, taking an intermediate reference configuration corresponding to the optimal configuration parameter as a target reference configuration of the current time step, and carrying out global nonlinear finite element analysis on the target reference configuration to update state variables of the current time step based on the target reference configuration. Numerical value anomalies such as negative volume, grid overturning and the like caused by serious distortion of the current configuration are effectively avoided, and simulation efficiency and numerical stability of nonlinear finite element analysis are improved.

Inventors

ZHOU QIUPING
DING HUA
DENG JIADONG
LI XUEGUI

Assignees

深圳十沣科技有限公司

Dates

Publication Date: 20260508
Application Date: 20251118

Claims (9)

1. A method for adaptively determining a configuration based on a lagrangian finite element of any configuration, the method comprising: Acquiring an initial configuration of a problem to be analyzed; constructing a continuously-changing configuration interpolation parameter and an objective function based on mechanical state parameters of units and nodes of the current time step and the last time step, wherein the configuration interpolation parameter is used for defining any intermediate reference configuration between an initial configuration and the current configuration, and the objective function is an index reflecting the geometric quality of a grid or the stability of the numerical value of a self-configuration; Searching an optimal configuration parameter for enabling the objective function to reach an optimal value in the configuration interpolation parameter based on an optimization algorithm, and taking an intermediate reference configuration corresponding to the optimal configuration parameter as a target reference configuration of the current time step; Performing global nonlinear finite element analysis on the target reference configuration to update state variables of a current time step based on the target reference configuration; Global nonlinear finite element analysis is performed on the target reference configuration to achieve updating of state variables of a current time step based on the target reference configuration, including: Calculating a deformation gradient and a velocity gradient of the target reference configuration; calculating a strain tensor and a strain rate tensor based on the target reference configuration according to the deformation gradient and the speed gradient; And performing constitutive integration based on the deformation gradient, the speed gradient, the strain tensor and the strain rate tensor to update the state variable of the current time step based on the target reference configuration.
2. The configuration adaptive determination method according to claim 1, wherein the objective function includes the following: The smallest jacobian among all units of the current time step, the objective function being aimed at maximizing the value of the smallest jacobian; the minimum unit length in all units in the current time step, and the objective function aims at maximizing the minimum unit length; The objective function is targeted at a minimum magnitude of the numerical oscillation resulting from the execution of the heuristic constitutive integration based on the candidate configuration.
3. The method for adaptively determining a configuration according to claim 1, wherein the determining means of the optimal configuration parameters further comprises: Giving an optimal configuration parameter in the configuration interpolation parameter based on an AI algorithm, and taking an intermediate reference configuration corresponding to the optimal configuration parameter as a target reference configuration of the current time step; or giving an optimal configuration parameter in the configuration interpolation parameter based on an empirical formula, and taking an intermediate reference configuration corresponding to the optimal configuration parameter as a target reference configuration of the current time step.
4. The configuration adaptive determination method according to claim 2, wherein the searching for an optimal configuration parameter that brings the objective function to an optimal value within the configuration interpolation parameters based on an optimization algorithm for the jacobian includes: Searching a first candidate parameter in the value range of the configuration interpolation parameter based on an optimization algorithm, and generating a first reference configuration based on the first candidate parameter; Performing jacobian analysis on the first reference configuration based on the objective function, and determining a minimum value of the jacobian of the first reference configuration; and continuing the iterative processing until the minimum value of the jacobian is determined to be the maximum value, and taking the candidate parameter corresponding to the jacobian as the optimal configuration parameter.
5. The method of adaptive configuration determination according to claim 1, wherein the deformation gradient and the velocity gradient in the target reference configuration are determined by the following formula: ; Wherein, the Is that Target reference configuration relative to time step The deformation gradient of the configuration at the time step, Is that The coordinates of the nodes of the configuration at the time step, Is that The coordinates of the nodes of the configuration at the time step, Is that The velocity gradient of the target reference profile at the time step, Is that Target reference configuration under 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 last time step t and the current time step An intermediate time step in between.
6. The configuration adaptive determination method according to claim 1, wherein the strain tensor and the strain rate tensor are determined by the following formula: ; ; Wherein, the Is that Target reference configuration relative to time step The strain tensor of the time-step configuration, I is the identity matrix, Is that Target reference configuration relative to time step The deformation gradient of the configuration at the time step, Is that Target reference configuration relative to time step The strain rate tensor of the configuration at time step, D, is the deformation rate.
7. A configuration adaptive determining device based on arbitrary configuration lagrangian finite elements, characterized in that the configuration adaptive determining device comprises: the acquisition module is used for acquiring the initial configuration of the problem to be analyzed; The function construction module is used for constructing a continuously-changing configuration interpolation parameter and an objective function based on mechanical state parameters of units and nodes of the current time step and the last time step, wherein the configuration interpolation parameter is used for defining any intermediate reference configuration between an initial configuration and the current configuration, and the objective function is an index reflecting the geometric quality of a grid or the stability of the numerical value of the integral of the configuration; the configuration optimization module is used for searching an optimal configuration parameter for enabling the objective function to reach an optimal value in the configuration interpolation parameters based on an optimization algorithm, and taking an intermediate reference configuration corresponding to the optimal configuration parameter as a target reference configuration of the current time step; The analysis module is used for carrying out global nonlinear finite element analysis on the target reference configuration so as to update the state variable of the current time step based on the target reference configuration, and comprises the following steps: Calculating a deformation gradient and a velocity gradient of the target reference configuration; calculating a strain tensor and a strain rate tensor based on the target reference configuration according to the deformation gradient and the speed gradient; And performing constitutive integration based on the deformation gradient, the speed gradient, the strain tensor and the strain rate tensor to update the state variable of the current time step based on the target reference configuration.
8. An electronic device comprising a processor, a memory and a bus, the memory storing machine-readable instructions executable by the processor, the processor and the memory in communication via the bus when the electronic device is in operation, the machine-readable instructions being executable by the processor to perform the steps of the method for adaptive configuration determination based on lagrangian finite elements of arbitrary configuration as claimed in any one of claims 1 to 6.
9. A computer-readable storage medium, characterized in that the computer-readable storage medium has stored thereon a computer program which, when executed by a processor, performs the steps of the configuration adaptive determination method based on arbitrary configuration lagrangian finite elements as claimed in any one of claims 1 to 6.

Description

Configuration self-adaptive determination method, device, equipment and medium based on Lagrange finite element with arbitrary configuration Technical Field The application relates to the technical field of computational mechanics, in particular to a method, a device, equipment and a medium for self-adaptive determination of a configuration based on Lagrange finite elements of any configuration. Background In finite element analysis of nonlinear continuous media mechanics, particularly in problems involving large deformations, large strains (e.g., high-speed impact, explosion molding, metal plastic working, etc.), the kinematics and constitutive behavior of the material must be defined and numerically integrated under a well-defined reference configuration. Because the object can generate remarkable geometric deformation in the loading process, the initial configuration and the current configuration have obvious difference, so that how to select a proper reference configuration to ensure the accuracy and the calculation stability of stress updating becomes a key problem in nonlinear finite element analysis. The prior art generally adopts two fixed reference configuration strategies (1) taking an initial configuration as a reference, using a second type Piola-Kirchhoff stress and a Green-Lagrange strain tensor, being applicable to path-independent materials (such as super elastic rubber), but being difficult to accurately describe elastic plastic materials subjected to complex deformation history, and (2) taking a current time step configuration as a reference, constructing constitutive relations based on Cauchy stress and Almansi strain, and being widely applied to processing path-dependent materials (such as metal elastoplasticity) in commercial finite element software (such as LS-DYNA and Abaqus). Although the method can better reflect the local deformation state, under the condition of large deformation, serious distortion (such as distortion, overturning or overstretching) occurs along with the unit, so that the jacobian is negative, the grid quality is rapidly reduced, and the numerical value is unstable and even the solving is interrupted. In summary, the main defect in the prior art is that the selection mode of the reference configuration is fixed and stiff, and cannot be adaptively adjusted according to the actual deformation state, so that the problems of grid distortion aggravation, numerical oscillation, solving failure, forced shrinkage of time step and the like are easy to occur under the large deformation working condition. Therefore, a new method for dynamically selecting the optimal reference configuration to improve the calculation robustness and efficiency on the premise of keeping the finite element topology unchanged is needed. Disclosure of Invention In view of the above, the present application aims to provide a method, a device and a medium for adaptive configuration determination based on Lagrange finite elements with arbitrary configurations, which can realize any intermediate configuration from an initial configuration to a current configuration as a reference frame of the integral of the configuration by introducing continuously adjustable configuration interpolation parameters. On the basis, the optimal configuration parameters are automatically searched by combining the objective function, numerical anomalies such as negative volume, grid overturning and the like caused by serious distortion of the current configuration are effectively avoided, and the simulation efficiency and the numerical stability of nonlinear finite element analysis are improved. The embodiment of the application provides a configuration self-adaptive determination method based on Lagrangian finite elements with arbitrary configurations, which comprises the following steps: Acquiring an initial configuration of a problem to be analyzed; constructing a continuously-changing configuration interpolation parameter and an objective function based on mechanical state parameters of units and nodes of the current time step and the last time step, wherein the configuration interpolation parameter is used for defining any intermediate reference configuration between an initial configuration and the current configuration, and the objective function is an index reflecting the geometric quality of a grid or the stability of the numerical value of a self-configuration; Searching an optimal configuration parameter for enabling the objective function to reach an optimal value in the configuration interpolation parameter based on an optimization algorithm, and taking an intermediate reference configuration corresponding to the optimal configuration parameter as a target reference configuration of the current time step; and carrying out global nonlinear finite element analysis on the target reference configuration so as to update the state variable of the current time step based on the target reference configuration. In one