Fundamental frequency topological optimization method and device for continuous fiber reinforced composite material structure

Abstract

The invention relates to a fundamental frequency topological optimization method and device for a continuous fiber reinforced composite structure, and the method comprises the steps: obtaining the material attribute parameters of a target fiber reinforced composite; calculating an element stiffness matrix and a partial derivative matrix of the sampling direction vector of the design variable; the design variables are filtered, and an element stiffness matrix approximate value is solved; calculating a template stiffness matrix of each node of each grid level; calculating a smooth residual error of the densest grid hierarchy after preprocessing, and calculating an approximate feature vector of the densest grid hierarchy; calculating a target function value according to a design variable and the closest grid level approximate feature vector to obtain a sensitivity value; and updating the design variable until a preset number of iterations is reached, and determining an optimization design result. Therefore, the problems that in the related technology, due to the fact that the memory of a GPU global memory is limited, the efficiency of solving the large-scale characteristic value problem through a double-circulation method is low, and large-scale topological optimization solving of the fiber reinforced composite material with the maximum structure fundamental frequency is difficult are solved.

Description

Technical Field

[0001] This application relates to the field of structural optimization technology, and in particular to a method and apparatus for optimizing the fundamental frequency topology of a continuous fiber reinforced composite material structure. Background Technology

[0002] Currently, fiber-reinforced composite materials have become core materials in aerospace, high-end equipment, and other fields due to their excellent specific strength, specific stiffness, and designability. With the development of additive manufacturing technology, components with complex three-dimensional topologies and spatially continuously varying fiber orientations have become possible. Topology optimization is a powerful tool for achieving the design of such high-performance lightweight structures. However, topology optimization for maximizing the fundamental frequency of such materials faces severe challenges: high-resolution discretization of the three-dimensional structure leads to a huge model size; the spatially varying fiber orientation makes the stiffness matrix of each element different; maximizing the fundamental frequency as an eigenvalue optimization problem has extremely high solution costs; the repetition frequency phenomenon makes the objective function non-differentiable; and in GPU (Graphics Processing Unit) accelerated computing, storing or computing the different element stiffness matrices faces dual constraints of GPU memory and efficiency.

[0003] In related technologies, multiple interpolation schemes are used to suppress spurious modes that occur during the optimization process, aggregation methods or boundary schemes are used to handle the repetition phenomenon, and multi-level discretization strategies are used to accelerate the solution process in order to cope with the computational burden brought about by large-scale discrete models.

[0004] However, in related technologies, it is difficult to efficiently process the fundamental frequency topology optimization of large-scale three-dimensional composite materials with spatially varying fiber orientations while ensuring accuracy. Due to the limited global memory of GPUs, the stiffness matrices of each element in the large-scale topology optimization problem of fiber-reinforced composite materials cannot be stored. The double-loop method is inefficient in solving large-scale eigenvalue problems, making it difficult to solve the large-scale topology optimization of fiber-reinforced composite materials that maximizes the structural fundamental frequency. This problem urgently needs to be improved. Summary of the Invention

[0005] This application provides a method and apparatus for optimizing the fundamental frequency topology of continuous fiber-reinforced composite structures, in order to solve the problems in related technologies, such as the inability to store the stiffness matrix of each element in large-scale topology optimization problems of fiber-reinforced composites due to the limited global memory of GPUs, the low efficiency of the double loop method in solving large-scale eigenvalue problems, and the difficulty in solving large-scale topology optimization problems of fiber-reinforced composites that maximize the fundamental frequency of the structure.

[0006] The first aspect of this application provides a fundamental frequency topology optimization method for a continuous fiber-reinforced composite material structure, comprising the following steps: obtaining material property parameters of the target fiber-reinforced composite material and determining design variables of a pre-constructed topology optimization model; calculating the element stiffness matrix and partial derivative matrix of the sampling direction vector of the design variables based on the material property parameters and a preset number of sampling points; filtering the design variables to solve for an approximate value of the element stiffness matrix based on the element stiffness matrix and the partial derivative matrix; and transferring the template stiffness matrix between each mesh level based on the approximate value of the element stiffness matrix. The process involves calculating the template stiffness matrix for each node in each grid level, calculating the smoothed residual of the densest grid level after preprocessing based on the template stiffness matrix, and calculating the approximate eigenvector of the densest grid level based on the smoothed residual. The objective function value is then calculated based on the design variables and the approximate eigenvector of the densest grid level, and a sensitivity value is obtained based on the objective function value. The current design variables are updated based on the objective function value and the sensitivity value until a preset number of iterations is reached, thus determining the optimized design result of the target fiber-reinforced composite material.

[0007] Through the above technical means, the embodiments of this application can obtain material property parameters, calculate the element stiffness matrix and its partial derivative matrix with respect to the sampling direction vector for each sampling direction vector based on the material property parameters and the preset number of sampling points, filter the design variables respectively, use the geometric multigrid preprocessing conjugate gradient method iterative solver to calculate the approximate eigenvector of the densest grid level, calculate the objective function based on the current design variables and the approximate eigenvector of the densest grid level, perform sensitivity analysis based on whether a repetition frequency occurs, update the design variables, until the preset number of iterations is reached, and output a new optimized design, thereby improving the approximate accuracy of the element stiffness matrix, balancing the contradiction between the storage consumption of GPU global memory and computing performance, saving memory access time and computing time, improving the computational efficiency of the algorithm, and enabling the optimization algorithm to correctly perform sensitivity analysis under repetition frequency conditions, and finally obtain a clear topological structure and continuously changing fiber direction.

[0008] Optionally, in one embodiment of this application, the step of calculating the element stiffness matrix and partial derivative matrix of the sampling direction vector of the design variable based on the material property parameters and the preset number of sampling points includes: determining the sampling direction vector of the design variable based on the preset number of sampling points; constructing the constitutive relation matrix of the orthotropic material based on the material property parameters; and calculating the element stiffness matrix and the partial derivative matrix based on the constitutive relation matrix of the orthotropic material and the sampling direction vector.

[0009] Through the above technical means, the embodiments of this application can adopt the method of pre-calculating and storing the element stiffness matrix and partial derivative matrix corresponding to the sampling direction vector, which solves the problems that the stiffness matrix of each element in the large-scale topology optimization problem of fiber-reinforced composite materials cannot be stored due to the limited global memory of the GPU, and the low efficiency of dynamically calculating the element stiffness matrix in the finite element solution process.

[0010] Optionally, in one embodiment of this application, the formula for the approximate value of the element stiffness matrix is: , , in, The element stiffness matrix corresponding to the actual design variables. This is the stiffness matrix of the sampling element corresponding to the sampling angle obtained by mapping from the actual angle variable. and is the interpolation function for the mass matrix of the stiffness matrix.

[0011] Through the above technical means, the embodiments of this application can calculate the approximate value of the element stiffness matrix according to the Taylor expansion formula, which reduces the huge computational overhead caused by repeatedly calculating the element stiffness matrix in the iteration, and improves the computational efficiency and accuracy.

[0012] Optionally, in one embodiment of this application, the design variables include density design variables and fiber orientation design variables, and the filtering expression for the density design variables is: , in, Design variables for the filtered density. Design variables for the density. For volume, For weighting functions; The filtering expression for the fiber orientation design variable is: , in, Design variables for the fiber orientation after filtration. Design variables for the density. For volume, This is the weighting function.

[0013] Through the above-mentioned technical means, the embodiments of this application can filter density design variables and fiber orientation design variables, thereby avoiding the checkerboard phenomenon, ensuring the grid independence and manufacturability of the design results, smoothing the fiber orientation change, and improving the practical engineering value of the optimization results.

[0014] Optionally, in one embodiment of this application, the expression for the template stiffness matrix transfer relationship between each mesh level is: , in, For the template stiffness matrix of each node in a coarser mesh level, for The summation index corresponding to the direction, for The summation index corresponding to the direction, for Direction corresponds to summation index, and The weights passed to the template stiffness matrix between different mesh levels. This is the template stiffness matrix for each node in a denser mesh layer.

[0015] Through the above technical means, the embodiments of this application can clarify the quantitative transfer rules of template stiffness matrix between different grid levels, calculate the template stiffness matrix of each node in each grid level, realize the accurate and efficient transfer calculation of template stiffness matrix between levels, and thus greatly accelerate the convergence speed of eigenvalue solution.

[0016] Optionally, in one embodiment of this application, the step of calculating the smoothed residual of the densest mesh layer after preprocessing based on the template stiffness matrix of each node in each mesh layer, and calculating the approximate eigenvector of the densest mesh layer based on the smoothed residual of the densest mesh layer after preprocessing, includes: calculating the initial residual of the densest mesh layer based on the template stiffness matrix of each node in each mesh layer, a preset initial approximate eigenvector, and a preset right-hand side term; transferring the initial residual of the densest mesh layer to the coarsest mesh layer to obtain the constrained residual of the coarsest mesh layer, and based on the overall stiffness matrix of the coarsest mesh layer and the coarsest... The constrained residuals of the mesh levels are used to solve for the constrained approximate eigenvectors of each node in the coarsest mesh level. These constrained approximate eigenvectors are then passed to the densest mesh level to obtain the extended approximate eigenvectors of each node in the densest mesh level. Based on the template stiffness matrix of the densest mesh level and the extended approximate eigenvectors of each node in the densest mesh level, the extended residuals of the densest mesh level are calculated. Based on the extended residuals of the densest mesh level, the preprocessed smooth residuals of the densest mesh level are obtained. Based on the preprocessed smooth residuals of the densest mesh level, the approximate eigenvectors of the densest mesh level are calculated.

[0017] Through the above-mentioned technical means, the embodiments of this application can use a geometric multigrid preprocessing conjugate gradient method iterative solver to calculate the approximate eigenvector of the densest grid level, which greatly reduces the computational complexity and overall computational cost. At the same time, through the hierarchical transfer of residuals, preprocessing and smoothing, and the combined use of the stiffness / template stiffness matrices of each grid level, the accuracy of the final solved approximate eigenvector of the densest grid level is guaranteed, providing reliable eigenvector support for the accurate calculation of the subsequent objective function and sensitivity value.

[0018] A second aspect of this application provides a fundamental frequency topology optimization device for a continuous fiber-reinforced composite material structure, comprising: an acquisition module for acquiring material property parameters of a target fiber-reinforced composite material and determining design variables of a pre-constructed topology optimization model; a first calculation module for calculating the element stiffness matrix and partial derivative matrix of the sampling direction vector of the design variables based on the material property parameters and a preset number of sampling points; a solution module for filtering the design variables to solve for an approximate value of the element stiffness matrix based on the element stiffness matrix and the partial derivative matrix; and a second calculation module for calculating the approximate value of the element stiffness matrix and the template stiffness matrix between each mesh level. The system employs a transfer relationship to calculate the template stiffness matrix of each node in each grid level; a third calculation module calculates the smoothed residual of the densest grid level after preprocessing based on the template stiffness matrix of each node in each grid level, and calculates the approximate eigenvector of the densest grid level based on the smoothed residual of the densest grid level; a fourth calculation module calculates the objective function value based on the design variables and the approximate eigenvector of the densest grid level, and obtains the sensitivity value based on the objective function value; and an optimization module updates the current design variables based on the objective function value and the sensitivity value until a preset number of iterations is reached, thereby determining the optimized design result of the target fiber-reinforced composite material.

[0019] Through the above technical means, the embodiments of this application can obtain material property parameters, calculate the element stiffness matrix and its partial derivative matrix with respect to the sampling direction vector for each sampling direction vector based on the material property parameters and the preset number of sampling points, filter the design variables respectively, use the geometric multigrid preprocessing conjugate gradient method iterative solver to calculate the approximate eigenvector of the densest grid level, calculate the objective function based on the current design variables and the approximate eigenvector of the densest grid level, perform sensitivity analysis based on whether a repetition frequency occurs, update the design variables, until the preset number of iterations is reached, and output a new optimized design, thereby improving the approximate accuracy of the element stiffness matrix, balancing the contradiction between the storage consumption of GPU global memory and computing performance, saving memory access time and computing time, improving the computational efficiency of the algorithm, and enabling the optimization algorithm to correctly perform sensitivity analysis under repetition frequency conditions, and finally obtain a clear topological structure and continuously changing fiber direction.

[0020] Optionally, in one embodiment of this application, the first calculation module includes: a determining unit, configured to determine the sampling direction vector of the design variable according to a preset number of sampling points; a constructing unit, configured to construct the constitutive relation matrix of the orthotropic material according to the material property parameters; and a first calculation unit, configured to calculate the element stiffness matrix and the partial derivative matrix based on the constitutive relation matrix of the orthotropic material and the sampling direction vector.

[0021] Through the above technical means, the embodiments of this application can adopt the method of pre-calculating and storing the element stiffness matrix and partial derivative matrix corresponding to the sampling direction vector, which solves the problems that the stiffness matrix of each element in the large-scale topology optimization problem of fiber-reinforced composite materials cannot be stored due to the limited global memory of the GPU, and the low efficiency of dynamically calculating the element stiffness matrix in the finite element solution process.

[0022] Optionally, in one embodiment of this application, the formula for the approximate value of the element stiffness matrix is: , , in, The element stiffness matrix corresponding to the actual design variables. This is the stiffness matrix of the sampling element corresponding to the sampling angle obtained by mapping from the actual angle variable. and is the interpolation function for the mass matrix of the stiffness matrix.

[0023] Through the above technical means, the embodiments of this application can calculate the approximate value of the element stiffness matrix according to the Taylor expansion formula, which reduces the huge computational overhead caused by repeatedly calculating the element stiffness matrix in the iteration, and improves the computational efficiency and accuracy.

[0024] Optionally, in one embodiment of this application, the design variables include density design variables and fiber orientation design variables, and the filtering expression for the density design variables is: , in, Design variables for the filtered density. Design variables for the density. For volume, For weighting functions; The filtering expression for the fiber orientation design variable is: , in, Design variables for the fiber orientation after filtration. Design variables for the density. For volume, This is the weighting function.

[0025] Through the above-mentioned technical means, the embodiments of this application can filter density design variables and fiber orientation design variables, thereby avoiding the checkerboard phenomenon, ensuring the grid independence and manufacturability of the design results, smoothing the fiber orientation change, and improving the practical engineering value of the optimization results.

[0026] Optionally, in one embodiment of this application, the expression for the template stiffness matrix transfer relationship between each mesh level is: , in, For the template stiffness matrix of each node in a coarser mesh level, for The summation index corresponding to the direction, for The summation index corresponding to the direction, for Direction corresponds to summation index, and The weights passed to the template stiffness matrix between different mesh levels. This is the template stiffness matrix for each node in a denser mesh layer.

[0027] Through the above technical means, the embodiments of this application can clarify the quantitative transfer rules of template stiffness matrix between different grid levels, calculate the template stiffness matrix of each node in each grid level, realize the accurate and efficient transfer calculation of template stiffness matrix between levels, and thus greatly accelerate the convergence speed of eigenvalue solution.

[0028] Optionally, in one embodiment of this application, the third calculation module includes: a second calculation unit, configured to calculate the initial residual of the densest mesh layer based on the template stiffness matrix of each node in each mesh layer, a preset initial approximate eigenvector, and a preset right-hand term; and a solution unit, configured to transfer the initial residual of the densest mesh layer to the coarsest mesh layer to obtain the constrained residual of the coarsest mesh layer, and solve for the constrained approximate eigenvector of each node in the coarsest mesh layer based on the overall stiffness matrix of the coarsest mesh layer and the constrained residual of the coarsest mesh layer; the third calculation unit... The first unit is used to transfer the constrained approximate feature vectors of each node in the coarsest mesh level to the densest mesh level to obtain the extended approximate feature vectors of each node in the densest mesh level, and calculate the extended residual of the densest mesh level based on the template stiffness matrix of the densest mesh level and the extended approximate feature vectors of each node in the densest mesh level; the second unit is used to obtain the smoothed residual of the densest mesh level after preprocessing based on the extended residual of the densest mesh level, and calculate the approximate feature vector of the densest mesh level based on the smoothed residual after preprocessing based on the densest mesh level.

[0029] Through the above-mentioned technical means, the embodiments of this application can use a geometric multigrid preprocessing conjugate gradient method iterative solver to calculate the approximate eigenvector of the densest grid level, which greatly reduces the computational complexity and overall computational cost. At the same time, through the hierarchical transfer of residuals, preprocessing and smoothing, and the combined use of the stiffness / template stiffness matrices of each grid level, the accuracy of the final solved approximate eigenvector of the densest grid level is guaranteed, providing reliable eigenvector support for the accurate calculation of the subsequent objective function and sensitivity value.

[0030] A third aspect of this application provides an electronic device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the fundamental frequency topology optimization method for continuous fiber reinforced composite material structures as described in the above embodiments.

[0031] A fourth aspect of this application provides a non-volatile computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method for optimizing the fundamental frequency topology of a continuous fiber-reinforced composite structure.

[0032] A fifth aspect of this application provides a computer program product that stores a computer program that, when executed by a processor, implements the above-described method for optimizing the fundamental frequency topology of a continuous fiber-reinforced composite material structure.

[0033] This application embodiment can obtain material property parameters, calculate the element stiffness matrix and its partial derivative matrix with respect to the sampling direction vector for each sampling direction vector based on the material property parameters and a preset number of sampling points, filter the design variables, and use a geometric multigrid preprocessing conjugate gradient method iterative solver to calculate the approximate eigenvector of the densest grid level. The objective function is calculated based on the current design variables and the approximate eigenvector of the densest grid level. Sensitivity analysis is performed based on whether a repetition frequency occurs, and the design variables are updated until a preset number of iterations is reached, outputting a new optimized design. This improves the approximate accuracy of the element stiffness matrix, balancing the contradiction between GPU global memory consumption and computational performance, saving memory access time and computation time, improving the computational efficiency of the algorithm, and enabling the optimization algorithm to correctly perform sensitivity analysis under repetition frequency conditions, ultimately obtaining a clear topology and continuously changing fiber orientation. Therefore, it solves the problems in related technologies, such as the inability to store element stiffness matrices in large-scale topology optimization problems of fiber-reinforced composite materials due to GPU global memory limitations, the low efficiency of the double-loop method in solving large-scale eigenvalue problems, and the difficulty in solving large-scale topology optimization problems of fiber-reinforced composite materials that maximize the structural fundamental frequency.

[0034] Additional aspects and advantages of this application will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of this application. Attached Figure Description

[0035] The above and / or additional aspects and advantages of this application will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein: Figure 1 This is a flowchart illustrating a fundamental frequency topology optimization method for a continuous fiber reinforced composite structure according to an embodiment of this application. Figure 2 This is a schematic diagram of a topology optimization problem according to an embodiment of this application; Figure 3 This is a flowchart of a method for fundamental frequency topology optimization of continuous fiber reinforced composite structures according to an embodiment of this application; Figure 4 This is a schematic diagram illustrating an angle variable definition method according to an embodiment of this application; Figure 5 The flowchart of the "V" loop algorithm for the geometric multigrid preprocessing method according to an embodiment of this application is shown. Figure 6 This is an iterative history diagram of the first three characteristic frequencies provided according to an embodiment of this application; Figure 7 This is a schematic diagram illustrating the optimization results provided according to an embodiment of this application; Figure 8 This is a comparative diagram of optimization results provided according to an embodiment of this application; Figure 9 This is a schematic diagram of a fundamental frequency topology optimization device for a continuous fiber reinforced composite material structure provided in an embodiment of this application; Figure 10 This is a schematic diagram of the structure of an electronic device provided according to an embodiment of this application.

[0036] Figure label: 10-Continuous fiber reinforced composite material structure fundamental frequency topology optimization device; 100-Acquisition module, 200-First calculation module, 300-Solving module, 400-Second calculation module, 500-Third calculation module, 600-Fourth calculation module, 700-Optimization module; 1001-Memory, 1002-Processor, 1003-Communication interface. Detailed Implementation

[0037] The embodiments of this application are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application.

[0038] The following description, with reference to the accompanying drawings, outlines a method and apparatus for optimizing the fundamental frequency topology of continuous fiber-reinforced composite structures according to embodiments of this application. Addressing the issues raised in the background section, such as the limitation of GPU global memory leading to the inability to store the stiffness matrices of individual elements in large-scale topology optimization problems of fiber-reinforced composite materials, and the low efficiency of the double-loop method for solving large-scale eigenvalue problems, which makes it difficult to solve large-scale topology optimization problems of fiber-reinforced composite materials maximizing the fundamental frequency, this application provides a method for optimizing the fundamental frequency topology of continuous fiber-reinforced composite structures. In this method, material property parameters are obtained, and the element stiffness matrix corresponding to each sampling direction vector and its partial derivative matrix with respect to the sampling direction vector are calculated based on the material property parameters and a preset number of sampling points. The design variables are then filtered accordingly. This paper proposes a geometric multigrid preprocessing conjugate gradient method iterative solver to calculate the approximate eigenvectors of the densest grid level. Based on the current design variables and the approximate eigenvectors of the densest grid level, the objective function is calculated. Sensitivity analysis is performed based on the occurrence of frequency repetition, and the design variables are updated until a preset number of iterations is reached, outputting a new optimized design. This improves the approximate accuracy of the element stiffness matrix, balancing the conflict between GPU global memory consumption and computational performance, saving memory access and computation time, and improving the algorithm's computational efficiency. This allows the optimization algorithm to correctly perform sensitivity analysis under frequency repetition conditions, ultimately obtaining a clear topology and continuously changing fiber orientation. Therefore, this paper solves the problems in related technologies, such as the inability to store the element stiffness matrices in large-scale topology optimization problems of fiber-reinforced composite materials due to GPU global memory limitations, the low efficiency of the double-loop method in solving large-scale eigenvalue problems, and the difficulty in solving large-scale topology optimization problems of fiber-reinforced composite materials that maximize the structural fundamental frequency.

[0039] Specifically, Figure 1 This is a schematic flowchart illustrating a method for fundamental frequency topology optimization of a continuous fiber reinforced composite structure provided in an embodiment of this application.

[0040] like Figure 1 As shown, the method for optimizing the fundamental frequency topology of a continuous fiber reinforced composite structure includes the following steps: In step S101, the material property parameters of the target fiber-reinforced composite material are obtained, and the design variables of the pre-built topology optimization model are determined.

[0041] It is understood that the material property parameters in the embodiments of this application can be used to characterize the inherent physical and mechanical properties of the target continuous fiber reinforced composite material; the topology optimization model can be understood as a mathematical model with the goal of maximizing the structural fundamental frequency and the material distribution and fiber orientation as optimization objects; the design variables may include density design variables and fiber orientation design variables represented by Cartesian coordinates.

[0042] In actual implementation, the embodiments of this application can input the property parameters of the target fiber-reinforced composite material (transversely isotropic material), the size of the solved finite element model, the size of the design domain (which may contain non-design domains), the boundary condition definition, the size and distribution location of the non-structural mass, the Cartesian mesh model resolution, the geometric multi-mesh level, and the structural topology optimization parameters, including but not limited to the filtering radius of density and fiber orientation variables, the number of sampling points for fiber orientation variables, and the convergence conditions of the iterative solver, into the host memory and copy them into the GPU global memory.

[0043] Furthermore, embodiments of this application can define the design domain, boundary conditions, and unstructured mass distribution of the topology optimization model, initialize the design variables of the pre-built topology optimization model, wherein the design variables include density design variables and fiber orientation design variables, and initialize the initial guess of the approximate eigenvector. The density and fiber orientation design variables of each element are declared and initialized in the GPU global memory; field variables are declared to store the element stiffness matrix corresponding to each sampled fiber orientation and the partial derivative matrix of the element stiffness matrix with respect to each fiber orientation design variable; field variables are initialized to store the block template matrix and preprocessing matrix corresponding to all nodes in each mesh level; variables required for numerical processing such as design variable filtering, sensitivity filtering, regularization, etc. are initialized; and the initial guess of the approximate eigenvector is generated.

[0044] For example, the mathematical model for the topology optimization problem is as follows: , in, Design variables for density. These are the fiber direction design variables in Cartesian coordinates. and These are the overall stiffness matrix and the mass matrix, respectively. The structure is clustered at the first characteristic frequency. Characteristic frequencies in These are the corresponding eigenmodes after the quality matrix has been normalized. For the volume of each unit, For the volume of the entire design domain, This represents the volume fraction.

[0045] Initialize design variables =0.3, =0, the initial guessed feature vector is set to be randomly generated. ,in The total degrees of freedom are denoted as . Since the subspace iteration method is used to solve the eigenvalue problem, the subspace dimension is usually chosen as . The number of sampling points was set to 10,000, and both the density filter radius and the angle filter radius were set to 1.5 times the unit size.

[0046] The embodiments of this application can obtain the core material property parameters of the target composite material and determine the design variables of the topology optimization model, laying accurate and matching basic data for subsequent optimization steps such as matrix calculation, stiffness analysis, and eigenvector solving, and ensuring the orderly start of the entire topology optimization process.

[0047] In step S102, the element stiffness matrix and partial derivative matrix of the sampling direction vector of the design variable are calculated based on the material property parameters and the preset number of sampling points.

[0048] It is understood that the number of preset sampling points in this embodiment can be set to 10,000. The number of preset sampling points can be set by those skilled in the art according to the actual situation, and no specific limitation is made here. The element stiffness matrix can be a matrix used to describe the mechanical properties of the element. The partial derivative matrix can be used to reflect the rate of change of the stiffness matrix relative to the design variables.

[0049] In actual implementation, the embodiments of this application can determine the sampling vector according to the preset number of sampling points, calculate the element stiffness matrix and the partial derivative matrix of the element stiffness matrix with respect to the sampling vector corresponding to the sampling vector, and store them in the GPU global memory.

[0050] Specifically, in this embodiment, the fiber orientation variable sampling points can be determined according to the preset number of sampling points. Based on the property parameters of the target fiber-reinforced composite material and the fiber orientation variable sampling points, the element stiffness matrix corresponding to each group of sampled fiber orientations and the partial derivative matrix of each element stiffness matrix with respect to the sampled fiber orientation variable are calculated. The element stiffness matrix corresponding to each group of sampled orientation vectors and the partial derivative matrix of each element stiffness matrix with respect to the sampled fiber orientation variable are stored in the GPU global memory.

[0051] The embodiments of this application can calculate the element stiffness matrix and partial derivative matrix corresponding to the sampling direction vector of the design variable by combining material property parameters and the preset number of sampling points. This achieves accurate quantitative characterization of the element stiffness characteristics under the scenario of spatial variation of fiber direction, and provides reliable matrix data support for the subsequent approximate solution of stiffness matrix.

[0052] Optionally, in one embodiment of this application, calculating the element stiffness matrix and partial derivative matrix of the sampling direction vector of the design variable based on material property parameters and a preset number of sampling points includes: determining the sampling direction vector of the design variable based on the preset number of sampling points; constructing the constitutive relation matrix of the orthotropic material based on the material property parameters; and calculating the element stiffness matrix and partial derivative matrix based on the constitutive relation matrix and sampling direction vector of the orthotropic material.

[0053] It is understood that the constitutive relation matrix of orthotropic materials in the embodiments of this application can be used as a mechanical matrix to characterize the linear correspondence between stress and strain of orthotropic materials, and can accurately adapt to the orthotropic mechanical properties of continuous fiber reinforced composite materials due to the directional arrangement of fibers.

[0054] For example, embodiments of this application can use a preset number of sampling points. Determine the sampling vector The coordinates of all sampling points are calculated using the Fibonacci lattice point coordinate calculation formula, as follows: , Construct the constitutive relation matrix of the orthotropic material based on the property parameters of the target fiber-reinforced composite material; calculate the corresponding element stiffness matrix and partial derivative matrix based on the constitutive relation matrix of the orthotropic material and the sampled fiber direction vector.

[0055] The element stiffness matrix corresponding to each group of sampled fiber direction vectors is: , in, It is a shape function matrix consisting of 8 submatrices. The integration region represented by each unit.

[0056] Wherein, submatrix It can be represented as: , In the formula, This is the element stiffness matrix corresponding to the fiber direction of each sample. This represents the material constitutive relation matrix corresponding to the sampled fiber direction in the global coordinate system. It is a shape function matrix consisting of 8 submatrices. The integral region represented by each element. Continuous fiber-reinforced composites are typically modeled as transversely isotropic materials, and their stress-strain relationship in the principal coordinate system can be expressed as: ,in , The stiffness matrix can be calculated from the inverse of the flexibility matrix: , in, The Cartesian parameterization method introduces a set of mutually orthogonal basis vectors. , and The basis vectors in the global coordinate system are as follows: Figure 4As shown. Therefore, the stiffness matrix in the global coordinate system can be obtained by rotating the stiffness matrix in the principal coordinate system: , in, It is the stress rotation matrix, which can be represented as: , The partial derivative matrix of the element stiffness matrix with respect to the sampling fiber direction vector in each group of sampled fiber directions is calculated using the finite difference method. , , .

[0057] The embodiments of this application can adopt the method of pre-calculating and storing the element stiffness matrix and partial derivative matrix corresponding to the sampling direction vector, which solves the problems that the stiffness matrix of each element in the large-scale topology optimization problem of fiber-reinforced composite materials cannot be stored due to the limited global memory of the GPU, and the low efficiency of dynamically calculating the element stiffness matrix in the finite element solution process.

[0058] In step S103, the design variables are filtered to obtain an approximate value of the element stiffness matrix based on the element stiffness matrix and the partial derivative matrix.

[0059] It is understood that filtering design variables in this application embodiment can avoid the checkerboard phenomenon and make the fiber direction change smooth; the approximate value of the element stiffness matrix can be understood as the element stiffness matrix corresponding to the current actual design variables, which is obtained quickly through interpolation.

[0060] In practical implementation, the embodiments of this application can filter the density design variables and fiber orientation design variables to obtain filtered density design variables and filtered fiber orientation design variables. The density design variables are filtered using a filtering method to obtain filtered density design variables. Based on the fiber-direction filter radius, design variables for the fiber direction in the Cartesian coordinate system are applied respectively. Filtering is performed to obtain the filtered fiber direction vector. The filtered fiber direction vector is normalized to obtain .

[0061] Furthermore, based on the parallel approach between elements, the element stiffness matrix and partial derivative matrix corresponding to each group of sampled fiber direction vectors are processed according to the Taylor expansion formula to solve for the approximate value of the element stiffness matrix.

[0062] The embodiments of this application can filter design variables and solve their approximate values ​​by combining the element stiffness matrix and the partial derivative matrix, which ensures the correctness of the optimization direction, reduces the calculation and storage cost of the actual value of the element stiffness matrix, and makes the form of the stiffness matrix more suitable for subsequent multi-grid matrix calculations, laying an efficient computational foundation for subsequent multi-grid template stiffness matrix calculations.

[0063] Optionally, in one embodiment of this application, the design variables include density design variables and fiber orientation design variables, and the filtering expression for the density design variables is: , in, Design variables for the filtered density. Design variables for density. For volume, For weighting functions; The filtering expression for the fiber orientation design variable is: , in, Design variables for the fiber orientation after filtration. Design variables for density. For volume, This is the weighting function.

[0064] It is understood that the density design variable in the embodiments of this application can be understood as a design variable characterizing the spatial distribution of material density in a continuous fiber reinforced composite material structure; the fiber orientation design variable can be understood as a design variable characterizing the spatial arrangement direction of fibers.

[0065] In actual implementation, the embodiments of this application can filter density design variables and angle design variables. Density filtering is expressed as follows: , Fiber orientation variable filtering can be similarly represented as follows: , in, , The design variables are the density and fiber orientation after filtration, respectively. This is the weighting function. After filtering, the fiber direction vector needs to be further normalized to a unit vector to ensure the rotational stiffness matrix is ​​correctly parameterized. .

[0066] The embodiments of this application can filter density design variables and fiber orientation design variables, thereby avoiding the checkerboard phenomenon, ensuring the grid independence and manufacturability of the design results, smoothing the fiber orientation changes, and improving the practical engineering value of the optimization results.

[0067] Optionally, in one embodiment of this application, the formula for approximating the element stiffness matrix is: , , in, This is the element stiffness matrix corresponding to the actual design variables. This is the stiffness matrix of the sampling element corresponding to the sampling angle obtained by mapping from the actual angle variable. and is the interpolation function for the mass matrix of the stiffness matrix.

[0068] It is understood that the interpolation function in the embodiments of this application can be understood as a function used to perform weighted calculations between the values ​​of two or more sampling points (corresponding to the sampling direction).

[0069] In actual implementation, the embodiments of this application can be based on parallel inter-unit operation, and the element stiffness matrix and partial derivative matrix corresponding to each group of sampled fiber directions can be processed according to the Taylor expansion formula to solve for the approximate value of the element stiffness matrix.

[0070] Among them, since the improved RAMP (Rational Approximation of Material Properties) method is used to solve for the approximate value of the element stiffness matrix, its expression is:

[0071]

[0072] in, The interpolation functions for the element stiffness matrix corresponding to the actual design variables, and the mass matrix of the stiffness matrix, can be expressed as follows:

[0073] This is the stiffness matrix of the sampling element corresponding to the sampling angle obtained by mapping from the actual angle variable.

[0074] The embodiments of this application can calculate an approximate value of the element stiffness matrix based on the Taylor expansion formula, which reduces the huge computational overhead caused by repeatedly calculating the element stiffness matrix in the iteration, and improves computational efficiency and accuracy.

[0075] In step S104, based on the approximate value of the element stiffness matrix and the template stiffness matrix transfer relationship between each mesh level, the template stiffness matrix of each node in each mesh level is calculated.

[0076] It is understood that in the embodiments of this application, the mesh level can be understood as dividing the finite element model into levels of different coarseness according to the mesh resolution; the node can be understood as the vertex or center of the mesh in the coarse mesh level; the stiffness matrix can be used to calculate the contribution of its node template matrix.

[0077] In actual implementation, the embodiments of this application can calculate the template stiffness matrix of each node in each mesh level based on the approximate value of the element stiffness matrix, the template stiffness matrix solution format, and the template stiffness matrix transfer relationship between each mesh level, and store the template stiffness matrices of all other levels except the densest mesh level in the GPU global memory.

[0078] For example, the embodiments of this application can calculate the template matrices of each level required by the assembly-free geometric multigrid preprocessing method. The calculation process adopts a parallel approach between nodes. The calculation process of the template matrices corresponding to the 27 adjacent nodes of each node is assigned to a separate GPU thread. The 27 nodes belong to the 8 units adjacent to the central node. When the stiffness matrix of a certain adjacent unit is used to calculate the contribution of its node template matrix, the sampling direction vector with the largest inner product with the filtered fiber direction vector in that unit is used as the sampling fiber direction of that unit. The unit stiffness matrix and the partial derivative matrix of the unit stiffness matrix with respect to the sampling direction vector are obtained directly from the GPU global memory according to the index. The approximate value of the unit stiffness matrix is ​​calculated according to the Taylor expansion formula.

[0079] The embodiments of this application can calculate the template stiffness matrix of each node in each grid level based on the approximate value of the element stiffness matrix and the template stiffness matrix transfer relationship between grid levels. This realizes the effective transfer and reuse of stiffness information between grids of different resolutions, avoids the repetitive operation caused by calculating the stiffness matrix separately for each grid level, optimizes the calculation process, and improves the overall calculation efficiency.

[0080] Optionally, in one embodiment of this application, the expression for the template stiffness matrix transfer relationship between each mesh level is: , in, For the template stiffness matrix of each node in a coarser mesh level, for The summation index corresponding to the direction, for The summation index corresponding to the direction, for Direction corresponds to summation index, and The weights passed to the template stiffness matrix between different mesh levels. This is the template stiffness matrix for each node in a denser mesh layer.

[0081] In actual implementation, the template stiffness matrix transfer relationship between each mesh level in this embodiment can be as follows:

[0082] in, For the template stiffness matrix of each node in a coarser mesh level, for The summation index corresponding to the direction, for The summation index corresponding to the direction, for Direction corresponds to summation index, , These are all weights transferred between different mesh levels using the template stiffness matrix. This is the template stiffness matrix for each node in a denser mesh layer.

[0083] The embodiments of this application can clearly define the quantitative transfer rules of template stiffness matrix between different grid levels, calculate the template stiffness matrix of each node in each grid level, realize the accurate and efficient transfer calculation of template stiffness matrix between levels, and thus greatly accelerate the convergence speed of eigenvalue solution.

[0084] In step S105, the smooth residual of the densest grid layer after preprocessing is calculated based on the template stiffness matrix of each node in each grid layer, and the approximate eigenvector of the densest grid layer is calculated based on the smooth residual of the densest grid layer after preprocessing.

[0085] It is understood that in the embodiments of this application, the smoothed residual can be understood as the value obtained after smoothing the residual; the approximate eigenvector can be understood as the structural eigenvector obtained by approximate solution.

[0086] In actual implementation, the embodiments of this application can be based on the overall quality matrix of the current iteration step. and right end item The smooth residuals of the densest grid layer after preprocessing are calculated based on the template stiffness matrix of each node in each grid layer. The smooth residuals of the densest grid layer after preprocessing are then processed using the preprocessing conjugate gradient method to obtain the approximate eigenvectors of the densest grid layer.

[0087] The embodiments of this application can solve the smooth residuals and approximate eigenvectors of the densest grid level after preprocessing by step according to the template stiffness matrix of each grid level. This avoids the direct nested solution of large-scale generalized eigenvalue problems, greatly reducing the computational complexity and cost of eigenvalue optimization in the process of maximizing the fundamental frequency. At the same time, through the preprocessing and smoothing of the residuals, the numerical fluctuation of the residuals is effectively reduced, and the solution accuracy of the approximate eigenvectors is improved, providing core eigenvector parameters for the accurate calculation of the subsequent objective function.

[0088] Optionally, in one embodiment of this application, the smoothed residual of the densest mesh layer after preprocessing is calculated based on the template stiffness matrix of each node in each mesh layer, and the approximate eigenvector of the densest mesh layer is calculated based on the smoothed residual of the densest mesh layer after preprocessing, including: calculating the initial residual of the densest mesh layer based on the template stiffness matrix of each node in each mesh layer, a preset initial approximate eigenvector, and a preset right-hand side term; the initial residual of the densest mesh layer is passed to the coarsest mesh layer to obtain the constrained residual of the coarsest mesh layer, and the final residual is calculated based on the overall stiffness matrix of the coarsest mesh layer and the coarsest mesh layer. The constrained residuals at the lattice level are used to solve for the constrained approximate eigenvectors of each node at the coarsest lattice level. These constrained approximate eigenvectors are then passed to the densest lattice level to obtain the extended approximate eigenvectors of each node at the densest lattice level. Based on the template stiffness matrix and the extended approximate eigenvectors of each node at the densest lattice level, the extended residuals of the densest lattice level are calculated. Based on the extended residuals of the densest lattice level, the preprocessed smooth residuals of the densest lattice level are obtained. Finally, based on the preprocessed smooth residuals of the densest lattice level, the approximate eigenvectors of the densest lattice level are calculated.

[0089] It is understood that, in the embodiments of this application, the preset initial approximate feature vector can be the approximate feature vector of the current iteration step. The preset initial approximate feature vector can be set by those skilled in the art according to the actual situation, and no specific restrictions are imposed here; the preset right-hand term is The preset right-hand term can be set by those skilled in the art according to the actual situation, and no specific restrictions are imposed here; the initial residual can be understood as the deviation value corresponding to the initial solution value of the eigenvector under the densest grid level; the restricted residual can be understood as the residual after the initial residual is passed to the coarsest grid level and scaled; the restricted approximate eigenvector can be understood as the eigenvector solved based on the restricted residual at the coarsest grid level; the extended approximate eigenvector can be understood as the eigenvector after the restricted approximate eigenvector is passed back to the densest grid level and scaled back; the extended residual can be understood as the residual calculated based on the extended approximate eigenvector.

[0090] For example, embodiments of this application can use the "V" loop algorithm of inter-element parallelism and geometric multigrid to calculate the initial residual of the densest grid level based on the template stiffness matrix of each node in each grid level and the right-hand side of the preset initial guess eigenvector.

[0091] A constraint method is used to transfer the initial residual of the densest mesh level to the coarsest mesh level to obtain the constraint residual of the coarsest mesh level. Then, a direct method is used to solve for the constraint approximate eigenvectors of each node of the coarsest mesh level based on the overall stiffness matrix of the coarsest mesh level and the constraint residual of the coarsest mesh level.

[0092] The confinement approximate eigenvectors of each node in the coarsest mesh level are transferred to the densest mesh level using the continuation method, resulting in the continuation approximate eigenvectors of each node in the densest mesh level. The continuation residual of the densest mesh level is then calculated based on the template stiffness matrix of the densest mesh level and the continuation approximate eigenvectors of each node in the densest mesh level.

[0093] A post-smoothing method is used to process the extended residuals of the densest grid level to obtain the smoothed residuals of the densest grid level after preprocessing.

[0094] The preprocessing conjugate gradient method is used to obtain the current approximate feature vector of each node in the densest grid level based on the smooth residual of the densest grid level.

[0095] Updating the approximate eigenvector of the current iteration step involves the following process: calculate and Solving low-dimensional eigenvalue problems Update the approximate eigenvector of the current iteration step. .

[0096] The embodiments of this application can use a geometric multigrid preprocessing conjugate gradient method iterative solver to calculate the approximate eigenvector of the densest grid level, which greatly reduces the computational complexity and overall computational cost. At the same time, through the hierarchical transfer of residuals, preprocessing and smoothing, and the combined use of the stiffness / template stiffness matrices of each grid level, the accuracy of the final solved approximate eigenvector of the densest grid level is guaranteed, providing reliable eigenvector support for the accurate calculation of the subsequent objective function and sensitivity value.

[0097] In step S106, the objective function value is calculated based on the design variables and the approximate eigenvector of the densest grid level, and the sensitivity value is obtained based on the objective function value.

[0098] It is understood that, in the embodiments of this application, the objective function value can be understood as a quantitative index that characterizes the magnitude of the fundamental frequency of the structure, calculated based on the design variables and the approximate eigenvector; the sensitivity value can be understood as the partial derivative of the objective function with respect to the design variables, characterizing the degree of influence of small changes in the design variables on the objective function value.

[0099] In actual implementation, the embodiments of this application can use the Rayleigh quotient to solve for approximate eigenvalues ​​based on the current design variables and the approximate eigenvectors of the densest grid level, use the cluster mean method to calculate the objective function value of the current iteration step, and perform sensitivity analysis on the objective function value and constraints based on whether the current structural fundamental frequency has a repetition frequency to obtain the sensitivity value.

[0100] For example, embodiments of this application can use the Rayleigh quotient to solve for approximate eigenvalues ​​based on the current design variables and the approximate eigenvectors of the densest mesh level. The cluster mean method is used to calculate the objective function value of the current iteration step. Sensitivity analysis was performed on the objective function value and constraints to obtain the sensitivity value.

[0101] Specifically, the sensitivity value of the objective function to the design variables is calculated based on whether the current structural fundamental frequency exhibits frequency repetition. When the... When there is no repeated frequency in the fundamental frequency of the next optimization iteration, the sensitivity of the fundamental frequency to the design variables can be calculated as follows; , When the The second optimization iteration exists At the first repetition frequency, the sensitivity of the fundamental frequency to design variables can be calculated as follows: .

[0102] The embodiments of this application can use the cluster mean method to calculate the objective function value, avoiding the problem that a single fundamental frequency is not differentiable with respect to the design variables when the repetition frequency occurs. This enables the optimization algorithm to correctly perform sensitivity analysis under the repetition frequency condition and ultimately obtain a clear topology and continuously changing fiber orientation.

[0103] In step S107, the current design variables are updated based on the objective function value and sensitivity value until the preset number of iterations is reached, and the optimized design result of the target fiber-reinforced composite material is determined.

[0104] It is understood that the preset number of iterations in this embodiment can be 300. The preset number of iterations can be set by those skilled in the art according to the actual situation, and no specific limitation is made here.

[0105] In actual implementation, the embodiments of this application can update the current design variables according to the objective function value and sensitivity value to obtain a new optimized design until the preset number of iterations is reached and the new optimized design is output.

[0106] Specifically, the density design variables are updated based on the objective function value and sensitivity value using the ZPR (Zhang-Paulino-Ramos) method to obtain new density design variables. The fiber orientation design variables are updated based on the moving asymptote-like convex approximation method to obtain new fiber orientation design variables. It is then determined whether the current number of optimization iterations has reached the preset maximum number. If it has, the iteration ends and a new optimized design is output; otherwise, the iteration continues.

[0107] The embodiments of this application can iteratively update the design variables according to the objective function value and the sensitivity value until the number of iterations is reached, and determine the optimized design result. By iteratively updating, the design variables are gradually adjusted in the direction of maximizing the fundamental frequency, realizing the continuous optimization and improvement of the structural fundamental frequency, making the optimization result more in line with the preset optimization goal. The optimized design result takes into account both the maximization of the fundamental frequency of the continuous fiber reinforced composite material structure and the lightweight requirement, effectively realizing high-performance topology optimization of composite material structure.

[0108] Specifically, it can be combined with Figures 2 to 8 As shown, the working principle of the fundamental frequency topology optimization method for continuous fiber reinforced composite material structures in this application is explained in detail with a specific embodiment.

[0109] The following uses a three-dimensional cantilever beam structure obtained after topology optimization as an example to illustrate the finite element analysis of large-scale fiber-reinforced composite materials. In this structure, the left end face of the initial cubic design domain is a fixed constraint, with a height of 1.0m, a length of 3.0m, and a width of 1.0m. Figure 2 As shown. The number of elements after discretizing the design domain into a finite element model. It can be represented as: Longitudinal elastic modulus of fiber-reinforced composites 132×10 9 Pa, transverse elastic modulus It is 9.6 × 10 9 Pa, Poisson's ratio It is 0.258. The in-plane shear modulus is 0.35. It is 5.8 × 10 9Pa. A total of 1215 kg of distributed unstructured mass is applied to the lower edge of the right end face of the structure. The dashed plane in the middle of the design domain represents the symmetry plane that imposes mandatory symmetry constraints on the design variables of density and fiber orientation. A volume constraint of 30% is applied with the optimization objective of maximizing the fundamental frequency of the structure.

[0110] like Figure 2 As shown, embodiments of this application may include the following steps: Step S301: Obtain the preset fiber-reinforced composite material property parameters, and define the design domain, boundary conditions, and non-structural mass distribution of the topology optimization model.

[0111] The mathematical model for the topology optimization problem can be established in the embodiments of this application as follows: , in, Design variables for density. These are the fiber direction design variables in Cartesian coordinates. and These are the overall stiffness matrix and the mass matrix, respectively. The structure is clustered at the first characteristic frequency. Characteristic frequencies in These are the corresponding eigenmodes after the quality matrix has been normalized. For the volume of each unit, For the volume of the entire design domain, This represents the volume fraction.

[0112] Step S302: Initialize the density and fiber orientation design variables and the initial guess values ​​of the approximate eigenvectors.

[0113] In this embodiment, design variables can be initialized. =0.3, =0, the initial guessed feature vector is set to be randomly generated. ,in The total degrees of freedom are denoted as . Since the subspace iteration method is used to solve the eigenvalue problem, the subspace dimension is usually chosen as . The number of sampling points was set to 10,000, and both the density filter radius and the angle filter radius were set to 1.5 times the unit size.

[0114] Step S303: Determine the sampling vector according to the preset number of sampling points, calculate the element stiffness matrix and partial derivative matrix corresponding to the sampling vector, and store the partial derivative matrix of the sampling vector in the GPU global memory.

[0115] In this embodiment, the coordinates of all sampling points can be calculated based on the Fibonacci lattice point coordinate calculation formula, according to the number of sampling points. The specific calculation formula is as follows: , The element stiffness matrix corresponding to each group of sampling points is calculated as follows:

[0116] in, It is a shape function matrix consisting of 8 submatrices.

[0117] Wherein, submatrix It can be represented as: , In the formula, This is the element stiffness matrix corresponding to the fiber direction of each sample. This represents the material constitutive relation matrix corresponding to the fiber direction sampled in the global coordinate system. It is a shape function matrix consisting of 8 submatrices. The integral region represented by each element. Continuous fiber-reinforced composites are typically modeled as transversely isotropic materials, and their stress-strain relationship in the principal coordinate system can be expressed as: ,in , The stiffness matrix can be calculated from the inverse of the flexibility matrix: , in The Cartesian parameterization method introduces a set of mutually orthogonal basis vectors. , and The basis vectors in the global coordinate system are as follows: Figure 3 As shown. Therefore, the stiffness matrix in the global coordinate system can be obtained by rotating the stiffness matrix in the principal coordinate system:

[0118] in It is the stress rotation matrix, which can be represented as: , The partial derivative matrix of the element stiffness matrix with respect to the sampling fiber direction vector in each group of sampled fiber directions is calculated using the finite difference method. , , .

[0119] Step S304: Filter the density variable; filter and normalize the fiber orientation vector.

[0120] In this embodiment, to avoid the checkerboard pattern and smooth the fiber orientation changes, density design variables and angle design variables are filtered. The density filtering is expressed as follows: , Fiber orientation variable filtering can be similarly represented as follows: , in, , The design variables are the density and fiber orientation after filtration, respectively. This is the weighting function. After filtering, the fiber direction vector needs to be further normalized to a unit vector to ensure the rotational stiffness matrix is ​​correctly parameterized. .

[0121] Step S305: Based on the parallel element method, the element stiffness matrix and partial derivative matrix corresponding to the sampled fiber direction vector are processed according to the Taylor expansion, and the approximate value of the element stiffness matrix is ​​calculated.

[0122] In this embodiment, an approximate value of the element stiffness matrix can be calculated based on the Taylor expansion formula. The calculation process is as follows: .

[0123] Step S306: Based on the approximate value of the element stiffness matrix, the solution format of the template stiffness matrix, and the template stiffness matrix transfer relationship between each mesh level, calculate the template stiffness matrix of each mesh level, and store all template stiffness matrices except for the densest level to the GPU global memory.

[0124] In this embodiment, the template matrices of each level required by the assembly-free geometric multigrid preprocessing method can be calculated. The calculation process adopts a parallel approach between nodes. The calculation process of the template matrices corresponding to the 27 adjacent nodes of each node is assigned to a separate GPU thread. The 27 nodes belong to the 8 units adjacent to the central node. When the stiffness matrix of a certain adjacent unit is used to calculate the contribution of its node template matrix, the sampling direction vector with the largest inner product with the filtered fiber direction vector in the unit is used as the sampling fiber direction of the unit. The unit stiffness matrix and the partial derivative matrix of the unit stiffness matrix with respect to the sampling direction vector calculated in step 3 are obtained directly from the GPU global memory according to the index. The approximate value of the unit stiffness matrix is ​​calculated according to the Taylor expansion formula.

[0125] Step S307: Calculate the right-hand side terms of the linear equation based on the mass matrix and approximate eigenvectors of the current iteration step.

[0126] In this embodiment, the overall quality matrix of the current iteration step can be calculated. and right end item .

[0127] Step S308: Calculate the preprocessed smooth residuals based on the template stiffness matrix of each grid level, and use the preprocessed conjugate gradient method to calculate the approximate eigenvectors of the densest grid level.

[0128] In this application, the embodiments may employ, as follows: Figure 5 The "V-loop" algorithm shown performs a geometric multimesh preprocessing process, the flow of which includes: This application embodiment may include the following steps: Step S501: Calculate the preprocessing matrix for each level.

[0129] Step S502: Pre-smoothing process.

[0130] Step S503: Calculate the residual of the current grid level.

[0131] Step S504: Transfer the residuals to the next mesh layer using the constraint formula.

[0132] Step S505: Transfer the residuals to the next mesh layer using the constraint formula.

[0133] Step S506: Determine if it is the coarsest level mesh. If yes, proceed to step S508; otherwise, proceed to step S507.

[0134] Step S507: Set the current mesh level to a coarser level.

[0135] Step S508: Solve the coarsest level linear equations using the direct method.

[0136] Step S509: Calculate the approximate eigenvectors of the second coarser level using the extension formula.

[0137] Step S510: Calculate the residual of the current grid level.

[0138] Step S511: Post-smoothing process.

[0139] Step S512: Determine if it is the densest level mesh. If yes, end; otherwise, proceed to step S509.

[0140] The preprocessing matrices required for each level of the assembly-free geometric multimesh method are calculated and stored in the GPU global memory; pre-smoothing is performed on the densest level; the residuals of the linear equations of the densest level are calculated; the residuals are passed to the next densest level as right-hand terms of the linear equations using a constraint method, and the above process is repeated until the coarsest level; on the coarsest level, the global stiffness matrix is ​​assembled, and the linear equations are solved directly using the Cholesky decomposition method; the approximate eigenvector values ​​of the next coarsest level are corrected using an extension method, and this step is repeated until the approximate eigenvector solution of the densest level is obtained; post-smoothing is performed on the densest level.

[0141] At the coarsest level, the calculation process of assembling the overall stiffness matrix and solving the linear equations using the direct method based on Cholesky decomposition is completed by CPU (Central Processing Unit), and the displacement data of each node is copied to the global memory of the GPU. All other calculations are completed by GPU in parallel.

[0142] Step S309: Based on the current design variables and approximate eigenvectors, calculate the approximate eigenvalues ​​using the Rayleigh quotient and perform sensitivity analysis.

[0143] Among them, the embodiments of this application can calculate and Solving low-dimensional eigenvalue problems Update the approximate eigenvector of the current iteration step. Based on the stiffness matrix and approximate eigenvectors of each element, and using the Rayleigh quotient... Find the approximate eigenvalues ​​for the current iteration step; and apply the cluster mean method. Calculate the objective function value for the current iteration step.

[0144] Furthermore, this application embodiment performs sensitivity analysis. When the... When there is no repeated frequency in the fundamental frequency of the next optimization iteration, the sensitivity of the fundamental frequency to the design variables can be calculated as follows;

[0145] When the The second optimization iteration exists At the first repetition frequency, the sensitivity of the fundamental frequency to design variables can be calculated as follows: .

[0146] Step S310: Update the design variables based on the objective function value and sensitivity analysis results until the preset number of iterations is reached, and output the optimized result for judgment. In this application embodiment, the design variables can be optimized and updated: the density design variable is updated using the ZPR method, and the angle design variable is updated using an explicit convex approximation method similar to a moving asymptote, resulting in a new optimized design.

[0147] Step S310: Determine whether convergence has occurred. If yes, end the process; otherwise, proceed to step S304.

[0148] In this embodiment, the iteration can be determined as follows: determine whether the number of optimization iterations has reached 300. If it has reached 300, the convergence condition is met, the iteration ends, and the optimization result is output. If the convergence condition is not met, jump to step four to continue the iteration.

[0149] The following describes the optimization design of the cantilever beam structure to maximize the structural fundamental frequency using the methods and dual-loop methods of the embodiments of this application. The embodiments of this application are run on a computer equipped with an Intel(R) Xeon(R) Gold 6240 and an NVIDIA Tesla V100 GPU.

[0150] The results show that the examples can simultaneously optimize the density and fiber orientation of large-scale fiber-reinforced composites, and obtain clear topological structures and continuously varying fiber orientation designs. Figure 6 The iterative history of the first three characteristic frequencies is shown, with the fundamental frequency significantly increasing from 166.92 rad / s to 459.94 rad / s. In the early stages of optimization iteration, the first two characteristic frequencies gradually became repetition frequencies and remained so until the end of the optimization process; the third characteristic frequency was consistently much higher than the first two. Therefore, the sensitivity analysis method considering repetition frequencies proposed in this application is necessary and effective. The topology optimization results are as follows... Figure 7 As shown in Table 1, the runtime statistics of the optimization algorithm are presented. Table 1 compares the results of the method in this embodiment and the double-loop method. Figure 8 The comparison of optimization results obtained by the dual-loop method shown in the table reveals that the method proposed in this application yields topological structures and fiber orientations with minimal differences. Table 1 shows that the fundamental frequency values ​​of the optimization results from the two methods are almost identical. Furthermore, the optimization algorithm proposed in this application significantly improves computational efficiency compared to the traditional dual-loop method, greatly saving time costs associated with the large-scale fiber-reinforced composite topology optimization problem of maximizing the fundamental frequency. It also achieves a reasonable balance between the storage cost and computational time cost of the anisotropic material element stiffness matrix, which is of great significance in practical applications.

[0151] Table 1

[0152] The fundamental frequency topology optimization method for continuous fiber reinforced composite structures proposed in this application can obtain material property parameters, calculate the element stiffness matrix and its partial derivative matrix with respect to the sampling direction vector for each sampling direction vector based on the material property parameters and the preset number of sampling points, filter the design variables respectively, use a geometric multigrid preprocessing conjugate gradient method iterative solver to calculate the approximate eigenvector of the densest grid level, calculate the objective function based on the current design variables and the approximate eigenvector of the densest grid level, perform sensitivity analysis based on whether a repetition frequency occurs, update the design variables, and output a new optimized design after reaching the preset number of iterations. This improves the approximate accuracy of the element stiffness matrix, balances the contradiction between GPU global memory storage consumption and computing performance, saves memory access time and computing time, improves the computational efficiency of the algorithm, and enables the optimization algorithm to correctly perform sensitivity analysis under repetition frequency conditions, and finally obtain a clear topology and continuously changing fiber direction. This solves the problem in related technologies where the limited global memory of GPUs prevents the storage of stiffness matrices for each element in large-scale topology optimization problems of fiber-reinforced composite materials, and the low efficiency of the double-loop method in solving large-scale eigenvalue problems makes it difficult to solve large-scale topology optimization problems of fiber-reinforced composite materials that maximize the fundamental frequency of the structure.

[0153] Next, referring to the accompanying drawings, a continuous fiber reinforced composite material structure fundamental frequency topology optimization device according to an embodiment of this application is described.

[0154] Figure 9 This is a schematic diagram of the structure of the continuous fiber reinforced composite material structure fundamental frequency topology optimization device according to an embodiment of this application.

[0155] like Figure 9 As shown, the continuous fiber reinforced composite material structure fundamental frequency topology optimization device 10 includes: an acquisition module 100, a first calculation module 200, a solution module 300, a second calculation module 400, a third calculation module 500, a fourth calculation module 600, and an optimization module 700.

[0156] The acquisition module 100 is used to acquire the material property parameters of the target fiber-reinforced composite material and determine the design variables of the pre-built topology optimization model.

[0157] The first calculation module 200 is used to calculate the element stiffness matrix and partial derivative matrix of the sampling direction vector of the design variables based on the material property parameters and the preset number of sampling points.

[0158] Solver module 300 is used to filter design variables to solve for approximate values ​​of the element stiffness matrix based on the element stiffness matrix and the partial derivative matrix.

[0159] The second calculation module 400 is used to calculate the template stiffness matrix of each node in each grid level based on the approximate value of the element stiffness matrix and the template stiffness matrix transfer relationship between each grid level.

[0160] The third calculation module 500 is used to calculate the smooth residual of the densest grid layer after preprocessing based on the template stiffness matrix of each node in each grid layer, and to calculate the approximate eigenvector of the densest grid layer based on the smooth residual of the densest grid layer after preprocessing.

[0161] The fourth calculation module 600 is used to calculate the objective function value based on the design variables and the approximate eigenvector of the densest grid level, and to obtain the sensitivity value based on the objective function value.

[0162] The optimization module 700 is used to update the current design variables based on the objective function value and sensitivity value until a preset number of iterations is reached, thereby determining the optimized design result of the target fiber-reinforced composite material.

[0163] Optionally, in one embodiment of this application, the first calculation module 200 includes: a determination unit, a construction unit, and a first calculation unit.

[0164] The determining unit is used to determine the sampling direction vector of the design variables based on the preset number of sampling points.

[0165] The building unit is used to construct the constitutive relation matrix of orthogonal anisotropic materials based on material property parameters.

[0166] The first computational unit is used to compute the unit stiffness matrix and partial derivative matrix based on the constitutive relation matrix and sampling direction vector of orthogonal anisotropic materials.

[0167] Optionally, in one embodiment of this application, the formula for approximating the element stiffness matrix is: , , in, This is the element stiffness matrix corresponding to the actual design variables. This is the stiffness matrix of the sampling element corresponding to the sampling angle obtained by mapping from the actual angle variable. and is the interpolation function for the mass matrix of the stiffness matrix.

[0168] Optionally, in one embodiment of this application, the design variables include density design variables and fiber orientation design variables, and the filtering expression for the density design variables is: , in, Design variables for the filtered density. Design variables for density. For volume, For weighting functions; The filtering expression for the fiber orientation design variable is: , in, Design variables for the fiber orientation after filtration. Design variables for density. For volume, This is the weighting function.

[0169] Optionally, in one embodiment of this application, the expression for the transfer relationship of the template stiffness matrix between each mesh level is: , in, For the template stiffness matrix of each node in a coarser mesh level, for The summation index corresponding to the direction, for The summation index corresponding to the direction, for Direction corresponds to summation index, and The weights passed to the template stiffness matrix between different mesh levels. This is the template stiffness matrix for each node in a denser mesh layer.

[0170] Optionally, in one embodiment of this application, the third calculation module 500 includes: a second calculation unit, a solution unit, a third calculation unit, and a fourth calculation unit.

[0171] The second calculation unit is used to calculate the initial residual of the densest grid level based on the template stiffness matrix of each node in each grid level, the preset initial approximate eigenvector, and the preset right-hand term.

[0172] The solver element is used to transfer the initial residual of the densest mesh level to the coarsest mesh level to obtain the constrained residual of the coarsest mesh level. Based on the overall stiffness matrix of the coarsest mesh level and the constrained residual of the coarsest mesh level, the constrained approximate eigenvectors of each node of the coarsest mesh level are solved.

[0173] The third calculation unit is used to transfer the constrained approximate eigenvectors of each node in the coarsest mesh level to the densest mesh level, obtain the extended approximate eigenvectors of each node in the densest mesh level, and calculate the extended residuals of the densest mesh level based on the template stiffness matrix of the densest mesh level and the extended approximate eigenvectors of each node in the densest mesh level.

[0174] The fourth calculation unit is used to obtain the smoothed residual after preprocessing of the densest grid level based on the extended residual of the densest grid level, and to calculate the approximate eigenvector of the densest grid level based on the smoothed residual after preprocessing of the densest grid level.

[0175] It should be noted that the foregoing explanation of the embodiment of the fundamental frequency topology optimization method for continuous fiber reinforced composite material structures also applies to the fundamental frequency topology optimization device for continuous fiber reinforced composite material structures in this embodiment, and will not be repeated here.

[0176] According to the continuous fiber reinforced composite material structure fundamental frequency topology optimization device proposed in this application, material property parameters can be obtained. Based on the material property parameters and the preset number of sampling points, the element stiffness matrix and its partial derivative matrix with respect to the sampling direction vector corresponding to each sampling direction vector are calculated. The design variables are filtered respectively. The geometric multigrid preprocessing conjugate gradient method iterative solver is used to calculate the approximate eigenvector of the densest grid level. The objective function is calculated based on the current design variables and the approximate eigenvector of the densest grid level. Sensitivity analysis is performed based on whether a repetition frequency occurs. The design variables are updated until the preset number of iterations is reached, and a new optimized design is output. This improves the approximate accuracy of the element stiffness matrix, thereby balancing the contradiction between the storage consumption of GPU global memory and the computing performance, saving memory access time and computing time, improving the computational efficiency of the algorithm, and enabling the optimization algorithm to correctly perform sensitivity analysis under repetition frequency conditions, and finally obtain a clear topology and continuously changing fiber direction. This solves the problem in related technologies where the limited global memory of GPUs prevents the storage of stiffness matrices for each element in large-scale topology optimization problems of fiber-reinforced composite materials, and the low efficiency of the double-loop method in solving large-scale eigenvalue problems makes it difficult to solve large-scale topology optimization problems of fiber-reinforced composite materials that maximize the fundamental frequency of the structure.

[0177] Figure 10 A schematic diagram of the structure of an electronic device provided in an embodiment of this application. The electronic device may include: The memory 1001, the processor 1002, and the computer program stored on the memory 1001 and capable of running on the processor 1002.

[0178] When the processor 1002 executes the program, it implements the fundamental frequency topology optimization method for continuous fiber reinforced composite material structures provided in the above embodiments.

[0179] Furthermore, electronic devices also include: Communication interface 1003 is used for communication between memory 1001 and processor 1002.

[0180] The memory 1001 is used to store computer programs that can run on the processor 1002.

[0181] The memory 1001 may include high-speed RAM memory, and may also include non-volatile memory, such as at least one disk storage device.

[0182] If the memory 1001, processor 1002, and communication interface 1003 are implemented independently, then the communication interface 1003, memory 1001, and processor 1002 can be interconnected via a bus to complete communication between them. The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus, etc. Buses can be categorized into address buses, data buses, control buses, etc. For ease of representation, Figure 10 The bus is represented by a single thick line, but this does not mean that there is only one bus or one type of bus.

[0183] Optionally, in a specific implementation, if the memory 1001, processor 1002, and communication interface 1003 are integrated on a single chip, then the memory 1001, processor 1002, and communication interface 1003 can communicate with each other through an internal interface.

[0184] The processor 1002 may be a central processing unit (CPU), an application specific integrated circuit (ASIC), or one or more integrated circuits configured to implement the embodiments of this application.

[0185] This application also provides a non-volatile computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method for optimizing the fundamental frequency topology of a continuous fiber-reinforced composite material structure.

[0186] This application also provides a computer program product storing a computer program that, when executed by a processor, implements the above-described method for optimizing the fundamental frequency topology of a continuous fiber-reinforced composite material structure.

[0187] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0188] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, "N" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0189] Any process or method described in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or N executable instructions for implementing custom logic functions or processes, and the scope of the preferred embodiments of this application includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as should be understood by those skilled in the art to which embodiments of this application pertain.

[0190] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of computer-readable media include: an electrical connection having one or more wires (electronic device), a portable computer disk drive (magnetic device), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Alternatively, the computer-readable medium may be paper or other suitable media on which the program can be printed, since the program can be obtained electronically by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in a computer memory.

[0191] It should be understood that the various parts of this application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, the N steps or methods can be implemented using software or firmware stored in memory and executed by a suitable instruction execution system. If implemented in hardware, as in another embodiment, it can be implemented using any one or more of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0192] Those skilled in the art will understand that all or part of the steps of the methods in the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, the program includes one or a combination of the steps of the method embodiments.

[0193] Furthermore, the functional units in the various embodiments of this application can be integrated into a processing module, or each unit can exist physically separately, or two or more units can be integrated into a module. The integrated module can be implemented in hardware or as a software functional module. If the integrated module is implemented as a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium.

[0194] The storage medium mentioned above can be a read-only memory, a disk, or an optical disk, etc. Although embodiments of this application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting this application. Those skilled in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of this application.

Claims

1. A method for fundamental frequency topology optimization of continuous fiber reinforced composite structures, characterized in that, Includes the following steps: Obtain the material property parameters of the target fiber-reinforced composite material and determine the design variables of the pre-built topology optimization model; Calculate the element stiffness matrix and partial derivative matrix of the sampling direction vector of the design variable based on the material property parameters and the preset number of sampling points; The design variables are filtered to obtain an approximate value of the element stiffness matrix based on the element stiffness matrix and the partial derivative matrix. Based on the approximate value of the element stiffness matrix and the template stiffness matrix transfer relationship between each mesh level, the template stiffness matrix of each node in each mesh level is calculated. The smooth residual of the densest grid layer after preprocessing is calculated based on the template stiffness matrix of each node in each grid layer, and the approximate feature vector of the densest grid layer is calculated based on the smooth residual of the densest grid layer after preprocessing. The objective function value is calculated based on the design variables and the approximate eigenvector of the densest grid level, and the sensitivity value is obtained based on the objective function value. The current design variables are updated based on the objective function value and the sensitivity value until a preset number of iterations is reached, thereby determining the optimized design result of the target fiber-reinforced composite material.

2. The method according to claim 1, characterized in that, The step of calculating the element stiffness matrix and partial derivative matrix of the sampling direction vector of the design variable based on the material property parameters and the preset number of sampling points includes: The sampling direction vector of the design variable is determined based on the preset number of sampling points; Construct the constitutive relation matrix of the orthogonal anisotropic material based on the material property parameters; Based on the constitutive relation matrix of the orthogonal anisotropic material and the sampling direction vector, the element stiffness matrix and the partial derivative matrix are calculated.

3. The method according to claim 1, characterized in that, The formula for the approximate value of the element stiffness matrix is: ， ， in, The element stiffness matrix corresponding to the actual design variables. This is the stiffness matrix of the sampling element corresponding to the sampling angle obtained by mapping from the actual angle variable. and is the interpolation function for the mass matrix of the stiffness matrix.

4. The method according to claim 1, characterized in that, The design variables include density design variables and fiber orientation design variables. The filtering expression for the density design variable is as follows: ， in, Design variables for the filtered density. Design variables for the density. For volume, For weighting functions; The filtering expression for the fiber orientation design variable is: ， in, Design variables for the fiber orientation after filtration. Design variables for the density. For volume, This is the weighting function.

5. The method according to claim 1, characterized in that, The expression for the template stiffness matrix transfer relationship between each mesh level is: ， in, For the template stiffness matrix of each node in a coarser mesh level, for The summation index corresponding to the direction, for The summation index corresponding to the direction, for Direction corresponds to summation index, and The weights passed to the template stiffness matrix between different mesh levels. This is the template stiffness matrix for each node in a denser mesh layer.

6. The method according to claim 1, characterized in that, The step of calculating the smoothed residual of the densest grid layer after preprocessing based on the template stiffness matrix of each node in each grid layer, and calculating the approximate eigenvector of the densest grid layer based on the smoothed residual of the densest grid layer after preprocessing, includes: Based on the template stiffness matrix, preset initial approximate eigenvector and preset right-hand term of each node in each grid level, calculate the initial residual of the densest grid level; The initial residual of the densest mesh level is passed to the coarsest mesh level to obtain the constrained residual of the coarsest mesh level. Based on the overall stiffness matrix of the coarsest mesh level and the constrained residual of the coarsest mesh level, the constrained approximate eigenvectors of each node of the coarsest mesh level are solved. The constrained approximate eigenvectors of each node in the coarsest mesh level are passed to the densest mesh level to obtain the extended approximate eigenvectors of each node in the densest mesh level. Based on the template stiffness matrix of the densest mesh level and the extended approximate eigenvectors of each node in the densest mesh level, the extended residual of the densest mesh level is calculated. Based on the extended residual of the densest grid level, the smoothed residual after preprocessing of the densest grid level is obtained, and based on the smoothed residual after preprocessing of the densest grid level, the approximate feature vector of the densest grid level is calculated.

7. A fundamental frequency topology optimization device for continuous fiber reinforced composite material structures, characterized in that, include: The acquisition module is used to acquire the material property parameters of the target fiber-reinforced composite material and determine the design variables of the pre-built topology optimization model; The first calculation module is used to calculate the element stiffness matrix and partial derivative matrix of the sampling direction vector of the design variable based on the material property parameters and the preset number of sampling points. The solution module is used to filter the design variables in order to solve for an approximate value of the element stiffness matrix based on the element stiffness matrix and the partial derivative matrix. The second calculation module is used to calculate the template stiffness matrix of each node in each grid level based on the approximate value of the element stiffness matrix and the template stiffness matrix transfer relationship between each grid level. The third calculation module is used to calculate the smooth residual of the densest grid layer after preprocessing based on the template stiffness matrix of each node in each grid layer, and to calculate the approximate feature vector of the densest grid layer based on the smooth residual of the densest grid layer after preprocessing. The fourth calculation module is used to calculate the objective function value based on the design variables and the approximate feature vector of the densest grid level, and to obtain the sensitivity value based on the objective function value; The optimization module is used to update the current design variables based on the objective function value and the sensitivity value until a preset number of iterations is reached, thereby determining the optimized design result of the target fiber-reinforced composite material.

8. An electronic device, characterized in that, include: The memory, the processor, and the computer program stored in the memory and capable of running on the processor, wherein the processor executes the program to implement the fundamental frequency topology optimization method for continuous fiber reinforced composite structures as described in any one of claims 1-6.

9. A non-volatile computer-readable storage medium having a computer program stored thereon, characterized in that, The program is executed by the processor to implement the fundamental frequency topology optimization method for continuous fiber reinforced composite structures as described in any one of claims 1-6.

10. A computer program product, comprising a computer program, characterized in that, The computer program is executed to implement the fundamental frequency topology optimization method for continuous fiber reinforced composite structures as described in any one of claims 1-6.

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