A structure topology optimization method and system based on unit strain energy sensitivity
Patent Information
- Application Number
- CN202610908034.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-06-23
- Publication Date
- 2026-10-09
AI Technical Summary
[0004]本申请提供一种基于单元应变能敏度的结构拓扑优化方法及系统，以至少解决现有优化方法效率及精度较低的技术问题
本申请提出了一种基于单元应变能敏度的结构拓扑优化方法及系统，所述方法包括：步骤1：获取待优化结构的有限元模型，初始化设计域内各单元的相对密度；步骤2：根据当前的相对密度，通过材料插值模型计算各单元的弹性模量，并将所述弹性模量赋予所述有限元模型中的对应单元；步骤3：调用有限元求解器对赋材后的模型进行结构分析，并提取每个单元的应变能；步骤4：基于各单元的应变能计算待优化结构的整体柔顺度及其对相对密度的敏度；步骤5：对所述敏度进行过滤和投影处理，得到处理后的敏度；步骤6：利用优化算法及所述处理后的敏度更新所述相对密度；步骤7：判断优化过程是否满足收敛条件；若否，则返回步骤2；若是，则输出待优化结构的分布拓扑结果。本申请提出的技术方案，显著提高了大规模复杂结构拓扑优化的计算效率和数值稳定性。
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Abstract
Description
Technical Field
[0001] This application relates to the field of structural optimization technology, and in particular to a structural topology optimization method and system based on element strain energy sensitivity. Background Technology
[0002] Topology optimization is an advanced structural design method that finds the optimal material distribution under given design space, constraints, and performance indicators. It plays a crucial role in lightweighting and performance improvement in fields such as aerospace, automotive, and civil engineering. Variable density methods, especially the penalty method for solid isotropic materials, are among the most widely used methods in continuum topology optimization. They introduce continuous design variables to represent the pseudo-density of elements and force the intermediate density to cluster towards the 0-1 ends through a penalty factor, thereby obtaining a clear topological configuration.
[0003] However, traditional topology optimization processes based on the variable density method suffer from a core computational bottleneck: sensitivity analysis. Sensitivity, the derivative of the objective function with respect to design variables, is crucial information driving the direction of optimization iterations. Traditional methods typically require extracting and operating the overall stiffness matrix and its inverse matrix to calculate the sensitivity of objective functions such as overall compliance. For large and complex structures, the finite element model is enormous, and storing, extracting, and inverting the overall stiffness matrix consumes huge computational resources, resulting in low computational efficiency and even failure to converge due to harsh numerical conditions. Although commercial finite element software possesses powerful mechanical analysis capabilities, its native interface usually does not directly provide convenient overall stiffness matrix manipulation functions, making the process of directly integrating efficient optimization algorithms with mature finite element analysis complex and cumbersome. Especially in the field of offshore wind power engineering, fixed wind turbine foundations (such as jacket structures) are massive in scale and operate in harsh environments, simultaneously bearing multiple complex loads such as wind loads, wave loads, ocean current loads, and even netting impacts. Topology optimization design for such structures faces challenges such as a large number of model elements, complex load conditions, and high computational costs. Therefore, there is an urgent need for an efficient and stable topology optimization scheme that can utilize the efficient solvers of commercial finite element software while avoiding complex global matrix operations. Summary of the Invention
[0004] This application provides a structural topology optimization method and system based on element strain energy sensitivity, which at least solves the technical problems of low efficiency and accuracy of existing optimization methods.
[0005] The first aspect of this application proposes a structural topology optimization method based on element strain energy sensitivity, the method comprising:
[0006] Step 1: Obtain the finite element model of the structure to be optimized and initialize the relative density of each element in the design domain; Step 2: Based on the current relative density, calculate the elastic modulus of each element using a material interpolation model, and assign the elastic modulus to the corresponding element in the finite element model; Step 3: Call the finite element solver to perform structural analysis on the material-equipped model and extract the strain energy of each element; Step 4: Calculate the overall compliance of the structure to be optimized and its sensitivity to relative density based on the strain energy of each element; Step 5: Filter and project the sensitivity to obtain the processed sensitivity; Step 6: Update the relative density using the optimization algorithm and the processed sensitivity; Step 7: Determine whether the optimization process meets the convergence condition; if not, return to step 2; if yes, output the distribution topology result of the structure to be optimized.
[0007] Preferably, during the initial design, a portion of the finite element model is set as a non-design domain, and the relative density of the elements within the non-design domain remains unchanged during the optimization process. The non-design domain includes the main leg structure of the offshore wind turbine jacket structure. During initial design, symmetric constraints are applied to the design domain, including planar symmetric constraints or rotational symmetric constraints. The loads borne by the finite element model include: wind turbine operating load, wave load, and netting load; The structure to be optimized is the fixed foundation support structure for offshore wind power.
[0008] Furthermore, the material interpolation model is a penalty model for solid isotropic materials; The calculation formula for the material interpolation model is as follows:
[0009] In the formula, Let e be the elastic modulus of element e. Let p be the projected density of element e, and p be the penalty factor. Let be the elastic modulus of the solid material corresponding to the structure to be optimized. It is the minimum elastic modulus.
[0010] Furthermore, the formula for calculating the sensitivity is as follows:
[0011] In the formula, Let be the sensitivity value under the projected density of element e, and c be the overall compliance. Let e be the strain energy of element e.
[0012] Furthermore, the filtering and projection processing of the sensitivity includes: The sensitivity is filtered based on a preset filter radius and using a density filtering method. Based on preset projection parameters, the filtered sensitivity is projected using the Heaviside function projection method. The preset projection parameters increase as the number of iterations increases.
[0013] Furthermore, updating the relative density using the optimization algorithm and the processed sensitivity includes: Based on the processed sensitivity and volume constraint sensitivity The update coefficients of the construction optimization criterion method for each design unit are determined, wherein the formula is used. Calculate the update coefficients, where, Let e be the update coefficient for cell e. For Lagrange multipliers, Let e be the volume of element e; The Lagrange multipliers are solved iteratively using the bisection method, and the relative density is updated using the solved Lagrange multipliers and the update coefficients. The formula for calculating the relative density is as follows:
[0014] in, The numerical damping coefficient is... The relative density of the updated element e, This is the minimum value of the preset relative density. Let be the current relative density of element e.
[0015] Furthermore, determining whether the optimization process satisfies the convergence condition includes: Determine the relative change in the overall compliance of the current iteration step compared to the overall compliance of the previous iteration step, and the absolute value of the difference between the relative density of the current iteration step and the relative density of the previous iteration step for each design unit. Based on the absolute value of the difference between the relative density of the current iteration step and the relative density of the previous iteration step for each design unit, select the maximum absolute change. When the relative change is less than or equal to a preset first threshold and the maximum absolute change is less than or equal to a preset second threshold, or when the current iteration step is equal to a preset maximum number of iteration steps, the optimization process is judged to meet the convergence condition.
[0016] A second aspect of this application proposes a structural topology optimization system based on element strain energy sensitivity, comprising: The initialization module is used to obtain the finite element model of the structure to be optimized and initialize the relative density of each element in the design domain. The first calculation module is used to calculate the elastic modulus of each element based on the current relative density using a material interpolation model, and to assign the elastic modulus to the corresponding element in the finite element model. The extraction module is used to call the finite element solver to perform structural analysis on the material-applied model and extract the strain energy of each element. The first calculation module is used to calculate the overall compliance of the structure to be optimized and its sensitivity to relative density based on the strain energy of each element. The processing module is used to filter and project the sensitivity to obtain the processed sensitivity. The update module is used to update the relative density using the optimization algorithm and the processed sensitivity; The judgment module is used to determine whether the optimization process meets the convergence condition; if not, it returns to the first calculation module; if yes, it outputs the distribution topology result of the structure to be optimized.
[0017] 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 when the processor executes the program, it implements the method described in the first aspect embodiment.
[0018] A fourth aspect of this application provides a computer-readable storage medium having a computer program stored thereon that, when executed by a processor, implements the method described in the first aspect.
[0019] The technical solutions provided by the embodiments of this application have at least the following beneficial effects: This application proposes a structural topology optimization method and system based on element strain energy sensitivity. The method includes: Step 1: Obtaining the finite element model of the structure to be optimized and initializing the relative density of each element in the design domain; Step 2: Calculating the elastic modulus of each element using a material interpolation model based on the current relative density, and assigning the elastic modulus to the corresponding element in the finite element model; Step 3: Calling the finite element solver to perform structural analysis on the material-assigned model and extracting the strain energy of each element; Step 4: Calculating the overall compliance of the structure to be optimized and its sensitivity to relative density based on the strain energy of each element; Step 5: Filtering and projecting the sensitivity to obtain the processed sensitivity; Step 6: Updating the relative density using the optimization algorithm and the processed sensitivity; Step 7: Determining whether the optimization process meets the convergence condition; if not, returning to Step 2; if yes, outputting the distributed topology result of the structure to be optimized. The technical solution proposed in this application significantly improves the computational efficiency and numerical stability of topology optimization for large-scale complex structures.
[0020] 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
[0021] 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 structural topology optimization method based on element strain energy sensitivity according to an embodiment of this application; Figure 2 A detailed flowchart of a structural topology optimization method based on element strain energy sensitivity according to an embodiment of this application; Figure 3 This is a structural diagram of a structural topology optimization system based on element strain energy sensitivity according to an embodiment of this application. Detailed Implementation
[0022] 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.
[0023] This application proposes a structural topology optimization method and system based on element strain energy sensitivity. The method includes: Step 1: Obtaining the finite element model of the structure to be optimized and initializing the relative density of each element in the design domain; Step 2: Calculating the elastic modulus of each element using a material interpolation model based on the current relative density, and assigning the elastic modulus to the corresponding element in the finite element model; Step 3: Calling the finite element solver to perform structural analysis on the material-assigned model and extracting the strain energy of each element; Step 4: Calculating the overall compliance of the structure to be optimized and its sensitivity to relative density based on the strain energy of each element; Step 5: Filtering and projecting the sensitivity to obtain the processed sensitivity; Step 6: Updating the relative density using the optimization algorithm and the processed sensitivity; Step 7: Determining whether the optimization process meets the convergence condition; if not, returning to Step 2; if yes, outputting the distributed topology result of the structure to be optimized. The technical solution proposed in this application significantly improves the computational efficiency and numerical stability of topology optimization for large-scale complex structures.
[0024] The following description, with reference to the accompanying drawings, illustrates a structural topology optimization method and system based on element strain energy sensitivity, according to embodiments of this application.
[0025] Example 1 Figure 1This is a flowchart illustrating a structural topology optimization method based on element strain energy sensitivity according to an embodiment of this application, as shown below. Figure 1 As shown, the method includes: Step 1: Obtain the finite element model of the structure to be optimized and initialize the relative density of each element in the design domain; It should be noted that during the initial design, some regions in the finite element model are set as non-design domains. The relative density of elements in the non-design domains remains unchanged during the optimization process. The non-design domains include the main leg structure of the offshore wind turbine jacket structure. During initial design, symmetric constraints are applied to the design domain, including planar symmetric constraints or rotational symmetric constraints. The loads borne by the finite element model include: wind turbine operating load, wave load, and netting load; The structure to be optimized is the fixed foundation support structure for offshore wind power.
[0026] Step 2: Based on the current relative density, calculate the elastic modulus of each element using a material interpolation model, and assign the elastic modulus to the corresponding element in the finite element model; In this embodiment of the disclosure, the material interpolation model is a penalty model for solid isotropic materials; The calculation formula for the material interpolation model is as follows:
[0027] In the formula, Let e be the elastic modulus of element e. Let p be the projected density of element e, and p be the penalty factor. Let be the elastic modulus of the solid material corresponding to the structure to be optimized. It is the minimum elastic modulus.
[0028] Step 3: Call the finite element solver to perform structural analysis on the material-equipped model and extract the strain energy of each element; Step 4: Calculate the overall compliance of the structure to be optimized and its sensitivity to relative density based on the strain energy of each element; In this embodiment of the disclosure, the sensitivity is calculated as follows:
[0029] In the formula, Let be the sensitivity value under the projected density of element e, and c be the overall compliance. Let e be the strain energy of element e.
[0030] Step 5: Filter and project the sensitivity to obtain the processed sensitivity; In this embodiment of the disclosure, step 5 specifically includes: The sensitivity is filtered based on a preset filter radius and using a density filtering method. Based on preset projection parameters, the filtered sensitivity is projected using the Heaviside function projection method. The preset projection parameters increase as the number of iterations increases.
[0031] Step 6: Update the relative density using the optimization algorithm and the processed sensitivity; In this embodiment of the disclosure, step 6 specifically includes: Based on the processed sensitivity and volume constraint sensitivity The update coefficients of the construction optimization criterion method for each design unit are determined, wherein the formula is used. Calculate the update coefficients, where, Let e be the update coefficient for cell e. For Lagrange multipliers, Let e be the volume of element e; The Lagrange multipliers are solved iteratively using the bisection method, and the relative density is updated using the solved Lagrange multipliers and the update coefficients. The formula for calculating the relative density is as follows:
[0032] in, The numerical damping coefficient is... The relative density of the updated element e, This is the minimum value of the preset relative density. Let be the current relative density of element e.
[0033] Step 7: Determine whether the optimization process meets the convergence condition; if not, return to step 2; if yes, output the distribution topology result of the structure to be optimized.
[0034] In this embodiment of the disclosure, determining whether the optimization process satisfies the convergence condition includes: Determine the relative change in the overall compliance of the current iteration step compared to the overall compliance of the previous iteration step, and the absolute value of the difference between the relative density of the current iteration step and the relative density of the previous iteration step for each design unit. Based on the absolute value of the difference between the relative density of the current iteration step and the relative density of the previous iteration step for each design unit, select the maximum absolute change. When the relative change is less than or equal to a preset first threshold and the maximum absolute change is less than or equal to a preset second threshold, or when the current iteration step is equal to a preset maximum number of iteration steps, the optimization process is judged to meet the convergence condition.
[0035] It should be noted that the formula for calculating the relative change is as follows: In the formula, It is a relative change. The overall compliance of the current iteration step k. The overall compliance of the k-1 iteration step.
[0036] The maximum absolute change The calculation formula is In the formula, Let e be the relative density of unit e in the k-th iteration step. Let be the relative density of unit e in the (k-1)th iteration step.
[0037] It should be noted that this embodiment utilizes Ansys finite element software to bypass the complex stiffness matrix extraction step in the topology optimization process, expressing the sensitivity as a function of the element strain energy. By extracting the strain energy of the elements, the sensitivity and objective function are calculated. After optimization, the corresponding material elastic modulus is transferred back to Ansys to complete the optimization iteration.
[0038] like Figure 2 The specific implementation steps are as follows: 1. By calling the command stream through Ansys, the finite element model is read in, and the number of elements, number of nodes, and coordinates of the element centers in the design domain are extracted; 2. Initialize design variables, preprocess filter functions, and set other OC or MMA and loop parameters; 3. Enter the loop, and exit the loop if the change in the design variable meets a certain difference or the maximum loop count is reached; 4. Python reads model parameters, performs material interpolation, and outputs material files; 5. Python calls Ansys to read the material file, assign materials to each element, perform finite element calculations, and output the element strain energy; 6. Calculate the objective function and sensitivity; 7. Projection and filtering of objective function sensitivity and material volume sensitivity; 8. MMA solution; 9. Design variables for filtering and projection; 10. Determine whether the convergence has occurred based on the convergence criteria; 11. If the convergence condition is met, perform post-processing and export of the results.
[0039] By following the steps above, we define the finite element model that requires topology optimization, specify the design domain and non-design domain, and Python will automatically call AnsysAPDL to complete the topology optimization iteration. By making full use of Python's rich interfaces, we can continuously optimize the algorithm and improve the program's versatility, stability and efficiency.
[0040] In summary, the structural topology optimization method based on element strain energy sensitivity proposed in this embodiment significantly improves the computational efficiency and numerical stability of topology optimization for large-scale complex structures.
[0041] Example 2 Figure 3 Here is a structural diagram of a structural topology optimization system based on element strain energy sensitivity according to an embodiment of this application, as shown below. Figure 3 As shown, the system includes: Initialization module 100 is used to obtain the finite element model of the structure to be optimized and initialize the relative density of each element in the design domain; It should be noted that during the initial design, some regions in the finite element model are set as non-design domains. The relative density of elements in the non-design domains remains unchanged during the optimization process. The non-design domains include the main leg structure of the offshore wind turbine jacket structure. During initial design, symmetric constraints are applied to the design domain, including planar symmetric constraints or rotational symmetric constraints. The loads borne by the finite element model include: wind turbine operating load, wave load, and netting load; The structure to be optimized is the fixed foundation support structure for offshore wind power.
[0042] The first calculation module 200 is used to calculate the elastic modulus of each element based on the current relative density using a material interpolation model, and to assign the elastic modulus to the corresponding element in the finite element model. It should be noted that the material interpolation model is a penalty model for solid isotropic materials; The calculation formula for the material interpolation model is as follows:
[0043] In the formula, Let e be the elastic modulus of element e. Let p be the projected density of element e, and p be the penalty factor. Let be the elastic modulus of the solid material corresponding to the structure to be optimized. It is the minimum elastic modulus.
[0044] Extraction module 300 is used to call the finite element solver to perform structural analysis on the material-applied model and extract the strain energy of each element; The first calculation module 400 is used to calculate the overall compliance of the structure to be optimized and its sensitivity to relative density based on the strain energy of each element. It should be noted that the formula for calculating the sensitivity is as follows:
[0045] In the formula, Let be the sensitivity value under the projected density of element e, and c be the overall compliance. Let e be the strain energy of element e.
[0046] The processing module 500 is used to filter and project the sensitivity to obtain the processed sensitivity. Update module 600 is used to update the relative density using the optimization algorithm and the processed sensitivity; The judgment module 700 is used to determine whether the optimization process meets the convergence condition; if not, it returns to the first calculation module; if yes, it outputs the distribution topology result of the structure to be optimized.
[0047] In this embodiment of the disclosure, the processing module 500 is further configured to: The sensitivity is filtered based on a preset filter radius and using a density filtering method. Based on preset projection parameters, the filtered sensitivity is projected using the Heaviside function projection method. The preset projection parameters increase as the number of iterations increases.
[0048] In this embodiment of the disclosure, the update module 600 is further configured to: Based on the processed sensitivity and volume constraint sensitivity The update coefficients of the construction optimization criterion method for each design unit are determined, wherein the formula is used. Calculate the update coefficients, where, Let e be the update coefficient for cell e. For Lagrange multipliers, Let e be the volume of element e; The Lagrange multipliers are solved iteratively using the bisection method, and the relative density is updated using the solved Lagrange multipliers and the update coefficients. The formula for calculating the relative density is as follows:
[0049] in, The numerical damping coefficient is... The relative density of the updated element e, This is the minimum value of the preset relative density. Let be the current relative density of element e.
[0050] In this embodiment of the disclosure, the determination module 700 is further configured to: Determine the relative change in the overall compliance of the current iteration step compared to the overall compliance of the previous iteration step, and the absolute value of the difference between the relative density of the current iteration step and the relative density of the previous iteration step for each design unit. Based on the absolute value of the difference between the relative density of the current iteration step and the relative density of the previous iteration step for each design unit, select the maximum absolute change. When the relative change is less than or equal to a preset first threshold and the maximum absolute change is less than or equal to a preset second threshold, or when the current iteration step is equal to a preset maximum number of iteration steps, the optimization process is judged to meet the convergence condition.
[0051] In summary, the structural topology optimization system based on element strain energy sensitivity proposed in this embodiment significantly improves the computational efficiency and numerical stability of topology optimization for large-scale complex structures.
[0052] Example 3 To implement the above embodiments, this disclosure also proposes an electronic device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, it implements the method described in Embodiment 1.
[0053] Example 4 To implement the above embodiments, this disclosure also proposes a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method described in Embodiment 1.
[0054] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are 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.
[0055] Any process or method description in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or more 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.
[0056] 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 structural topology optimization method based on element strain energy sensitivity, characterized in that, The method includes: Step 1: Obtain the finite element model of the structure to be optimized and initialize the relative density of each element in the design domain; Step 2: Based on the current relative density, calculate the elastic modulus of each element using a material interpolation model, and assign the elastic modulus to the corresponding element in the finite element model; Step 3: Call the finite element solver to perform structural analysis on the material-equipped model and extract the strain energy of each element; Step 4: Calculate the overall compliance of the structure to be optimized and its sensitivity to relative density based on the strain energy of each element; Step 5: Filter and project the sensitivity to obtain the processed sensitivity; Step 6: Update the relative density using the optimization algorithm and the processed sensitivity; Step 7: Determine whether the optimization process meets the convergence condition; if not, return to step 2; if yes, output the distribution topology result of the structure to be optimized.
2. The method as described in claim 1, characterized in that, During the initial design, a portion of the finite element model is designated as a non-design domain. The relative density of elements within the non-design domain remains unchanged during the optimization process. The non-design domain includes the main leg structure of the offshore wind turbine jacket structure. During initial design, symmetric constraints are applied to the design domain, including planar symmetric constraints or rotational symmetric constraints. The loads borne by the finite element model include: wind turbine operating load, wave load, and netting load; The structure to be optimized is the fixed foundation support structure for offshore wind power.
3. The method as described in claim 2, characterized in that, The material interpolation model is a penalty model for solid isotropic materials; The calculation formula for the material interpolation model is as follows: In the formula, Let e be the elastic modulus of element e. Let p be the projected density of element e, and p be the penalty factor. Let be the elastic modulus of the solid material corresponding to the structure to be optimized. It is the minimum elastic modulus.
4. The method as described in claim 3, characterized in that, The sensitivity is calculated as follows: In the formula, Let be the sensitivity value under the projected density of element e, and c be the overall compliance. Let e be the strain energy of element e.
5. The method as described in claim 4, characterized in that, The filtering and projection processing of the sensitivity includes: The sensitivity is filtered based on a preset filter radius and using a density filtering method. Based on preset projection parameters, the filtered sensitivity is projected using the Heaviside function projection method. The preset projection parameters increase as the number of iterations increases.
6. The method as described in claim 5, characterized in that, The step of updating the relative density using the optimization algorithm and the processed sensitivity includes: Based on the processed sensitivity and volume constraint sensitivity The update coefficients of the construction optimization criterion method for each design unit are determined, wherein the formula is used. Calculate the update coefficients, where, Let e be the update coefficient for cell e. For Lagrange multipliers, Let e be the volume of element e; The Lagrange multipliers are solved iteratively using the bisection method, and the relative density is updated using the solved Lagrange multipliers and the update coefficients. The formula for calculating the relative density is as follows: in, The numerical damping coefficient is... The relative density of the updated element e, This is the minimum value of the preset relative density. Let be the current relative density of element e.
7. The method as described in claim 6, characterized in that, The determination of whether the optimization process meets the convergence condition includes: Determine the relative change in the overall compliance of the current iteration step compared to the overall compliance of the previous iteration step, and the absolute value of the difference between the relative density of the current iteration step and the relative density of the previous iteration step for each design unit. Based on the absolute value of the difference between the relative density of the current iteration step and the relative density of the previous iteration step for each design unit, select the maximum absolute change. When the relative change is less than or equal to a preset first threshold and the maximum absolute change is less than or equal to a preset second threshold, or when the current iteration step is equal to a preset maximum number of iteration steps, the optimization process is judged to meet the convergence condition.
8. A structural topology optimization system based on element strain energy sensitivity, characterized in that, The system includes: The initialization module is used to obtain the finite element model of the structure to be optimized and initialize the relative density of each element in the design domain. The first calculation module is used to calculate the elastic modulus of each element based on the current relative density using a material interpolation model, and to assign the elastic modulus to the corresponding element in the finite element model. The extraction module is used to call the finite element solver to perform structural analysis on the material-applied model and extract the strain energy of each element. The first calculation module is used to calculate the overall compliance of the structure to be optimized and its sensitivity to relative density based on the strain energy of each element. The processing module is used to filter and project the sensitivity to obtain the processed sensitivity. The update module is used to update the relative density using the optimization algorithm and the processed sensitivity; The judgment module is used to determine whether the optimization process meets the convergence condition; if not, it returns to the first calculation module; if yes, it outputs the distribution topology result of the structure to be optimized.
9. An electronic device, characterized in that, include: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the program, implements the method as described in any one of claims 1-7.
10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the method as described in any one of claims 1-7.