SABRE-based variable density method structure topology optimization method and device
By constructing a finite element model and iteratively optimizing the pseudo-density of materials based on the SABRE-based variable density method, the problem of high complexity in existing topology optimization design is solved, and more efficient structural performance optimization is achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-03-06
- Publication Date
- 2026-04-03
AI Technical Summary
In existing technologies, topology optimization design methods based on foreign commercial software have failed to fully explore their inherent potential, and user operation is limited, resulting in high complexity of topology optimization design and difficulty in maximizing structural performance.
The SABRE-based variable density method is adopted. By constructing a finite element model, dividing the mesh nodes, giving the material pseudo density, calculating the elastic modulus and material volume, and iteratively optimizing the material pseudo density to minimize the overall strain energy and control the material usage, the final topology optimization design region is formed.
This reduces the complexity of topology optimization, improves the efficiency of structural topology optimization, and achieves more efficient structural performance optimization.
Smart Images
Figure CN121786912A_ABST
Abstract
Description
Technical Field
[0001] This application belongs to the field of structural topology optimization design, specifically relating to a variable density method and apparatus for structural topology optimization based on SABRE. Background Technology
[0002] Structural topology optimization is a commonly used optimization design method in the product concept design stage and one of the main means of innovative structural configuration design. Although topology optimization is more difficult to implement than structural shape and size optimization, it also brings greater openness and is an important foundation for technological innovation and new structural design. The essence of structural topology optimization can be simply described as: within a given design space, given loads and boundary conditions, seeking the optimal material distribution that satisfies specific performance constraints. Applying structural topology optimization methods can improve structural performance while reducing structural weight. With the development of structural topology optimization technology, structural topology optimization technology based on variable density methods has been widely used in aerospace, automotive, and mechanical fields. Currently, mainstream foreign commercial software such as ANSYS, ABAQUS, and Optistruct have all incorporated topology optimization design functions, enabling the topology optimization design of complex structures. The domestic structural analysis CAE software SABRE has the function of solving static and dynamic responses of structures and can independently replace the relevant functions of mainstream foreign commercial software.
[0003] Based on the topology optimization design of the aforementioned foreign commercial software, users often treat the topology optimization finite element solution and optimization calculation as a "black box," neglecting the inherent connection between the topology optimization design itself and the structural finite element solver and optimizer. They cannot deeply explore the potential of the topology optimization method and can only consider the structural topology optimization of finite response based on the operation methods provided by the software itself. This creates a certain barrier to the development of the topology optimization method itself and the progress of cutting-edge structural optimization technologies. Summary of the Invention
[0004] To address the aforementioned issues, this application provides a SABRE-based variable density method and apparatus for structural topology optimization.
[0005] The first aspect of this application provides a variable density method for structural topology optimization based on SABRE, which mainly includes:
[0006] Step S1: Construct the finite element model of the structure and define the topology optimization design region of the structure;
[0007] Step S2: Divide the topology optimization design region into multiple grid nodes and give an initial pseudo-density of material for each grid node;
[0008] Step S3: Calculate the elastic modulus and material volume of each grid node based on the pseudo-density of the material at each grid node;
[0009] Step S4: Determine the overall strain energy of the structure under a specified external load based on the SABRE variable density method, and determine the total volume of material used in the supporting structure.
[0010] Step S5: With the goal of minimizing the overall strain energy and the constraint that the total volume of material used is lower than the set volume fraction, iteratively optimize the pseudo density of the material at each grid node.
[0011] Step S6: Identify the regions corresponding to grid nodes with material pseudo-density below the threshold as empty regions, forming the final topology optimization design region.
[0012] Preferably, step S3 further includes:
[0013] Calculate the elastic modulus of each grid node using the following formula. :
[0014] ;
[0015] in, Let i be the updated elastic modulus of the i-th node. Let i be the elastic modulus before the update of the i-th node. Let p be the pseudo-density of the material at the current iteration number of the i-th node, and p be the penalty factor.
[0016] Calculate the material volume of each mesh node using the following formula:
[0017] ;
[0018] in, The updated material volume for the i-th node. Let be the volume when the i-th node is a solid material.
[0019] Preferably, the penalty factor is set to 3.
[0020] Preferably, in step S5, the termination condition for iteratively optimizing the pseudo-density of the material at each grid node is reaching the set number of iterations, or the rate of change of the overall strain energy is lower than the set value.
[0021] Preferably, in step S5, when iteratively optimizing the material pseudo-density of each grid node, the material pseudo-density is updated by the filtered variable sensitivity.
[0022] The second aspect of this application provides a variable density structural topology optimization device based on SABRE, mainly comprising:
[0023] The topology optimization design region determination module is used to construct the finite element model of the structure and define the topology optimization design region of the structure.
[0024] The material pseudo-density assignment module is used to divide the topology optimization design region into multiple grid nodes and assign an initial material pseudo-density to each grid node.
[0025] The node attribute calculation module is used to calculate the elastic modulus and material volume of each grid node based on the pseudo density of the material of each grid node.
[0026] The overall strain energy calculation module is used to determine the overall strain energy of a structure under a specified external load based on the SABRE variable density method, as well as to determine the total volume of material used in the supporting structure.
[0027] The variable iteration update module is used to iteratively optimize the pseudo density of the material at each grid node with the goal of minimizing the overall strain energy and the constraint that the total volume of material usage is lower than a set volume fraction.
[0028] The optimized structure generation module is used to identify the regions corresponding to mesh nodes with material pseudo-density below a threshold as empty regions, thus forming the final topology optimization design region.
[0029] Preferably, the node attribute calculation module includes:
[0030] The elastic modulus calculation unit is used to calculate the elastic modulus of each mesh node according to the following formula:
[0031] ;
[0032] in, Let i be the updated elastic modulus of the i-th node. Let i be the elastic modulus before the update of the i-th node. Let p be the pseudo-density of the material at the current iteration number of the i-th node, and p be the penalty factor.
[0033] The material volume calculation unit is used to calculate the material volume of each mesh node according to the following formula:
[0034] ;
[0035] in, The updated material volume for the i-th node. Let be the volume when the i-th node is a solid material.
[0036] Preferably, the penalty factor is set to 3.
[0037] Preferably, in the variable iteration update module, the termination condition for iteratively optimizing the material pseudo density of each grid node is reaching a set number of iterations, or the rate of change of the overall strain energy is lower than a set value.
[0038] Preferably, in the variable iteration update module, when iteratively optimizing the material pseudo-density of each grid node, the material pseudo-density is updated through filtered variable sensitivity.
[0039] This application reduces the complexity of topology optimization implementation and improves the efficiency of structural topology optimization. Attached Figure Description
[0040] Figure 1 This is a flowchart of a preferred embodiment of the SABRE-based variable density structural topology optimization method of this application.
[0041] Figure 2 This is a schematic diagram of the mesh division of the topology optimization design region in this application.
[0042] Figure 3 This is a schematic diagram of the optimized structure of this application. Detailed Implementation
[0043] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions in the embodiments of this application will be described in more detail below with reference to the accompanying drawings. In the drawings, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The described embodiments are only some, not all, of the embodiments of this application. 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. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application. The embodiments of this application will be described in detail below with reference to the accompanying drawings.
[0044] The first aspect of this application provides a variable density method for structural topology optimization based on SABRE, such as... Figure 1 As shown, it mainly includes:
[0045] Step S1: Construct the finite element model of the structure and define the topology optimization design region of the structure;
[0046] Step S2: Divide the topology optimization design region into multiple grid nodes and give an initial pseudo-density of material for each grid node;
[0047] Step S3: Calculate the elastic modulus and material volume of each grid node based on the pseudo-density of the material at each grid node;
[0048] Step S4: Determine the overall strain energy of the structure under a specified external load based on the SABRE variable density method, and determine the total volume of material used in the supporting structure.
[0049] Step S5: With the goal of minimizing the overall strain energy and the constraint that the total volume of material used is lower than the set volume fraction, iteratively optimize the pseudo density of the material at each grid node.
[0050] Step S6: Identify the regions corresponding to grid nodes with material pseudo-density below the threshold as empty regions, forming the final topology optimization design region.
[0051] In step S1, taking a cantilever beam as an example, a finite element model is constructed as follows: Figure 2 As shown, the entire cantilever beam region is designated as topology optimization design region I. The left side of topology optimization design region I is constrained by boundary II. Topology optimization design region I has a length of 1500mm, a width of 600mm, and a thickness of 1mm. In step S2, finite element mesh nodes are generated. The element size of the mesh nodes is 20mm, the elastic modulus E = 210Gpa, and the Poisson's ratio μ = 0.3. The lower right corner of topology optimization design region I is... Figure 1 A concentrated load is applied in the direction shown, with a vertical load of 1000N. The grid nodes are numbered starting from the bottom left corner as 1 and increasing by 1 to the right, arranged in a serpentine pattern throughout the structure. The last element is the top right corner element, with an element number of n of 2250. That is, there are a total of 2250 grid nodes in the design area.
[0052] Step S2 requires further specifying the initial pseudo-density of the material for each mesh node. It's important to note that pseudo-density is a key concept in structural topology optimization, particularly widely used in density-based methods. It's an artificially introduced variable used to describe the distribution of material within the design domain. By relating pseudo-density to material physical properties (such as elastic modulus), the topology optimization problem is transformed into a problem of optimal material distribution. In variable density methods, pseudo-density is typically defined as the relative density of each finite element, ranging from 0 to 1. A pseudo-density close to 1 indicates that the element is solid material, while a value close to 0 indicates voids or no material. (Reference) Figure 2 and Figure 3 This application requires [to address / to address] Figure 2 The initial structure shown is subjected to topology optimization, and finally optimized into Figure 3The structure shown retains solid material in some areas and is empty in others. Assuming that 40% of the volume needs to be retained and the other 60% is empty, the initial pseudo-density of the material of all mesh nodes can be set to 0.4. In the subsequent optimization process, the pseudo-density of the material of some mesh nodes gradually approaches 1, and the pseudo-density of the material of other mesh nodes gradually approaches 0 (to ensure the smooth progress of the solution, the lower limit of the design variable is set to a small value greater than 0, which is set to 0.001 here). Without considering the overall increment, the final overall volume of the structure is reduced by 60%. Correspondingly, this application will subsequently limit the overall increment through the constraint conditions mentioned in step S5, that is, set the optimized volume to be less than 40% of the initial volume.
[0053] In step S3, the elastic modulus and the total material volume are calculated based on the material pseudo-density. The elastic modulus is used to participate in the calculation of the subsequent optimization objective, and the material volume is used to participate in the calculation of the subsequent constraint conditions.
[0054] In some alternative implementations, step S3 further includes:
[0055] Calculate the elastic modulus of each grid node using the following formula. :
[0056] ;
[0057] in, Let i be the updated elastic modulus of the i-th node. Let i be the elastic modulus before the update of the i-th node. Let p be the pseudo-density of the material at the current iteration number of the i-th node, and p be the penalty factor.
[0058] Calculate the material volume of each mesh node using the following formula:
[0059] ;
[0060] in, The updated material volume for the i-th node. Let be the volume when the i-th node is a solid material.
[0061] In this embodiment, the volume of each node when it is a solid material can be calculated using a unit size of 20mm and a thickness of 1mm, i.e., 20mm × 20mm × 1mm = 400mm. 3 .
[0062] In some alternative implementations, the penalty factor is set to 3.
[0063] In step S4, SABRE is invoked to complete the model analysis, which determines the overall strain energy of the structure under a specified external load and the total volume of material used in the supporting structure. First, SABRE is used to solve for the overall stiffness matrix K and the displacement vector U under the external load F. Then, the overall strain energy f is calculated based on the strain energy formula:
[0064] .
[0065] Then, in step S5, after determining the optimization objective and constraints, iterative optimization is performed. The optimization objective is to minimize the overall strain energy f, and the constraints are as follows:
[0066] KU=F;
[0067] ;
[0068] The optimization variable is the pseudo-density of the material in the aforementioned 2250 mesh nodes. .
[0069] in, To support the total volume of structural materials used, The structural material volume when each design unit is filled with material; This is the upper limit of the volume fraction of the material used, which is 40% as given in the previous example.
[0070] In some alternative implementations, in step S5, the termination condition for iteratively optimizing the pseudo-density of the material at each grid node is reaching a set number of iterations, or the rate of change of the overall strain energy is lower than a set value.
[0071] In this embodiment, the set value is typically 0.001.
[0072] In some alternative implementations, during step S5, when iteratively optimizing the material pseudo-density of each grid node, the material pseudo-density is updated using filtered variable sensitivity.
[0073] In this embodiment, the sensitivity of the overall structural strain energy function to each design variable is first calculated using the relationship between the structural stiffness matrix and the material elastic modulus. The sensitivity of the overall structural material fraction to each design variable is then calculated using the chain rule, followed by sensitivity filtering.
[0074] Variable sensitivity filtering is calculated using the following formula:
[0075] .
[0076] In the formula: , The filter radius; It is the center distance between neighboring units i and k. At that time, the sensitivity converges to the original sensitivity; while At that time, the sensitivity of each unit is basically equal. By giving appropriate To ensure that the sensitivity of adjacent cells changes smoothly and reduce the fluctuation of cell density values in adjacent cells, thereby eliminating the checkerboard pattern, the sensitivity filtering radius in this embodiment is set to twice the cell size.
[0077] Finally, in step S6, nodes below a threshold (e.g., 0.01) are designated as holes, constructing a structure as follows: Figure 3 The topology shown.
[0078] A second aspect of this application provides a SABRE-based variable density structural topology optimization device corresponding to the above method, mainly comprising:
[0079] The topology optimization design region determination module is used to construct the finite element model of the structure and define the topology optimization design region of the structure.
[0080] The material pseudo-density assignment module is used to divide the topology optimization design region into multiple grid nodes and assign an initial material pseudo-density to each grid node.
[0081] The node attribute calculation module is used to calculate the elastic modulus and material volume of each grid node based on the pseudo density of the material of each grid node.
[0082] The overall strain energy calculation module is used to determine the overall strain energy of a structure under a specified external load based on the SABRE variable density method, as well as to determine the total volume of material used in the supporting structure.
[0083] The variable iteration update module is used to iteratively optimize the pseudo density of the material at each grid node with the goal of minimizing the overall strain energy and the constraint that the total volume of material usage is lower than a set volume fraction.
[0084] The optimized structure generation module is used to identify the regions corresponding to mesh nodes with material pseudo-density below a threshold as empty regions, thus forming the final topology optimization design region.
[0085] In some optional implementations, the node attribute calculation module includes:
[0086] The elastic modulus calculation unit is used to calculate the elastic modulus of each mesh node according to the following formula:
[0087] ;
[0088] in, Let i be the updated elastic modulus of the i-th node. Let i be the elastic modulus before the update of the i-th node. Let p be the pseudo-density of the material at the current iteration number of the i-th node, and p be the penalty factor.
[0089] The material volume calculation unit is used to calculate the material volume of each mesh node according to the following formula:
[0090] ;
[0091] in, The updated material volume for the i-th node. Let be the volume when the i-th node is a solid material.
[0092] In some alternative implementations, the penalty factor is set to 3.
[0093] In some optional implementations, in the variable iteration update module, the termination condition for iteratively optimizing the material pseudo density of each grid node is reaching a set number of iterations, or the rate of change of the overall strain energy is lower than a set value.
[0094] In some alternative implementations, during the iterative optimization of the material pseudo-density of each grid node in the variable iteration update module, the material pseudo-density is updated by a filtered variable sensitivity.
[0095] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.
Claims
1. A variable density structural topology optimization method based on SABRE, characterized in that, Includes the following steps: Step S1: Construct the finite element model of the structure and define the topology optimization design region of the structure; Step S2: Divide the topology optimization design region into multiple grid nodes and give an initial pseudo-density of material for each grid node; Step S3: Calculate the elastic modulus and material volume of each grid node based on the pseudo-density of the material at each grid node; Step S4: Determine the overall strain energy of the structure under a specified external load based on the SABRE variable density method, and determine the total volume of material used in the supporting structure. Step S5: With the goal of minimizing the overall strain energy and the constraint that the total volume of material used is lower than the set volume fraction, iteratively optimize the pseudo density of the material at each grid node. Step S6: Identify the regions corresponding to grid nodes with material pseudo-density below the threshold as empty regions, forming the final topology optimization design region.
2. The SABRE-based variable density structural topology optimization method according to claim 1, characterized in that, Step S3 further includes: Calculate the elastic modulus of each grid node using the following formula. : ； in, Let i be the updated elastic modulus of the i-th node. Let i be the elastic modulus before the update of the i-th node. Let p be the pseudo-density of the material at the current iteration number of the i-th node, and p be the penalty factor. Calculate the material volume of each mesh node using the following formula: ； in, The updated material volume for the i-th node. Let be the volume when the i-th node is a solid material.
3. The SABRE-based variable density structural topology optimization method according to claim 2, characterized in that, The penalty factor is set to 3.
4. The SABRE-based variable density structural topology optimization method according to claim 1, characterized in that, In step S5, the termination condition for iterative optimization of the material pseudo density of each grid node is reaching the set number of iterations, or the rate of change of the overall strain energy is lower than the set value.
5. The SABRE-based variable density structural topology optimization method according to claim 1, characterized in that, In step S5, when iteratively optimizing the pseudo-density of the material at each grid node, the pseudo-density of the material is updated by the filtered variable sensitivity.
6. A variable density method structure topology optimization device based on SABRE, characterized in that, include: The topology optimization design region determination module is used to construct the finite element model of the structure and define the topology optimization design region of the structure. The material pseudo-density assignment module is used to divide the topology optimization design region into multiple grid nodes and assign an initial material pseudo-density to each grid node. The node attribute calculation module is used to calculate the elastic modulus and material volume of each grid node based on the pseudo density of the material of each grid node. The overall strain energy calculation module is used to determine the overall strain energy of a structure under a specified external load based on the SABRE variable density method, as well as to determine the total volume of material used in the supporting structure. The variable iteration update module is used to iteratively optimize the pseudo density of the material at each grid node with the goal of minimizing the overall strain energy and the constraint that the total volume of material usage is lower than a set volume fraction. The optimized structure generation module is used to identify the regions corresponding to mesh nodes with material pseudo-density below a threshold as empty regions, thus forming the final topology optimization design region.
7. The SABRE-based variable density structural topology optimization device according to claim 6, characterized in that, The node attribute calculation module includes: The elastic modulus calculation unit is used to calculate the elastic modulus of each mesh node according to the following formula: ； in, Let i be the updated elastic modulus of the i-th node. Let i be the elastic modulus before the update of the i-th node. Let p be the pseudo-density of the material at the current iteration number of the i-th node, and p be the penalty factor. The material volume calculation unit is used to calculate the material volume of each mesh node according to the following formula: ； in, The updated material volume for the i-th node. Let be the volume when the i-th node is a solid material.
8. The SABRE-based variable density structural topology optimization device according to claim 7, characterized in that, The penalty factor is set to 3.
9. The SABRE-based variable density structural topology optimization device according to claim 6, characterized in that, In the variable iteration update module, the termination condition for iterative optimization of the material pseudo density of each grid node is reaching the set number of iterations, or the rate of change of the overall strain energy is lower than the set value.
10. The SABRE-based variable density structural topology optimization device according to claim 6, characterized in that, In the variable iteration update module, when iteratively optimizing the material pseudo-density of each grid node, the material pseudo-density is updated through filtered variable sensitivity.