Lattice structure optimization design method and equipment combining multivariable cutting level set and progressive optimization

Abstract

The invention belongs to the technical field related to structure optimization design, and discloses a lattice structure optimization design method and device combining a multivariable cutting level set and progressive optimization, and the method comprises the steps: (1) building a lattice structure optimization model by taking structure flexibility as a target function and cutting height as a design variable; (2) performing finite element analysis based on the lattice structure optimization model to obtain a structure volume fraction; (3) if the current number of iterations is an odd number or the structural volume fraction is lower than the set threshold value, calculating the sensitivity of the target function and the constraint function to the design variable, and updating the design variable by adopting a moving asymptote algorithm based on the obtained sensitivity; if the number of iterations is an even number and the volume fraction of the structure exceeds a set threshold value, calculating a unit sensitivity degree so as to obtain a sensitivity degree of the virtual microstructure, and removing a part of the virtual microstructure based on the sensitivity degree of the virtual microstructure; and a final lattice structure is further obtained. According to the invention, the optimization efficiency is improved.

Description

Technical Field

[0001] This invention belongs to the technical field of structural optimization design, and more specifically, relates to a method and device for optimizing lattice structures by combining multivariable level set cutting with incremental optimization. Background Technology

[0002] Lattice structures are composed of interconnected rods or beams arranged in a periodic or aperiodic manner. With their excellent specific stiffness, high specific strength, and outstanding energy absorption performance, these structures demonstrate great potential in a wide range of engineering applications. In the design process of lattice structures, micro-geometric features and macro-topological layout can be synergistically optimized to fully utilize design space and improve overall structural performance. With the rapid development of additive manufacturing technology, high-precision manufacturing of complex lattice structures has gradually become possible. However, the limited resolution of 3D printing processes restricts further reduction in the feature size of lattice structures. Therefore, effectively controlling the minimum micro-dimensions is a crucial issue that urgently needs to be addressed in the optimization design stage of lattice structures.

[0003] In the prior art, patent CN201911415301.X discloses a multivariate horizontal segmentation method for topology optimization of cellular structures. This method utilizes multiple basic level set functions and their cutting functions to describe the shape and topology of the microstructures, ensuring the design freedom of the cellular structure and the connectivity between microstructures. However, this technique does not consider the minimum size control of the microstructures, leading to the appearance of extremely small features in the optimized structure, which fails to meet the resolution requirements of 3D printing processes. Patent CN202010850986.7 discloses a multivariate cutting level set optimization method for topology optimization of porous structures. This method employs higher-order cutting functions and maps the microstructure prototype from a square mesh to a quadrilateral mesh, solving the optimization problem of porous structures with complex geometries. However, this technique still does not consider the fabrication feasibility of the structure. Patent CN202310548993.5 discloses a data-driven dual-scale structural optimization design method, which uses a homogenization method to establish a database of cutting height (input) and equivalent elasticity matrix (output), thereby achieving efficient optimization of dual-scale structures. However, this technique still produces extremely fine features that are unmanufacturable, making it difficult to meet the size limitations of 3D printing processes. To ensure the manufacturability of such structures, patent CN202411122013.6 discloses a macro-micro dual-scale structural topology optimization method that can control the minimum size of microstructures. It defines microstructure size constraints by introducing topological variables, ensuring that the optimized structure can be directly manufactured by 3D printing. However, this technique requires additional size-related constraints, increasing the complexity of the optimization model and reducing optimization efficiency to some extent. Summary of the Invention

[0004] In view of the above-mentioned defects or improvement needs of the existing technology, the present invention provides a lattice structure optimization design method and device that combines multivariate level set cutting and progressive optimization, which aims to solve the problem of low optimization efficiency of existing lattice structure optimization methods.

[0005] To achieve the above objectives, according to one aspect of the present invention, a method for optimizing the design of lattice structures by combining multivariate level set segmentation with asymptotic optimization is provided, comprising the following steps:

[0006] (1) Divide the structural design domain of the lattice structure to be optimized into a single cell, and then divide the single cell into elements; (2) Define multiple basic level set functions within each unit cell. And set the initial cutting height. To describe virtual microstructures This yields the initial virtual microstructure within each unit cell; among which, ; (3) Arbitrary virtual microstructures are combined using Boolean operations to obtain actual microstructures. This leads to the formation of the initial overall lattice structure. ; (4) Structural flexibility The objective function is the cutting height. Set a threshold for structural volume fraction as a design variable. Upper limit of cutting height and lower limit To establish an optimization model for the lattice structure; (5) After determining the boundary conditions of the lattice structure to be optimized based on the initial overall lattice structure, perform finite element analysis based on the lattice structure optimization model to obtain the structural volume fraction. (6) If the current iteration number is odd or the structural volume fraction is lower than the set threshold, calculate the sensitivity of the objective function and constraint function to the design variables, and update the design variables based on the obtained sensitivity using the moving asymptote algorithm; if the iteration number is even and the structural volume fraction exceeds the set threshold, calculate the unit sensitivity number, and then obtain the sensitivity number of the virtual microstructure, and remove part of the virtual microstructure based on the sensitivity number of the virtual microstructure. (7) Determine whether the convergence condition is met. If it is met, generate the final lattice structure; otherwise, proceed to step (5) until convergence.

[0007] Furthermore, virtual microstructures Composed of multiple basic level set functions and corresponding cutting height The formula is: , in, For single cell The coordinates of any point within the interior.

[0008] Furthermore, the actual microstructure All by A virtual microstructure The specific calculation formula is obtained through Boolean operations:

[0009] Then, all the actual microstructures are combined into an initial overall lattice structure. The corresponding mathematical expression is: .

[0010] Furthermore, the mathematical expression of the lattice structure optimization model is:

[0011] In the formula, For the overall external force vector, This is the global displacement vector. For the overall stiffness matrix, This represents the volume fraction of the current structure.

[0012] Furthermore, the upper limit of the cutting height. Minimum structural feature size required by 3D printing process The relationship is as follows:

[0013] in, It is the magnitude of the gradient of the basic level set function.

[0014] Furthermore, single cells Inner Virtual Microstructure The sensitivity number is obtained by adding the sensitivity numbers of the units that make up the virtual microstructure, and the specific calculation formula is as follows: , in, For single cell Internal composition of the first The first virtual microstructure The sensitivity number of each unit is calculated using the following formula: , in, To form the first The first virtual microstructure The stiffness matrix of each element is calculated using the following formula: , in, To form the first The first virtual microstructure The volume fraction of solid material in each unit.

[0015] Furthermore, spatial filtering is applied to the sensitivity number of the virtual microstructure, and the specific calculation formula is as follows: , in, The weighting factor is calculated as follows: , in, For the filter radius, For the first The first cell and the first The Euclidean distance between the center points of each unit cell is then used to perform time filtering on the spatially filtered virtual microstructure sensitivity number. The specific calculation formula is as follows: , in, and These represent the current iteration number and the previous iteration number, respectively.

[0016] Furthermore, for each virtual microstructure, the sensitivity scores of all its non-empty individuals are sorted in ascending order, yielding... The removal rate for each virtual microstructure is set to be 1. Based on the removal rate and the resulting ranking, non-empty virtual microstructures that rank higher in the ranking are removed. For the current number The total number of non-empty individuals of the virtual microstructure.

[0017] The present invention also provides a manufacturable design system for lattice structures that combines multivariate level set cutting with incremental optimization. The system includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to perform the lattice structure optimization design method that combines multivariate level set cutting with incremental optimization as described above.

[0018] The present invention also provides a computer-readable storage medium storing machine-executable instructions, which, when invoked and executed by a processor, cause the processor to implement the lattice structure optimization design method described above, which combines multivariate level set cutting with asymptotic optimization.

[0019] In summary, compared with the prior art, the lattice structure optimization design method and equipment combining multivariate level set cutting and progressive optimization provided by the present invention have the following beneficial effects: 1. This invention sets a cutting height limit to constrain the minimum size of the microstructure. Without introducing additional constraints, it achieves control over the minimum size of the microstructure, reduces computational load, improves optimization efficiency, and lowers optimization costs.

[0020] 2. This invention provides a lattice structure optimization design method combining multivariate level set cutting and incremental optimization. It utilizes a basic level set function and its cutting height to describe virtual microstructures, and combines these with Boolean operations to obtain the actual microstructures, thus forming the overall lattice structure. A cutting height limit is set to constrain the minimum size of the microstructure. Based on sensitivity information, a moving asymptote algorithm is used to update the cutting height. Based on the incremental optimization approach, inefficient virtual microstructures are removed, alternating with the former. Therefore, without introducing additional constraints, this method has high computational efficiency, achieves macro- and micro-topological optimization of the lattice structure, and ensures that the optimized structure maintains good mechanical properties and meets the dimensional requirements of 3D printing processes.

[0021] 3. This invention introduces a progressive optimization strategy to ensure that the overall lattice structure changes in macroscopic topological configuration. Attached Figure Description

[0022] Figure 1 This is a flowchart of a lattice structure optimization design method that combines multivariate level set cutting with progressive optimization, provided by an embodiment of the present invention. Figure 2 This is an optimized schematic diagram of the planar cantilever beam structure provided in the embodiments of the present invention; Figure 3 This is the initial design drawing of the lattice structure in the embodiment of the present invention; Figure 4 This is an image showing the optimized result obtained using the method provided by this invention in an embodiment of the invention; Figure 5 This is the optimized result diagram obtained by using the traditional multivariate level set cutting method in the embodiments of the present invention. Detailed Implementation

[0023] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0024] This invention provides a lattice structure optimization design method that combines multivariable cutting level sets with progressive optimization. The optimization design method effectively realizes lattice structure topology optimization considering minimum microscale control, and solves the manufacturability design problem of lattice structures for 3D printing processes.

[0025] The optimization design method mainly includes the following steps: (1) Divide the structural design domain of the lattice structure to be optimized into a single cell, and then divide the single cell into units.

[0026] In one implementation, a given structural design domain and the structural design domain Divided into a certain number of units , The total number of cells is defined as the total number of units, and each cell is divided into a certain number of units.

[0027] (2) Define multiple basic level set functions within each unit cell. ,correspond A microstructure prototype was created, and an initial cut height was set. To describe virtual microstructures This yields the initial virtual microstructure within each unit cell.

[0028] Virtual microstructure Composed of multiple basic level set functions and corresponding cutting height The specific calculation formula is as follows: , in, For single cell The coordinates of any point within the interior.

[0029] (3) Arbitrary virtual microstructures are combined using Boolean operations to obtain actual microstructures. This leads to the formation of the initial overall lattice structure. .

[0030] Actual microstructure All by A virtual microstructure The specific calculation formula is obtained through Boolean operations:

[0031] Then, all the actual microstructures are combined into an initial overall lattice structure. The corresponding mathematical expression is: .

[0032] (4) Structural flexibility The objective function is the cutting height. Set a threshold for structural volume fraction as a design variable. Upper limit of cutting height and lower limit A lattice structure optimization model is established; the mathematical expression of the lattice structure optimization model is:

[0033] In the formula, For the overall external force vector, This is the global displacement vector. For the overall stiffness matrix, This represents the volume fraction of the current structure.

[0034] Cutting height limit Minimum structural feature size required by 3D printing process The relationship is as follows:

[0035] in, It is the magnitude of the gradient of the basic level set function.

[0036] (5) After determining the boundary conditions of the lattice structure to be optimized based on the initial overall lattice structure, perform finite element analysis based on the lattice structure optimization model to obtain the current structural flexibility value and structural volume fraction.

[0037] Finite element analysis is performed based on the lattice structure optimization model to obtain the overall displacement vector, and the current structural flexibility value is calculated based on the overall displacement vector.

[0038] When performing finite element analysis, the global stiffness matrix From the complete element stiffness matrix Assembled The specific calculation formula is as follows: , in, and These are the stiffness matrices for the real element and the empty element, respectively. For the first The volume fraction of solid material in each unit is calculated using the following formula: , in, This is the Heaviside approximation function. For the first The area occupied by each unit.

[0039] (6) If the current iteration number is odd or the structural volume fraction is lower than the set threshold, calculate the sensitivity of the objective function and constraint function to the design variables, and update the design variables based on the obtained sensitivity using the moving asymptote algorithm; if the iteration number is even and the structural volume fraction exceeds the set threshold, calculate the unit sensitivity number, and then obtain the sensitivity number of the virtual microstructure, and remove part of the virtual microstructure based on the sensitivity number of the virtual microstructure.

[0040] Sensitivity of the objective function (structural flexibility) to the design variable (cutting height) The calculation formula is: , in, For the first The coordinates of the center of each unit; The element displacement vector; Let be the element stiffness matrix, and its partial derivatives with respect to design variables. The formula for calculation is: , Similarly, the sensitivity of the constraint function to the design variables is calculated as follows: , Where, partial derivatives It can be calculated using the finite difference method.

[0041] unit cell Inner Virtual Microstructure The sensitivity number is obtained by adding the sensitivity numbers of the units that make up the virtual microstructure, and the specific calculation formula is as follows: , in, For single cell Internal composition of the first The first virtual microstructure The sensitivity number of each unit is calculated using the following formula: , in, To form the first The first virtual microstructure The stiffness matrix of each element is calculated using the following formula: , in, To form the first The first virtual microstructure The volume fraction of solid material in each unit.

[0042] To ensure the stability of the numerical calculation, the sensitivity number of the virtual microstructure is first spatially filtered. The specific calculation formula is as follows: , in, The weighting factor is calculated as follows: , in, For the filter radius, For the first The first cell and the first The Euclidean distance between the center points of each unit cell is then used to perform time filtering on the spatially filtered virtual microstructure sensitivity number. The specific calculation formula is as follows: , in, and These represent the current iteration number and the previous iteration number, respectively.

[0043] For each virtual microstructure, sort the sensitivity scores of all its non-empty individuals in ascending order to obtain... , For the current number The total number of non-empty individuals of each virtual microstructure is given, and the removal rate for each virtual microstructure is set to be 1. Based on this, non-empty virtual microstructures with low sensitivity are removed.

[0044] (7) Determine whether the convergence condition is met. If it is met, generate the final lattice structure; otherwise, proceed to step (5) until convergence.

[0045] The present invention will be further described in detail below with reference to specific embodiments.

[0046] Please see Figure 2 This embodiment uses the problem of minimizing the flexibility of a planar cantilever beam structure with concentrated loads as an example to explain the present invention. A 2 m × 1 m rectangular design domain is given. D A fixed left end of the region is fixed, and a concentrated load of 1 N is applied at the midpoint of the right end of the region. The cantilever beam structure is then optimized to minimize its flexibility, i.e., maximize its stiffness.

[0047] Please see Figure 1 The flowchart illustrates the following steps in this embodiment of the lattice structure optimization design method, which combines multivariate level set segmentation with progressive optimization: 1. Define the rectangular design domain Divided into a certain number of square units If its side length is 0.1 m, then the total number of unit cells is... If the size is 20 × 10, and each unit cell is divided into 40 × 40 units, then the unit size in the entire design domain is 800 × 400. 2. Define four basic level set functions within each unit cell. These correspond to four types of microstructure prototypes, while virtual microstructures... These basic level set functions and corresponding cutting height The specific calculation formula is as follows: ,in For single cell Set the coordinates of any point within the area, and then set the initial cutting height. To describe the initial virtual microstructure In this embodiment, the selected basic level set function The expressions are as follows: , , , , Among them, the function , , and The expressions are as follows: , , , , In addition, the initial cutting height of all virtual microstructures was set to 0.9.

[0048] 3. In each unit cell In this process, four virtual microstructures are combined using Boolean operations to obtain the initial actual microstructure. The specific calculation formula is as follows: , Then combine all the actual microstructures into Figure 3 The initial overall lattice structure shown The corresponding mathematical expression is ; 4. Based on structural flexibility The objective function is the cutting height. Set a threshold for structural volume fraction as a design variable. Upper limit of cutting height and lower limit A lattice structure optimization model is established, and its mathematical expression is: , in, For the overall external force vector, This is the global displacement vector. For the overall stiffness matrix, This represents the volume fraction of the current structure. Note the upper limit of the cutting height. Minimum structural feature size required by 3D printing process The relationship is as follows: , in, The gradient magnitude of the basic level set function can be obtained in this embodiment based on the expression of the level set function selected in step ②. If set If it is 7.5 mm, then the corresponding It is 0.4; 5. To avoid singularity in the stiffness matrix, the elastic moduli of the solid material and the virtual weak material are set to 1 Pa and 10 Pa, respectively. 3 Pa, both have a Poisson's ratio of 0.3, and the stiffness matrix of the real element composed entirely of solid material is denoted as Pa. The stiffness matrix of the empty element composed entirely of virtual weak materials is denoted as... The calculation formulas for both are as follows: , , in, For unit area, The strain-displacement matrix, and These are the elasticity matrices for solid materials and virtual weak materials, respectively. It is an area infinitesimal element; it is important to note that the matrix... The matrix is ​​obtained by taking the partial derivatives of the unit shape functions. and The element stiffness matrix within the design domain is calculated from the elastic modulus and Poisson's ratio, using the following formula: , in, For the first The volume fraction of solid material in each unit is calculated as follows: , in, For the first The area occupied by each unit This is the Heaviside approximation function. In this embodiment, the specific expression of this function is: , Among them, parameters and The values ​​are 10. 3 4. After completing the calculation of all element stiffness matrices, assemble them to form the overall stiffness matrix. Determine the boundary conditions of the structure and solve the force equilibrium equations. Obtain the global displacement vector And according to the formula and Calculate the current structural flexibility value and volume fraction respectively, where This represents the total number of elements within the design domain. 6. If the number of iterations is odd or the structural volume fraction is below the set threshold of 0.5, then calculate the sensitivity of the objective function (structural flexibility) to the design variable (cutting height). The specific formula is as follows: , in, For the first The coordinates of the center of each unit For element displacement vectors, the element stiffness matrix is... For design variables partial derivatives The calculation formula is: , Similarly, the sensitivity of the constraint function to the design variables is calculated using the following formula: , Where, partial derivatives It can be calculated by the finite difference method, and then the cutting height is updated by the moving asymptote algorithm based on the obtained sensitivity, and a new lattice structure is generated.

[0049] If the number of iterations is even and the structure volume fraction exceeds the set threshold of 0.5, then the unit cell is calculated. Internal composition virtual microstructure Unit sensitivity number The specific formula is as follows: , in, To form the first The first virtual microstructure The stiffness matrix of each element is calculated using the following formula: , in, To form the first The first virtual microstructure The volume fraction of solid material in each unit will then form the virtual microstructure. The sensitivity number of the virtual microstructure is obtained by adding the sensitivity numbers of the individual units. The specific formula is as follows: , To ensure the stability of the numerical calculation, the sensitivity number of the virtual microstructure is first spatially filtered, and the specific formula is as follows: , in, The weighting factor is calculated as follows: , in, For the filter radius, For the first The first cell and the first The Euclidean distance between the center points of each unit cell is used, and then the spatially filtered virtual microstructure sensitivity number is subjected to temporal filtering, with the specific formula as follows: , in, and Let these represent the current iteration number and the previous iteration number, respectively. For each virtual microstructure, sorting the sensitivity numbers of all its non-empty individuals in ascending order, we can obtain... , For the current number The total number of non-empty virtual microstructures is determined, and the deletion rate for each virtual microstructure is set to 2%. Based on this, non-empty virtual microstructures with low sensitivity are removed. 7. Evaluate whether the convergence criterion is met. The specific formula is as follows: , in For compliance error, For volume fraction error, and If the convergence criterion is not met, take 0.2%. If the convergence criterion is not met, repeat steps 5 to 7 until convergence is achieved; otherwise, stop the iteration and generate the final lattice structure.

[0050] The optimization results of the preferred embodiment of the present invention are as follows: The optimized lattice structure is as follows Figure 4 As shown, the compliance value is 55.02. In contrast, the lattice structure optimized using the original multivariate cut level set method is shown below. Figure 5As shown, the compliance value is 52.74. Although the structure obtained by the original method has slightly higher stiffness, it has extremely fine microstructural features and does not meet the minimum size requirements of 3D printing. Therefore, considering the size constraints of actual manufacturing, the lattice structure optimization design method combining multivariate cutting level sets and progressive optimization provided by this invention is more advantageous. It can ensure that the optimized lattice structure maintains good mechanical properties, while effectively controlling the minimum microscopic size of the optimal structure.

[0051] The present invention also provides a manufacturable design system for lattice structures that combines multivariate level set cutting with incremental optimization. The system includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to perform the lattice structure optimization design method that combines multivariate level set cutting with incremental optimization as described above.

[0052] The present invention also provides a computer-readable storage medium storing machine-executable instructions, which, when invoked and executed by a processor, cause the processor to implement the lattice structure optimization design method described above, which combines multivariate level set cutting with asymptotic optimization.

[0053] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A lattice structure optimization design method combining multivariate level set segmentation and asymptotic optimization, characterized in that, The steps are as follows: (1) Divide the structural design domain of the lattice structure to be optimized into a single cell, and then divide the single cell into elements; (2) Define multiple basic level set functions within each unit cell. And set the initial cutting height. To describe virtual microstructures This yields the initial virtual microstructure within each unit cell; among which, ; (3) Arbitrary virtual microstructures are combined using Boolean operations to obtain actual microstructures. This leads to the formation of the initial overall lattice structure. ; (4) Structural flexibility The objective function is the cutting height. Set a structural volume fraction threshold as a design variable. Upper limit of cutting height and lower limit To establish an optimization model for the lattice structure; (5) After determining the boundary conditions of the lattice structure to be optimized based on the initial overall lattice structure, perform finite element analysis based on the lattice structure optimization model to obtain the structural volume fraction. (6) If the current iteration number is odd or the structural volume fraction is lower than the set threshold, calculate the sensitivity of the objective function and constraint function to the design variables, and update the design variables based on the obtained sensitivity using the moving asymptote algorithm; if the iteration number is even and the structural volume fraction exceeds the set threshold, calculate the unit sensitivity number, and then obtain the sensitivity number of the virtual microstructure, and remove part of the virtual microstructure based on the sensitivity number of the virtual microstructure. (7) Determine whether the convergence condition is met. If it is met, generate the final lattice structure; otherwise, proceed to step (5) until convergence.

2. The lattice structure optimization design method combining multivariate level set cutting and asymptotic optimization as described in claim 1, characterized in that: Virtual microstructure Composed of multiple basic level set functions and corresponding cutting height The formula is: ， in, For single cell The coordinates of any point within the area.

3. The lattice structure optimization design method combining multivariate level set cutting and asymptotic optimization as described in claim 2, characterized in that: Actual microstructure All by A virtual microstructure The specific calculation formula is obtained through Boolean operations: Then, all the actual microstructures are combined into an initial overall lattice structure. The corresponding mathematical expression is: 。 4. The lattice structure optimization design method combining multivariate level set cutting and asymptotic optimization as described in claim 3, characterized in that: The mathematical expression for the lattice structure optimization model is: In the formula, For the overall external force vector, This is the global displacement vector. For the overall stiffness matrix, This represents the volume fraction of the current structure.

5. The lattice structure optimization design method combining multivariate level set cutting and asymptotic optimization as described in any one of claims 1-4, characterized in that: Cutting height limit Minimum structural feature size required by 3D printing process The relationship is as follows: in, It is the magnitude of the gradient of the basic level set function.

6. The lattice structure optimization design method combining multivariate level set cutting and asymptotic optimization as described in claim 1, characterized in that: unit cell Inner Virtual Microstructure The sensitivity number is obtained by adding the sensitivity numbers of the units that make up the virtual microstructure, and the specific calculation formula is as follows: ， in, For single cell Internal composition of the first The first virtual microstructure The sensitivity number of each unit is calculated using the following formula: ， in, To form the first The first virtual microstructure The stiffness matrix of each element is calculated using the following formula: ， in, To form the first The first virtual microstructure The volume fraction of solid material in each unit.

7. The lattice structure optimization design method combining multivariate level set cutting and asymptotic optimization as described in claim 6, characterized in that: Spatial filtering is applied to the sensitivity number of the virtual microstructure, and the specific calculation formula is as follows: ， in, The weighting factor is calculated as follows: ， in, For the filter radius, For the first The first cell and the first The Euclidean distance between the center points of each unit cell is then used to perform time filtering on the spatially filtered virtual microstructure sensitivity number. The specific calculation formula is as follows: ， in, and These represent the current iteration number and the previous iteration number, respectively.

8. The lattice structure optimization design method combining multivariate level set cutting and asymptotic optimization as described in claim 1, characterized in that: For each virtual microstructure, sort the sensitivity scores of all its non-empty individuals in ascending order to obtain... The removal rate for each virtual microstructure is set to be 1. Based on the removal rate and the resulting ranking, non-empty virtual microstructures that rank higher in the ranking are removed. For the current number The total number of non-empty individuals of the virtual microstructure.

9. A manufacturable design system for lattice structures that combines multivariable level set segmentation with asymptotic optimization, characterized in that: The system includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it performs the lattice structure optimization design method combining multivariate level set cutting and progressive optimization as described in any one of claims 1-8.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores machine-executable instructions, which, when invoked and executed by a processor, cause the processor to implement the lattice structure optimization design method combining multivariate level set cutting and asymptotic optimization as described in any one of claims 1-8.

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