A macro-micro collaborative topology optimization design method for continuous fiber additive manufacturing

Abstract

The present application relates to a kind of macroscopic and microscopic synergic topology optimization design method of continuous fiber additive manufacturing, constructs the square cell of filling continuous fiber and obtains the mapping relationship of fiber parameter, cell geometric parameter and equivalent material performance based on homogenization method, according to the manufacturing characteristics of continuous fiber single filament bundle composite material, construct fiber divergence constraint model, and with the maximum structural stiffness as design goal, using parameterized topology optimization design idea, by regulating cell geometric parameter, fiber parameter obtains the continuous fiber trans-scale structure of stiffness performance optimum;According to the numerical value of design variable, the continuous of discrete design variable is realized using wave projection method, and the continuous fiber distribution is obtained, and the manufacturing filament bundle scheme is formed according to the size of manufacturing equipment nozzle and fiber content;The present application greatly improves the load bearing advantage of trans-scale structure local and whole of additive continuous fiber composite material that can be synergic regulated, realizes the integrated design of macroscopic and microscopic synergic regulation.

Description

Technical Field

[0001] This invention relates to the field of structural optimization in composite additive manufacturing, specifically to a structural optimization design method for continuous fiber additive manufacturing that combines continuous fiber parameters and structural topology optimization. Background Technology

[0002] Continuous fiber reinforced polymer composites (CFRPCs), using polymers as the matrix and continuous fibers as reinforcement, possess advantages such as high strength-to-weight ratio, low coefficient of thermal expansion, long fatigue performance, good corrosion resistance, and high thermal conductivity. Fiber-reinforced composites based on additive manufacturing, with their innovative development model of "integrating structural performance design with digital manufacturing," represent a promising new combination of technology and materials for the future. This process is simple, requires no molds, has high material utilization, and is mold-free, significantly reducing the manufacturing cost of composite components and providing a new approach to composite material processing. It features moldless, integrated, and rapid prototyping of multi-scale, multi-level composite structures, showing great potential in achieving the integration of lightweight, high-strength materials with complex structural functions. It allows for arbitrary arrangement of materials according to load requirements and structural shape, enabling overall / local controllability of the structural performance. However, this combination of new materials and processes has unique forming characteristics and constraints. For example, fiber orientation and arrangement are highly related to structural forming performance; different fiber content and fiber form also directly affect structural performance; during the manufacturing process of continuous fiber reinforced composites, the curvature of the fiber layout will determine the final structural performance to a certain extent; in order to maintain the continuity of load transfer, it is necessary to ensure the spatial continuity of fiber angle changes, etc.

[0003] Currently, research on the structural design of fiber-reinforced composite materials based on additive manufacturing is still incomplete. Most studies employ traditional geometric infilling path planning methods, such as grid contour filling, contour offset path filling, and hybrid path filling, to prepare solid prototypes. Some researchers further consider the anisotropic mechanical properties of continuous fiber-reinforced composites, analyzing the stress transmission paths of fibers in the composite material to extract key stress lines, thereby optimizing and improving the structure. By adjusting the fiber distribution and strength, the mechanical and durability properties of the composite material can be improved. Alternatively, level set functions are used to characterize the composite material. By defining a function in three-dimensional space and determining the position of materials and pores based on the sign of the function value, the geometry of the composite material can be constructed. However, these methods present a sequential design and manufacturing process, failing to fully consider the characteristics of simultaneous local and overall controllability of fiber materials and the process characteristics. They cannot achieve control over the local fiber material volume ratio within the structure; problems such as excessively small corners and unreasonable layouts may also occur during printing, severely affecting the mechanical properties of the optimized structure and making it difficult to achieve the goal of integrated design of complex multi-scale structures and processes. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the present invention aims to provide a macro-micro collaborative topology optimization design method for continuous fiber additive manufacturing. This method fully considers the load-bearing characteristics of cross-scale structures to design reasonable microstructures. Based on the characteristics of fiber additive manufacturing, a model describing the fiber layout is established, and the mechanical properties of the structure are synergistically controlled from both microstructure geometric parameters and fiber parameters to achieve integrated design of cross-scale structures of continuous fiber reinforced composite materials.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] A macro-micro collaborative topology optimization design method for continuous fiber additive manufacturing specifically includes the following steps:

[0007] 1) Construct a microstructure unit cell filled with continuous fiber composite material and calculate the equivalent material properties. Considering a 2.5-dimensional structure under a single load condition, where the two principal stress directions are perpendicularly distributed, a microstructure geometric unit cell with four perpendicularly intersecting sides is adopted to generate a more reasonable load-bearing structure. The variable parameters of the material are: fiber volume fraction and fiber orientation; the variable parameters of the microstructure unit cell are: the length and width of the hollow region; based on the energy homogenization method, the mapping relationship between the above adjustable parameters and the equivalent material mechanical properties is obtained. Specifically, the equivalent material elasticity matrix D of the microstructure unit cell is obtained based on the homogenization method. H The equivalent material elasticity matrix is ​​multiplied by a rotation matrix to obtain the material elasticity matrix associated with the fiber direction.

[0008] 2) Construct a fiber layout divergence model. For FDM continuous fiber additive manufacturing, reducing fiber overlap and aligning the distribution improves manufacturability. Fiber angles and continuous fiber paths can be transformed into a vector field representation problem. By vector decomposing the fiber bundle distribution, the total fiber volume is calculated using the microstructure geometric unit cell side length parameters and fiber volume fraction. Taking the microstructure direction B as an example: V fB(A) =(1-Gap)V f The fiber bundle distribution vector is decomposed along the diagonal of the unit cell, and the sum of the fiber quantities at all ingress and egress nodes of the element boundary node is defined as the same. Where V f The corresponding fiber volume ratio, Gap is the printing spacing, and V is the printing pitch. fB(A) Fiber content, The fiber content entering the unit. The fiber content of the unit.

[0009] 3) Establish a macro-micro synergistic optimization design model for continuous fiber reinforced composites. Based on the mapping relationship between design parameters and equivalent material properties and the fiber distribution divergence model obtained in steps 1) and 2), the geometric parameters of microstructure unit cells and fiber parameters (content and orientation) are used as design variables, the overall structural compliance is minimized as the design objective, and the overall structural mass fraction and the fiber content at unit nodes are used as constraints to obtain a macro-micro synergistic optimization model. The fiber orientation can be introduced into the design model by multiplying the equivalent material matrix by a rotation matrix.

[0010] 4) Establish a finite element analysis model. Discretize the design region and, based on bilinear quadrilateral elements, determine the stiffness matrix k of the discrete element e in the finite element analysis. e It can be represented as: k e =∫∫ Ω B T DBdΩ, where B is the geometric matrix, D is the equivalent material elasticity matrix, and Ω is the discrete element integration region. The element stiffness matrix is ​​assembled, and the structure is subjected to finite element analysis to obtain the structural nodal displacements.

[0011] 5) Calculate the objective function and sensitivity. Based on the structural node displacements obtained in step 4), filter the parametric design variables and calculate the objective function of the topology optimization structure, i.e., the structural strain energy; as well as the sensitivity of the objective function and constraints to the design variables. In this model, the filtering method used is image-based opening and closing operations.

[0012] 6) Optimize and update parametric design variables. Based on the GCMMA algorithm, the objective function and sensitivity obtained in step 5) are calculated, and the design variables are iteratively updated to obtain new parametric design variables;

[0013] 7) Determine if the iteration meets the convergence condition. Determine whether the geometric parameters and fiber parameters of the design variables in step 6) simultaneously meet the convergence condition, i.e., the change in the design variable values ​​between the two iterations is less than 0.001. If the convergence condition is not met, continue the iteration; if it is met, stop the loop and obtain the corresponding design variable values ​​in the final discrete element.

[0014] 8) Achieve visualization of continuous fiber layout and matching of manufacturing scheme. Based on the design variable distribution finally obtained in step 7), and using the wave projection concept, calculate the scalar field in the design domain that is compatible with the design variables, and obtain two orthogonal projection functions based on this scalar field; introduce the real-time adjustable fiber content value into the wave projection equation to form a parametrically adjustable double field superposition, and achieve direct matching between the material content obtained from the design and the manufacturing tow scheme based on the nozzle size of the manufacturing equipment and the optimized local fiber content.

[0015] Beneficial effects:

[0016] This invention proposes a cross-scale structural optimization design method based on continuous fiber additive composites, breaking through the limitations of traditional continuous fiber topological solid structure design. Compared with existing methods, it considers the material and process characteristics of additive continuous fiber composites more deeply. Employing a parameter optimization design method based on homogenization, it introduces fiber volume fraction variables into the material model, thereby achieving coordinated design of the macroscopic topology and local fiber volume fractions. It establishes a mapping relationship between fiber parameters, microstructure geometric parameters, and mechanical properties, fully considering the high controllability of material parameters in additively manufactured continuous fiber composites. Furthermore, it constructs a divergence constraint model describing the fiber layout and establishes a mathematical model considering angular constraints during manufacturing. This significantly improves the cross-scale structural load-bearing advantages of additive continuous fiber composites, enabling coordinated control of both local and overall load-bearing capacity, and achieving integrated design with coordinated macro- and micro-level control.

[0017] This invention has good applicability. It adopts the parametric topology optimization design concept and obtains a continuous fiber cross-scale structure with optimal stiffness performance by adjusting the unit cell geometry parameters and fiber parameters. It introduces fiber content, fiber orientation and fiber layout divergence constraints into the cross-scale structure optimization design and additive manufacturing. It achieves precise control of the composite material parameters and load-bearing requirements during the printing process, effectively solving the current problem of integrated design and manufacturing of complex structures of continuous fiber reinforced composite materials, thereby promoting the development of additive continuous fiber composite structure optimization design. Attached Figure Description

[0018] Figure 1 This is a flowchart of the macro-micro collaborative topology optimization design method of the present invention.

[0019] Figure 2 This is a schematic diagram of a single microstructure cell of the continuous fiber composite bundle constructed according to the present invention.

[0020] Figure 3 This is a schematic diagram of the fiber layout divergence decomposition constructed according to the present invention.

[0021] Figure 4 This is a schematic diagram of the node definition method for the fiber layout divergence constraint unit constructed in this invention.

[0022] Figure 5 This is a diagram showing the initial design domain and boundary conditions for an implementation example of the present invention.

[0023] Figure 6 The variable distribution diagram is used to implement the calculation example of this invention.

[0024] Figure 7 This is a partial diagram showing the distribution of optimized variables in a numerical example of the present invention.

[0025] Figure 8 This is a schematic diagram illustrating a continuous fiber composite tow manufacturing scheme for an implementation example of the present invention. Detailed Implementation

[0026] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0027] This invention proposes a macro-micro collaborative optimization design method for continuous fiber additive manufacturing. Based on the homogenization method, it obtains the equivalent material properties related to the microstructure unit cell parameters and fiber parameters. According to the manufacturing characteristics of continuous fiber monofilament bundles, it constructs a fiber distribution divergence constraint model and establishes a microstructure unit cell parameter and fiber parameter control model. This enables the collaborative optimization design of the macroscopic topology and local fiber content of the structure, and ensures that the fiber layout meets the high manufacturability constraints. This maximizes the structural characteristics of high degree of freedom in controlling the mechanical properties of continuous fiber structures in additive manufacturing.

[0028] In the additive manufacturing process of composite materials, the resin matrix of the selected continuous fiber reinforced composite material includes thermoplastic resin materials such as polylactic acid (PLA), ABS, nylon, polyimide (PI), or polyether ether ketone (PEEK); the fiber reinforcing phase of the selected continuous fiber reinforced composite material includes continuous fiber materials such as carbon fiber, aramid fiber, glass fiber, and basalt fiber, as well as metal wire bundles such as copper wire and silver wire.

[0029] like Figure 1 A macro-micro collaborative topology optimization design method for continuous fiber additive manufacturing includes the following steps:

[0030] 1) Construct a square microstructure unit cell filled with continuous fiber composite material, referring to... Figure 2 Continuous fiber composite bundles are distributed on the four sides of the geometric unit cell. Based on the energy homogenization method, the macroscopic equivalent material elasticity matrix D of the microstructure unit cell is obtained. H:

[0031]

[0032] In the formula, E A and E B These are the equivalent elastic moduli in the transverse and longitudinal directions of the microstructure unit cell, respectively, and their calculation methods are as follows: E A =2.201v fA +3.167, E B =2.201v fB +3.167, of which and These represent the fibrous volume fractions in the transverse and longitudinal directions of the microstructure unit cell, respectively, and G is the shear modulus, calculated as follows:

[0033] By multiplying the equivalent material elasticity matrix by a rotation matrix, a fiber orientation variable is introduced:

[0034] D(A,B,θ,v fA ,v fB ) = R T (θ)D H (A,B,v fA ,v fB R(θ)

[0035] In the formula:

[0036] 2) Construct a fiber distribution divergence model. For example... Figure 3 The fiber bundle distribution is decomposed into vectors, and the fiber bundle distribution vector is defined as V. fiB V can be calculated using the microstructure geometric unit cell side length parameter and fiber volume ratio: fB(A) =(1-Gap)V f The fiber bundle distribution vector is decomposed along the diagonal of the unit cell, and defined as the fibers entering the unit cell. and fibers leaving the unit cell in Therefore, the definition of satisfying the non-scattering constraint is: internal nodes satisfy the condition that the fiber quantity of entering and exiting nodes is the same, and boundary nodes satisfy the condition that the sum of the fiber quantity of all entering and exiting nodes is the same. Figure 4 This is the definition method for a single-cell node, where blue represents boundary nodes and black represents internal nodes;

[0037] 3) Establish a macro-micro synergistic optimization design model for continuous fiber reinforced composites. In the optimization model, the design variables are defined as the side length (A, B) of the central hole in the microstructure geometric unit cell and the fiber volume fraction in the solid material. And the fiber angle θ. Fiber mass fraction constraints and fiber distribution divergence constraints are applied, with the overall structural compliance being minimized as the design objective. The side lengths of the microstructure unit cell pores are all greater than 0 and less than 1, and the fiber angle θ ranges from [-π / 2, π / 2]. The optimization design model is as follows:

[0038]

[0039] In the formula, g Ai Let A be the geometric width of the microstructure in the i-th unit along direction A. Let ρ be the geometric width of the microstructure in the B direction in the i-th unit. f Density of continuous fiber phase materials, ρ r Density of the resin matrix phase material, m B S is the fiber area along the B direction in the microstructure unit. B =(1-A)B, m A S is the fiber area along direction A in the microstructure unit. A =(1-B)A,S AB Let d be the area of ​​the overlapping fiber portion in the AB direction. max The maximum width of the hole. and The minimum and maximum volume ratios, ε represents the distribution of unit node fibers in agglomeration, and ε is the divergence distribution threshold.

[0040] 4) Establish a finite element analysis model. Discretize the geometric design domain using bilinear quadrilateral elements, set the element size, apply boundary conditions (loads and constraints), and calculate the nodal displacement response of the structural elements based on the equilibrium equations.

[0041] 5) Calculate the objective function and sensitivity. Based on the structural node displacements obtained in step 4), filter the parametric design variables by performing opening-then-closing and closing-then-opening operations on the design variables respectively, and then take the average value. The calculation formula is as follows:

[0042]

[0043] In the formula:

[0044] Where, x e The design variable values ​​for unit e.

[0045] After obtaining the filtered design variable values, the objective function of the topology optimization structure, i.e., the structural strain energy, is calculated based on these values; as well as the sensitivity of the objective function and constraints to the design variables. The sensitivity calculation formula is as follows:

[0046] The sensitivity of the objective function to the design variables (parameterized design variables are collectively referred to as ) can be written as:

[0047]

[0048] The sensitivity of fiber layout divergence constraints to design variables can be written as:

[0049]

[0050] Taking the transverse direction A of the fiber layout element decomposition as an example, the sensitivity calculation formula is as follows:

[0051] Fiber usage in Unit A direction:

[0052] The formula for solving the sensitivity of fiber components at unit nodes is as follows: (taking node 1 as an example, the same applies to the other nodes).

[0053] Node 1, fiber infeed in direction A:

[0054] A-direction fiber and divergence: Ω i Internal nodes of the structure Sensitivity: V l : The internal nodes contained in unit l

[0055] 6) Optimize and update parametric design variables. Based on the GCMMA iterative algorithm and the obtained objective function and sensitivity calculation, iteratively update the design variables to obtain new design parameters.

[0056] 7) Determine if the iteration meets the convergence condition. Determine whether the geometric parameters and fiber parameters of the design variables in step 6) simultaneously meet the convergence condition, i.e., the change in the design variable values ​​between the two iterations is less than 0.001. If the convergence condition is not met, continue the iteration; if it is met, stop the loop and obtain the final design variable values ​​of the discrete element response.

[0057] The finite element solution program, optimization program, continuous fiber visualization and path program in steps 1)-7) were all written in Matlab. Those skilled in the art can also use C#, C++ or Fortran as needed.

[0058] In step 5), the topology optimization solution uses the optimization criterion method, the moving asymptote method, the sequential linear programming method, the sequential quadratic programming method, the interior point method, the effective set method, or the trust region effective algorithm.

[0059] For specific examples of the present invention, please refer to Figures 5-8 Taking the classic cantilever beam structure as an example, we carried out macro-micro collaborative optimization design of continuous fiber composite materials. The specific implementation is as follows:

[0060] The initial design domain and boundary conditions of the cantilever beam are as follows: Figure 5 As shown, the design domain is a 60×90mm area, with one side fixed. An input force F = 100N is applied to the middle of the right side of the cantilever beam. The overall structural mass fraction is constrained to 30%, and the filter radius is Rmin = 1.5. The design domain is discretized into 60×90 finite element elements. The mechanical properties of the resin matrix and continuous fibers are shown in the table. Table 1 Material Properties

[0061] Based on the established macro-micro collaborative optimization design method, the cantilever beam example is optimized. Figure 6 This is the optimal design variable distribution diagram. The optimization results show that, for this boundary condition and design domain configuration, the microstructure geometry and fiber content are relatively high at the upper and lower left corners of the structure and at the loading point on the right end. Furthermore, the design variables exhibit a gradual distribution at the connection points of these locations, forming a reasonable and continuous force transmission path (such as...). Figure 7 (Partial view), the design variable values ​​in other areas are relatively small. By leveraging the rational material layout in topological thinking, the design of high structural rigidity and lightweight structure can be effectively achieved. Furthermore, by filtering the design variables, a continuous distribution of fiber angles is formed to facilitate the subsequent formation of continuous fiber paths and make manufacturing easier.

[0062] Figure 8 Based on the idea of ​​wave function projection, a constrained least squares formula is constructed to obtain the wave function at high resolution. At the same time, the microstructure geometric width and fiber volume ratio information are introduced into the formula to form a continuous fiber distribution with adjustable local fiber content. Based on the manufacturing equipment size, the nozzle size in the robotic arm printing, i.e. the minimum size of the composite filament bundle, is considered. The nozzle size is matched with the fiber distribution content obtained by the design to obtain a continuous fiber distribution directly related to the manufacturing scheme.

[0063] In summary, this invention proposes a macro-micro co-optimization design method for additive manufacturing continuous fiber composites. Based on continuous fiber additive manufacturing technology and considering its characteristics, this method aims to maximize structural stiffness. It performs cross-scale parallel optimization design on fiber layout, local / overall fiber content, fiber orientation, and structural density. First, a rectangular unit cell filled with continuous fibers is constructed. Equivalent material parameters related to microstructure geometry and fiber parameters are obtained using a homogenization method. To avoid mechanical property degradation caused by large rotations during continuous fiber additive manufacturing, a fiber local divergence constraint model is constructed based on the manufacturing characteristics of fiber monofilament bundles. Based on the aforementioned material parameters and manufacturing constraint model, a macro-micro co-optimization design model for cross-scale structures of additive manufacturing continuous fiber composites is established. The design variables are updated using a gradient-based GCMMA algorithm. Based on the design variable values ​​obtained from the optimization design, two orthogonally superimposed projection fields are formed using wave projection to obtain a manufacturing scheme matching the number of fiber bundles. This achieves co-design of the overall structural topology distribution and local fiber content, fundamentally leveraging the advantages of high degree of freedom and topology optimization in additive manufacturing of continuous fiber materials.

[0064] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A macro-micro collaborative topology optimization design method for continuous fiber additive manufacturing, characterized in that, Includes the following steps: 1) Construct microstructure unit cells of continuous fiber composite materials, obtain the equivalent material elastic matrix of the microstructure unit cells based on the homogenization method, multiply the equivalent material elastic matrix by the rotation matrix, and then obtain the material elastic matrix related to the fiber direction, that is, obtain the equivalent material properties related to the microstructure unit cell parameters and fiber parameters. 2) Based on the manufacturing characteristics of continuous fiber monofilament composite materials, a fiber layout divergence constraint model is constructed; 3) Establish a macro-micro synergistic optimization design model for continuous fiber reinforced composites. With the minimum overall structural compliance as the design objective, fiber mass fraction constraints and fiber layout divergence constraints are applied to obtain the macro-micro synergistic optimization model. The established macro-micro synergistic optimization design model is as follows: ； In the formula, Let A be the geometric width of the microstructure in the i-th unit along direction A. Let be the geometric width of the microstructure in the B direction in the i-th unit; Density of continuous fiber phase material; Density of the resin matrix phase material; The fiber area in the B direction of the microstructure unit , The fiber area in direction A in the microstructure unit , Let be the area of ​​the overlapping fiber portion in the AB direction. The maximum width of the hole. and The minimum and maximum volume ratios, The fiber distribution of the unit nodes is cohesive. The threshold for the divergence distribution; 4) Establish a finite element analysis model; 5) Calculate the objective function and sensitivity. 6) Optimize and update parametric design variables; 7) Determine whether the design iteration meets the convergence condition. If it does, output the values ​​of the design variables obtained by optimization. Otherwise, perform finite element analysis again and update the design variables until the convergence condition is met.

2. The macro-micro collaborative topology optimization design method for continuous fiber additive manufacturing according to claim 1, characterized in that, Step 2) Specifically, based on the actual manufacturing characteristics of single-filament continuous fiber composite materials, a unit node fiber decomposition model is constructed. The overall fiber content information of the unit is decomposed to the fiber boundary nodes and defined as the amount of fiber flowing into and out of the unit. An equation is established to make the amount of fiber flowing into and out of the unit equal. The P-norm is used to aggregate all units to generate a fiber layout divergence constraint model.

3. The macro-micro collaborative topology optimization design method for continuous fiber additive manufacturing according to claim 1, characterized in that, Step 4) Specifically, the design domain is defined, and the design domain of the macro-micro co-optimization model is discretized into several finite element elements. Each finite element element includes four nodes. The initial values ​​of the optimization model are defined, boundary conditions are applied, and based on finite element analysis, the element displacement of each finite element element in the continuous fiber design domain is output.

4. The macro-micro collaborative topology optimization design method for continuous fiber additive manufacturing according to claim 3, characterized in that, Step 5) Specifically, the element compliance of each finite element is calculated based on the nodal displacement of each finite element obtained in step 4). The design variables are filtered using a graph-based method to obtain the filtered design variable values. Based on these values, the objective function of the topology optimization structure is calculated, and the sensitivities of the objective function and constraint function to the design variables of each finite element are obtained by taking the derivatives.

5. The macro-micro collaborative topology optimization design method for continuous fiber additive manufacturing according to claim 4, characterized in that, In step 6), based on the GCMMA algorithm and the objective function and sensitivity obtained in step 5), the design variables are iteratively updated to obtain new parameterized design variables.

6. The macro-micro collaborative topology optimization design method for continuous fiber additive manufacturing according to claim 1, characterized in that, The design variable values ​​output in step 7) are discrete distributions dependent on finite elements. Based on this, and based on the wave projection concept, the fiber content, microstructure parameters and fiber orientation parameters in the design variables are integrated into two orthogonal projection fields. Based on the orthogonal projection fields, according to the nozzle diameter of the single-filament additive manufacturing machine and the fiber content at different positions in the structure, an interpolation model is used to match the filament quantity manufacturing scheme, forming a filament manufacturing scheme, and then visualized.

7. The macro-micro collaborative topology optimization design method for continuous fiber additive manufacturing according to claim 4, characterized in that, In step 5), the topology optimization solution uses the optimization criterion method, moving asymptotic method, sequential linear programming method, sequential quadratic programming method, interior point method, effective set method, or trust region effective algorithm.

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