Strength-constrained topology optimization design method for shell-porous filling structures

Abstract

The present invention discloses a strength-constrained topological optimization design method for a shell-porous filling structure, comprising: discretizing the design domain using finite elements according to the characteristics of the design structure; introducing two sets of design variables to optimize the shell structure and the internal porous filling structure respectively; for static strength design problems, using a modified solid isotropic material interpolation model with a penalty factor to describe the elastic modulus and density of the material, and for dynamic strength design problems, using a modified polynomial interpolation model to describe the elastic modulus of the material; constructing a robust strength-constrained topological optimization model to solve the sensitivity of the objective function to the design variables; and using a moving asymptotic algorithm for optimization design. The present invention can simplify the design of porous structure material properties, which is conducive to reducing the difficulty of numerical implementation.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-scale structure topology optimization design, and in particular to a strength-constrained topology optimization design method for a shell-porous filling structure. Background Art

[0002] Mechanical structure design includes single-scale structure design and multi-scale structure design. For single-scale structure design, only the construction of macro structure is realized; while multi-scale structure design includes the integrated design of macro structure and micro structure. The optimization design of micro structure makes multi-scale structure have greater design freedom. Many scholars believe that multi-scale structure is expected to become a new generation of lightweight structure with excellent performance. For example, the shell-porous filling structure composed of dense shell and porous internal filling is a lightweight structure with good damage resistance and stability. How to realize the shell-porous filling multi-scale structure has become a research hotspot today.

[0003] The current shell-porous filling structure design method has the following defects:

[0004] (1) For the shell-porous filling structure, the porous structure filled inside is a major component, and the existing porous structure design methods are often based on the idea of ​​"scale separation" to design macroscopic and microscopic structures separately. This type of method assumes that a limited number of microstructures are uniformly distributed in the macroscopic structure, and the design model is simple and the computational cost is low. However, this type of method greatly reduces the microstructure design domain, which is not conducive to achieving structural design with better performance.

[0005] (2) At present, there is still a design method that mainly focuses on stiffness performance to carry out structural design, and there is little research on design methods for structural strength. However, in engineering practice, structural strength performance is crucial to structural safety. Ignoring the analysis and design of structural strength will result in a structure that is unconvincing. Therefore, the development of strength design methods for shell-porous filling structures is an urgent direction to be solved. Summary of the invention

[0006] In view of the defects of the prior art and the need for improvement, the present invention provides a strength constrained topological optimization design method for a shell-porous filling structure, which fully considers the demand for structural strength in actual engineering problems, and comprehensively considers the static strength and dynamic strength of the shell and porous filling structure. The design method can avoid structural strength failure and has stronger engineering applicability.

[0007] To achieve the above object, the present invention is implemented through the following technical solutions:

[0008] The present invention provides a strength-constrained topological optimization design method for a shell-porous filling structure, which is applicable to the structural design of a dense shell and a porous internal filling structure, and includes:

[0009] Step 1: Based on the characteristics of the design structure, use finite elements to discretize the design domain and set relevant parameters including material parameters and optimization parameters;

[0010] Step 2: Introduce two sets of design variables to optimize the shell structure and the internal porous filling structure respectively. After a series of numerical operations, output three sets of intermediate physical field variables, and use different projection coefficients to generate three sets of intermediate erosion field variables.

[0011] Step 3: For static strength design problems, the modified solid isotropic material interpolation model with penalty factor is used to describe the elastic modulus and density of the material. For dynamic strength design problems, the modified polynomial interpolation model is used to describe the elastic modulus of the material.

[0012] Step 4: Construct a robust strength constrained topology optimization model, perform finite element analysis on the structure, and calculate the objective function and response values ​​of each constraint function in the optimization model;

[0013] Step 5: According to the derivative rule of composite function and the derivative method of adjoint variables, solve the sensitivity of the objective function, global volume fraction, local volume fraction and maximum stress response function of the structure to the design variables;

[0014] Step 6: Use the moving evolutionary algorithm to optimize the design. The objective function solved in steps 4 and 5 and the response values ​​and sensitivity information of each constraint are used as the input conditions of the moving evolutionary algorithm to solve the optimization problem and iteratively update the design variables.

[0015] Exemplarily, the strength-constrained topology optimization design method for a shell-porous filling structure further includes:

[0016] Step 7: Repeat steps 2 to 6 to update the design variables multiple times until the current design meets the optimization convergence conditions and the optimization process is stopped.

[0017] Exemplarily, in step 2, the series of numerical operations include: filtering, projecting, and solving density space gradient on the two groups of design variables at least once.

[0018] Exemplarily, in step 2, the two sets of design variables introduced include a first design variable μ and a second design variable v. The first design variable μ is filtered, gradient normed, and projected at least once to obtain two sets of intermediate variables: and τ, the second design variable v is filtered and projected to obtain a set of intermediate variables ψ, where the filtering operation is used to avoid the checkerboard pattern and identify the boundary, and the projection operation is used to generate a clear structure. The total variable field of the shell and filling structure is expressed as three sets of intermediate variables The combination of τ and ψ corresponds to

[0019] Exemplarily, step 2 also includes:

[0020] A local volume constraint is introduced to ensure the porosity of the internal filling structure. v It is expressed as: Among them, N e is the number of units in the partition structure, P v is the local volume aggregation parameter, represents the local volume fraction near the i-th unit;

[0021] The erosion field variable is introduced to construct a robust topology optimization model, and the erosion field projection coefficient η is used. ero , and obtain the erosion field variables

[0022] Exemplarily, in step three, the elastic modulus and density of the material, namely:

[0023]

[0024]

[0025] Among them, E(ξ i ) and ρ(ξ i ) represent the elastic modulus and density of the material of the ith unit, E0 and ρ0 represent the elastic modulus and density of the solid material, respectively. It is expressed as:

[0026]

[0027]

[0028] Here, e is a small amount to avoid the singularity of stiffness and is set to e = 10 -6 , p E and p ρ are the penalty factors for elastic modulus and density, respectively, set to p E =3 and p ρ =1,χ( ξ i, p) is expressed as:

[0029]

[0030] Exemplarily, in step three, for the dynamic strength design problem, a modified polynomial interpolation model is used to describe the elastic modulus of the material, namely:

[0031]

[0032] Among them, setting p E =5 and p E，2 =1.

[0033] Exemplarily, in step 4, the objective function and the response values ​​of each constraint function are expressed as follows:

[0034]

[0035]

[0036]

[0037]

[0038]

[0039] Among them, the objective function c is the physical field flexibility c and the erosion field flexibility c ero The weighting coefficient w is initially 0.1 and increases by 0.1 every 50 iterations until it reaches a maximum value of 0.9. v is the global volume fraction of the structure, l v is the local volume fraction of the structure, φ is the maximum stress response function of the structure, For the global volume constraint defined, is the local volume constraint defined, and are the stress constraints for the physical field and erosion field structures respectively.

[0040] In the above embodiments, the structural design method of the dense shell and the porous internal filling structure is based on the idea of ​​full-scale analysis. There is no need to separate the macrostructure and the microstructure at different scales, thus simplifying the design of the material properties of the porous structure and reducing the difficulty of numerical implementation.

[0041] In some exemplary embodiments, structural strength constraints under static loads and dynamic loads are considered respectively, and structural enhancement design under static and dynamic conditions is achieved. Since too many constraints are not imposed on the design of the porous structure, the reduction of the structural design domain is avoided, and the optimal design of structural performance can be well achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0043] Figure 1 It is a partial flow chart of a strength-constrained topology optimization design method for a shell-porous filling structure provided by an embodiment of the present invention;

[0044] Figure 2 is a schematic diagram of the physical field and the erosion field in an embodiment of the present invention, wherein: Figure 2 (a) Taking the L-shaped structure as an example, the generation of physical field and erosion field structure when different projection coefficients are used is illustrated; Figure 2 (b) illustrates the projection curves under different projection coefficients; Figure 2 (c) describes the effect of the projection coefficient on the structure size;

[0045] Figure 3 It is a schematic diagram of the topology optimization design area and boundary in Example 1 of the present invention;

[0046] Figure 4 is a schematic diagram of the optimization results of the shell and the porous filling structure in Example 1 of the present invention;

[0047] Figure 5 Schematic diagram of the topology optimization design area and boundary and load conditions in Example 2 of the present invention;

[0048] Figure 6 It is a schematic diagram of the optimization results of the shell-porous filling structure in Example 2 of the present invention. DETAILED DESCRIPTION

[0049] In order to make the purpose, technical solution and advantages of the embodiment of the present invention clearer, the technical solution of the embodiment of the present invention will be further described in detail below in conjunction with the drawings of the embodiment of the present invention. Obviously, the described embodiment is a part of the embodiment of the present invention, not all of the embodiments. Based on the described embodiment of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0050] Unless otherwise defined, the technical or scientific terms used in the present invention shall have the common meanings understood by persons with ordinary skills in the field to which the present invention belongs. "Include" or "comprising" and similar words mean that the elements, objects, methods, schemes, systems, and devices that appear before the word include the elements, objects, methods, schemes, systems, and devices listed after the word and their equivalents, but do not exclude other elements, objects, methods, schemes, systems, and devices.

[0051] Combination Figure 1 This embodiment provides a strength-constrained topology optimization design method for a shell-porous filling structure, which is suitable for the structural design of a dense shell and a porous internal filling structure, including:

[0052] Step 1: Based on the characteristics of the design structure, use finite elements to discretize the design domain and set relevant parameters including material parameters and optimization parameters;

[0053] Step 2: Introduce two sets of design variables to optimize the shell structure and the internal porous filling structure respectively. After a series of numerical operations, output three sets of intermediate physical field variables, and use different projection coefficients to generate three sets of intermediate erosion field variables.

[0054] Step 3: For static strength design problems, the modified solid isotropic material interpolation model with penalty factor is used to describe the elastic modulus and density of the material. For dynamic strength design problems, the modified polynomial interpolation model is used to describe the elastic modulus of the material.

[0055] Step 4: Construct a robust strength constrained topology optimization model, perform finite element analysis on the structure, and calculate the objective function and response values ​​of each constraint function in the optimization model;

[0056] Step 5: According to the derivative rule of composite function and the derivative method of adjoint variables, solve the sensitivity of the objective function, global volume fraction, local volume fraction and maximum stress response function of the structure to the design variables;

[0057] Step 6: Use the moving evolutionary algorithm to optimize the design. The objective function solved in steps 4 and 5 and the response values ​​and sensitivity information of each constraint are used as the input conditions of the moving evolutionary algorithm to solve the optimization problem and iteratively update the design variables.

[0058] In the above embodiments, the structural design method of the dense shell and the porous internal filling structure is based on the idea of ​​full-scale analysis. There is no need to separate the macrostructure and the microstructure at different scales, thus simplifying the design of the material properties of the porous structure and reducing the difficulty of numerical implementation.

[0059] In some exemplary embodiments, structural strength constraints under static loads and dynamic loads are considered respectively, and structural enhancement design under static and dynamic conditions is achieved. Since too many constraints are not imposed on the design of the porous structure, the reduction of the structural design domain is avoided, and the optimal design of structural performance can be well achieved.

[0060] In addition, the strength-constrained topology optimization design method for the shell-porous filling structure also includes:

[0061] Step 7: Repeat steps 2 to 6 to update the design variables multiple times until the current design meets the optimization convergence conditions and the optimization process is stopped.

[0062] In some exemplary embodiments, in step 2, two sets of design variables are introduced to optimize the shell structure and the internal porous filling structure respectively. After a series of numerical operations, including filtering, projection, density space gradient solution, etc., three sets of intermediate physical field variables are output. In addition, in order to construct a robust topology optimization model in step 4, different projection coefficients are used to generate three sets of intermediate erosion field variables at the same time.

[0063] (1) Shell and porous filling structure generation process

[0064] like Figure 1 As shown, the design variable μ is filtered, projected, filtered, gradient normed, and projected to obtain two sets of intermediate variables. and τ; on the other hand, the design variable ν is filtered and projected to obtain a set of intermediate variables ψ. Multiple filtering and projection operations are performed throughout the process, where filtering operations are used to avoid checkerboard patterns and identify boundaries, and projection operations are used to generate clear structures. Specifically, Helmholtz partial differential filtering and threshold projection are used:

[0065]

[0066] Where γ can represent the variable fields μ and ν; r represents the filter size control parameter; η is the projection threshold, and β is the projection control parameter.

[0067] To identify the structural boundaries, the variable field Filter and then solve for the gradient norm:

[0068]

[0069] Last pair Projection is performed to obtain the shell variable field τ. At this point, all three sets of intermediate variables have been obtained, and the final shell and filling structure variable field can be expressed as a combination of three sets of intermediate variables:

[0070]

[0071] Furthermore, in order to ensure the porosity of the internal filling structure, it is necessary to introduce additional local volume constraints:

[0072]

[0073] Where N e is the number of units in the partition structure, P v is the local volume aggregation parameter, Represents the local volume fraction near the i-th unit, which is achieved by the following filtering operation:

[0074]

[0075] (2) Introduction of erosion field

[0076] In order to construct a robust topology optimization model in step 4, it is necessary to generate erosion field variables simultaneously in step 2. Figure 2 A schematic diagram of erosion field generation is shown, where Figure 2 (a) Taking the L-shaped structure as an example, the generation of physical field and erosion field structure when different projection coefficients are used is illustrated; Figure 2 (b) illustrates the projection curves under different projection coefficients; Figure 2 (c) describes the effect of the projection coefficient on the structure size. Using the erosion field projection coefficient η ero (>η), again according to Figure 1 The process shown can obtain the erosion field variables:

[0077]

[0078] Step 3: For the static strength design problem, the modified solid isotropic material with penalty factor interpolation model (MSIMP) is used to describe the elastic modulus and density of the material, that is:

[0079]

[0080] Among them, E(ξ i ) and ρ(ξ i ) represent the elastic modulus and density of the material of the ith unit, E0 and ρ0 represent the elastic modulus and density of the solid material, respectively. It is expressed as:

[0081]

[0082] Here, e is a small amount to avoid the singularity of stiffness and is set to e = 10 -6 , p E and p ρare the penalty factors for elastic modulus and density, respectively, set to p E =3 and p ρ =1,χ(ξ i , p) is expressed as:

[0083]

[0084] For the dynamic strength design problem, the mismatch of the above interpolation method in the low-density area will cause local modal problems. Therefore, a modified polynomial interpolation scheme (MPIS) is used to describe the elastic modulus of the material, namely:

[0085]

[0086] in It is expressed as:

[0087]

[0088] Among them, setting p E =5 and p E，2 =1.

[0089] In some embodiments, step 4: in order to achieve minimum size control in the structural design process, a robust strength constraint topology optimization model is constructed; then a finite element analysis is performed on the structure to calculate the objective function and the response values ​​of each constraint function in the optimization model:

[0090]

[0091] Among them, the objective function is the physical field flexibility c and the erosion field flexibility c ero The weighting coefficient w is initially o.1 and increases by 0.1 every 50 iterations until it reaches a maximum value of 0.9; g v is the global volume fraction of the structure, l v is the local volume fraction of the structure, φ is the maximum stress response function of the structure, For the global volume constraint defined, is the local volume constraint defined, and are the stress constraints for the physical field and erosion field structures respectively.

[0092] (1) Specifically, the structural flexibility is expressed as:

[0093] c=F T U (13)

[0094] Among them, F is the external load vector and U is the physical field displacement vector.

[0095] (2) The local volume fraction of the structure is expressed as:

[0096]

[0097] (3) In order to ensure that the internal structure is evenly filled and avoid excessive blank areas, it is assumed that all units just meet the local volume constraints. Therefore, the global volume fraction of the structure is expressed as:

[0098]

[0099] (4) In the finite element method environment, the structural stress response of the i-th element is expressed as:

[0100]

[0101] where σ i is the stress vector of the i-th unit, D0 is the constitutive matrix of the solid material, B is the strain-displacement matrix of the i-th unit, u i is the node displacement vector of the i-th element.

[0102] In order to avoid stress singularities, the element stresses are relaxed:

[0103]

[0104] where p s is the stress relaxation coefficient. For static and dynamic problems, p is set s = 0.5 and p s = 1. Considering that the material follows the von Mises yield criterion, the von Mises equivalent stress of unit i is calculated as:

[0105]

[0106] where V is the stress coefficient matrix:

[0107]

[0108] Finally, in order to reduce the optimization computation cost, the local stress responses are aggregated into a global stress response:

[0109]

[0110] Where P is the stress aggregation coefficient. For dynamic strength design problems, the global stress response is expanded to:

[0111]

[0112] Where N tRepresents the total time steps of dynamic analysis; in order to improve the accuracy of the aggregation function fitting the maximum stress of the structure, a correction factor η is introduced. Finally, the maximum stress response function of the structure is expressed as:

[0113] φ=ησ PN (twenty two)

[0114] The correction factor η is initially set to 1 and is updated with iterations:

[0115]

[0116] Where n represents the current topology optimization iteration step.

[0117] In some exemplary embodiments, step 5: solve the sensitivity of the objective function, global volume fraction, local volume fraction, and maximum stress response function of the structure to the design variables according to the composite function derivation rule and the adjoint variable derivation method; for any function f(ξ), its sensitivity to the design variable μ j and v j The sensitivity analysis of can be expressed using the chain rule:

[0118]

[0119] in, and It can be deduced from formula (1) to formula (2); and are all zero for all objective and constraint functions; the remaining terms are derived in detail later.

[0120] (1) Solve the sensitivity of structural flexibility according to the adjoint variable method:

[0121]

[0122] Among them, x represents three intermediate variables τ and ψ; k0 represents the unit stiffness matrix of the solid material; for the three intermediate variables, Write separately:

[0123]

[0124] (2) The sensitivity of the local volume fraction is written as:

[0125]

[0126] in and It can be deduced from formula (14):

[0127]

[0128] (3) The sensitivity of the global volume fraction is written as:

[0129]

[0130] (4) Then the sensitivity derivation of the maximum stress response function is given. First, for the static strength problem, according to the adjoint variable method, a set of Lagrange multipliers λ and static equilibrium equations are introduced. At this time, the stress response function can be written as:

[0131]

[0132] Then, the relative intermediate variables on both sides of equation (36) are Taking the derivative of τ and ψ, we get:

[0133]

[0134] By using the arbitrariness of Lagrange multipliers, we can eliminate item:

[0135]

[0136] In formula (37) and It can be directly obtained:

[0137]

[0138] Finally, the derivative of the stress response function can be written as:

[0139]

[0140] For the dynamic strength problem, according to the adjoint variable method, three sets of Lagrange multipliers and dynamic equilibrium equations are introduced. At this time, the stress response function can be written as:

[0141]

[0142] Here, R, S, and Q represent the kinetic equilibrium equations and the assumptions of the Newmark implicit iteration strategy:

[0143]

[0144] Then, we take the derivative of both sides of equation (36) and sort them out to get:

[0145]

[0146] Using the arbitrariness of Lagrange multipliers, we can eliminate and item:

[0147]

[0148] In formula (43) and It can be directly obtained:

[0149]

[0150] Finally, the derivative of the stress response function can be written as:

[0151]

[0152] In some exemplary embodiments, step six: using a moving incremental algorithm (MMA) for optimization design, using the objective function solved in steps three and four and the response values ​​and sensitivity information of each constraint as input conditions of the MMA optimization algorithm, solving the optimization problem, and iteratively updating the design variables.

[0153] Step 7: Repeat steps 2 to 6 to update the design variables multiple times until the current design meets the optimization convergence conditions and the optimization process is stopped.

[0154] To facilitate understanding of the present invention, two two-dimensional examples are given below to further illustrate the present invention. For these two two-dimensional examples, the material elastic modulus is set to 190000Mpa, the Poisson's ratio is 0.3, and the density is 8×10 -9 t / mm 3 .

[0155] In one possible implementation, the initial design domain is as follows: Figure 3 As shown in the figure, the structure is divided into 57600 quadrilateral grids, the top edge of the structure is fixed, and a vertical downward concentrated force is applied to the upper right corner. The force is 500N and is evenly distributed to the 15mm edge. Set the stress aggregation coefficient P = 12, the local volume aggregation coefficient P v = 8. Filter radius R μ =20, R μ =2 and R ψ =4.

[0156] In the above embodiment, the global volume constraint is set with the goal of minimizing the structural flexibility. Local Volume Constraints Stress Constraint The structure is topologically optimized, and the optimization results are as follows: Figure 4 As shown, Figure 4 (a) shows the optimized structure. Figure 4 (b) depicts the stress distribution cloud diagram of the structure. It can be seen that the optimized structure presents a clear shell-porous filling topology, and there is a smooth transition at the corner to prevent stress concentration.

[0157] The above embodiments can demonstrate the effectiveness of the static strength design method of the shell and porous filling structure proposed in the present invention.

[0158] In another exemplary embodiment, the initial design domain is as follows: Figure 5 As shown in (a), the structure is divided into 45,000 quadrilateral grids, the x-direction degrees of freedom on the left side of the structure are constrained, the y-direction degrees of freedom on the lower right corner are constrained, and a vertical downward velocity boundary is imposed on the 10 mm edge of the upper left corner. The velocity magnitude is as follows: Figure 5 As shown in (b), the parameter in the figure is set to v0 = 3 × 10 3 mm / s,t max =100μs, t0=5μs, and set the dynamic analysis time step Δt=1μs. Set the stress aggregation coefficient P=20, the local volume aggregation coefficient P v = 8. Filter radius R μ =8, R μ =2 and R ψ =2.5.

[0159] In the above embodiment, the global volume constraint is set with the goal of minimizing the structural flexibility. Local Volume Constraints Stress Constraint The structure is topologically optimized, and the optimization results are as follows: Figure 6 As shown, Figure 6 (a) shows the optimized structure. Figure 6 (b) depicts the stress distribution cloud diagram of the structure. It can be seen that the optimized structure presents a clear shell-porous filling topology, and the structural stress level is well controlled under the stress constraint.

[0160] The above embodiments demonstrate the effectiveness of the dynamic strength design method of the shell and porous filling structure proposed in the present invention.

[0161] It should also be noted that the above is a preferred embodiment of the present invention. It should be noted that although the preferred embodiment of the present invention has been described, once the basic creative concept of the present invention is known, a number of improvements and modifications can be made by a person skilled in the art without departing from the principles of the present invention, and these improvements and modifications should also be regarded as the protection scope of the present invention. Therefore, the attached claims are intended to be interpreted as including the preferred embodiment and all changes and modifications that fall within the scope of the embodiments of the present invention.

Claims

1. A strength-constrained topological optimization design method for a shell-porous filling structure, characterized in that: include: Step 1: Based on the characteristics of the design structure, use finite elements to discretize the design domain and set relevant parameters including material parameters and optimization parameters; Step 2: Introduce two sets of design variables to optimize the shell structure and the internal porous filling structure respectively. After a series of numerical operations, output three sets of intermediate physical field variables, and use different projection coefficients to generate three sets of intermediate erosion field variables. Step 3: For static strength design problems, the modified solid isotropic material interpolation model with penalty factor is used to describe the elastic modulus and density of the material. For dynamic strength design problems, the modified polynomial interpolation model is used to describe the elastic modulus of the material. Step 4: Construct a robust strength constrained topology optimization model, perform finite element analysis on the structure, and calculate the objective function and response values ​​of each constraint function in the optimization model; Step 5: According to the derivative rule of composite function and the derivative method of adjoint variables, solve the sensitivity of the objective function, global volume fraction, local volume fraction and maximum stress response function of the structure to the design variables; Step 6: Use the moving evolutionary algorithm to optimize the design. The objective function solved in steps 4 and 5 and the response values ​​and sensitivity information of each constraint are used as the input conditions of the moving evolutionary algorithm to solve the optimization problem and iteratively update the design variables.

2. The strength-constrained topology optimization design method for a shell-porous filling structure according to claim 1 is characterized in that: Also includes: Step 7: Repeat steps 2 to 6 to update the design variables multiple times until the current design meets the optimization convergence conditions and the optimization process is stopped.

3. The strength-constrained topology optimization design method for a shell-porous filling structure according to claim 1 is characterized in that: In step 2, a series of numerical operations are performed, including: filtering, projecting, and density space gradient solving for the two sets of design variables at least once.

4. The strength-constrained topology optimization design method for a shell-porous filling structure according to claim 3 is characterized in that: In step 2, the two sets of design variables are introduced, including the first design variable μ and the second design variable ν. The first design variable μ is filtered, gradient normed and projected at least once to obtain two sets of intermediate variables: and τ, the second design variable ν is filtered and projected to obtain a set of intermediate variables ψ, where the filtering operation is used to avoid the checkerboard pattern and identify the boundary, and the projection operation is used to generate a clear structure. The total variable field of the shell and filling structure is expressed as three sets of intermediate variables The combination of τ and ψ corresponds to 5. The strength-constrained topology optimization design method for a shell-porous filling structure according to claim 4 is characterized in that: Step 2 also includes: A local volume constraint is introduced to ensure the porosity of the internal filling structure. v It is expressed as: Among them, N e is the number of units in the partition structure, P υ is the local volume aggregation parameter, represents the local volume fraction near the i-th unit; The erosion field variable is introduced to construct a robust topology optimization model, and the erosion field projection coefficient η is used. ero , we get the erosion field variable 6. The strength-constrained topology optimization design method for a shell-porous filling structure according to claim 1, characterized in that: In step three, the elastic modulus and density of the material, namely: Among them, E(ξ i ) and ρ(ξ i ) represent the elastic modulus and density of the material of the ith unit, E0 and ρ0 represent the elastic modulus and density of the solid material, It is expressed as: Here, e is a small amount to avoid the singularity of stiffness and is set to e = 10 -6 ,p E and p ρ are the penalty factors for elastic modulus and density, respectively, set to p E =3 and p ρ =1,χ(ξ i , p) is expressed as:

7. The strength-constrained topology optimization design method for a shell-porous filling structure according to claim 6 is characterized in that: In step 3, for the dynamic strength design problem, a modified polynomial interpolation model is used to describe the elastic modulus of the material, namely: Among them, setting p E =5 and p E，2 =1.

8. The strength-constrained topology optimization design method for a shell-porous filling structure according to claim 1, characterized in that: In step 4, the objective function and the response values ​​of each constraint function are expressed as follows: Among them, the objective function is the physical field flexibility c and the erosion field flexibility c ero The weighting coefficient w is initially 0.1 and increases by 0.1 every 50 iterations until it reaches a maximum value of 0.

9. υ is the global volume fraction of the structure, l υ is the local volume fraction of the structure, φ is the maximum stress response function of the structure, For the global volume constraint defined, For the local volume constraint defined, and are the stress constraints for the physical field and erosion field structures respectively.

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