Continuum multi-material structure topology optimization method for vehicle lightweight design

Abstract

The application relates to a continuum multi-material structure topology optimization method for lightweight design of a carrier, which comprises the following steps: S1, establishing a finite element model of a continuum structure, and initializing related parameters of multi-material topology optimization; S2, decoupling a continuum structure multi-material topology optimization problem into a series of two-phase material topology optimization sub-problems based on an alternating active phase algorithm framework, and solving in a two-phase material topology optimization sub-program; S3, dynamically updating a filtering radius of each phase material; S4, judging whether to terminate the continuum structure multi-material topology optimization, and outputting an optimization result. Through the method of dynamically updating the filtering radius in the multi-material topology optimization process, the application effectively simplifies the material distribution of the optimization result, suppresses the emergence of bifurcated structures, simultaneously introduces manufacturing constraints, so that the multi-material topology optimization result meets the geometric characteristics defined by a manufacturing process, and the manufacturability of the multi-material topology optimization result is improved.

Description

Technical Field

[0001] This invention belongs to the field of multi-material structure topology optimization technology, and specifically relates to a method for topology optimization of continuum multi-material structures for lightweight vehicle design. Background Technology

[0002] Multimaterial structures exhibit superior overall and local performance compared to single-material structures. However, current multimaterial structure design heavily relies on the engineering experience of designers. Yet, when designing and developing complex structures, relying solely on engineers' experience is insufficient to fully realize the potential of multimaterial structures. To fully unleash the potential performance of multimaterial structures, multimaterial topology optimization can be used. Multimaterial topology optimization technology combines the advantages of high material utilization in topology optimization design with the strong comprehensive performance of multimaterial structures, expanding the design space of ordinary single-material topology optimization and enabling the acquisition of structures with even higher overall performance. In recent years, with the increasing demand for lightweight structures in the vehicle manufacturing industry and the emergence of more high-performance materials, the application of multimaterial structures has expanded. Developing multimaterial topology optimization technology that can achieve lightweight structures, functional integration, and maximized performance has become one of the important research directions in the field of topology optimization.

[0003] However, current multi-material topology optimization results often result in complex structures with poor manufacturability, serving only as conceptual designs for designers and being difficult to directly fabricate using conventional manufacturing processes. The manufacturability of multi-material topology optimization results urgently needs improvement. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention provides a continuous multi-material structure topology optimization method for lightweight vehicle design. By using a method of dynamically updating the filter radius during the multi-material topology optimization process, it not only effectively simplifies the material distribution of the optimization results but also suppresses the occurrence of bifurcation structures, improves the manufacturability of the multi-material topology optimization results, and plays a positive role in the transfer from the multi-material structure design end to the manufacturing end.

[0005] The technical solution adopted in this invention is a topology optimization method for continuum multi-material structures for lightweight vehicle design, which includes the following steps:

[0006] S1. Establish a finite element model of the continuum structure and initialize the relevant parameters for multi-material topology optimization.

[0007] S2. Based on the alternating activation phase algorithm framework, the multi-material topology optimization problem of the continuum structure is decoupled into a series of two-phase material topology optimization sub-problems, and solved in the two-phase material topology optimization subroutine.

[0008] S3. After all phase material design variables have been updated once, determine whether to execute the dynamic update of the filter radius. The determination condition is as follows:

[0009]

[0010] Where Δρ represents the infinite norm of the difference between the design variables of all phase materials in the current iteration and the previous iteration. If the current iteration is the k-th iteration, then X k X represents the design variables for all phase materials in the current iteration. k-1 Let represent the design variables for all phase materials in the previous iteration; ΔC represents the difference between the objective function of the current iteration and the previous iteration. If the current iteration is the k-th iteration, then C... k C represents the objective function value of the current iteration. k-1 ρ represents the objective function value of the previous iteration; r and C r Represent the design variable threshold and objective function threshold that control the update of the filter radius, respectively; r represents the current filter radius; R min Indicates the final filtration radius;

[0011] If the conditions for dynamically updating the filter radius are met, then the current filter radius r and the design variable threshold ρ are updated as follows: R :

[0012]

[0013] The weighting coefficients for the sensitivity of other units within the filtering radius of each unit are recalculated according to the following formula:

[0014]

[0015] Among them, w e Δ(e,i) represents the weighting coefficient; Δ(e,i) represents the distance between the centroids of element i and element e.

[0016] If the conditions for dynamically updating the filter radius are not met, proceed to step S4;

[0017] S4. Determine whether to terminate multi-material topology optimization. If the maximum value of the absolute change of each unit design variable in the current external iteration and the previous external iteration is greater than the preset value, and the cumulative number of external iterations has not exceeded the set maximum number of iterations, then return to step S2 for further iterative optimization. If the maximum value of the absolute change of each unit design variable between two consecutive external iterations is less than the preset value, or the cumulative number of external iterations exceeds the set maximum number of iterations, then terminate the iterative process of multi-material topology optimization and output the optimization results.

[0018] Preferably, the initialization of relevant parameters of the multi-material continuous structure in step S1 specifically includes the following steps:

[0019] S11. Define the material properties of each phase material;

[0020] S12. Mesh the design domain for each phase material;

[0021] S13. Apply constraints and loads to the mesh model of each phase material;

[0022] S14. Perform filtration pretreatment on each phase material, that is, calculate the weighting coefficient of the sensitivity of other units within the filtration radius of each unit.

[0023] S15. Define the unit mapping relationship of each phase material according to the type of manufacturing constraint applied;

[0024] S16. Initialize the design variables for each phase material.

[0025] Preferably, in step S2, the order of the design variables of each phase material input into the two-phase material topology optimization subroutine must follow the principle of decreasing influence of material properties on the objective function. That is, for the topology optimization problem of the maximum structural stiffness of n-phase materials, if the elastic moduli of the n-phase materials are E1, E2, ..., E n And satisfying E1>E2>…>E n To determine the relationship, first select the two-phase material design variables with elastic moduli E1 and E2 and input them into the two-phase material topology optimization subroutine for solution, and then input the design variables of the remaining phase materials into the two-phase material topology optimization subroutine for solution in sequence.

[0026] Preferably, the solution to the two-phase material topology optimization sub-problem in step S2 adopts the SIMP material difference model, which specifically includes the following steps:

[0027] S21. Based on the SIMP material interpolation model, construct an interpolation model applicable to any multiphase material. The expression of the multiphase material interpolation model is as follows:

[0028]

[0029] Among them, E i E represents the Young's modulus of the i-th unit; p represents the penalty factor (p>1); j ρ represents the elastic modulus of the j-th material; i，j ρ represents the percentage of the volume occupied by the j-th phase material in the i-th unit, and ρ i，j The following relationship must be satisfied:

[0030]

[0031] S22. A multiphase material interpolation model is used to construct the overall stiffness matrix with planar four-node rectangular elements and corresponding to the shape of the design domain. Finite element analysis is performed on the multiphase material interpolation model to obtain the displacement vector U of each discrete element node in the finite element model.

[0032] S23. Based on the mathematical model of topology optimization, with minimizing structural compliance as the objective and limiting the volume ratio of each phase material as the constraint, a mathematical model for the topology optimization subproblem of two-phase materials in a continuous structure is established. The model expression is as follows:

[0033]

[0034] Where C represents structural flexibility; K represents the overall structural stiffness matrix; F and U represent the nodal load vector and nodal displacement vector, respectively; v e V represents the volume of a single unit cell. * j This represents the preset volume of the j-th phase material; the subscript 'a' indicates the material with a higher elastic modulus input into the two-phase material topology optimization subroutine; l i and u i The design variable ρ for the j-th phase material of the i-th unit i,j The upper and lower bounds; X represents the design variable matrix of size m×n, as follows:

[0035]

[0036] Where m represents the total number of element meshes in the finite element mesh model; n represents the number of phases of candidate materials in multi-material topology optimization; i satisfies 1≤i≤m; j satisfies 1≤j≤n;

[0037] S24. Solve for the sensitivity of the objective function to the design variables, and the expression of the objective function is:

[0038]

[0039] Where, ρ i，a E represents the percentage of volume occupied by phase a material in the i-th unit; a and E b U represents the elastic modulus of the two materials input into the two-phase material topology optimization subroutine. Subscript 'a' indicates the material with the higher elastic modulus, and subscript 'b' indicates the material with the lower elastic modulus. k0 is the element stiffness matrix when the elastic modulus is 1. i Let be the displacement vector of the i-th element node.

[0040] S25. Perform projection calculation on the original unit sensitivity according to the unit mapping relationship, and the projection calculation uses the maximum value projection;

[0041] S26. Perform sensitivity filtering on the sensitivity obtained from the projection in step S25, with the following expression:

[0042]

[0043] in, Indicates the sensitivity after filtration; Ω e ρ represents the set of all elements within a radius r centered at element i; e，j This represents the percentage of the volume occupied by the j-th phase material in the e-th unit within a radius r centered at unit i. γ is a constant; to avoid division by zero, γ is set to a very small positive number. e The weight coefficient of the e-th cell within a radius r centered at cell i is calculated using the following formula:

[0044]

[0045] Where r represents the filtration radius; Δ(e,i) represents the distance between the centroids of element i and element e;

[0046] S27. Using the optimization criterion method, with the goal of minimizing structural flexibility and the constraint of limiting the volume ratio of each phase material in the structure, the sensitivity of the filtered variables is solved iteratively using flexibility and the volume ratio of each phase material.

[0047] S28. Determine whether the number of iterations of the current two-phase material topology optimization subproblem is greater than the preset number. If the number of iterations of the current two-phase material topology optimization subproblem is greater than or equal to the preset number, then end the solution of the two-phase material topology optimization subproblem and output the updated design variables to step S2 to proceed to the next step; if the number of iterations of the current two-phase material topology optimization subproblem is less than the preset number, then continue the solution of the two-phase material topology optimization subproblem.

[0048] The features and beneficial effects of this invention are:

[0049] This invention provides a topology optimization method for continuous multi-material structures used in lightweight vehicle design. By using a dynamic update of the filter radius during the multi-material topology optimization process, the material distribution of the optimization results is effectively simplified, and the occurrence of bifurcation structures is suppressed. At the same time, by introducing manufacturing constraints, the multi-material topology optimization results meet the geometric characteristics specified by some manufacturing processes, thus improving the manufacturability of the optimization results. This has a positive effect on the transfer of multi-material structures from the design end to the manufacturing end. Attached Figure Description

[0050] Figure 1 This is a flowchart of the topology optimization method for two-phase materials in a continuum structure according to the present invention;

[0051] Figure 2a This is a schematic diagram showing the results of a preferred embodiment of the cantilever beam under unconstrained conditions in preferred embodiment 1 of the present invention;

[0052] Figure 2b This is a schematic diagram of the results of the preferred embodiment considering the horizontal symmetry constraint in preferred embodiment 1 of the present invention;

[0053] Figure 2c This is a schematic diagram of the results of a preferred embodiment considering vertical plane symmetry constraints in preferred embodiment 1 of the present invention;

[0054] Figure 2d This is a schematic diagram of the preferred embodiment of the present invention, which considers the symmetry constraints of two planes in preferred embodiment 1.

[0055] Figure 3a This is a schematic diagram showing the results of a preferred embodiment of the S-shaped beam without constraints in preferred embodiment 2 of the present invention;

[0056] Figure 3b This is a schematic diagram of the preferred embodiment of the S-shaped beam under the maximum projection function in preferred embodiment 2 of the present invention;

[0057] Figure 3c This is a schematic diagram of the preferred embodiment of the S-shaped beam under the average projection function in preferred embodiment 2 of the present invention;

[0058] Figure 4a This is a schematic diagram showing the results of a preferred embodiment of the three-dimensional cantilever beam without manufacturing constraints in preferred embodiment 3 of the present invention;

[0059] Figure 4b This is a schematic diagram of the preferred embodiment of the three-dimensional cantilever beam under compression constraint in preferred embodiment 3 of the present invention;

[0060] Figure 4c This is a side view of the preferred embodiment of the three-dimensional cantilever beam under compression constraint in the preferred embodiment 3 of the present invention. Detailed Implementation

[0061] To fully describe the technical content, structural features, objectives, and effects of this invention, a detailed description will be provided below in conjunction with the accompanying drawings.

[0062] This invention provides a topology optimization method for continuum multi-material structures used in lightweight vehicle design, such as... Figure 1 As shown, it includes the following steps:

[0063] S1. Establish the finite element model of the continuum structure and initialize the relevant parameters for multi-material topology optimization. This includes the following steps:

[0064] S11. Define the material properties of each phase material;

[0065] S12. Mesh the design domain for each phase material;

[0066] S13. Apply constraints and loads to the mesh model of each phase material;

[0067] S14. Perform filtration pretreatment on each phase material, that is, calculate the weighting coefficient of the sensitivity of other units within the filtration radius of each unit.

[0068] S15. Define the unit mapping relationship of each phase material according to the type of manufacturing constraint applied;

[0069] S16. Initialize the design variables for each phase material.

[0070] S2. Based on the alternating activation phase algorithm framework, the multi-material topology optimization problem of a continuum structure is decoupled into a series of two-phase material topology optimization subproblems, and the design variables corresponding to each phase material are input into the two-phase material topology optimization subroutine for processing. The order of the design variables of each phase material input into the two-phase material topology optimization subroutine must follow the principle of decreasing influence of material properties on the objective function. That is, for the topology optimization problem of the maximum structural stiffness of n-phase materials, if the elastic moduli of the n-phase materials are E1, E2, ..., E... n And satisfying E1>E2>…>E n To determine the relationship, first select the two-phase material design variables with elastic moduli E1 and E2 and input them into the two-phase material topology optimization subroutine for solution. Then, sequentially input the design variables of the remaining phase materials into the two-phase material topology optimization subroutine for solution. For example... Figure 1 In this example, a=1 and b=2 represent the elastic moduli of the two-phase materials, corresponding to E1 and E2 respectively, and the same applies to other cases. The corresponding two-phase material topology optimization subproblem is solved using the SIMP material difference model, specifically including the following steps:

[0071] S21. Based on the SIMP material interpolation model, construct an interpolation model applicable to any multiphase material. The expression for the multiphase material interpolation model is:

[0072]

[0073] Among them, E i E represents the Young's modulus of the i-th unit; p represents the penalty factor (p>1); j ρ represents the elastic modulus of the j-th material; i，j ρ represents the percentage of the volume occupied by the j-th phase material in the i-th unit, and ρ i，j The following relationship must be satisfied:

[0074]

[0075] S22. A multiphase material interpolation model is used to construct the overall stiffness matrix of the planar four-node rectangular elements, which corresponds to the shape of the design domain. Finite element analysis is performed on the multiphase material interpolation model to obtain the displacement vector U of each discrete element node in the finite element model.

[0076] S23. Based on the mathematical model of topology optimization, with minimizing structural compliance as the objective and limiting the volume ratio of each phase material as the constraint, a mathematical model for the topology optimization subproblem of two-phase materials in a continuous structure is established. The model expression is as follows:

[0077]

[0078] Where C represents structural flexibility; K represents the overall structural stiffness matrix; F and U represent the nodal load vector and nodal displacement vector, respectively; v e V represents the volume of a single unit cell. * j The j-th phase material represents the preset volume; a and b represent the materials with higher elastic moduli input into the two-phase material topology optimization subroutine; l i and u i The design variable ρ for the j-th phase material of the i-th unit i,j The upper and lower bounds; X represents the design variable matrix of size m×n, as follows:

[0079]

[0080] Where m represents the total number of element meshes in the finite element mesh model; n represents the number of phases of candidate materials in multi-material topology optimization.

[0081] S24. Solve for the sensitivity of the objective function to the design variables, where the objective function expression is:

[0082]

[0083] Where, ρ i，a E represents the percentage of volume occupied by phase a material in the i-th unit; a and E b Let represent the elastic modulus of the two materials input into the two-phase material topology optimization subroutine. Subscript a indicates the material with the higher elastic modulus, and subscript b indicates the material with the lower elastic modulus. k0 is the element stiffness matrix when the elastic modulus is 1, and Ui is the displacement vector of the i-th element node.

[0084] S25. Perform projection calculation on the original unit sensitivity according to the unit mapping relationship, and the projection calculation uses the maximum value projection.

[0085] S26. Perform sensitivity filtering on the sensitivity obtained from the projection in step S25, with the following expression:

[0086]

[0087] in, Indicates the sensitivity after filtration; Ω e ρ represents the set of all elements within a radius r centered at element i; e，j This represents the percentage of the volume occupied by the j-th phase material in the e-th unit within a radius r centered at unit i. γ is a constant; to avoid division by zero, γ is set to a very small positive number. e The weight coefficient of the e-th cell within a radius r centered at cell i is calculated using the following formula:

[0088]

[0089] Where r represents the filtration radius; Δ(e,i) represents the distance between the centroids of element i and element e.

[0090] S27. Using the optimization criterion method, with the goal of minimizing structural flexibility and the constraint of limiting the volume ratio of each phase material in the structure, the sensitivity of the filtered variables is solved iteratively using the flexibility and the volume ratio of each phase material.

[0091] S28. Determine whether the number of iterations of the current two-phase material topology optimization subproblem is greater than the preset number. If the number of iterations of the current two-phase material topology optimization subproblem is greater than or equal to the preset number, then end the solution of the two-phase material topology optimization subproblem and output the updated design variables to step S2 to proceed to the next step; if the number of iterations of the current two-phase material topology optimization subproblem is less than the preset number, then continue the solution of the two-phase material topology optimization subproblem.

[0092] S3. After all phase material design variables have been updated once, determine whether to execute the dynamic update of the filter radius. The determination condition is as follows:

[0093]

[0094] Where Δρ represents the infinite norm of the difference between the design variables of all phase materials in the current iteration and the previous iteration; ΔC represents the difference between the objective function of the current iteration and the previous iteration; ρ r and C r Represent the design variable threshold and objective function threshold that control the update of the filter radius, respectively; r represents the current filter radius; R min This indicates the final filtration radius.

[0095] If the conditions for dynamically updating the filter radius are met, then the current filter radius r and the design variable threshold ρ are updated as follows: R :

[0096]

[0097] The weighting coefficients for the sensitivity of other units within the filtering radius of each unit are recalculated according to the following formula:

[0098]

[0099] Among them, w e Δ(e,i) represents the weighting coefficient; Δ(e,i) represents the distance between the centroids of element i and element e.

[0100] If the conditions for dynamically updating the filter radius are not met, proceed to step S4.

[0101] S4. Determine whether to terminate multi-material topology optimization. If the maximum value of the absolute change of each unit design variable in the current external iteration and the previous external iteration is greater than the preset value, and the cumulative number of external iterations has not exceeded the set maximum number of iterations, then return to step S2 for further iterative optimization. If the maximum value of the absolute change of each unit design variable between two consecutive external iterations is less than the preset value, or the cumulative number of external iterations exceeds the set maximum number of iterations, then terminate the iterative process of multi-material topology optimization and output the optimization results.

[0102] The following preferred embodiments are provided to verify the effectiveness of this method. The material properties of all the numerical preferred embodiments are shown in Table 1, and the volume percentage of each phase material is given in the specific preferred embodiments. In the preferred embodiments, the two-dimensional design domain is discretized using 4-node square plane strain elements, and the three-dimensional design domain is discretized using 8-node hexahedral strain solid elements. All side lengths of the plane strain elements and solid strain elements are 1 mm. The design domain size is in mm, and the load is in N.

[0103] Table 1 Material properties of preferred embodiments with manufacturing constraints

[0104]

[0105] Preferred embodiment 1: Cantilever beam

[0106] The manufacturing process of generating symmetrical structures is common in industry, but in multi-material topology optimization, asymmetric load boundary conditions or asymmetric constraints can lead to optimization results that do not meet symmetry conditions, making manufacturing difficult. Figure 2 shows a comparison of the results of the preferred embodiment with symmetric constraints applied. The design domain size, load, and boundary conditions are also marked in the figure. The design domain was discretized into 7200 plane strain elements, with the volume percentage of each phase material being V*=[0.16,0.1,0.1,0.64]. The initial filter radius R0 was set to 16, and the final filter radius R... min Set to 1.5. Among them... Figure 2a The result for the unconstrained cantilever beam (C = 14.8) is as follows. Figure 2b To account for the results of the horizontal symmetry constraint (C = 16.3); Figure 2c The result is taken into account for the vertical plane symmetry constraint (C = 21.4); Figure 2d The result is to consider the symmetry constraints of the two planes simultaneously (C = 24.8).

[0107] Preferred embodiment 2: S-shaped beam

[0108] Pattern repetition constraints induce recurring structural shapes in parts or the whole of a structure in a controllable manner, commonly seen in structures with periodic repetition. Figure 3 shows a comparison of the results of a preferred embodiment of an S-shaped beam with pattern repetition constraints applied. In this preferred embodiment, the design domain consists of three identical rectangular sub-design domains (black dashed boxes in the figure), each with dimensions of 100×50. Loads and boundary conditions are marked in the figure, and the design domain is discretized into 15,000 plane strain elements. The volume fraction of each phase material is V*=[0.16,0.1,0.1,0.64]. In this preferred embodiment, the initial filtration radius R0 is set to 12, and the final filtration radius R... min Set to 1.5. Among them... Figure 3a The result is unconstrained (C = 75.8). Figure 3b The preferred embodiment of the style repetition constraint using the maximum projection function (C = 127.2) yielded the following results. Figure 3c The preferred embodiment of the pattern repetition constraint using the mean projection function yields results (C = 128.6).

[0109] Preferred embodiment 3: Three-dimensional cantilever beam

[0110] In multi-material topology optimization, the extrusion constraint requires the cross-section of the entire component to have a constant shape so that the structure can be manufactured through an extrusion process. Figure 4 shows a three-dimensional cantilever beam with the same cross-section obtained by applying the extrusion constraint. It can be seen that the extrusion constraint algorithm significantly simplifies the structure. The figure shows the design domain size, load (uniformly distributed load q = 1), and boundary conditions of the preferred embodiment. The design domain is discretized into 12000 solid strain elements. The volume fraction of each material phase is V* = [0.2, 0.1, 0.1, 0.6]. In this preferred embodiment, the initial filter radius R0 is set to 3, and the final filter radius R... min Set to 1.5. Among them... Figure 4a The result is for an unconstrained preferred embodiment (C = 218.5). Figure 4b The results for the preferred embodiment using extrusion constraints (C = 351.7) are as follows: Figure 4c This is a side view of the corresponding optimization results.

[0111] All the above preferred embodiments, compared with the optimization results without manufacturing constraints, show that the optimization results obtained by this method satisfy the preset geometric features, which are beneficial to making it easier to manufacture this type of structure in production.

[0112] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A topology optimization method for a continuum multi-material structure for lightweight vehicle design, characterized in that, It includes the following steps: S1. Establish a finite element model of the continuum structure and initialize the relevant parameters for multi-material topology optimization. S2. Based on the alternating activation phase algorithm framework, the multi-material topology optimization problem of the continuum structure is decoupled into a series of two-phase material topology optimization sub-problems, and solved in the two-phase material topology optimization subroutine. S3. After all phase material design variables have been updated once, determine whether to execute the dynamic update of the filter radius. The determination condition is as follows: Where Δρ represents the infinite norm of the difference between the design variables of all phase materials in the current iteration and the previous iteration. If the current iteration is the k-th iteration, then X k X represents the design variables for all phase materials in the current iteration. k-1 Let represent the design variables for all phase materials in the previous iteration; ΔC represents the difference between the objective function of the current iteration and the previous iteration. If the current iteration is the k-th iteration, then C... k C represents the objective function value of the current iteration. k-1 ρ represents the objective function value of the previous iteration; r and C r Represent the design variable threshold and objective function threshold that control the update of the filter radius, respectively; r represents the current filter radius; R min Indicates the final filtration radius; If the conditions for dynamically updating the filter radius are met, then the current filter radius r and the design variable threshold ρ are updated as follows: r : The weighting coefficients for the sensitivity of other units within the filtering radius of each unit are recalculated according to the following formula: Among them, w e Represents the weighting coefficient; Δ(e,i) represents the distance between the centroids of element i and element e; If the conditions for dynamically updating the filter radius are not met, proceed to step S4; S4. Determine whether to terminate multi-material topology optimization. If the maximum value of the absolute change of each unit design variable in the current external iteration and the previous external iteration is greater than the preset value, and the cumulative number of external iterations has not exceeded the set maximum number of iterations, then return to step S2 for further iterative optimization. If the maximum value of the absolute change of each unit design variable between two consecutive external iterations is less than the preset value, or the cumulative number of external iterations exceeds the set maximum number of iterations, then terminate the iterative process of multi-material topology optimization and output the optimization results.

2. The topology optimization method for continuum multi-material structures for lightweight vehicle design according to claim 1, characterized in that, Step S1 initializes the relevant parameters of the multi-material continuous structure, specifically including the following steps: S11. Define the material properties of each phase material; S12. Mesh the design domain for each phase material; S13. Apply constraints and loads to the mesh model of each phase material; S14. Perform filtration pretreatment on each phase material, that is, calculate the weighting coefficient of the sensitivity of other units within the filtration radius of each unit. S15. Define the unit mapping relationship of each phase material according to the type of manufacturing constraint applied; S16. Initialize the design variables for each phase material.

3. The topology optimization method for continuum multi-material structures for lightweight vehicle design according to claim 1, characterized in that, In step S2, the order of the design variables for each phase material input into the two-phase material topology optimization subroutine must follow the principle of decreasing influence of material properties on the objective function. That is, for the topology optimization problem of the maximum structural stiffness of n-phase materials, if the elastic moduli of the n-phase materials are E1, E2, ..., E... n And satisfying E1>E2>…>E n To determine the relationship, first select the two-phase material design variables with elastic moduli E1 and E2 and input them into the two-phase material topology optimization subroutine for solution, and then input the design variables of the remaining phase materials into the two-phase material topology optimization subroutine for solution in sequence.

4. The topology optimization method for continuum multi-material structures for lightweight vehicle design according to claim 3, characterized in that, The solution to the two-phase material topology optimization sub-problem in step S2 adopts the SIMP material difference model, which specifically includes the following steps: S21. Based on the SIMP material interpolation model, construct an interpolation model applicable to any multiphase material. The expression of the multiphase material interpolation model is as follows: Among them, E i E represents the Young's modulus of the i-th unit; p represents the penalty factor (p>1); j ρ represents the elastic modulus of the j-th material; i，j ρ represents the percentage of the volume occupied by the j-th phase material in the i-th unit, and ρ i，j The following relationship must be satisfied: S22. A multiphase material interpolation model is used to construct the overall stiffness matrix of the planar four-node rectangular elements, which corresponds to the shape of the design domain. Finite element analysis is performed on the multiphase material interpolation model to obtain the displacement vector U of each discrete element node in the finite element model. S23. Based on the mathematical model of topology optimization, with minimizing structural compliance as the objective and limiting the volume ratio of each phase material as the constraint, a mathematical model for the topology optimization subproblem of two-phase materials in a continuous structure is established. The model expression is as follows: Where C represents structural flexibility; K represents the overall structural stiffness matrix; F and U represent the nodal load vector and nodal displacement vector, respectively; v e Represents the volume of a single unit. This represents the preset volume of the j-th phase material; the subscript 'a' indicates the material with a higher elastic modulus input into the two-phase material topology optimization subroutine; l i and u i The design variable ρ for the j-th phase material of the i-th unit i,j The upper and lower bounds; X represents the design variable matrix of size m×n, as follows: Where m represents the total number of element meshes in the finite element mesh model; n represents the number of phases of candidate materials in multi-material topology optimization; i satisfies 1≤i≤m; j satisfies 1≤j≤n; S24. Solve for the sensitivity of the objective function to the design variables, and the expression of the objective function is: Where, ρ i，a E represents the percentage of volume occupied by phase a material in the i-th unit; a and E b U represents the elastic modulus of the two materials input into the two-phase material topology optimization subroutine. Subscript 'a' indicates the material with the higher elastic modulus, and subscript 'b' indicates the material with the lower elastic modulus. k0 is the element stiffness matrix when the elastic modulus is 1. i Let be the displacement vector of the i-th element node; S25. Perform projection calculation on the original unit sensitivity according to the unit mapping relationship, and the projection calculation uses the maximum value projection; S26. Perform sensitivity filtering on the sensitivity obtained from the projection in step S25, with the following expression: in, Indicates the sensitivity after filtration; Ω e ρ represents the set of all elements within a radius r centered at element i; e，j This represents the percentage of the volume occupied by the j-th phase material in the e-th unit within a radius r centered at unit i. γ is a constant; to avoid division by zero, γ is set to a very small positive number. e The weight coefficient of the e-th cell within a radius r centered at cell i is calculated using the following formula: Where r represents the filtration radius; Δ(e,i) represents the distance between the centroids of element i and element e; S27. Using the optimization criterion method, with the goal of minimizing structural flexibility and the constraint of limiting the volume ratio of each phase material in the structure, the sensitivity of the filtered variables is solved iteratively using flexibility and the volume ratio of each phase material. S28. Determine whether the number of iterations of the current two-phase material topology optimization subproblem is greater than the preset number. If the number of iterations of the current two-phase material topology optimization subproblem is greater than or equal to the preset number, then end the solution of the two-phase material topology optimization subproblem and output the updated design variables to step S2 to proceed to the next step; if the number of iterations of the current two-phase material topology optimization subproblem is less than the preset number, then continue the solution of the two-phase material topology optimization subproblem.

Images