Apparatus and method for inverse design of zoned periodic hierarchical structures considering material strength

Abstract

The application provides a kind of partition periodic hierarchical structure reverse design device and method considering material strength, with such features, including data input module, for inputting specified parameters;Data processing module, for generating variables according to inputted specified parameters;Design variable optimization module with collaborative optimization column formula stored, for obtaining the value of macrostructure design variable and the value of microstructure design variable by iterative optimization of generated variables combined with collaborative optimization column formula;And, structure generation module, for processing the value of macrostructure design variable and the value of microstructure design variable obtained, to obtain the partition periodic hierarchical structure data of specified required structure.The partition periodic hierarchical structure reverse design device and method considering material strength of the application can realize that designed partition multilevel structure meets both specified volume fraction requirement and specified stress requirement.

Description

Technical Field

[0001] This invention belongs to the field of structural design, specifically relating to a reverse design device and method for a partitioned periodic hierarchical structure that takes into account material strength. Background Technology

[0002] Many high-performance structures in nature, such as animal skeletons and plant roots, often exhibit different structural characteristics at different scales. Therefore, designing structural configurations at different length scales to obtain high-performance structures is considered one of the directions for the development of next-generation lightweight structures. The reverse design method for partitioned periodic hierarchical structures is often based on topology optimization theory. Using the required material volume and mass as inputs, and employing numerical methods such as optimization algorithms and finite element analysis, the macroscopic configuration, microstructure configuration, and distribution are used as optimization objects to iteratively solve for the partitioned periodic hierarchical structure.

[0003] Existing partitioned periodic hierarchical design models focus on maximum stiffness design under volume constraints. This approach may result in local stresses exceeding material strength, impacting structural safety and durability. Existing reverse design methods for partitioned periodic hierarchical structures that consider material strength often pre-define the initial distribution of microstructures using methods such as cluster analysis, and then perform collaborative design of macro- and micro-structural configurations. During the optimization process, as the macro-configuration changes, the optimal distribution of microstructures inevitably changes as well. Pre-defining the microstructure distribution restricts the design space.

[0004] In summary, existing reverse design methods for partitioned periodic hierarchical structures that consider material strength cannot achieve collaborative optimization design of partitioned multi-level macro- and micro-structures and microstructure distributions under strength constraints. Summary of the Invention

[0005] This invention is made to solve the above-mentioned problems, and aims to provide a reverse design device and method for partitioned periodic hierarchical structures that takes into account material strength.

[0006] This invention provides a reverse design device for a partitioned periodic hierarchical structure considering material strength. It is used to obtain the desired structure based on the specified boundary and load-bearing capacity of the desired structure, the initial values ​​of macroscopic structural design variables, the initial values ​​of microstructural design variables, the minimum values ​​of macroscopic and microstructural design variables, the dimensions of the macroscopic structure, the number of macroscopic units, the number of macroscopic structural design variables, the dimensions of the microstructure, the number of microunits, the number of microstructural design variables, the number of microstructure types, the volume fraction of each microstructure, the volume fraction of each microstructure occupying the macroscopic design domain, the elastic modulus of the material, and the strength of the material. The partitioned periodic hierarchical structure data has the following characteristics: a data input module for users to input the boundary conditions and bearing capacity of the desired structure, the initial values ​​of macroscopic design variables, the initial values ​​of microstructural design variables, the minimum values ​​of macroscopic and microstructural design variables, the dimensions of the macroscopic structure, the number of macroscopic units, the number of macroscopic structural design variables, the dimensions of the microstructure, the number of micro-units, the number of microstructural design variables, the number of microstructural types, the volume fraction of each type of microstructure, the volume fraction of each type of microstructure in the macroscopic design domain, the elastic modulus of the material, and the strength of the material; a data processing module for... The system calculates the periodic displacement matrix of the microstructure and the displacement vector of the macrostructure based on the specified boundary and bearing capacity of the required structure, macroscopic design variables, microstructural design variables, minimum values ​​of macroscopic and microstructural design variables, dimensions of the macrostructure, number of macroscopic elements, number of macrostructural design variables, dimensions of the microstructure, number of micro-elements, number of microstructural design variables, number of types of microstructures, and elastic modulus of the material. The design variable optimization module stores the co-optimization formula and updates the values ​​of the macrostructural design variables and microstructural design variables based on the periodic displacement matrix of the microstructure, the displacement vector of the macrostructure, the strength of the material, the volume fraction of each microstructure, the volume fraction of each microstructure occupying the macrostructural design domain, and the co-optimization formula. The iteration module stores preset iteration termination conditions and determines whether the iteration is complete based on the iteration termination conditions and the values ​​of the macrostructural and microstructural design variables. If yes, the structure generation module is executed; otherwise, the data processing module is executed. The structure generation module processes the updated values ​​of the macrostructural design variables and microstructural design variables to obtain the partitioned periodic hierarchical structure data of the specified required structure. The expression of the co-optimization formula is:

[0007]

[0008] In the formula This represents the design variable for the ξ-th material in the i-th macroscopic unit. N represents the design variable for the ξ-th material in the i-th micro-unit. M and N m N represents the number of macro-structure and micro-structure design variables, respectively.C σ represents the number of microstructure types. a It refers to the strength of the material, K. M The stiffness matrix represents the macroscopic structure; Let χ represent the stiffness matrix of the ξ-th microstructure. ξ Let U represent the periodic displacement matrix of the ξ-th microstructure. M Displacement vector representing macroscopic structure Let F represent the test load matrix of the ξ-th microstructure. M Let represent the load vector of the macroscopic structure, and c be the correction factor updated iteratively. This represents the P-norm stress of all microstructures in a multi-level structure. Here, g1 represents the volume constraint function of the macroscopic configuration, g1(ρ)≤0 indicates the volume constraint of the macroscopic configuration, and g2 represents the stress constraint function of the multi-level structure. ρ represents the stress constraint of the multi-level structure, g3 represents the volume constraint function of the microstructure configuration, g3(γ)≤0 represents the volume constraint of the microstructure configuration, and ρ min γ represents the minimum value of the macroscopic structural design variables. min This represents the minimum value of the microstructure design variables. The macrostructure design variables include the design variables of all materials in all macrostructure units, while the microstructure design variables include the design variables of all microstructure units.

[0009] The reverse design apparatus for partitioned periodic hierarchical structures considering material strength provided by this invention may also have the following feature: In each iteration, the co-optimization formula updates the design variables through sensitivity, and the expression for the sensitivity of the objective function to the macroscopic structural design variables is: The expression for the sensitivity of the objective function to the microstructure design variables is: The expression for the sensitivity of the stress constraint function to macroscopic structural design variables is as follows: The expression for the sensitivity of the stress constraint function to the microstructure design variables is as follows: In the formula, ω = 1, 2, ..., N r T denotes transpose, λ denotes the adjoint vector of the macroscopic displacement vector, and N D P represents the number of columns in the adjoint matrix. N It refers to P N Power of 1.

[0010] The reverse design apparatus for partitioned periodic hierarchical structures considering material strength provided by this invention may also have the following feature: wherein the P-norm stress of all microstructures in the multi-level structure is considered. The expression is: In the formula P N It refers to P NThe power of , vm represents the von Mises stress. This represents the von Mises stress in the j-th micro-element at the i-th macro-element.

[0011] The reverse design apparatus for partitioned periodic hierarchical structures considering material strength provided by this invention may also have the following feature: wherein the von Mises stress of the j-th micro-unit at the i-th macro-unit is... The expression is:

[0012] In the formula, E0 is the elastic modulus of the material, and q is the penalty parameter. It is the von Mises stress of the j-th micro-unit of the ξ-th microstructure at the i-th macro-unit.

[0013] The reverse design apparatus for partitioned periodic hierarchical structures considering material strength provided by this invention may also have the following feature: the von Mises stress of the j-th micro-unit of the ξ-th microstructure at the i-th macro-unit. The expression is: In the formula, T represents the transpose, and V is the von Mises matrix. Let be the stress vector of the j-th micro-unit of the ξ-th microstructure at the i-th macro-unit.

[0014] The reverse design apparatus for partitioned periodic hierarchical structures considering material strength provided by this invention may also have the following feature: wherein the stress vector of the j-th micro-unit of the ξ-th microstructure at the i-th macro-unit is... The expression is: In the formula It is the equivalent uniform strain of the macroscopic unit, D0 is the elasticity matrix of the material, and is the identity matrix. It is the geometric matrix of the j-th micro-unit. It is the periodic displacement matrix of the ξ-th microstructure.

[0015] The reverse design apparatus for partitioned periodic hierarchical structures considering material strength provided by this invention may also have the following feature: wherein the expression for the correction factor is: In the formula c k Let δ represent the correction factor in the k-th iteration, and δ represent the update period of the correction factor.

[0016] This invention also provides a reverse design method for a partitioned periodic hierarchical structure considering material strength. This method is used to obtain partitioned periodic hierarchical structure data for a specified desired structure based on the boundary conditions and bearing capacity of the specified structure, initial values ​​of macroscopic structural design variables, initial values ​​of microstructural design variables, minimum values ​​of macroscopic and microstructural design variables, dimensions of the macroscopic structure, number of macroscopic units, number of macroscopic structural design variables, number of microstructural design variables, number of microstructural types, volume fraction of each microstructural type, volume fraction of each microstructural type occupying the macroscopic design domain, elastic modulus of the material, and strength of the material. The method is characterized by: Step S1, based on the boundary conditions and bearing capacity of the specified desired structure, macroscopic structural design variables, microstructural design variables, minimum values ​​of macroscopic and microstructural design variables, dimensions of the macroscopic structure, number of macroscopic units, and macroscopic structural design variables... Step S2: Calculate the periodic displacement matrix of the microstructure and the displacement vector of the macrostructure based on the number of microstructures, the size of the microstructure, the number of micro-units, the number of microstructure design variables, the number of microstructure types, and the elastic modulus of the material. Step S3: Update the values ​​of the macrostructure design variables and microstructure design variables based on the periodic displacement matrix of the microstructure, the displacement vector of the macrostructure, the strength of the material, the volume fraction of each microstructure, the volume fraction of each microstructure occupying the macrostructure design domain, and the co-optimization formula. Step S4: Determine whether the iteration is complete based on the iteration termination condition and the values ​​of the macrostructure design variables and microstructure design variables. If yes, execute the structure generation module; otherwise, execute the data processing module. Step S5: Process the updated values ​​of the macrostructure design variables and microstructure design variables to obtain the partitioned periodic hierarchical structure data of the specified desired structure.

[0017] The expression for the collaborative optimization formula is as follows:

[0018]

[0019] In the formula This represents the design variable for the ξ-th material in the i-th macroscopic unit. N represents the design variable for the ξ-th material in the i-th micro-unit. M and N m N represents the number of macro-structure and micro-structure design variables, respectively. C σ represents the number of microstructure types. a It refers to the strength of the material, K. M The stiffness matrix represents the macroscopic structure; Let χ represent the stiffness matrix of the ξ-th microstructure. ξ Let U represent the periodic displacement matrix of the ξ-th microstructure. M Displacement vector representing macroscopic structure Let F represent the test load matrix of the ξ-th microstructure. MLet represent the load vector of the macroscopic structure, and c be the correction factor updated iteratively. This represents the P-norm stress of all microstructures in a multi-level structure. Here, g1 represents the volume constraint function for the macroscopic configuration, and g1(ρ)≤0 indicates the volume constraint of the macroscopic structural configuration; g2 represents the stress constraint function for the multi-level structure. ρ represents the stress constraint of the multi-level structure, g3 represents the volume constraint function of the microstructure configuration, g3(γ)≤0 represents the volume constraint of the microstructure configuration, and ρ min γ represents the minimum value of the macroscopic structural design variables. min This represents the minimum value of the microstructure design variables. The macrostructure design variables include the design variables of all materials in all macrostructure units, and the values ​​of the microstructure design variables include the design variables of all microstructure units.

[0020] The role and effect of invention

[0021] According to the reverse design apparatus and method for partitioned periodic hierarchical structures considering material strength of the present invention, stress constraints and volume constraints participate together in the process of updating the values ​​of design variables using a collaborative optimization formula. Simultaneously, the influence of material strength is considered in the collaborative optimization formula, resulting in a partitioned multi-level structure that ultimately satisfies both the specified volume fraction requirement and the specified stress requirement. Therefore, the reverse design apparatus and method for partitioned periodic hierarchical structures considering material strength of the present invention can achieve the reverse design of partitioned multi-level structures that meet material strength requirements. Attached Figure Description

[0022] Figure 1 This is a block diagram of a reverse design device for a partitioned periodic hierarchical structure considering material strength in an embodiment of the present invention;

[0023] Figure 2 This is a single-cell diagram of the microstructure in an embodiment of the present invention;

[0024] Figure 3 This is a diagram showing the single-cell distribution of the multi-level structure in an embodiment of the present invention;

[0025] Figure 4 This is a diagram of the partitioned periodic hierarchical structure shape designed in an embodiment of the present invention;

[0026] Figure 5 This is a force cloud diagram of the multi-level structure in an embodiment of the present invention;

[0027] Figure 6 This is a flowchart illustrating the reverse design method for a partitioned periodic hierarchical structure considering material strength in an embodiment of the present invention. Detailed Implementation

[0028] To make the technical means, creative features, objectives and effects of the present invention easy to understand, the following embodiments, in conjunction with the accompanying drawings, specifically illustrate the reverse design device and method for a partitioned periodic hierarchical structure considering material strength.

[0029] This embodiment provides a reverse design device for a partitioned periodic hierarchical structure considering material strength. It is used to obtain partitioned periodic hierarchical structure data for a specified structure based on the boundary conditions and bearing capacity of the desired structure, the initial values ​​of macroscopic design variables, the initial values ​​of microstructure design variables, the minimum values ​​of macroscopic and microstructure design variables, the dimensions of the macrostructure, the number of macroscopic units, the number of macroscopic structure design variables, the dimensions of the microstructure, the number of microunits, the number of microstructure design variables, the number of types of microstructures, the volume fraction of each type of microstructure, the volume fraction of each type of microstructure occupying the macroscopic design domain, the elastic modulus of the material, and the strength of the material.

[0030] In this embodiment, the boundary condition for the required structure is specified as a cantilever beam, the required structural bearing capacity is 100N, the initial value of the macroscopic design variable is 0.1, the initial value of the microstructural design variable is 0.6, and the minimum value of both macroscopic and microstructural design variables is 1×10⁻⁶. -6 The macrostructure has dimensions of 120mm × 50mm, the number of macro units and the number of macrostructure design variables are 120 × 50, the microstructure has dimensions of 1mm × 1mm, the number of micro units and the number of microstructure design variables are 30 × 30, the number of microstructure types is 4, there are 3 types of microstructures with a volume fraction of 60%, 1 type with a volume fraction of 100%, each type of microstructure occupies a volume fraction of 10% of the macrostructure design domain, the elastic modulus of the material is 1GPa and the strength of the material is 60MPa.

[0031] Figure 1 This is a block diagram of a reverse design device for a partitioned periodic hierarchical structure considering material strength, as described in an embodiment of the present invention.

[0032] like Figure 1 As shown, the reverse design device 100 for a partitioned periodic hierarchical structure considering material strength in this embodiment includes a data input module 10, a data processing module 20, a design variable optimization module 30, an iteration module 40, and a structure generation module 50.

[0033] The data input module 10 is used by the user to input the boundary and bearing capacity of the specified structure, the initial value of the macro design variables, the initial value of the micro structure design variables, the minimum value of the macro structure and micro structure design variables, the size of the macro structure, the number of macro elements, the number of macro structure design variables, the size of the micro structure, the number of micro elements, the number of micro structure design variables, the number of types of micro structures, the volume fraction of each type of micro structure, the volume fraction of each type of micro structure in the macro design domain, the elastic modulus of the material, and the strength of the material.

[0034] The data processing module 20 is used to calculate the periodic displacement matrix of the microstructure and the displacement vector of the macrostructure based on the specified boundary and bearing capacity of the required structure, macrostructure design variables, microstructure design variables, minimum values ​​of macrostructure and microstructure design variables, dimensions of the macrostructure, number of macro elements, number of macrostructure design variables, dimensions of the microstructure, number of micro elements, number of microstructure design variables, number of types of microstructures and elastic modulus of the material.

[0035] The design variable optimization module 30 stores a collaborative optimization formula. Based on the periodic displacement matrix of the microstructure, the displacement vector of the macrostructure, the strength of the material, the volume fraction of each microstructure, the volume fraction of each microstructure in the macro design domain, and the collaborative optimization formula, it updates the values ​​of the macrostructure design variables and the microstructure design variables.

[0036] The expression for the collaborative optimization formula is as follows:

[0037]

[0038] In the formula This represents the design variable for the ξ-th material in the i-th macroscopic unit. N represents the design variable for the ξ-th material in the i-th micro-unit. M and N m N represents the number of macro-structure and micro-structure design variables, respectively. C σ represents the number of microstructure types. a It refers to the strength of the material, K. M The stiffness matrix represents the macroscopic structure; Let χ represent the stiffness matrix of the ξ-th microstructure. ξ Let U represent the periodic displacement matrix of the ξ-th microstructure. M Displacement vector representing macroscopic structure Let F represent the test load matrix of the ξ-th microstructure. M Let represent the load vector of the macroscopic structure, and c be the correction factor updated iteratively. This represents the P-norm stress of all microstructures in a multi-level structure. Here, g1 represents the volume constraint function of the macroscopic configuration, g1(ρ)≤0 indicates the volume constraint of the macroscopic configuration, and g2 represents the stress constraint function of the multi-level structure. ρ represents the stress constraint of the multi-level structure, g3 represents the volume constraint function of the microstructure configuration, g3(γ)≤0 represents the volume constraint of the microstructure configuration, and ρ min γ represents the minimum value of the macroscopic structural design variables. min This represents the minimum value of the microstructure design variables. The macrostructure design variables include the design variables of all materials in all macrostructure units, and the values ​​of the microstructure design variables include the design variables of all microstructure units.

[0039] The reverse design apparatus for partitioned periodic hierarchical structures considering material strength provided by this invention may also have the following feature: In each iteration, the co-optimization formula updates the design variables through sensitivity, and the expression for the sensitivity of the objective function to the macroscopic structural design variables is: The expression for the sensitivity of the objective function to the microstructure design variables is: The expression for the sensitivity of the stress constraint function to macroscopic structural design variables is as follows: The expression for the sensitivity of the stress constraint function to the microstructure design variables is as follows: In the formula, ω = 1, 2, ..., N r T denotes transpose, λ denotes the adjoint vector of the macroscopic displacement vector, and N D P represents the number of columns in the adjoint matrix. N It refers to P N Power of 1.

[0040] The reverse design apparatus for partitioned periodic hierarchical structures considering material strength provided by this invention may also have the following feature: wherein the P-norm stress of all microstructures in the multi-level structure is considered. The expression is: In the formula P N It refers to P N The power of , vm represents the von Mises stress. This represents the von Mises stress in the j-th micro-element at the i-th macro-element.

[0041] The reverse design apparatus for partitioned periodic hierarchical structures considering material strength provided by this invention may also have the following feature: wherein the von Mises stress of the j-th micro-unit at the i-th macro-unit is... The expression is:

[0042] In the formula, E0 is the elastic modulus of the material, and q is the penalty parameter. It is the von Mises stress of the j-th micro-unit of the ξ-th microstructure at the i-th macro-unit.

[0043] The reverse design apparatus for partitioned periodic hierarchical structures considering material strength provided by this invention may also have the following feature: the von Mises stress of the j-th micro-unit of the ξ-th microstructure at the i-th macro-unit. The expression is: In the formula, T represents the transpose, and V is the von Mises matrix. Let be the stress vector of the j-th micro-unit of the ξ-th microstructure at the i-th macro-unit.

[0044] The reverse design apparatus for partitioned periodic hierarchical structures considering material strength provided by this invention may also have the following feature: wherein the stress vector of the j-th micro-unit of the ξ-th microstructure at the i-th macro-unit is... The expression is: In the formula It is the equivalent uniform strain of the macroscopic unit, D0 is the elasticity matrix of the material, and is the identity matrix. It is the geometric matrix of the j-th micro-unit. It is the periodic displacement matrix of the ξ-th microstructure.

[0045] The reverse design apparatus for partitioned periodic hierarchical structures considering material strength provided by this invention may also have the following feature: wherein the expression for the correction factor is: In the formula c k Let δ represent the correction factor in the k-th iteration, and δ represent the update period of the correction factor.

[0046] The iteration module 40 stores preset iteration termination conditions, which are used to determine whether the iteration is complete based on the iteration termination conditions and the values ​​of macro-structure design variables and micro-structure design variables. In this embodiment, if the difference between the values ​​of macro-structure design variables and micro-structure design variables obtained in the current iteration and the values ​​of macro-structure design variables and micro-structure design variables obtained in the previous iteration is less than 0.01, then the structure generation module 50 is executed. If the difference between the values ​​of macro-structure design variables and micro-structure design variables obtained in the current iteration and the values ​​of macro-structure design variables and micro-structure design variables obtained in the previous iteration is greater than 0.01, then the data processing module 20 is executed.

[0047] The structure generation module 50 processes the updated values ​​of the macroscopic structure design variables and the microstructure design variables to obtain the partitioned periodic hierarchical structure data of the specified structure. In this embodiment, the partitioned periodic hierarchical structure data includes the structural information of the specified structure and the structural information of each microstructure.

[0048] Figure 2 This is a single-cell diagram of the microstructure in an embodiment of the present invention.

[0049] like Figure 2 As shown, A, B, C, and D are the structural information of four microstructures generated through collaborative optimization. The white parts are voids, i.e., regions without material, while the non-white parts are regions with material.

[0050] Figure 3 This is a diagram showing the single-cell distribution of the multi-level structure in this experiment.

[0051] like Figure 3 As shown, the structural information of the required structure, i.e. the cantilever beam, includes the location distribution of the above four microstructures.

[0052] Figure 4 This is a diagram of the partitioned periodic hierarchical structure shape designed in an embodiment of the present invention.

[0053] like Figure 4 As shown, the structural information of the required structure, i.e. the cantilever beam, includes the microstructure. The microstructure is reasonably distributed, and the volume of the macrostructure and the porosity of the microstructure can be effectively controlled.

[0054] Figure 5 This is a stress cloud diagram of a multi-level structure in an embodiment of the present invention.

[0055] like Figure 5 As can be seen, the light to dark color bars represent the increasing stress in the multi-level structure. Therefore, the maximum stress in the designed structure is below 60 MPa. Thus, this embodiment of the invention can achieve reverse design of a cantilever beam that meets strength requirements under a given load.

[0056] The following description, in conjunction with the accompanying drawings, explains the process of using the partitioned periodic hierarchical structure reverse design device 100, which considers material strength, to perform a partitioned periodic hierarchical structure reverse design method.

[0057] Figure 6 This is a flowchart illustrating the reverse design method for a partitioned periodic hierarchical structure considering material strength in an embodiment of the present invention.

[0058] like Figure 6 As shown, the reverse design method for partitioned periodic hierarchical structures considering material strength includes the following steps:

[0059] Step S1: Using the data processing module 20, the periodic displacement matrix of the microstructure and the displacement vector of the macrostructure are calculated based on the boundary conditions and bearing capacity of the specified required structure, macroscopic design variables, microstructure design variables, minimum values ​​of macrostructure and microstructure design variables, dimensions of the macrostructure, number of macrostructure elements, number of macrostructure design variables, dimensions of the microstructure, number of microstructure elements, number of microstructure design variables, number of types of microstructures and elastic modulus of the material.

[0060] Step S2: Using the design variable optimization module 30, update the values ​​of the macrostructure design variables and the microstructure design variables based on the periodic displacement matrix of the microstructure, the displacement vector of the macrostructure, the strength of the material, the volume fraction of each microstructure, the volume fraction of each microstructure occupying the macrostructure design domain, and the collaborative optimization formula.

[0061] Step S3: The iteration module 40 determines whether the iteration is complete based on the iteration termination condition and design variables. If yes, the structure generation module 50 is executed; otherwise, the data processing module 20 is executed.

[0062] Step S4: The updated values ​​of macroscopic structural design variables and microstructural design variables are processed using the structure generation module 50 to obtain the partitioned periodic hierarchical structure data of the specified required structure.

[0063] The role and effect of the embodiments

[0064] The reverse design apparatus and method for partitioned periodic hierarchical structures considering material strength according to embodiments of the present invention, in the process of optimizing design variables using a collaborative optimization formula, both stress constraints and volume constraints participate, and the influence of material strength is considered in the collaborative optimization formula. The final designed partitioned multi-level structure satisfies both specified volume fraction requirements and specified stress requirements. In summary, the reverse design apparatus and method for partitioned periodic hierarchical structures considering material strength according to the present invention can achieve the reverse design of partitioned multi-level structures that meet material strength requirements.

[0065] Furthermore, based on the progressive homogenization method to approximate the local stress of the microstructure, compared with the full-scale analysis method, higher accuracy stress can be obtained with lower computational cost.

[0066] Furthermore, this invention achieves the optimization design of macroscopic configuration and microstructure distribution based on discrete materials methods, and realizes the synergistic optimization design of macroscopic and microscopic configuration and microstructure distribution by constructing a new stress interpolation function to describe local stress.

[0067] Those skilled in the art should understand that this invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to this invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A reverse design device for a partitioned periodic hierarchical structure considering material strength, used to obtain partitioned periodic hierarchical structure data for a specified desired structure based on the boundary conditions and bearing capacity of the specified desired structure, the initial values ​​of macroscopic structural design variables, the initial values ​​of microstructural design variables, the minimum values ​​of macroscopic and microstructural design variables, the dimensions of the macroscopic structure, the number of macroscopic units, the number of macroscopic structural design variables, the dimensions of the microstructure, the number of microunits, the number of microstructural design variables, the number of types of microstructures, the volume fraction of each type of microstructure, the volume fraction of each microstructure and solid material occupying the macroscopic design domain, the elastic modulus of the material, and the strength of the material, characterized in that, include: The data input module is used by the user to input the boundary conditions and bearing capacity of the specified structure, the initial values ​​of the macroscopic structural design variables, the initial values ​​of the microstructural design variables, the minimum values ​​of the macroscopic and microstructural design variables, the dimensions of the macroscopic structure, the number of macroscopic elements, the number of macroscopic structural design variables, the dimensions of the microstructure, the number of micro-elements, the number of microstructural design variables, the number of types of microstructures, the volume fraction of each type of microstructure, the volume fraction of each type of microstructure in the macroscopic design domain, the elastic modulus of the material, and the strength of the material. The data processing module is used to calculate the periodic displacement matrix of the microstructure and the displacement vector of the macrostructure based on the specified required structure's boundary and bearing capacity, the macrostructure design variables, the microstructure design variables, the minimum values ​​of the macrostructure and microstructure design variables, the size of the macrostructure, the number of macro elements, the number of macrostructure design variables, the size of the microstructure, the number of micro elements, the number of microstructure design variables, the number of types of microstructures, and the elastic modulus of the material. The design variable optimization module stores a collaborative optimization formula. Based on the periodic displacement matrix of the microstructure, the displacement vector of the macrostructure, the strength of the material, the volume fraction of each microstructure, the volume fraction of each microstructure occupying the macro design domain, and the collaborative optimization formula, it updates the values ​​of the macrostructure design variables and the microstructure design variables. The iteration module stores preset iteration termination conditions, which are used to determine whether the iteration is complete based on the iteration termination conditions and the values ​​of the macro-structure design variables and micro-structure design variables. If yes, the structure generation module is executed; otherwise, the data processing module is executed. The structure generation module processes the updated values ​​of the macroscopic structure design variables and the microstructure design variables to obtain partitioned periodic hierarchical structure data for the specified desired structure. The expression for the collaborative optimization formula is as follows: In the formula This represents the design variable for the ξ-th material in the i-th macroscopic unit. N represents the design variable for the ξ-th material in the j-th micro-unit. M and N m N represents the number of macro-structure and micro-structure design variables, respectively. C σ represents the number of microstructure types. a It refers to the strength of the material, K. M The stiffness matrix represents the macroscopic structure; Let χ represent the stiffness matrix of the ξ-th microstructure. ξ Let U represent the periodic displacement matrix of the ξ-th microstructure. M Displacement vector representing macroscopic structure Let F represent the test load matrix of the ξ-th microstructure. M Let represent the load vector of the macroscopic structure, and c be the correction factor updated iteratively. This represents the P-norm stress of all microstructures in a multi-level structure. Here, g1 represents the volume constraint function of the macroscopic structure, where g1(ρ)≤0 indicates the volume constraint of the macroscopic structure; g2 represents the stress constraint function of the multi-level structure. ρ represents the stress constraint of the multi-level structure, g3 represents the volume constraint function of the microstructure configuration, g3(γ)≤0 represents the volume constraint of the microstructure configuration, and ρ min γ represents the minimum value of the macroscopic structural design variables. min This represents the minimum value of the microstructure design variables. The macroscopic structural design variables include the design variables of all materials of all macroscopic units, and the values ​​of the microstructural design variables include the design variables of all micro-units.

2. The reverse design device for a partitioned periodic hierarchical structure considering material strength according to claim 1, characterized in that: in, In each iteration, the collaborative optimization formula updates the design variables using sensitivity. The expression for the sensitivity of the objective function to the macroscopic structural design variables is as follows: The expression for the sensitivity of the objective function to the microstructure design variables is as follows: The expression for the sensitivity of the stress constraint function to the macroscopic structural design variables is as follows: The expression for the sensitivity of the stress constraint function to the microstructure design variables is as follows: In the formula, ω = 1, 2, ..., N r T denotes transpose, λ denotes the adjoint vector of the macroscopic displacement vector, and N D P represents the number of columns in the adjoint matrix. N It refers to P N Power of 1.

3. The reverse design device for a partitioned periodic hierarchical structure considering material strength according to claim 1, characterized in that: in, The P-norm stress of all microstructures in the multi-level structure The expression is: In the formula P N It refers to P N The power of 1, vm represents the von Mises stress. This represents the von Mises stress in the j-th micro-element at the i-th macro-element.

4. The reverse design device for a partitioned periodic hierarchical structure considering material strength according to claim 3, characterized in that: in, The von Mises stress of the j-th micro-unit at the i-th macro-unit. The expression is: In the formula, E0 is the elastic modulus of the material, and q is the penalty parameter, which takes a value of 0-1. It is the von Mises stress of the j-th micro-unit of the ξ-th microstructure at the i-th macro-unit.

5. The reverse design device for a partitioned periodic hierarchical structure considering material strength according to claim 4, characterized in that: in, The von Mises stress of the j-th micro-unit of the ξ-th microstructure at the i-th macro-unit. The expression is: In the formula, T represents the transpose, and V is the von Mises matrix. Let be the stress vector of the j-th micro-unit of the ξ-th microstructure at the i-th macro-unit.

6. The reverse design device for a partitioned periodic hierarchical structure considering material strength according to claim 5, characterized in that: in, The stress vector of the j-th micro-unit of the ξ-th microstructure at the i-th macro-unit. The expression is: In the formula It represents the equivalent uniform strain of the macroscopic unit, where D0 is the elastic matrix of the material and I is the identity matrix. It is the geometric matrix of the j-th micro-unit. It is the periodic displacement matrix of the ξ-th microstructure.

7. The reverse design device for a partitioned periodic hierarchical structure considering material strength according to claim 1, characterized in that: in, The expression for the correction factor is: In the formula c k Let δ represent the correction factor in the k-th iteration, and δ represent the update period of the correction factor.

8. A reverse design method for a partitioned periodic hierarchical structure considering material strength, used to obtain partitioned periodic hierarchical structure data for a specified desired structure based on the boundary conditions and bearing capacity of the specified desired structure, the initial values ​​of design variables for the macrostructure, the initial values ​​of design variables for the microstructure, the minimum values ​​of design variables for the macrostructure and microstructure, the dimensions of the macrostructure, the number of macro elements, the number of design variables for the macrostructure, the dimensions of the microstructure, the number of micro elements, the number of design variables for the microstructure, the number of types of microstructures, the volume fraction of each type of microstructure, the volume fraction of each microstructure and solid material occupying the macro design domain, the elastic modulus of the material, and the strength of the material, characterized in that: Step S1: Calculate the periodic displacement matrix of the microstructure and the displacement vector of the macrostructure based on the specified boundary conditions and bearing capacity of the required structure, the macrostructure design variables, the microstructure design variables, the minimum values ​​of the macrostructure and microstructure design variables, the dimensions of the macrostructure, the number of macro elements, the number of macrostructure design variables, the dimensions of the microstructure, the number of micro elements, the number of microstructure design variables, the number of types of microstructures, and the elastic modulus of the material. Step S2: Update the values ​​of the macrostructure design variables and the microstructure design variables based on the periodic displacement matrix of the microstructure, the displacement vector of the macrostructure, the strength of the material, the volume fraction of each microstructure, the volume fraction of each microstructure occupying the macrostructure design domain, and the collaborative optimization formula. Step S3: Determine whether the iteration is complete based on the iteration termination condition and the values ​​of the macro-structure design variables and micro-structure design variables. If yes, proceed to step S4; otherwise, proceed to step S1. Step S4: Process the updated values ​​of the macroscopic structural design variables and the microstructural design variables to obtain the partitioned periodic hierarchical structure data of the specified desired structure. The expression for the collaborative optimization formula is as follows: In the formula This represents the design variable for the ξ-th material in the i-th macroscopic unit. N represents the design variable for the ξ-th material in the i-th micro-unit. M and N m N represents the number of macro-structure and micro-structure design variables, respectively. C σ represents the number of microstructure types. a It refers to the strength of the material, K. M The stiffness matrix represents the macroscopic structure; Let χ represent the stiffness matrix of the ξ-th microstructure. ξ Let U represent the periodic displacement matrix of the ξ-th microstructure. M Displacement vector representing macroscopic structure Let F represent the test load matrix of the ξ-th microstructure. M Let represent the load vector of the macroscopic structure, and c be the correction factor updated iteratively. This represents the P-norm stress of all microstructures in a multi-level structure. Here, g1 represents the volume constraint function for the macroscopic configuration, g1(ρ)≤0, indicating the volume constraint of the macroscopic structural configuration, and g2 represents the stress constraint function for the multi-level structure. ρ represents the stress constraint of the multi-level structure, g3 represents the volume constraint function of the microstructure configuration, g3(γ)≤0 represents the volume constraint of the microstructure configuration, and ρ min γ represents the minimum value of the macroscopic structural design variables. min This represents the minimum value of the microstructure design variables. The macrostructure design variables include the design variables of all materials in all macrostructure units, and the values ​​of the microstructure design variables include the design variables of all microstructure units.

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