Multi-material microstructure and macrostructure concurrent geometric topology optimization method, device, equipment and medium

Abstract

The application provides a multi-material microstructure and macrostructure concurrent isometric topology optimization method, device, equipment and medium, relates to the isometric topology optimization technical field, and the method comprises the following steps: based on the macroscopic design variable and the microscopic design variable of the multi-material structure to be optimized, taking the global stress constraint function constructed based on the equivalent yield strength of the microscopic unit corresponding to the multi-material structure to be optimized as a constraint condition, taking the minimization of the structure quality as an optimization target, constructing a preset isometric topology optimization model, calculating the sensitivity and updating the macroscopic design variable and the microscopic design variable by using an MMA optimizer based on the sensitivity, until the preset convergence condition is met, obtaining the target macroscopic design variable and the target microscopic design variable; based on the target macroscopic design variable and the target microscopic design variable, the isometric topology optimization design is performed on the multi-material structure to be optimized, and the structure lightweight optimization design target is realized while ensuring that the maximum von mises stress of the structure meets the stress constraint condition.

Description

Technical Field

[0001] The present application relates to the technical field of isogeometric topology optimization, and in particular to a method, device, equipment and medium for concurrent isogeometric topology optimization of multi-material microstructures and macrostructures. Background Art

[0002] Composite materials are made from multiple component materials, exhibiting distinct properties and the ability to produce multiple functions, resulting in superior performance at a low cost. Multiphase composite materials with periodic microstructures are attracting increasing attention due to their high design flexibility. One of their greatest advantages is the ability to achieve lightweight structures while maintaining structural strength, which is increasingly important in engineering applications such as aviation, aerospace, and automotive.

[0003] Performing dual-scale topological optimization of the microstructure and macrostructure of periodic materials during the design phase can achieve optimal material properties while saving material consumption. The indicator that characterizes the strength of a structure is the structural stress state, that is, the maximum stress does not exceed the yield strength of the material. Currently, multi-material topological optimization research considering stress constraints is mostly based on the multi-material topological optimization design of macrostructures, which makes it impossible to fully utilize the combined performance advantages of multiple materials. Often, a corresponding global stress constraint needs to be constructed for each material, which will increase the stress conditions of the optimization problem and increase the computational cost.

[0004] Therefore, it is necessary to provide a concurrent isogeometric topology optimization method for multi-material microstructures and macrostructures considering stress constraints. Summary of the Invention

[0005] The purpose of this application is to address the above problems and provide a method, system, equipment and medium for concurrent geometric topology optimization of multi-material microstructures and macrostructures, so as to achieve the goal of structural lightweight optimization design while ensuring that the maximum von Mises stress of the structure meets the stress constraints.

[0006] In a first aspect, the present application provides a method for concurrent isogeometric topology optimization of multi-material microstructures and macrostructures, comprising:

[0007] Based on the macro-design variables and micro-design variables of the multi-material structure to be optimized, with a global stress constraint function as a constraint condition and minimization of structural mass as the optimization goal, a preset isogeometric topology optimization model of the multi-material structure to be optimized is constructed; wherein the global stress constraint function is constructed based on the equivalent yield strength of the micro-units corresponding to the multi-material structure to be optimized;

[0008] Sensitivity of the preset isometric topological optimization model is calculated, and the macroscopic design variable and the microscopic design variable are updated by using the MMA optimizer based on the sensitivity until a preset convergence condition is met, to obtain a target macroscopic design variable and a target microscopic design variable;

[0009] Based on the target macroscopic design variable and the target microscopic design variable, an isometric topological optimization design is performed on the multi-material structure to be optimized.

[0010] According to the technical scheme provided in the present application, based on the macroscopic design variable and the microscopic design variable of the multi-material structure to be optimized, a preset isometric topological optimization model of the multi-material structure to be optimized is constructed with a global stress constraint function as a constraint condition and with minimization of structure mass as an optimization target, including:

[0011] Based on the geometric model parameter information of the multi-material structure to be optimized, a macroscopic structure design domain and a microscopic structure design domain of the multi-material structure to be optimized are generated, and a macroscopic design variable corresponding to the macroscopic structure design domain and a microscopic design variable corresponding to the microscopic structure design domain are determined;

[0012] Based on the macroscopic design variable and the microscopic design variable, an initial isometric topological optimization model of the multi-material structure to be optimized is constructed with minimization of structure mass as an optimization target and with von Mises stress at the center of an element as a constraint condition;

[0013] The equivalent yield strength of a microscopic element corresponding to the microscopic structure design domain is calculated by a QP relaxation method and a DMO interpolation method, and a global stress constraint function is constructed according to the equivalent yield strength of the microscopic element;

[0014] The constraint condition of the initial isometric topological optimization model is updated according to the global stress constraint function, to obtain the preset isometric topological optimization model.

[0015] According to the technical scheme provided in the present application, based on the macroscopic design variable and the microscopic design variable, an initial isometric topological optimization model of the multi-material structure to be optimized is constructed with minimization of structure mass as an optimization target and with von Mises stress at the center of an element as a constraint condition, including:

[0016] According to the formula:

[0017]

[0018] An initial isometric topological optimization model of the multi-material structure to be optimized is constructed; wherein x M is a macroscopic design variable, that is, a macroscopic design domain control point density; x m is a microscopic design variable, that is, a macroscopic design domain control point density; N P,M is a number of macroscopic design domain control points, NP,m is the number of control points in the micro-design domain, M is the structural mass, is the relative density of the macro unit after threshold projection processing, ρ M is the equivalent density of the macro unit, is the volume of the Nth macro unit, is the overall stiffness matrix of the macrostructure, U M is the macro displacement vector, U M is the macroscopic external load vector, is the overall stiffness matrix of the microstructure, U m is the microscopic displacement vector, F m is the microscopic external load vector, is the maximum von Mises stress of material t, is the relative density of the microscopic unit after threshold projection processing, q is the stress relaxation coefficient, is the yield strength of material t, K m is the material type, N m is the number of microscopic units, N M is the number of macro units, is the relative density of the macrostructure control point i, is the relative density of material t corresponding to the jth microscopic design domain control point, and All are fixed values.

[0019] According to the technical solution provided in this application, the equivalent yield strength of the micro-unit corresponding to the microstructure design domain is calculated by the QP relaxation method and the DMO interpolation method, including:

[0020] According to the formula:

[0021]

[0022] Calculate the equivalent yield strength of the micro-element, where is the equivalent yield strength of the nth micro-element, K m For the material type, is the weight, is the yield strength of material t, is the relative density of the micro unit n corresponding to the material t after threshold projection processing, q is the stress relaxation coefficient, is the relative density of the micro unit n corresponding to the material k after the threshold projection processing, and s is the penalty coefficient.

[0023] According to the technical solution provided by the present application, constructing a global stress constraint function based on the equivalent yield strength of the micro unit includes:

[0024] According to the formula:

[0025]

[0026] Construct the global stress constraint function; where g1 is the global stress constraint function, σ max is the actual maximum stress, N m is the number of microscopic units, N M is the number of macro units, Expressed as the von Mises stress of the nth microelement under the Nth macroelement, is the equivalent yield strength of the nth micro-element, p is the P norm value, C is the scaling factor, is the Young's modulus of the micro-element after DMO interpolation, I is the element matrix, B m is the strain-displacement matrix at the center of the micro-element, U m is the displacement matrix of the nth micro-element under a given strain field, is the strain vector at the center of the macro unit.

[0027] According to the technical solution provided by the present application, the macro-design variables and the micro-design variables are updated using an MMA optimizer based on the sensitivity until a preset convergence condition is met, thereby obtaining target macro-design variables and target micro-design variables, including:

[0028] updating the macro-design variables and the micro-design variables using an MMA optimizer based on the sensitivity, and obtaining changes in the macro-design variables and the micro-design variables after each update;

[0029] If it is determined that the changes in the macro-design variables and the micro-design variables are less than a preset threshold, the current macro-design variables and the micro-design variables are used as the target macro-design variables and the target micro-design variables;

[0030] Alternatively, the macro-design variables and the micro-design variables are updated using an MMA optimizer based on the sensitivity, and the number of iterations after each update is obtained;

[0031] If it is determined that the number of iterations reaches a preset number, the current macro-design variables and micro-design variables are used as the target macro-design variables and target micro-design variables.

[0032] According to the technical solution provided in this application, the calculation of the sensitivity of the preset isogeometric topology optimization model includes:

[0033] According to the formula:

[0034]

[0035] Calculate the sensitivity of the preset geometric topology optimization model; wherein the function is the objective function or global stress constraint function, the design variable x i is a macro design variable or a micro design variable, S i is the set of macro-units composed of control points in the macro-design domain or the set of micro-units composed of control points in the micro-design domain. is the relative density of cell j calculated directly from the control points, for The relative density of unit j after threshold projection, x i is the relative density of control point i.

[0036] In a second aspect, the present application provides a device for concurrent iso-geometric topology optimization of multi-material microstructures and macrostructures, comprising:

[0037] a model construction module for constructing a preset isogeometric topology optimization model of the multi-material structure to be optimized based on the macro-design variables and micro-design variables of the multi-material structure to be optimized, with a global stress constraint function as a constraint condition and minimization of structural mass as an optimization goal; wherein the global stress constraint function is constructed based on the equivalent yield strength of the micro-units corresponding to the multi-material structure to be optimized;

[0038] a calculation and updating module, configured to calculate the sensitivity of the preset isogeometric topology optimization model, and update the macro-design variables and the micro-design variables using an MMA optimizer based on the sensitivity until a preset convergence condition is met, thereby obtaining target macro-design variables and target micro-design variables;

[0039] The optimization design module is used to perform isogeometric topology optimization design on the multi-material structure to be optimized based on the target macro-design variables and the target micro-design variables.

[0040] In a third aspect, the present application provides an electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the method described above when executing the computer program.

[0041] In a fourth aspect, the present application provides a computer-readable storage medium having a computer program stored thereon, and the computer program implements the method described above when executed by a processor.

[0042] Compared with the prior art, the beneficial effects of the present application are as follows: the method, device, equipment and medium for concurrent isogeometric topology optimization of multi-material microstructures and macrostructures provided by the present application are based on the macro design variables and micro design variables of the multi-material structure to be optimized, with the global stress constraint function constructed based on the equivalent yield strength of the micro units corresponding to the multi-material structure to be optimized as the constraint condition, and with minimization of structural mass as the optimization goal, a preset isogeometric topology optimization model is constructed, the sensitivity is calculated and the macro design variables and micro design variables are updated using the MMA optimizer based on the sensitivity until the preset convergence conditions are met, and the target macro design variables and target micro design variables are obtained; based on the target macro design variables and target micro design variables, the multi-material structure to be optimized isogeometric topology optimization design is performed. By adopting the DMO interpolation and QP relaxation method, a calculation method for the equivalent yield strength of multi-material units is proposed, which can be effectively used to realize stress verification when multiple materials exist in a unit at the same time during the optimization process; and by constructing a global stress constraint based on the equivalent yield strength of the micro units corresponding to the multi-material structure to be optimized, the stress constraint conditions are improved, which can effectively reduce the number of stress constraints when considering multiple materials, reduce the computational cost, and achieve structural lightweighting or other optimization goals while ensuring that the maximum von Mises stress of the structure meets the stress constraint conditions.

[0043] It should be understood that the description of technical features, technical solutions, beneficial effects or similar language in this application does not imply that all features and advantages can be realized in any single embodiment. On the contrary, it is understood that the description of a feature or beneficial effect means that a specific technical feature, technical solution or beneficial effect is included in at least one embodiment. Therefore, the description of a technical feature, technical solution or beneficial effect in this specification does not necessarily refer to the same embodiment. Furthermore, the technical features, technical solutions and beneficial effects described in the present embodiment can also be combined in any appropriate manner. Those skilled in the art will understand that the embodiment can be implemented without one or more specific technical features, technical solutions or beneficial effects of a specific embodiment. In other embodiments, additional technical features and beneficial effects can also be identified in specific embodiments that do not embody all embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to more clearly illustrate the technical solution in this embodiment, the following is a brief introduction to the drawings required for the description of the embodiment. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0045] Figure 1A flowchart of a method for concurrent isogeometric topology optimization of multi-material microstructures and macrostructures provided in an embodiment of the present application;

[0046] Figure 2 Schematic diagram of the elements affected by control points in a 2D isogeometric model with NURBS order 2;

[0047] Figure 3 Schematic diagram of the control points that constitute the unit in a 2D isogeometric model with URBS order 2;

[0048] Figure 4 Schematic diagram of periodic boundary conditions corresponding to a 2D isogeometric model with NURBS order 2;

[0049] Figure 5 Schematic diagram of three unit strain fields of 2D structure;

[0050] Figure 6 Schematic diagram of the transformation between the physical domain, parameter domain and integration domain in isogeometric analysis;

[0051] Figure 7 A schematic diagram of a device for concurrent isogeometric topology optimization of multi-material microstructures and macrostructures provided in an embodiment of the present application;

[0052] Figure 8 A schematic diagram of a computer system of an electronic device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0053] In order to enable those skilled in the art to better understand the technical solutions of the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the accompanying drawings. The description in this section is only exemplary and explanatory and should not have any limiting effect on the scope of protection of the present application. Specifically, the embodiments described are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without making creative work should fall within the scope of protection of the present application.

[0054] It should be noted that similar reference numerals and letters represent similar items in the following figures. Therefore, once an item is defined in one figure, it does not need to be further defined or explained in subsequent figures. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions. For example, a process, method, system, product or apparatus that includes a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units that are not explicitly listed or inherent to these processes, methods, products or apparatuses.

[0055] In order to make the technical solution of the present application clearer and easier to understand, the geometric topology optimization method of multi-material microstructure and macrostructure concurrently provided in the embodiment of the present application is introduced below.

[0056] like Figure 1 As shown in the figure, this figure is a flow chart of a method for concurrent isogeometric topology optimization of a multi-material microstructure and macrostructure provided by this embodiment, the method comprising the following steps:

[0057] S101. Based on the macro-design variables and micro-design variables of the multi-material structure to be optimized, with a global stress constraint function as a constraint condition and minimization of structural mass as an optimization goal, construct a preset isogeometric topology optimization model of the multi-material structure to be optimized; wherein the global stress constraint function is constructed based on the equivalent yield strength of the micro-units corresponding to the multi-material structure to be optimized;

[0058] Specifically, based on the geometric model parameter information of the multi-material structure to be optimized, the macro-structure design domain and the micro-structure design domain of the multi-material structure to be optimized are generated, and the macro-design variables corresponding to the macro-structure design domain and the micro-design variables corresponding to the micro-structure design domain are determined. Then, based on the macro-design variables and the micro-design variables, with the minimum structural mass as the optimization goal and the von Mises stress at the unit center as the constraint condition, an initial iso-geometric topology optimization model of the multi-material structure to be optimized is constructed, the equivalent yield strength of the micro-unit corresponding to the micro-structure design domain is calculated by the QP relaxation method and the DMO interpolation method, and a global stress constraint function is constructed according to the equivalent yield strength of the micro-unit. The constraint conditions of the initial iso-geometric topology optimization model are updated according to the global stress constraint function to obtain the preset iso-geometric topology optimization model.

[0059] S102, calculating the sensitivity of the preset isogeometric topology optimization model, and updating the macro-design variables and the micro-design variables using an MMA optimizer based on the sensitivity until a preset convergence condition is met, thereby obtaining target macro-design variables and target micro-design variables;

[0060] Specifically, the macro-design variables and micro-design variables corresponding to the preset convergence conditions are used as the target macro-design variables and the target micro-design variables; wherein the preset convergence conditions include that the changes in the macro-design variables and the micro-design variables are less than a preset threshold or the number of iterations reaches a preset number, and can also be other conditions, which can be set and adjusted according to actual conditions and are not specifically limited here.

[0061] S103 , performing isogeometric topology optimization design on the multi-material structure to be optimized based on the target macro-design variables and the target micro-design variables.

[0062] Specifically, the target macro-design variables and the target micro-design variables determine the target topological parameters corresponding to the multi-material microstructure and the macrostructure, and the multi-material microstructure and the macrostructure are optimized according to the target topological parameters.

[0063] The present application provides a method for concurrent isogeometric topology optimization of multi-material microstructures and macrostructures. Based on the macro-design variables and micro-design variables of the multi-material structure to be optimized, the method uses a global stress constraint function constructed based on the equivalent yield strength of the micro-units corresponding to the multi-material structure to be optimized as a constraint condition, and takes minimizing the structural mass as the optimization goal. A preset isogeometric topology optimization model is constructed, the sensitivity is calculated, and the macro-design variables and micro-design variables are updated using an MMA optimizer based on the sensitivity until the preset convergence conditions are met, thereby obtaining the target macro-design variables and target micro-design variables. Based on the target macro-design variables and target micro-design variables, the multi-material structure to be optimized isogeometric topology optimization design is performed. By adopting the DMO interpolation and QP relaxation method, a calculation method for the equivalent yield strength of multi-material units is proposed, which can be effectively used to realize stress verification when multiple materials exist in a unit at the same time during the optimization process; and by constructing a global stress constraint based on the equivalent yield strength of the micro units corresponding to the multi-material structure to be optimized, the stress constraint conditions are improved, which can effectively reduce the number of stress constraints when considering multiple materials, reduce the computational cost, and achieve structural lightweighting or other optimization goals while ensuring that the maximum von Mises stress of the structure meets the stress constraint conditions.

[0064] On the basis of the above embodiment, further, based on the macro-design variables and micro-design variables of the multi-material structure to be optimized, taking the global stress constraint function as the constraint condition and minimizing the structural mass as the optimization goal, a preset isogeometric topology optimization model of the multi-material structure to be optimized is constructed, including:

[0065] generating a macrostructure design domain and a microstructure design domain of the multi-material structure to be optimized based on geometric model parameter information of the multi-material structure to be optimized, and determining macrodesign variables corresponding to the macrostructure design domain and microdesign variables corresponding to the microstructure design domain;

[0066] Specifically, if Figure 2-3 As shown, based on the isogeometric analysis model of the multi-material structure to be optimized, the geometric model parameter information of the multi-material structure to be optimized is obtained, the finite element mesh is used to discretize the design domain from the macro and micro levels, the multi-material structure to be optimized is NURBS meshed, and the macro-structure design domain and micro-structure design domain of the multi-material structure to be optimized are generated. The control point density of the macro-structure design domain is used as the macro-design variable x M , taking the control point density of the macro-structure design domain as the micro-design variable xm .

[0067] Based on the macro-design variables and micro-design variables, an initial isogeometric topology optimization model of the multi-material structure to be optimized is constructed with minimum structural mass as the optimization goal and von Mises stress at the unit center as the constraint condition;

[0068] Calculating the equivalent yield strength of the micro-units corresponding to the microstructure design domain by using the QP relaxation method and the DMO interpolation method, and constructing a global stress constraint function according to the equivalent yield strength of the micro-units;

[0069] Specifically, based on the QP relaxation method and DMO interpolation method, the equivalent yield strength at the nth micro-element is obtained: The expression is:

[0070]

[0071] in, is the equivalent yield strength of the nth micro-element, K m For the material type, is the weight, is the yield strength of material t, is the relative density of the micro unit n corresponding to the material t after threshold projection processing, q is the stress relaxation coefficient, is the relative density of the micro unit n corresponding to the material k after the threshold projection processing, and the global stress constraint function is constructed according to the equivalent yield strength of the micro unit.

[0072] The constraint conditions of the initial isogeometric topology optimization model are updated according to the global stress constraint function to obtain the preset isogeometric topology optimization model.

[0073] Specifically, the constraint conditions of the initial isogeometric topology optimization model are replaced with the global stress constraint function to obtain the preset isogeometric topology optimization model.

[0074] On the basis of the above embodiment, further, based on the macro-design variables and the micro-design variables, with the minimum structural mass as the optimization goal and the von Mises stress at the unit center as the constraint condition, an initial isogeometric topology optimization model of the multi-material structure to be optimized is constructed, including:

[0075] According to the formula:

[0076]

[0077] Construct an initial isogeometric topology optimization model of the multi-material structure to be optimized; where x M is the macro design variable, i.e. the density of control points in the macro design domain; x mis the micro-design variable, i.e. the density of control points in the macro-design domain; N P,M is the number of control points in the macro design domain, N P,m is the number of control points in the micro-design domain, M is the structural mass, is the relative density of the macro unit after threshold projection processing, ρ M is the equivalent density of the macro unit, is the volume of the Nth macro unit, is the overall stiffness matrix of the macrostructure, U M is the macro displacement vector, F M is the macroscopic external load vector, is the overall stiffness matrix of the microstructure, U m is the microscopic displacement vector, F m is the microscopic external load vector, is the maximum von Mises stress of material t, is the relative density of the microscopic unit after threshold projection processing, q is the stress relaxation coefficient, is the yield strength of material t, K m is the material type, N m is the number of microscopic units, N M is the number of macro units, is the relative density of the macrostructure control point i, is the relative density of material t corresponding to the jth microscopic design domain control point, and All are fixed values.

[0078] Specifically, based on the macroscopic design variables and microscopic design variables, the Young's modulus field E is introduced. m With elastic matrix The corresponding relationship is as follows:

[0079]

[0080] Among them, ii,jj represents the control point number along the parameterized coordinates ξ and η, represents the density of the corresponding control point of the macro design variable, represents the density at the corresponding control point of the micro-design variable, represents the NURBS basis function corresponding to the control points numbered ii, j, r and l are the basis function orders along the ξ and η directions respectively, j M,ec and η M,ec are the parameter coordinates along the ξ and η directions at the center of the macro unit, are the relative density of macro units and micro units after threshold projection processing, I m 、Jm denote the total number of control points along the ξ and η directions in the microscopic design domain, I M 、J M denote the total number of control points along the ξ and η directions in the macro design domain, respectively; is the elastic matrix of macro unit N after interpolation, is the microstructure equivalent constitutive matrix, is the Young's modulus of the micro-element after DMO interpolation, K m is the material type, w n,t is the weight, E t is the Young's modulus of the solid material t, E min The minimum Young's modulus is preset to avoid the occurrence of singularity in the stiffness matrix, and is set to 0.001 MPa in this embodiment; is the relative density of the micro unit n corresponding to the material k after the threshold projection process, and s is a penalty coefficient greater than 1, which is set to 3 in this embodiment.

[0081] in, To pass such Figure 4 The equivalent constitutive matrix of the microstructure obtained by numerical homogenization calculation under the given periodic boundary conditions is expressed as follows:

[0082]

[0083] in, is the microstructure equivalent constitutive matrix, Ω m is the total volume (or area) of the microstructure, are the three displacement fields corresponding to a given unit strain, is the displacement matrix of the nth micro-element under a given strain field, which contains three columns, corresponding to the globally applied unit strain field (such as Figure 5 The three displacement fields generated by is the stiffness matrix of the nth micro-element, which is expressed as:

[0084]

[0085] in, is the stiffness matrix of the nth microelement, is the Young's modulus of the micro-element after DMO interpolation, B m is the strain-displacement matrix at the center of the micro-element, D0 is the elastic matrix corresponding to the elastic modulus of 1, and the Jacobian matrices J1 and J2 are the spatial variation relationships from the NURBS parameter domain to the physical domain and from the integral domain to the parameter domain, respectively (e.g. Figure 6 shown), ω a is the weight coefficient corresponding to the ath Gaussian integral point, N gis the number of Gaussian integration points.

[0086] The relative density x of the microscopic unit after threshold projection processing M,e 、x m,e After threshold projection, we get For example, the projection expression is:

[0087]

[0088] in, is the relative density of the macro unit after threshold projection processing, β is the projection curvature control parameter, the larger the β value is, the greater the curvature of the projection function curve is, δ is the projection threshold, and variables greater than δ approach 1 after projection, otherwise they approach 0. In this embodiment, δ is set to 0.5.

[0089] Maximum von Mises stress of material t It can be expressed as:

[0090]

[0091] Where V is the stress coefficient matrix. For the case of 2D plane stress structure optimization, we have:

[0092]

[0093] For the case of 3D plane stress structure optimization, we have:

[0094]

[0095] Stress vector The expression is:

[0096]

[0097] in, is the stress vector, is the relative density of the micro-unit after threshold projection processing, s is the penalty coefficient greater than 1, E t is the Young's modulus of the solid material t, D0 is the elastic matrix corresponding to the elastic modulus of 1, I is the unit matrix, B m is the strain-displacement matrix at the center of the micro-element, is the displacement matrix of the nth micro-element under a given strain field, is the strain vector at the center of the macro unit.

[0098] In summary, the initial isogeometric topology optimization model of the multi-material structure to be optimized is constructed as follows:

[0099]

[0100] Among them, x M is the macro design variable, i.e. the density of control points in the macro design domain; x m is the micro-design variable, i.e. the density of control points in the macro-design domain; N P,M is the number of control points in the macro design domain, N P,m is the number of control points in the micro-design domain, M is the structural mass, is the relative density of the macro unit after threshold projection processing, ρ M is the equivalent density of the macro unit, is the volume of the Nth macro unit, is the overall stiffness matrix of the macrostructure, U M is the macro displacement vector, F M is the macroscopic external load vector, is the overall stiffness matrix of the microstructure, U m is the microscopic displacement vector, F m is the microscopic external load vector, is the maximum von Mises stress of material t, is the relative density of the microscopic unit after threshold projection processing, q is the stress relaxation coefficient, is the yield strength of material t, K m is the material type, N m is the number of microscopic units, N M is the number of macro units, is the relative density of the macrostructure control point i, is the relative density of material t corresponding to the jth microscopic design domain control point, and All are preset fixed values. It should be noted that in this embodiment, the stress relaxation coefficient q is set to 2.5, which can be set and adjusted according to actual conditions and is not specifically limited here; and are all small values ​​to avoid singularity.

[0101] On the basis of the above embodiment, further, the equivalent yield strength of the micro-unit corresponding to the microstructure design domain is calculated by the QP relaxation method and the DMO interpolation method, including:

[0102] According to the formula:

[0103]

[0104] Calculate the equivalent yield strength of the micro-element, where is the equivalent yield strength of the nth micro-element, K m For the material type, is the weight, is the yield strength of material t, is the relative density of the micro unit n corresponding to the material t after threshold projection processing, q is the stress relaxation coefficient, is the relative density of the micro unit n corresponding to the material k after the threshold projection processing, and s is the penalty coefficient.

[0105] On the basis of the above embodiment, further, constructing a global stress constraint function according to the equivalent yield strength of the micro unit includes:

[0106] According to the formula:

[0107]

[0108] Construct the global stress constraint function; where g1 is the global stress constraint function, σ max is the actual maximum stress, N m is the number of microscopic units, N M is the number of macro units, Expressed as the von Mises stress of the nth microelement under the Nth macroelement, is the equivalent yield strength of the nth micro-element, p is the P norm value, C is the scaling factor, is the Young's modulus of the micro-element after DMO interpolation, I is the element matrix, B m is the strain-displacement matrix at the center of the micro-element, is the displacement matrix of the nth micro-element under a given strain field, is the strain vector at the center of the macro unit.

[0109] Specifically, after the equivalent yield strength of the micro-unit corresponding to the above-mentioned microstructure design domain is calculated by the QP relaxation method and the DMO interpolation method, the improved stress constraint function (i.e., the global stress constraint function) is:

[0110] g1=σ max -1≤0 (15)

[0111]

[0112] Among them, g1 is the global stress constraint function, σ max is the actual maximum stress, Expressed as the von Mises stress of the nth microelement under the Nth macroelement, is the equivalent yield strength of the nth microelement, and p is the P-norm value.

[0113] C is the scaling factor, and its value is as follows:

[0114]

[0115] in, Expressed as the von Mises stress of the nth microelement under the Nth macroelement, the von Mises stress at the nth microelement, is the equivalent yield strength of the nth microelement, and p is the P-norm value.

[0116] Furthermore, The expression is:

[0117]

[0118] in, is the Young's modulus of the micro-element after DMO interpolation, I is the element matrix, B m is the strain-displacement matrix at the center of the micro unit, D0 is the elastic matrix corresponding to the elastic modulus of 1, is the displacement matrix of the nth micro-element under a given strain field, is the strain vector at the center of the Nth macroelement.

[0119] In summary, the global stress constraint function is constructed as follows:

[0120]

[0121] Among them, g1 is the global stress constraint function, σ max is the actual maximum stress, N m is the number of microscopic units, N M is the number of macro units, Expressed as the von Mises stress of the nth microelement under the Nth macroelement, is the equivalent yield strength of the nth micro-element, p is the P norm value, C is the scaling factor, is the Young's modulus of the micro-element after DMO interpolation, I is the element matrix, B m is the strain-displacement matrix at the center of the micro-element, U m is the displacement matrix of the nth micro-element under a given strain field, is the strain vector at the center of the macro unit.

[0122] On the basis of the above embodiment, further, based on the sensitivity, the macro design variables and the micro design variables are updated using an MMA optimizer until a preset convergence condition is met, thereby obtaining target macro design variables and target micro design variables, including:

[0123] updating the macro-design variables and the micro-design variables using an MMA optimizer based on the sensitivity, and obtaining changes in the macro-design variables and the micro-design variables after each update;

[0124] If it is determined that the changes in the macro-design variables and the micro-design variables are less than a preset threshold, the current macro-design variables and the micro-design variables are used as the target macro-design variables and the target micro-design variables;

[0125] Alternatively, the macro-design variables and the micro-design variables are updated using an MMA optimizer based on the sensitivity, and the number of iterations after each update is obtained;

[0126] If it is determined that the number of iterations reaches a preset number, the current macro-design variables and micro-design variables are used as the target macro-design variables and target micro-design variables.

[0127] Specifically, in this embodiment, the preset threshold can be set to 0.002, and the preset number of times can be set to 100 times. The specific values ​​of the preset threshold and the preset number of times can be set and adjusted according to actual conditions and are not specifically limited here.

[0128] Based on the above embodiment, further, calculating the sensitivity of the preset isogeometric topology optimization model includes:

[0129] According to the formula:

[0130]

[0131] Calculate the sensitivity of the preset geometric topology optimization model; wherein the function is the objective function or global stress constraint function, the design variable x i is a macro design variable or a micro design variable, S i is the set of macro-units composed of control points in the macro-design domain or the set of micro-units composed of control points in the micro-design domain. is the relative density of cell j calculated directly from the control points, for The relative density of unit j after threshold projection, x i is the relative density of control point i.

[0132] Specifically, the sensitivity function It can be an objective function or a global stress constraint function, and the design variable x i It can be a macro design variable or a micro design variable, that is, the relative density of any control point in the macro design domain or the relative density of any control point in the micro design domain.

[0133] in:

[0134]

[0135]

[0136] where, is the relative density of the element j calculated directly from the control points, is the relative density of the element j after threshold projection, β is the projection curvature control parameter, and δ is the projection threshold, is the NURBS basis function corresponding to the control point i, ξ M,ec and η M,ec are the parametric coordinates along the ξ and η directions at the element center, respectively.

[0137] When the sensitivity function is the objective function, the sensitivity corresponding to the objective function is as follows:

[0138]

[0139] where M is the structure mass, ρ M is the equivalent density of the macro element, is the volume of the Nth macro element, is the relative density of the micro element after threshold projection.

[0140] When the sensitivity function is the global stress constraint function, the sensitivity corresponding to the global stress constraint function is calculated as follows:

[0141]

[0142] where g1 is the global stress constraint function, p is the P-norm value, is the equivalent yield strength of the nth micro element, denotes the von Mises stress of the nth micro element under the Nth macro element, is the relative density of the micro element after threshold projection.

[0143] For the macro structure, we have:

[0144]

[0145] where, denotes the von Mises stress of the nth micro element under the Nth macro element, is the Young's modulus of the micro element after DMO interpolation, B m is the strain-displacement matrix at the micro element center, D0 is the elastic matrix corresponding to the elastic modulus of 1, and I is the element matrix, is the displacement matrix of the nth micro element under the given strain field, is the strain vector at the macro element center, is the control point displacement index matrix corresponding to the Nth macro unit.

[0146] By the adjoint method we can get:

[0147]

[0148] Where, is the element stiffness matrix, U M is the macro displacement vector, K M is the overall stiffness matrix of the macrostructure, is the control point displacement index matrix corresponding to the Nth macro unit, and s is the penalty coefficient.

[0149] The Gaussian integral is expressed as

[0150]

[0151] Where, is the constitutive matrix calculated by the numerical homogenization method. The Jacobian matrices J1 and J2 are the spatial variation relationships from the NURBS parameter domain to the physical domain and from the integral domain to the parameter domain, respectively. a is the weight coefficient corresponding to the ath Gaussian integral point, N g is the number of Gaussian integration points.

[0152] For the micro-design domain, we have:

[0153]

[0154] Where, is the equivalent yield strength of the nth micro-element, is the relative density of the microscopic unit after threshold projection processing, K m For the material type, is the yield strength of material k.

[0155] Furthermore, there are:

[0156]

[0157]

[0158] Where q is the stress relaxation coefficient, is the relative density of the micro unit n corresponding to the material k after threshold projection processing, is the relative density of the micro unit n corresponding to the material i after the threshold projection processing, s is the penalty coefficient, is the maximum von Mises stress, is the stress vector, E k is the elastic modulus of material k.

[0159] Furthermore,

[0160]

[0161] Where, is the control point displacement index matrix corresponding to the nth micro unit, U M is the macro displacement vector, K M is the overall stiffness matrix of the macrostructure.

[0162] Specifically, there are:

[0163]

[0164] in, is the element stiffness matrix when the elastic modulus is 1, ω a is the weight coefficient corresponding to the ath Gaussian integral point, N g is the number of Gaussian integration points, Contains three displacement fields corresponding to unit strain, is the displacement matrix of the nth microelement under a given strain field, which contains three columns, corresponding to the three displacement fields generated by the globally applied unit strain field.

[0165] Combined with the above Figure 1-6 The method for concurrent geometric topology optimization of multi-material microstructures and macrostructures provided in the embodiment of the present application is introduced in detail. The device, electronic device and computer-readable storage medium for concurrent geometric topology optimization of multi-material microstructures and macrostructures provided in the embodiment of the present application will be introduced in conjunction with the accompanying drawings.

[0166] like Figure 7 As shown in the figure, this figure is a schematic diagram of the multi-material microstructure and macrostructure simultaneous geometric topology optimization device provided by the present application, and the device includes:

[0167] A model construction module 201 is configured to construct a preset isogeometric topology optimization model of the multi-material structure to be optimized based on the macro-design variables and micro-design variables of the multi-material structure to be optimized, with a global stress constraint function as a constraint condition and minimization of structural mass as an optimization goal; wherein the global stress constraint function is constructed based on the equivalent yield strength of the micro-units corresponding to the multi-material structure to be optimized;

[0168] A calculation and updating module 202 is configured to calculate the sensitivity of the preset isogeometric topology optimization model and update the macro-design variables and micro-design variables using an MMA optimizer based on the sensitivity until a preset convergence condition is met, thereby obtaining target macro-design variables and target micro-design variables.

[0169] The optimization design module 203 is used to perform isogeometric topology optimization design on the multi-material structure to be optimized based on the target macro-design variables and the target micro-design variables.

[0170] The multi-material microstructure and macrostructure concurrent iso-geometric topology optimization device provided in the embodiment of the present application can correspond to the execution of the multi-material microstructure and macrostructure concurrent iso-geometric topology optimization method described in the embodiment of the present application, and the above functions of each module of the system correspond to the implementation of Figure 1 For the sake of brevity, the corresponding process of the method shown will not be repeated here.

[0171] An embodiment of the present application also provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the concurrent geometric topology optimization method of multi-material microstructures and macrostructures as described in the above embodiment is implemented.

[0172] like Figure 8 As shown, the computer system 300 of the electronic device includes a CPU 301, which can perform various appropriate actions and processes according to the programs stored in the ROM 302 or the programs loaded from the storage unit 308 into the RAM 303. The RAM 303 also stores various programs and data required for system operation. The CPU 301, ROM 302, and RAM 303 are connected to each other via a bus 304. An I / O interface 305 is also connected to the bus 304. Here, CPU 301 represents a central processing unit, ROM 302 represents a read-only memory, RAM 303 represents a random access memory, and I / O represents input / output.

[0173] The following components are connected to the I / O interface 305: an input section 306 including a keyboard, a mouse, and the like; an output section 307 including devices such as a cathode ray tube, a liquid crystal display, and a speaker; a storage section 308 including devices such as a hard disk; and a communication section 309 including a network interface card such as a LAN card or a modem. The communication section 309 performs communication processing via a network such as the Internet. A drive 310 is also connected to the I / O interface 305 as needed. Removable media 311, such as a magnetic disk, an optical disk, a magneto-optical disk, or a semiconductor memory, is installed in the drive 310 as needed, so that computer programs read from the media can be installed in the storage section 308 as needed.

[0174] In particular, the process of the multi-material microstructure and macrostructure concurrent iso-geometric topology optimization method described in the above embodiment can be implemented as a computer software program. For example, an embodiment of the present application includes a computer program product, which includes a computer program carried on a computer-readable storage medium, and the computer program contains program code for executing the multi-material microstructure and macrostructure concurrent iso-geometric topology optimization method described in the above embodiment. In such an embodiment, the computer program can be downloaded and installed from the network through the communication part 309, and / or installed from the removable medium 311. When the computer program is executed by the CPU 301, the above-mentioned functions defined in the present computer system 300 are executed.

[0175] An embodiment of the present application also provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the method for concurrent geometric topology optimization of multi-material microstructures and macrostructures as described in the above embodiment is implemented.

[0176] Specifically, the computer-readable storage medium may be included in the electronic device described in the above embodiments, or may exist independently and not be incorporated into the electronic device. The computer-readable storage medium carries one or more programs. When executed by the electronic device, the electronic device implements the multi-material microstructure and macrostructure concurrent geometric topology optimization method described in the above embodiments.

[0177] It should be noted that the computer-readable storage medium described in this application may be a computer-readable signal medium or a computer-readable storage medium, or any combination thereof. Computer-readable storage media may include, for example, but are not limited to, electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems, devices, or components, or any combination thereof. More specific examples of computer-readable storage media may include, but are not limited to, an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory, read-only memory, erasable programmable read-only memory, optical fiber, a portable compact disk read-only memory, an optical storage device, a magnetic storage device, or any suitable combination thereof. In this application, a computer-readable storage medium may be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, device, or component. Furthermore, in this application, a computer-readable signal medium may include a data signal propagated in baseband or as part of a carrier wave, carrying computer-readable program code. This propagated data signal may take a variety of forms, including, but not limited to, electromagnetic signals, optical signals, or any suitable combination thereof.

[0178] This article uses specific examples to illustrate the principles and implementation methods of this application. The description of the above embodiments is only used to help understand the method and core ideas of this application. The above is only the preferred implementation method of this application. It should be pointed out that due to the limitations of textual expression, there are objectively infinite specific structures. For ordinary technicians in this technical field, without departing from the principles of the present invention, they can also make several improvements, modifications or changes, and can also combine the above technical features in an appropriate manner; these improvements, modifications, changes or combinations, or the direct application of the inventive concept and technical solution to other occasions without improvement, should be regarded as the scope of protection of this application.

Claims

1. A method for concurrent isogeometric topology optimization of multi-material microstructures and macrostructures, characterized in that: include: Based on the macro-design variables and micro-design variables of the multi-material structure to be optimized, with the global stress constraint function as the constraint condition, the minimization of the structural mass as the optimization goal, and the von Mises stress at the unit center as the constraint condition, an initial isogeometric topology optimization model of the multi-material structure to be optimized is constructed; the equivalent yield strength of the micro-unit corresponding to the microstructure design domain is calculated by the QP relaxation method and the DMO interpolation method, and a global stress constraint function is constructed according to the equivalent yield strength of the micro-unit; the constraint conditions of the initial isogeometric topology optimization model are updated according to the global stress constraint function, and a preset isogeometric topology optimization model of the multi-material structure to be optimized is constructed; wherein, the global stress constraint function is constructed based on the equivalent yield strength of the micro-unit corresponding to the multi-material structure to be optimized; the formula for constructing the global stress constraint function is: ； in, is the global stress constraint function, is the actual maximum stress, is the number of microscopic units, is the number of macro units, Expressed as The first macro unit The von Mises stress of a microscopic element, For the The equivalent yield strength of a micro-element, is the P norm value, C is the scaling factor, is the Young's modulus of the micro-element after DMO interpolation, is the unit matrix, is the strain-displacement matrix at the center of the micro-element, For the The displacement matrix of a microscopic unit under a given strain field is: is the strain vector at the center of the macro unit; Calculating the sensitivity of the preset isogeometric topology optimization model, and updating the macro-design variables and the micro-design variables using an MMA optimizer based on the sensitivity until a preset convergence condition is met, thereby obtaining target macro-design variables and target micro-design variables; Based on the target macro-design variables and the target micro-design variables, isogeometric topology optimization design is performed on the multi-material structure to be optimized.

2. The method according to claim 1, characterized in that The method constructs an initial isogeometric topology optimization model of the multi-material structure to be optimized based on the macro-design variables and micro-design variables of the multi-material structure to be optimized, with the global stress constraint function as a constraint condition, minimizing the structural mass as an optimization goal, and the von Mises stress at the unit center as a constraint condition, including: generating a macrostructure design domain and a microstructure design domain of the multi-material structure to be optimized based on geometric model parameter information of the multi-material structure to be optimized, and determining macrodesign variables corresponding to the macrostructure design domain and microdesign variables corresponding to the microstructure design domain; Based on the macro-design variables and micro-design variables, with minimizing the structural mass as the optimization goal and the von Mises stress at the unit center as the constraint condition, an initial isogeometric topology optimization model of the multi-material structure to be optimized is constructed.

3. The method according to claim 2, characterized in that Based on the macro-design variables and micro-design variables, with the minimum structural mass as the optimization goal and the von Mises stress at the unit center as the constraint condition, an initial isogeometric topology optimization model of the multi-material structure to be optimized is constructed, including: According to the formula: ； Construct an initial isogeometric topology optimization model of the multi-material structure to be optimized; is the macro design variable, i.e., the density of control points in the macro design domain; is the micro-design variable, i.e., the density of control points in the micro-design domain; is the number of control points in the macro design domain, is the number of control points in the micro-design domain, For structural quality, is the relative density of the macro unit after threshold projection processing, is the equivalent density of the macro unit, For the The volume of a macro unit, is the overall stiffness matrix of the macrostructure, is the macro displacement vector, is the macroscopic external load vector, is the overall stiffness matrix of the microstructure, is the microscopic displacement vector, is the microscopic external load vector, is the maximum von Mises stress of material t, is the relative density of the microscopic unit after threshold projection processing, is the stress relaxation coefficient, is the yield strength of material t, For the material type, is the number of microscopic units, is the number of macro units, is the relative density of the macrostructure control point i, is the relative density of material t corresponding to the jth microscopic design domain control point, and All are fixed values.

4. The method according to claim 3, characterized in that The equivalent yield strength of the micro-element corresponding to the microstructure design domain is calculated by the QP relaxation method and the DMO interpolation method, including: According to the formula: ； Calculate the equivalent yield strength of the micro-element, where For the The equivalent yield strength of a micro-element, For the material type, is the weight, is the yield strength of material t, is the relative density of the micro unit n corresponding to the material t after threshold projection processing, q is the stress relaxation coefficient, is the relative density of the micro unit n corresponding to the material k after the threshold projection processing, and s is the penalty coefficient.

5. The method according to claim 1, wherein The macro-design variables and the micro-design variables are updated using an MMA optimizer based on the sensitivity until a preset convergence condition is satisfied, thereby obtaining target macro-design variables and target micro-design variables, including: updating the macro-design variables and the micro-design variables using an MMA optimizer based on the sensitivity, and obtaining changes in the macro-design variables and the micro-design variables after each update; If it is determined that the changes in the macro-design variables and the micro-design variables are less than a preset threshold, the current macro-design variables and the micro-design variables are used as the target macro-design variables and the target micro-design variables; Alternatively, the macro-design variables and the micro-design variables are updated using an MMA optimizer based on the sensitivity, and the number of iterations after each update is obtained; If it is determined that the number of iterations reaches a preset number, the current macro-design variables and micro-design variables are used as the target macro-design variables and target micro-design variables.

6. The method according to claim 5, characterized in that The calculating the sensitivity of the preset isogeometric topology optimization model includes: According to the formula: ； Calculate the sensitivity of the preset geometric topology optimization model; wherein the function is the objective function or global stress constraint function, the design variable is a macro design variable or a micro design variable, is the set of macro-units composed of control points in the macro-design domain or the set of micro-units composed of control points in the micro-design domain. is the relative density of cell j calculated directly from the control points, for The relative density of unit j after threshold projection, is the relative density of control point i.

7. A device for concurrent isogeometric topology optimization of multi-material microstructures and macrostructures, characterized in that: include: A model construction module is used to construct an initial isogeometric topology optimization model of the multi-material structure to be optimized based on the macro-design variables and micro-design variables of the multi-material structure to be optimized, with a global stress constraint function as a constraint condition, minimization of structural mass as an optimization goal, and von Mises stress at the unit center as a constraint condition; the equivalent yield strength of the micro-unit corresponding to the microstructure design domain is calculated by the QP relaxation method and the DMO interpolation method, and a global stress constraint function is constructed according to the equivalent yield strength of the micro-unit; the constraint conditions of the initial isogeometric topology optimization model are updated according to the global stress constraint function to construct a preset isogeometric topology optimization model of the multi-material structure to be optimized; wherein the global stress constraint function is constructed based on the equivalent yield strength of the micro-unit corresponding to the multi-material structure to be optimized; the global stress constraint function construction formula is: ； in, is the global stress constraint function, is the actual maximum stress, is the number of microscopic units, is the number of macro units, Expressed as The first macro unit The von Mises stress of a microscopic element, For the The equivalent yield strength of a micro-element, is the P norm value, C is the scaling factor, is the Young's modulus of the micro-element after DMO interpolation, is the unit matrix, is the strain-displacement matrix at the center of the micro-element, For the The displacement matrix of a microscopic unit under a given strain field is: is the strain vector at the center of the macro unit; a calculation and updating module, configured to calculate the sensitivity of the preset isogeometric topology optimization model, and update the macro-design variables and the micro-design variables using an MMA optimizer based on the sensitivity until a preset convergence condition is met, thereby obtaining target macro-design variables and target micro-design variables; The optimization design module is used to perform isogeometric topology optimization design on the multi-material structure to be optimized based on the target macro-design variables and the target micro-design variables.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the computer program, the method according to any one of claims 1 to 6 is implemented.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method according to any one of claims 1 to 6 is implemented.

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