CN114282421B - A superstructure optimization method, system and device - Google Patents

Abstract

The present invention provides a superstructure optimization method, system and device. In the method of this embodiment, the topological configuration of the superstructure is described by the material distribution of two physical materials and one virtual material, wherein the virtual material is used to describe the distribution of empty materials. The optimization target is dynamically adjusted by judging the basic material combination. When the materials are all physical materials, the first optimization process including the thermal expansion coefficient optimization process is set. When the materials are virtual materials, the second optimization process including the Poisson's ratio process is set. Thus, iterative optimization of the thermal expansion coefficient and Poisson's ratio of the superstructure to be optimized is achieved, thereby effectively solving the technical problem that the optimization method of the superstructure in the prior art mainly focuses on a single function, such as only being able to optimize the negative Poisson's ratio, resulting in the function of the optimized superstructure being too single.

Description

A superstructure optimization method, system and device

Technical Field

The present invention relates to the technical field of metamaterials, and in particular to a method, system and device for optimizing a metastructure.

Background Art

Superstructures are artificial structures with novel functions built from traditional materials. In recent years, typical superstructures such as left-handed structures, "invisibility cloaks" and perfect lenses have gradually emerged in the fields of mechanics, optics, communications and other applications. Their special properties mainly depend on the special configuration formed by the basic materials. A large number of electromagnetic superstructures, mechanical superstructures, acoustic superstructures, thermal superstructures and new structures based on the fusion of superstructures and conventional materials have emerged one after another, forming an important growth point for new materials and new structures.

Among them, for mechanical superstructures, Poisson's ratio and thermal expansion are two important basic parameters; negative Poisson's ratio materials expand laterally when stretched, and vice versa. This unique function can improve the structure's resistance to fracture, impact, sound absorption and other properties; the thermal expansion coefficient is a parameter that characterizes the dimensional change of a material when the temperature increases. Negative thermal expansion coefficient and zero expansion coefficient can suppress and eliminate structural deformation caused by temperature changes, and are widely needed in high-precision instruments and aerospace; currently, superstructure optimization methods mainly focus on single-function optimization, such as only being able to optimize the negative Poisson's ratio, resulting in the optimized superstructure having too single function and being unable to meet the complex environmental requirements of multi-field coupling of mechanical fields and temperature fields.

Summary of the invention

The present invention provides a superstructure optimization method, system and device for solving the technical problem that the superstructure optimization methods in the prior art mainly focus on a single function, such as only being able to optimize the negative Poisson's ratio, resulting in the function of the optimized superstructure being too single.

An embodiment of the present invention provides a superstructure optimization method, the method comprising:

Acquire a superstructure to be optimized, wherein the material distribution in the superstructure to be optimized includes a physical material Mat-1, a physical material Mat-2, and a virtual material Mat-3;

Establishing a loop optimization process and inputting the superstructure to be optimized into the loop optimization process for optimization to generate an optimized superstructure.

The cyclic optimization process is to combine any two of the physical material Mat-1, the physical material Mat-2 and the virtual material Mat-3 to generate three combinations, and optimize the superstructure to be optimized in turn according to the three combinations;

In a combination where all materials are solid materials, the superstructure to be optimized is subjected to n first optimization processes; in a combination where virtual materials are included, the superstructure to be optimized is subjected to m second optimization processes, and when the first optimization process and the second optimization process are completed on the superstructure to be optimized, an optimized superstructure is generated; the first optimization process includes performing a thermal expansion coefficient optimization process on the superstructure to be optimized, and the second optimization process includes performing a Poisson's ratio optimization process on the superstructure.

In some embodiments of the present application, the optimizing the superstructure to be optimized in sequence according to the three combinations specifically includes:

The three combinations are judged in turn as to whether all the materials are combinations of solid materials.

If yes, performing the first optimization process d times on the superstructure to be optimized to generate a superstructure subjected to the first optimization process;

If not, the superstructure to be optimized is subjected to second optimization processing e times to generate a superstructure subjected to second optimization processing; the optimization process of the three combinations is traversed, and each optimization is inputted with the result of the previous optimization;

The above optimization process is repeated k times, with n first optimization processes and m second optimization processes performed in total, to generate an optimized superstructure.

In some embodiments of the present application, obtaining the superstructure to be optimized includes:

Obtain a superstructure, wherein the superstructure includes a finite element model of Ne units, and for any unit e, its design variable is the relative density of the material ρ _e =[ρ _e1 ρ _e2 ρ _e3 ];

The superstructure to be optimized is obtained by optimizing the relative density of the materials of each unit superstructure.

In some embodiments of the present application, the step of optimizing the thermal expansion coefficient of the superstructure to be optimized includes:

Acquiring parameters of a basic material in the superstructure to be optimized, wherein the parameters include elastic modulus, Poisson's ratio, thermal expansion coefficient, volume constraint, and relative density of the material;

Processing the parameters of the superstructure to be optimized based on the first objective function to obtain the superstructure after the first optimization process;

Among them, in the combination where all materials are solid materials, the first objective function is to minimize the sum of squares of thermal expansion coefficients, and the first objective function is specifically:

Find: _ρea (e∈Ne)

in, is the thermal expansion coefficient of the superstructure in different directions, the initial value of i is 1, the subscript H represents the equivalent performance of the superstructure, _ve is the _volume of unit e, _Va ^* is _the maximum volume fraction of material a; _ρea is the value when a=1 in the material relative density matrix _ρe =[ _ρe1ρe2ρe3 ]; ft is the first objective function; fv is the constraint function.

In some embodiments of the present application, performing Poisson's ratio optimization processing on the superstructure includes:

Acquiring parameters of a basic material in the superstructure to be optimized, wherein the parameters include elastic modulus, Poisson's ratio, thermal expansion coefficient, volume constraint, and relative density of the material;

Based on the parameter optimization of the superstructure to be optimized, the Poisson's ratio of the superstructure to be optimized is optimized by a second objective function to obtain a superstructure after a second optimization process.

Among them, in the combination including the virtual material, the second objective function is the minimization of the square of Poisson's ratio, and the second objective function is specifically:

Find: _ρea (e∈Ne)

in, is the equivalent Poisson's ratio of the superstructure in different directions, the subscript H represents the equivalent performance of the superstructure, _ve is the _volume of unit e, _Va ^* is the maximum volume fraction of material a; _ρea is the value when a= ₁ in the material relative density matrix _ρe =[ _ρe1ρe2ρe3 ]; fp is the second objective function; fv is the constraint function.

In some embodiments of the present application, the first optimization process and the second optimization process both further include finite element analysis processing and sensitivity calculation processing.

In some embodiments of the present application, the finite element analysis process includes:

Acquire mechanical parameters of basic materials in the current superstructure, wherein the mechanical parameters include elastic modulus, Poisson's ratio and thermal expansion coefficient;

The mechanical parameters are processed based on the homogenization theory to obtain the equivalent Poisson's ratio of the current superstructure in different directions. And the equivalent thermal expansion coefficient of the current superstructure in different directions

In some embodiments of the present application, the sensitivity calculation process includes:

Obtain the results of the finite element analysis process, including the equivalent Poisson's ratio of the current superstructure in different directions Equivalent thermal expansion coefficient of the current superstructure in different directions Homogenized equivalent elastic tensor C ^H and equivalent thermal stress tensor β ^H ;

The result is processed according to the chain rule to obtain the sensitivity of the first objective function ft The sensitivity of the second objective function fp and the sensitivity of the volume constraint fv

An embodiment of the present invention further provides a superstructure optimization system, the system comprising:

An acquisition module, the acquisition module is used to acquire a super structure to be optimized, wherein the basic materials in the super structure to be optimized include a physical material Mat-1, a physical material Mat-2 and a virtual material Mat-3;

A generation module, the generation module is used to establish a loop optimization process and input the super structure to be optimized into the loop optimization process for optimization, thereby generating an optimized super structure.

The cyclic optimization process is to combine any two of the physical material Mat-1, the physical material Mat-2 and the virtual material Mat-3 to generate three combinations, and optimize the superstructure to be optimized in turn according to the three combinations;

In a combination where all materials are solid materials, the superstructure to be optimized is subjected to n first optimization processes; in a combination where virtual materials are included, the superstructure to be optimized is subjected to m second optimization processes, and when the first optimization process and the second optimization process are completed on the superstructure to be optimized, an optimized superstructure is generated; the first optimization process includes performing a thermal expansion coefficient optimization process on the superstructure to be optimized, and the second optimization process includes performing a Poisson's ratio optimization process on the superstructure.

An embodiment of the present invention provides a superstructure optimization device, including a processor and a memory;

The memory is used to store program code and transmit the program code to the processor;

The processor is used to execute the above-mentioned superstructure optimization method according to the instructions in the program code.

It can be seen from the above technical solutions that the embodiments of the present invention have the following advantages:

The embodiment of the present invention provides a superstructure optimization method, system and optimization device, the method comprising: obtaining a superstructure to be optimized, wherein the material distribution in the superstructure to be optimized includes a physical material Mat-1, a physical material Mat-2 and a virtual material Mat-3; establishing a cyclic optimization process and inputting the superstructure to be optimized into the cyclic optimization process for optimization to generate an optimized superstructure, wherein the cyclic optimization process combines any two of the physical material Mat-1, the physical material Mat-2 and the virtual material Mat-3 to generate three combinations, and sequentially optimizes the superstructure to be optimized according to the three combinations; in a combination in which the materials are all physical materials, the superstructure to be optimized is subjected to n times of first optimization processing; in a combination including virtual materials, the superstructure to be optimized is subjected to m times of second optimization processing, and when the first optimization processing and the second optimization processing are completed on the superstructure to be optimized, an optimized superstructure is generated; the first optimization processing includes performing thermal expansion coefficient optimization processing on the superstructure to be optimized, and the second optimization processing includes performing Poisson's ratio optimization processing on the superstructure.

In the method of the present embodiment, virtual materials are introduced on the basis of the basic materials in the superstructure to be optimized, so as to form three different combinations according to any two combinations of the physical material Mat-1, the physical material Mat-2 and the virtual material Mat-3. Among the three combinations, when the materials are all physical materials, the first optimization treatment including the thermal expansion coefficient optimization treatment is set, and when the materials are the combination including the virtual materials, the second optimization treatment including the Poisson's ratio treatment is set, thereby realizing the optimization of the thermal expansion coefficient and the Poisson's ratio of the superstructure to be optimized, thereby effectively solving the technical problem that the optimization method of the superstructure in the prior art mainly focuses on a single function, such as optimizing only the negative Poisson's ratio, resulting in the function of the optimized superstructure being too single.

BRIEF DESCRIPTION OF THE DRAWINGS

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

FIG1 is a method flow chart of a superstructure optimization method, system and device provided by an embodiment of the present invention.

FIG. 2 is a flowchart of a method, system, and device for optimizing a superstructure provided by an embodiment of the present invention.

FIG. 3 is a diagram of an initialization structure of a concave configuration of a superstructure optimization method, system, and device provided by an embodiment of the present invention.

FIG4 is a graph showing a zero Poisson's ratio & zero thermal expansion concave superstructure topology optimization process and an objective function variation curve of a superstructure optimization method, system and device provided by an embodiment of the present invention.

FIG. 5 is a diagram showing the first concave and chiral multifunctional superstructure topology optimization results of a superstructure optimization method, system, and device provided by an embodiment of the present invention.

FIG. 6 is a diagram showing the second concave and chiral multifunctional superstructure topology optimization results of a superstructure optimization method, system, and device provided by an embodiment of the present invention.

FIG. 7 is a diagram showing the topological optimization results of the third concave and chiral multifunctional superstructure of a superstructure optimization method, system and device provided by an embodiment of the present invention.

FIG8 is a diagram showing the fourth concave and chiral multifunctional superstructure topology optimization results of a superstructure optimization method, system, and device provided by an embodiment of the present invention.

FIG. 9 is a diagram showing the topological optimization results of the fifth concave and chiral multifunctional superstructure of a superstructure optimization method, system and device provided by an embodiment of the present invention.

FIG. 10 is a diagram showing the sixth concave and chiral multifunctional superstructure topology optimization results of a superstructure optimization method, system, and device provided by an embodiment of the present invention.

FIG. 11 is a diagram showing the seventh concave and chiral multifunctional superstructure topology optimization results of a superstructure optimization method, system, and device provided by an embodiment of the present invention.

FIG. 12 is a system configuration diagram of a superstructure optimization method, system, and device provided in an embodiment of the present invention.

FIG. 13 is a device framework diagram of a superstructure optimization method, system, and device provided in an embodiment of the present invention.

DETAILED DESCRIPTION

The embodiments of the present invention provide a superstructure optimization method, system and device for solving the technical problem that the superstructure optimization methods in the prior art mainly focus on a single function, such as optimizing only the negative Poisson's ratio, resulting in the function of the optimized superstructure being too single.

In order to make the purpose, features and advantages of the present invention more obvious and easy to understand, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the embodiments described below are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

Unless otherwise defined, all technical and scientific terms used in the embodiments of the present invention have the same meanings as those commonly understood by those skilled in the art of the technical field of the embodiments of the present invention. The terms used in the present invention are only for the purpose of describing specific embodiments and are not intended to limit the present invention.

Before further describing the embodiments of the present invention in detail, the nouns and terms involved in the embodiments of the present invention are described first. The nouns and terms involved in the embodiments of the present invention are subject to the following explanations.

Superstructures: Artificial structures with novel functions built from traditional materials.

Poisson's ratio: refers to the ratio of the absolute value of the lateral normal strain to the axial normal strain when the material is subjected to unidirectional tension or compression, also called the lateral deformation coefficient. It is an elastic constant that reflects the lateral deformation of the material. The Poisson's ratio of most natural materials is positive, which means that they expand laterally under pressure, while zero Poisson is lateral invariant under pressure, and negative Poisson expands laterally under pressure. Positive Poisson, negative Poisson and zero Poisson can adjust the deformation of structures under mechanical loads, and therefore are widely used in engineering.

Thermal expansion coefficient: the change in length caused by a unit temperature change; in most cases, this coefficient is positive; that is, the temperature change is proportional to the length change, and the volume expands as the temperature rises; while zero expansion means no deformation due to heat, and negative expansion means contraction due to heat. Positive thermal expansion, negative thermal expansion, and zero expansion can adjust the deformation of the structure under thermal field loads, so there is an urgent application demand in aerospace and high-precision instruments.

Direct design method: structural design method based on experience and inspiration.

Topology optimization: It is a mathematical method to optimize the material distribution in a given area according to given load conditions, constraints and performance indicators. It is a kind of structural optimization method.

Material properties generally refer to elastic modulus, thermal expansion coefficient, and Poisson’s ratio;

Please refer to FIG. 1 , which is a method flow chart of a superstructure optimization method, system, and device provided by an embodiment of the present invention.

As shown in FIG. 1-11 , the present invention provides a superstructure optimization method, the method comprising:

Acquire a superstructure to be optimized, wherein the material distribution in the superstructure to be optimized includes a physical material Mat-1, a physical material Mat-2, and a virtual material Mat-3;

Establishing a loop optimization process and inputting the superstructure to be optimized into the loop optimization process for optimization to generate an optimized superstructure.

The cyclic optimization process is to combine any two of the physical material Mat-1, the physical material Mat-2 and the virtual material Mat-3 to generate three combinations, and optimize the superstructure to be optimized in turn according to the three combinations;

In a combination where all materials are solid materials, the superstructure to be optimized is subjected to n first optimization processes; in a combination containing virtual materials, the superstructure to be optimized is subjected to m second optimization processes, and when the first optimization process and the second optimization process are completed on the superstructure to be optimized by traversing all material combinations, an optimized superstructure is generated; the first optimization process includes performing thermal expansion coefficient optimization process on the superstructure to be optimized, and the second optimization process includes performing Poisson's ratio optimization process on the superstructure.

In the method of this embodiment, the topological configuration of the superstructure is described by the material distribution of two physical materials and one virtual material, wherein the virtual material is used to describe the distribution of empty materials. By judging the basic material combination to dynamically adjust the optimization target, two materials are randomly selected to exist in three combinations. Among the three combinations, when the materials are all physical materials, it is set to perform the first optimization process including the thermal expansion coefficient optimization process, and when the combination includes virtual materials, it is set to perform the second optimization process including the Poisson's ratio process, thereby realizing the optimization of the thermal expansion coefficient and the Poisson's ratio of the superstructure to be optimized, thereby effectively solving the technical problem that the optimization method of the superstructure in the prior art mainly focuses on a single function, such as only optimizing the negative Poisson's ratio, resulting in the function of the optimized superstructure being too single.

The superstructure optimization method of this embodiment comprises the following steps:

S1: obtaining a superstructure to be optimized, wherein the material distribution in the superstructure to be optimized includes a physical material Mat-1, a physical material Mat-2, and a virtual material Mat-3;

The basic material distribution of the superstructure to be optimized includes two solid materials Mat-1 and Mat-2 with different thermal expansion coefficients and a virtual material Mat-3 representing an empty material, and the initial geometric features are established by setting the material distribution in the model;

Wherein, obtaining the superstructure to be optimized includes:

Obtain a superstructure, wherein the superstructure includes a finite element model of Ne units, and for any unit e, its design variable is the relative density of the material ρ _e =[ρ _e1 ρ _e2 ρ _e3 ];

The superstructure to be optimized is obtained by optimizing the relative density of the materials of each unit superstructure.

Specifically, the superstructure can be discretized using four-node planar units to form a finite element model containing Ne units. For any unit e, its design variable is the relative density of the material ρ _e = [ρ _e1 ρ _e2 ρ _e3 ]; by optimizing the relative density of the material of each unit, the design of superstructures with different performances, that is, the superstructure to be optimized, can be achieved. For example, in order to obtain a superstructure with a concave or chiral configuration, the initial material distribution in the design area needs to be set in advance to induce the corresponding geometric features, and the superstructure with a concave or chiral configuration can be achieved by modifying the relative density of the material of each unit in the optimized design area.

S2: Establishing a loop optimization process and inputting the superstructure to be optimized into the loop optimization process for optimization to generate an optimized superstructure.

The cyclic optimization process is to combine any two of the physical material Mat-1, the physical material Mat-2 and the virtual material Mat-3 to generate three combinations, and optimize the superstructure to be optimized in turn according to the three combinations;

In a combination where all materials are solid materials, the superstructure to be optimized is subjected to n first optimization processes; in a combination where virtual materials are included, the superstructure to be optimized is subjected to m second optimization processes, and when the first optimization process and the second optimization process are completed on the superstructure to be optimized, an optimized superstructure is generated; the first optimization process includes performing a thermal expansion coefficient optimization process on the superstructure to be optimized, and the second optimization process includes performing a Poisson's ratio optimization process on the superstructure.

This embodiment achieves the optimization of the thermal expansion coefficient and Poisson's ratio of the configuration including the concave and chiral superstructure, and the concave and chiral superstructure can be adjusted according to requirements.

The optimization method of this embodiment forms the alternating objective function of the alternating phase field method by introducing the virtual material mat-3. In the alternating phase field method, the optimization sub-problems of each cycle are the same, which will lead to convergence instability. Therefore, the method of this embodiment is to set different optimization targets according to the material combination in the establishment of each cycle optimization sub-problem in the alternating phase field method and the target method; if the materials of the current combination are all solid materials, the optimization target of the sub-problem is the thermal expansion coefficient, and if there is a virtual material in the current material combination, the optimization target of the sub-problem is the Poisson's ratio, thereby realizing the dual-functional coupling of the Poisson's ratio and the thermal expansion coefficient, and achieving the dual optimization effect of the Poisson's ratio and the thermal expansion coefficient of the superstructure.

For example, the material combination sets preset material a and preset material b, and substitutes any two of the physical material Mat-1, the physical material Mat-2, and the virtual material Mat-3 into the preset material a and the preset material b to form three combinations: (1) a = mat-1, b = mat-2, (2) a = mat-2, b = mat-3, and (3) a = mat-1, b = mat-3; among which, in the combination of (1) a = mat-1, b = mat-2, both the preset material a and the preset material b are physical materials, while in the combinations of (2) a = mat-2, b = mat-3 and (3) a = mat-1, b = mat-3, there is a virtual material in the preset material a and the preset material b. By combining the three combinations The two situations are divided into two cases: the preset material a and the preset material b are both physical materials and there is a virtual material in the preset material a and the preset material b, and they are processed separately. When there is a virtual material in the preset material a and the preset material b, the Poisson's ratio optimization processing is performed on the superstructure to be optimized. When the preset material a and the preset material b are both physical materials, the thermal expansion coefficient optimization processing is performed on the superstructure. All material combinations are traversed to perform a complete first optimization processing and a second optimization processing on the superstructure to be optimized, and an optimized superstructure with dual functional coupling of Poisson's ratio and thermal expansion coefficient can be obtained, thereby realizing dual functional coupling of Poisson's ratio and thermal expansion coefficient, and achieving dual optimization effect of Poisson's ratio and thermal expansion coefficient on the superstructure.

In some embodiments of the present application, the optimizing the superstructure to be optimized in sequence according to the three combinations specifically includes:

The three combinations are judged in turn as to whether all the materials are combinations of solid materials.

If yes, performing the first optimization process d times on the superstructure to be optimized to generate a superstructure subjected to the first optimization process;

If not, the superstructure to be optimized is subjected to second optimization processing e times to generate a superstructure subjected to second optimization processing; the optimization process of the three combinations is traversed, and each optimization is inputted with the result of the previous optimization;

The above optimization process is repeated k times, with n first optimization processes and m second optimization processes performed in total, to generate an optimized superstructure.

When the thermal expansion coefficient processing and the Poisson's ratio processing reach a certain number of times, that is, when k is 80-150 times, preferably 120 times, the superstructure will converge and gradually become stable from the beginning to the end.

This is achieved by setting up an inner and outer loop. For example, an inner loop is first constructed. According to the combination (1) a=mat-1, b=mat-2 in which all materials are solid materials, the superstructure to be optimized is first optimized d times. After the d times of first optimization are completed, the superstructure that has completed the d times of first optimization is subjected to e times of second optimization according to the combination (2) a=mat-2, b=mat-3 containing virtual materials, and then output. Then, according to the combination (3) a=mat-1, b=mat-3 containing virtual materials, the superstructure that has completed the e times of second optimization is subjected to e times of second optimization. After the e times of second optimization are completed and output, an inner loop process is formed here. The inner loop selects the first optimization process or the second optimization process in a sequential manner by judging whether the materials of the three combinations are all solid materials.

The outer loop is: judging whether the superstructure after the second optimization process e times has been processed by the inner loop k times, if not, returning to the combination of (1) a=mat-1, b=mat-2 according to the material being a solid material, firstly performing the first optimization process d times on the superstructure to be optimized and restarting, until the inner loop is completed g times, then the inner loop ends, thereby outputting the optimized superstructure. Wherein, d is 3-6 times, preferably 5 times, e is 2-5 times, preferably 3 times, and k is 80-150 times, preferably 120 times.

There are many ways to perform the first optimization process and the second optimization process respectively for two of the three combinations, which will not be listed here. It can be concluded through reasonable deduction that after these optimization processes, an optimized superstructure can be generated.

The first optimization process includes thermal expansion coefficient processing, and the thermal expansion coefficient optimization process for the superstructure to be optimized includes:

Acquiring parameters of a basic material in the superstructure to be optimized, wherein the parameters include elastic modulus, Poisson's ratio, thermal expansion coefficient, volume constraint, and relative density of the material;

Processing the parameters of the superstructure to be optimized based on the first objective function to obtain the superstructure after the first optimization process;

Among them, in the combination where all materials are solid materials, the first objective function is a function related to the thermal expansion coefficient. Taking the optimization of zero thermal expansion coefficient as an example, the first objective function is to minimize the sum of squares of thermal expansion coefficients. The first objective function is specifically:

Find: _ρea (e∈Ne)

in, is the thermal expansion coefficient of the superstructure in different directions (different directions include horizontal and vertical directions), the initial value of i is 1, the subscript H represents the equivalent performance of the superstructure, _ve is _the volume of unit e, _Va ^* is the maximum volume fraction of material a; _ρea is the value when a=1 in the material relative density matrix _ρe =[ _{ρe1ρe2ρe3 ]} ; ft is the first objective function; fv is the constraint function;

The thermal expansion coefficient that can be optimized by the first objective function is used to adjust the relative density matrix ρ _e =[ρ _e1 ρ _e2 ρ _e3 ] of the superstructure to be optimized, so as to optimize the thermal expansion coefficient of the superstructure to be optimized;

When the thermal expansion coefficient is non-zero, the above formula may be modified accordingly.

The second optimization process includes Poisson's ratio processing, and the Poisson's ratio optimization process performed on the superstructure includes:

Acquiring parameters of a basic material in the superstructure to be optimized, wherein the parameters include elastic modulus, Poisson's ratio, thermal expansion coefficient, volume constraint, and relative density of the material;

Based on the parameter optimization of the superstructure to be optimized, the Poisson's ratio of the superstructure to be optimized is optimized by a second objective function to obtain a superstructure after a second optimization process.

Among them, in the combination including virtual materials, the second objective function is a function related to Poisson's ratio. Taking zero Poisson's ratio optimization as an example, the second objective function is the minimization of the square of Poisson's ratio. The second objective function is specifically:

Find: _ρea (e∈Ne)

in, is the equivalent Poisson's ratio of the superstructure in different directions (the different directions include horizontal and vertical directions), the subscript H represents the equivalent performance of the superstructure, _ve is _the volume of _unit e, _Va ^* is the maximum volume fraction of material a; _ρea is the value when a=1 in the material relative density matrix _ρe =[ _ρe1ρe2ρe3 ]; fp is the second objective function; and fv is the constraint function.

The optimized Poisson's ratio can be obtained through the second objective function, so as to adjust the relative density matrix ρ _e =[ρ _e1 ρ _e2 ρ _e3 ] of the superstructure to be optimized, so as to optimize the Poisson's ratio of the superstructure to be optimized.

When the Poisson's ratio is non-zero, the above formula may be modified accordingly.

Among them, the thermal expansion coefficient of the superstructure in different directions in the first optimization process of n times is The sensitivity of the first objective function ft and the sensitivity of the volume constraint fv All of them need to be actually obtained according to the currently optimized superstructure; similarly, the equivalent Poisson's ratio of the current superstructure in different directions The sensitivity of the second objective function fp and the sensitivity of the volume constraint fv It is also based on the actual results of the currently optimized superstructure. For the thermal expansion coefficient of the current superstructure in different directions And the equivalent Poisson's ratio of the current superstructure in different directions The sensitivity of the first objective function ft is obtained through finite element analysis. The sensitivity of the second objective function fp and the sensitivity of the volume constraint fv is obtained through sensitivity; that is, the first optimization process and the second optimization process both include finite element analysis and sensitivity calculation;

Each time the thermal expansion coefficient is optimized, it is necessary to perform finite element analysis and sensitivity calculation to obtain the thermal expansion coefficient of the current superstructure in different directions. Sensitivity of the first objective function ft and the sensitivity of the volume constraint fv In the process of substituting the above-mentioned thermal expansion coefficient optimization processing, the optimization process of the first objective function is realized, that is, if the thermal expansion coefficient optimization processing is n times, the finite element analysis processing and sensitivity calculation processing need to be performed n times;

Similarly, each time the Poisson's ratio optimization process is performed, it is necessary to calculate the equivalent Poisson's ratio of the current superstructure in different directions through finite element analysis and sensitivity calculation. The sensitivity of the second objective function fp and the sensitivity of the volume constraint fv In the process of substituting the above Poisson's ratio optimization processing, the optimization process of the second objective function is realized, that is, if the Poisson's ratio optimization processing is performed m times, then m times of finite element analysis processing and sensitivity calculation processing need to be performed.

Wherein, the finite element analysis process includes:

Acquire mechanical parameters of basic materials in the current superstructure, wherein the mechanical parameters include elastic modulus, Poisson's ratio and thermal expansion coefficient;

The mechanical parameters are processed based on the homogenization theory to obtain the equivalent Poisson's ratio of the current superstructure in different directions. And the equivalent thermal expansion coefficient of the current superstructure in different directions

Specifically, firstly, the relationship between the material properties (mechanical parameters) of the superstructure and the variable ρ _ea is established based on the SIMP material interpolation function, and the formula is as follows:

in is the elastic modulus of any base material m and is the thermal expansion coefficient of any base material m; p is the penalty function, generally ranging from 3 to 5. Note that the sum of the relative densities of the unit materials should be 1, that is:

Then, based on the homogenization theory, the equivalent Poisson's ratio of the current superstructure in different directions is solved in turn: Equivalent thermal expansion coefficient of the current superstructure in different directions Homogenized equivalent elastic tensor ^CH and equivalent thermal stress tensor ^βH :

(a) Homogenized equivalent elastic tensor ^CH :

Taking the two-dimensional problem as an example, |Y| is the area of the superstructure; i, j, k, l = 1, 2, ..., d represents the index vector; is the initial independent unit unit strain vector, including the horizontal direction Vertical direction and shear direction is the unknown strain field generated in the microstructure under the action of the initial strain, which can be solved based on the linear elastic equilibrium equation:

Where v is the virtual displacement field.

(b) Equivalent Poisson’s ratio of the current superstructure in different directions

(c) Equivalent thermal stress tensor β ^H

Where τ _pq is the applied heat load; is the unit cell strain field under unit thermal load, and by solving the linear elastic equilibrium equation, we can get:

Where v is the virtual displacement field.

(d) Equivalent thermal expansion coefficient of the current superstructure in different directions

The sensitivity calculation process includes:

Obtain the results of the finite element analysis process, including the equivalent Poisson's ratio of the current superstructure in different directions Equivalent thermal expansion coefficient of the current superstructure in different directions Homogenized equivalent elastic tensor C ^H and equivalent thermal stress tensor β ^H ;

The result is processed according to the chain rule to obtain the sensitivity of the first objective function ft The sensitivity of the second objective function fp and the sensitivity of the volume constraint fv

Specifically, as described above, the materials are defined as preset material a and preset material b. For the process of Poisson's ratio optimization or thermal expansion coefficient optimization, the material properties are obtained by the variable density method interpolation form based on the SIMP material interpolation function.

in, is the elastic modulus of the preset material a, is the thermal expansion coefficient of material a, is the elastic modulus of the preset material b, is the thermal expansion coefficient of the preset material b, p is the penalty parameter (ranging from 1 to 5); based on the homogenization theory, for the variable ρ _ea , the equivalent elastic modulus and the equivalent thermal stress tensor sensitivity The sensitivities are:

in, and The sensitivity is calculated by the material interpolation formula Eq:

Finally, the objective function ft sensitivity Sensitivity of fp and the sensitivity of the volume constraint fv We can get:

Where _ve is the volume of the e-th unit and the volume of all units in V.

Among them, according to the finite element analysis and sensitivity calculation results of the inner loop, the design variable ρ _ea is updated, and the algorithm operation is terminated when the convergence condition is met, and the optimized superstructure is output.

Specifically, the variables can be updated by the moving asymptote method, and when the convergence judgment condition is reached, the topology optimization design results are output.

Based on the method of this embodiment, the specific implementation is as follows:

Example 1:

In this example, two common engineering plastics PVA are used as the solid material mat-1 and Nylon is used as the solid material mat-2 (material properties are shown in Table 1) to design an inward-concave zero Poisson's ratio and zero thermal expansion multifunctional superstructure.

Table 1 Engineering material PVA, Nylon material properties

First, a multi-material topology optimization model is established, with the basic materials being PVA, Nylon, and the set virtual materials, represented by dark, light, and white, respectively. The initial geometric features are established by setting the material distribution within the model, as shown in Figure 3;

As shown in FIG4 , the above-mentioned superstructure optimization method is executed. Under the drive of the zero Poisson's ratio objective function (second objective function), the complex concave geometric configuration gradually appears when the Poisson's ratio optimization process is executed as described above; under the drive of the zero thermal expansion objective function (first objective function), the material distribution changes; as the optimization process progresses, the structural geometric configuration gradually becomes clear, and the isolated and disconnected material distribution is suppressed and eliminated; when n and m are both about 60; out is the number of steps completed by n and m at the same time, the first objective function and the second objective function gradually become stable, the structural configuration gradually becomes stable, and almost no changes occur, and the convergence condition is reached and terminated; the Poisson's ratio value of the superstructure generated by topology optimization is 0.057, and the thermal expansion coefficient is -0.571ppm/℃. It can be seen that by adopting the superstructure optimization method proposed in this embodiment, the optimization of near-zero superstructure can be achieved by using two common materials with different properties.

Example 2

By executing the Poisson's ratio optimization processing and thermal expansion optimization processing in the above optimization method, the topological optimization of various combination functions of Poisson's ratio and thermal expansion coefficient is realized. The optimization results include concave configuration and chiral configuration. The functional combinations include: negative Poisson's ratio & negative thermal expansion, negative Poisson's ratio & positive thermal expansion, positive Poisson's ratio & negative thermal expansion, positive Poisson's ratio & positive thermal expansion, etc., as shown in the following table. Poisson's ratio (PR) is a dimensionless value, and the unit of thermal expansion coefficient (CTE) is ppm/℃.

Table 2 Topology optimization results of concave and chiral multifunctional superstructures

As shown in FIG12 , this embodiment also provides a superstructure optimization system, the system comprising the following modules:

An acquisition module 201, the acquisition module 201 is used to acquire a super structure to be optimized, wherein the basic materials in the super structure to be optimized include a physical material Mat-1, a physical material Mat-2 and a virtual material Mat-3;

A generation module 202 is used to establish a loop optimization process and input the super structure to be optimized into the loop optimization process for optimization, thereby generating an optimized super structure.

The cyclic optimization process is to combine any two of the physical material Mat-1, the physical material Mat-2 and the virtual material Mat-3 to generate three combinations, and optimize the superstructure to be optimized in turn according to the three combinations;

In a combination where all materials are solid materials, the superstructure to be optimized is subjected to n first optimization processes; in a combination containing virtual materials, the superstructure to be optimized is subjected to m second optimization processes, and all material combinations are traversed to complete the first optimization process and the second optimization process on the superstructure to be optimized, thereby generating an optimized superstructure; the first optimization process includes performing thermal expansion coefficient optimization process on the superstructure to be optimized, and the second optimization process includes performing Poisson's ratio optimization process on the superstructure.

Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working processes of the systems, devices and units described above can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

As shown in FIG13 , this embodiment further provides a superstructure optimization device, the device comprising a processor 300 and a memory 301 ;

The memory 301 is used to store program code 302 and transmit the program code 302 to the processor;

The processor 300 is used to execute the steps in the above-mentioned superstructure optimization method according to the instructions in the program code 302 .

Exemplarily, the computer program 302 may be divided into one or more modules/units, which are stored in the memory 301 and executed by the processor 300 to complete the present application. The one or more modules/units may be a series of computer program instruction segments capable of completing specific functions, which are used to describe the execution process of the computer program 302 in the terminal device 30.

The terminal device 30 may be a computing device such as a desktop computer, a notebook, a PDA, a cloud server, etc. The terminal device may include, but not limited to, a processor 300 and a memory 301. Those skilled in the art may understand that FIG. 5 is only an example of the terminal device 30 and does not constitute a limitation on the terminal device 30. The terminal device 30 may include more or fewer components than shown in the figure, or may combine certain components, or different components. For example, the terminal device may also include input and output devices, network access devices, buses, etc.

The processor 300 may be a central processing unit (CPU), other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor, etc.

The memory 301 may be an internal storage unit of the terminal device 30, such as a hard disk or memory of the terminal device 30. The memory 301 may also be an external storage device of the terminal device 30, such as a plug-in hard disk, a smart memory card (SmartMediaCard, SMC), a secure digital (SecureDigital, SD) card, a flash card (FlashCard), etc. equipped on the terminal device 30. Further, the memory 301 may also include both an internal storage unit of the terminal device 30 and an external storage device. The memory 301 is used to store the computer program and other programs and data required by the terminal device. The memory 301 may also be used to temporarily store data that has been output or is to be output.

Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working processes of the systems, devices and units described above can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

In the several embodiments provided in the present application, it should be understood that the disclosed systems, devices and methods can be implemented in other ways. For example, the device embodiments described above are only schematic. For example, the division of the units is only a logical function division. There may be other division methods in actual implementation, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be an indirect coupling or communication connection through some interfaces, devices or units, which can be electrical, mechanical or other forms.

The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

In addition, each functional unit in each embodiment of the present invention may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit. The above-mentioned integrated unit may be implemented in the form of hardware or in the form of software functional units.

If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention is essentially or partly contributed to the prior art or all or part of the technical solution can be embodied in the form of a software product, and the computer software product is stored in a storage medium, including a number of instructions to enable a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk and other media that can store program codes.

As described above, the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features thereof may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims (9)

1. A method of optimizing a superstructure, the method comprising:

acquiring a super structure to be optimized, wherein the material distribution in the super structure to be optimized comprises a physical material Mat-1, a physical material Mat-2 and a virtual material Mat-3;

Establishing a cyclic optimization flow, inputting the superstructure to be optimized into the cyclic optimization flow for optimization to generate an optimized superstructure,

The cyclic optimization flow is formed by combining any two of a physical material Mat-1, a physical material Mat-2 and a virtual material Mat-3 to generate three combinations, and optimizing the superstructure to be optimized according to the three combinations in sequence;

In the combination that the materials are solid materials, carrying out first optimization treatment on the super structure to be optimized n times; in the combination containing virtual materials, the super structure to be optimized is subjected to m times of second optimization processing, and when the first optimization processing and the second optimization processing are completed on the super structure to be optimized, an optimized super structure is generated; the first optimization processing comprises thermal expansion coefficient optimization processing on the super structure to be optimized, and the second optimization processing comprises poisson ratio optimization processing on the super structure;

The optimizing processing of the to-be-optimized superstructure according to the three combinations in turn specifically comprises:

sequentially and respectively judging whether the materials are all combinations of solid materials or not for the three combinations,

If yes, performing d times of first optimization processing on the superstructure to be optimized, and generating a first optimized superstructure;

if not, performing e times of second optimization processing on the superstructure to be optimized, and generating a superstructure subjected to the second optimization processing; traversing the optimization processes of three combinations, wherein each optimization takes the previous optimization result as input;

and (3) circulating the optimization process k times, and carrying out n times of first optimization processing and m times of second optimization processing, so as to generate an optimized superstructure.

2. The method for optimizing a superstructure according to claim 1, wherein said obtaining a superstructure to be optimized comprises:

obtaining a superstructure, wherein the superstructure comprises a finite element model of Ne units, for any one

Italian unit e, the design variable of which is the relative density ρ _e＝[ρ_e1 ρ_e2 ρ_e3 of the material;

And obtaining the super structure to be optimized by optimizing the material relative density of the super structure of each unit.

3. The method for optimizing a superstructure according to claim 2, wherein said performing a thermal expansion coefficient optimization process on said superstructure to be optimized comprises:

Obtaining parameters of a base material in the super structure to be optimized, wherein the parameters comprise elastic modulus, poisson ratio, thermal expansion coefficient, volume constraint and relative material density;

Processing parameters of the superstructure to be optimized based on a first objective function, and obtaining a first optimized superstructure;

Wherein, in the combination that the materials are solid materials, the first objective function is a function related to the thermal expansion coefficient, specifically, the minimization of the sum of squares of the thermal expansion coefficients may be:

Find:ρ_ea(e∈Ne)

min:

s.t.:

wherein, For the thermal expansion coefficients of the super structure in different directions, the initial value of i is 1, the angle sign H represents the equivalent performance of the super structure, V _e is the volume of the unit e, and V _a ^* is the maximum volume fraction of the material a; ρ _ea is the value of a=1 in the relative density matrix ρ _e＝[ρ_e1 ρ_e2 ρ_e3 of the material; ft is a first objective function; fv is a constraint function.

4. The method of claim 1, wherein said poisson's ratio optimization of said superstructure comprises:

Obtaining parameters of a base material in the super structure to be optimized, wherein the parameters comprise elastic modulus, poisson ratio, thermal expansion coefficient, volume constraint and relative material density;

optimizing the Poisson's ratio of the superstructure to be optimized through a second objective function based on the parameter optimization of the superstructure to be optimized, obtaining a superstructure after a second optimization process,

Wherein, in the combination containing the virtual material, the second objective function is a poisson ratio related function, and specifically may be a minimization of poisson ratio square:

Find:ρ_ea(e∈Ne)

min:

s.t.:

wherein, For the equivalent poisson ratio of the superstructure in different directions, the angle sign H represents the equivalent performance of the superstructure, V _e is the volume of the unit e, and V _a ^* is the maximum volume fraction of the material a; ρ _ea is the value of a=1 in the relative density matrix ρ _e＝[ρ_e1 ρ_e2 ρ_e3 of the material; fp is the second objective function; fv is a constraint function.

5. The method of claim 1, wherein the first optimization process and the second optimization process each further comprise a finite element analysis process and a sensitivity calculation process.

6. The method of claim 5, wherein the finite element analysis process comprises:

Obtaining the mechanical parameters of a base material in the current super structure, wherein the mechanical parameters comprise elastic modulus, poisson ratio and thermal expansion coefficient;

based on a homogenization theory, the mechanical parameters are processed to obtain equivalent Poisson ratios of the current superstructure in different directions Equivalent thermal expansion coefficients of current superstructures in different directions

7. The method of optimizing a superstructure according to claim 6, wherein said sensitivity calculation process comprises:

Obtaining a result of finite element analysis processing, the result comprising equivalent poisson ratios of the current superstructure in different directions Equivalent thermal expansion coefficients of current superstructures in different directionsHomogenizing the equivalent elastic tensor C ^H and the equivalent thermal stress tensor β ^H;

Processing the result according to the chain rule to obtain the sensitivity of the first objective function ft Sensitivity of the second objective function fpSensitivity of volume constraint fv

8. A system for optimizing a superstructure, said system comprising:

The acquisition module is used for acquiring a super structure to be optimized, and the basic materials in the super structure to be optimized comprise a physical material Mat-1, a physical material Mat-2 and a virtual material Mat-3;

The generation module is used for establishing a circulation optimization flow and inputting the superstructure to be optimized into the circulation optimization flow for optimization to generate an optimized superstructure,

The cyclic optimization flow is formed by combining any two of a physical material Mat-1, a physical material Mat-2 and a virtual material Mat-3 to generate three combinations, and optimizing the superstructure to be optimized according to the three combinations in sequence;

In the combination that the materials are solid materials, carrying out first optimization treatment on the super structure to be optimized n times; in the combination containing virtual materials, the super structure to be optimized is subjected to m times of second optimization processing, and when the first optimization processing and the second optimization processing are completed on the super structure to be optimized, an optimized super structure is generated; the first optimization processing comprises thermal expansion coefficient optimization processing on the super structure to be optimized, and the second optimization processing comprises poisson ratio optimization processing on the super structure;

The optimizing processing of the to-be-optimized superstructure according to the three combinations in turn specifically comprises:

sequentially and respectively judging whether the materials are all combinations of solid materials or not for the three combinations,

If yes, performing d times of first optimization processing on the superstructure to be optimized, and generating a first optimized superstructure;

if not, performing e times of second optimization processing on the superstructure to be optimized, and generating a superstructure subjected to the second optimization processing; traversing the optimization processes of three combinations, wherein each optimization takes the previous optimization result as input;

and (3) circulating the optimization process k times, and carrying out n times of first optimization processing and m times of second optimization processing, so as to generate an optimized superstructure.

9. A super-structure optimizing device, comprising a processor and a memory;

the memory is used for storing program codes and transmitting the program codes to the processor;

The processor is configured to execute a method of optimizing a superstructure according to any one of claims 1-7 according to instructions in the program code.