Structural topology optimization method and apparatus

Abstract

The embodiment of the application discloses a structural topology optimization method and device, pseudo densities of each unit in a design domain are obtained based on a variable field of the design domain of a target structure; the pseudo density is used for describing whether the corresponding unit is a void; a maximum displacement in displacements of each node in a first specified area of the target structure is minimized as a target, and values of the variable field in the design domain are optimized under a plurality of constraint conditions; the node in the first specified area at least includes a vertex of each unit in the first specified area; the displacement of each node in the first specified area is determined based on the pseudo density of each unit in the design domain, and a material property related to temperature of each unit in the design domain and an association relationship between the material property and the temperature. The application considers the material property related to temperature in the process of topology optimization of the structure, optimizes the topology configuration of the structure working under a large temperature gradient, and the optimized topology structure is suitable for an environment with a large temperature gradient.

Description

Technical Field

[0001] This application relates to the field of engineering structural design technology, and more specifically, to a structural topology optimization method and apparatus. Background Technology

[0002] With the rapid development of the aerospace industry, thermal structures capable of withstanding higher temperatures and larger temperature gradients than conventional thermal structures have been widely used in high-speed aircraft. For example, according to the literature "Hyper-X hot structures design and comparison with flight data," the temperature range of the vertical tail fin of a Mach 7 aircraft can range from -12°C to 1163°C. In such cases, the physical and mechanical properties of materials such as alloys change significantly with temperature.

[0003] Structural topology optimization techniques have become the most effective tool for lightweight and performance design in engineering fields such as aerospace. However, thermal structures obtained based on existing structural topology optimization methods are only suitable for environments with small temperature gradients and cannot be applied to environments with large temperature gradients. Summary of the Invention

[0004] The purpose of this application is to provide a structural topology optimization method and apparatus, including the following technical solutions: A structural topology optimization method, the method comprising: The pseudo-density of each element within the design domain is obtained from the variable field of the design domain based on the target structure. Different variables in the variable field correspond to different elements of the design domain. The pseudo-density is used to describe whether the corresponding element is void. With the goal of minimizing the maximum displacement among the displacements of each node within the first specified region of the target structure, the values ​​of the variable field within the design domain are optimized under multiple constraints; the nodes within the first specified region include at least the vertices of each element within the first specified region. The displacement of each node within the first designated area is determined based on the pseudo density of each element within the design domain, the temperature-related material properties of each element within the design domain, and the correlation between the material properties and temperature. The multiple constraints include: When a heat flux is applied within the non-design domain of the target structure, the maximum temperature of each node in the second specified region of the target structure is less than or equal to a temperature threshold. The weighted sum of the volumes of all units within the design domain is less than or equal to a volume threshold, which is the product of a volume fraction threshold and the volume of the design domain. The variables in the variable field are greater than zero and less than or equal to 1.

[0005] Optionally, the temperature-related material properties mentioned above include: thermal conductivity, Young's modulus, Poisson's ratio, and coefficient of linear expansion.

[0006] Optionally, the process of determining the displacement of each node in the first specified region based on the pseudo-density of each element within the design domain, the temperature-related material properties of each element within the design domain, and the correlation between the material properties and temperature includes: The fundamental equations for the problem of heat conduction The solution is performed to obtain the temperature of each node of the target structure, where: This is a temperature vector composed of the temperatures of all nodes of the target structure; P For thermal load; Representation unit e Temperature; Representation unit e The thermal conductivity matrix; Indicates the number of units in the target structure; V e Representation unit e Volume; Representation unit e The gradient matrix of the shape function; T, as a superscript, denotes the matrix transpose operation; Representation unit e The thermal conductivity coefficient, through the... The first material interpolation process is performed to obtain the result. Representation unit e Solid materials at a temperature of Thermal conductivity coefficient at that time; Is with Column vectors of the same dimension are only related to the cell. e The element values ​​corresponding to each node are set to Other elements are set to zero. For unit e The number of nodes; Based on the temperature of each unit, as well as the pre-established functional relationship between the linear expansion coefficient and temperature, and the functional relationship between the elastic matrix and temperature, the linear expansion coefficient and elastic matrix of the solid material of each unit are obtained. Based on the elasticity matrix of the solid material of each unit and the stiffness matrix of the target structure. The stiffness matrix of the target structure is obtained by calculating the formula, and the formula for calculating the stiffness matrix is ​​as follows:

[0007] in, Representation unit e The stiffness matrix; Representation unit e The strain-displacement matrix; Representation unit e The elasticity matrix, through the... The result is obtained by performing a second material interpolation process; This indicates that the solid material is at a temperature of The elasticity matrix at that time; Based on the mechanical load and the thermal stress load caused by the temperature field, as well as the stiffness matrix of the target structure, the fundamental equations of the elasticity problem are solved to obtain the displacements of each node of the target structure; the fundamental equations of the elasticity problem are:

[0008] in, This represents the displacement vector formed by the displacements of each node of the target structure; This indicates a preset mechanical load; Indicates thermal stress load; Representation unit e Thermal stress load; , This is the reference temperature for material properties; This is a preset constant vector.

[0009] The above methods are optional, wherein, The formula for the first material interpolation process can be expressed as:

[0010] And / or, The formula for the second material interpolation process can be expressed as:

[0011] in, Representation unit e The pseudo-density; , , All of these are penalty factors.

[0012] Optionally, the process of optimizing the values ​​of the variable field within the design domain in the above method includes: Each time the displacement of each node in the first specified region is obtained, a first smooth approximation function representing the first maximum value function of the displacement of each node in the first specified region is obtained, and a second smooth approximation function representing the second maximum value function of the temperature of each node in the second specified region is obtained. The first smooth approximation function is:

[0013] The second smooth approximation function is:

[0014] in, , All are smooth approximation parameters; It is the set of nodes within the first specified region; It is a diagonal matrix, with only the diagonal elements corresponding to the target degrees of freedom of the selected nodes set to 1, and the rest set to 0; It is the set of nodes within the second specified region; This is the upper bound of the temperature constraint; The first sensitivity of the first smooth approximation function and the second sensitivity of the second smooth approximation function are derived using the adjoint method. The variables of each unit within the design domain are updated based on the first sensitivity and the second sensitivity.

[0015] Optionally, the process of deriving the first sensitivity of the first smooth approximation function using the adjoint method as described above includes: The first sensitivity of the first smooth approximation function is derived using the following formula:

[0016] Wherein, the adjoint vector and The following two adjoint equations are obtained:

[0017] in, .

[0018] Optionally, the process of deriving the second sensitivity of the second smooth approximation function using the adjoint method as described above includes: The second sensitivity of the second smooth approximation function is derived using the following formula:

[0019] Wherein, the adjoint vector The following adjoint equations were obtained by solving them using a solver: .

[0020] Optionally, in the process of optimizing the values ​​of the variable field within the design domain, the above method may be implemented. After each preset number of iterations, the penalty factor is increased. The value of the penalty factor is taken up to the value of the penalty factor. The first preset value has been reached; Each pair of the penalty factors An update is performed, and after a second preset number of iterations, the penalty factor is increased. The value of the penalty factor is taken up to the value of the penalty factor. The second preset value is reached; the second preset number of times is less than the first preset number of times. When the penalty factor After reaching the first preset value, and after a third preset number of iterations, the penalty factor is... Increase to the third preset value.

[0021] Optionally, in the process of optimizing the values ​​of the variable field within the design domain, the above method may be implemented. After each fourth preset number of iterations, the temperature threshold value is reduced until the temperature threshold value reaches the fourth preset value.

[0022] A structural topology optimization device, the device comprising: The pseudo-density acquisition module is used to obtain the pseudo-density of each element in the design domain based on the variable field of the design domain of the target structure. Different variables in the variable field correspond to different elements in the design domain. The pseudo-density is used to describe whether the corresponding element is void. The optimization module is used to optimize the values ​​of the variable field in the design domain under multiple constraints, with the goal of minimizing the maximum displacement among the displacements of each node in the first specified region of the target structure; the nodes in the first specified region include at least the vertices of each element in the first specified region. The displacement of each node within the first designated area is determined based on the pseudo density of each element within the design domain, the temperature-related material properties of each element within the design domain, and the correlation between the material properties and temperature. The multiple constraints include: When a heat flux is applied within the non-design domain of the target structure, the maximum temperature of each node in the second specified region of the target structure is less than or equal to a temperature threshold. The weighted sum of the volumes of all units within the design domain is less than or equal to a volume threshold, which is the product of a volume fraction threshold and the volume of the design domain. The variables in the variable field are greater than zero and less than or equal to 1.

[0023] An electronic device, comprising: Memory, used to store programs; A processor is configured to invoke and execute the program in the memory, thereby implementing the various steps of the structural topology optimization method as described in any of the preceding claims.

[0024] A readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the structural topology optimization method as described in any of the preceding claims.

[0025] As can be seen from the above scheme, the structural topology optimization method and apparatus provided in this application obtains the pseudo-density of each element in the design domain based on the variable field of the design domain of the target structure. Different variables in the variable field correspond to different elements in the design domain. The pseudo-density is used to describe whether the corresponding element is void. With the goal of minimizing the maximum displacement among the displacements of each node in the first specified region of the target structure, the values ​​of the variable field in the design domain are optimized under multiple constraints. The nodes in the first specified region include at least the vertices of each element in the first specified region. The displacements of each node in the first specified region are determined based on the pseudo-density of each element in the design domain, the temperature-related material properties of each element in the design domain, and the correlation between the material properties and temperature. The above-mentioned multiple constraints include: when a heat flux is applied in the non-design domain of the target structure, the maximum temperature of each node in the second specified region of the target structure is less than or equal to a temperature threshold; the weighted sum of the volumes of each element in the design domain is less than or equal to a volume threshold, and the volume threshold is the product of the volume fraction threshold and the volume of the design domain; the variables in the variable field are greater than zero and less than or equal to 1. This application considers temperature-related material properties during the topology optimization process, thereby optimizing the topology of the structure operating under large temperature gradients, making the optimized topology suitable for environments with large temperature gradients. Attached Figure Description

[0026] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0027] Figure 1 This is a flowchart illustrating an implementation of the structural topology optimization method provided in an embodiment of this application. Figure 2 An example diagram of the target structure provided in the embodiments of this application; Figure 3 A flowchart illustrating an implementation of this application for determining the displacement of each node within a first specified region based on the pseudo density of each element within the design domain, the temperature-related material properties of each element within the design domain, and the correlation between the material properties and temperature. Figure 4 A flowchart illustrating another implementation of the structural topology optimization method provided in this application embodiment; Figure 5 Examples of four optimization results obtained by applying four temperature constraints to the same structure, provided for embodiments of this application; Figure 6 The embodiments provided in this application are based on Figure 5 The iterative curves for topology optimization under different temperature constraints are shown. Figure 7 This is a schematic diagram of a topology optimization device provided in an embodiment of this application; Figure 8 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application.

[0028] The terms “first,” “second,” “third,” “fourth,” etc. (if present) in the specification, claims, and accompanying drawings are used to distinguish similar parts and are not necessarily used to describe a specific order or sequence. It should be understood that such use of data can be interchanged where appropriate so that the embodiments of this application described herein can be implemented in a sequence other than that illustrated herein. Detailed Implementation

[0029] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0030] This application introduces temperature-dependent material properties (TDMPs) during the topology optimization process, such as thermal conductivity. Young's modulus E Poisson's ratio v and coefficient of linear expansion wait.

[0031] like Figure 1 The diagram shown is a flowchart of one implementation of the structural topology optimization method provided in this application, which may include: Step S101: Obtain the pseudo-density of each element within the design domain based on the variable field of the design domain of the target structure. Different variables in the variable field correspond to different elements in the design domain; the pseudo-density is used to describe whether the corresponding element is void.

[0032] like Figure 2 The diagram shown is an example of a target structure provided in an embodiment of this application. In this example, the target structure is a rectangular plate with a length of 1.5m, a width of 0.5m, and a thickness of 0.01m. Figure 2 The application scenario of the target structure shown is as follows: the left edge of a rectangular plate is clamped and fixed, and the right edge is subjected to three uniformly distributed shear forces F1=F2=F3=50kN. A 0.01m × 0.08m region located at the center of the right edge (i.e., the black rectangular region on the right edge) is designated as the non-designable region (denoted as the non-design domain), and the other regions are the design domain. A heat flux is set on the right side of the non-designable region. q =10kW / m 2 The temperature of the left clamping edge is set to T 0 = 25℃.

[0033] This application divides the design domain and non-design domain of the target structure into finite element meshes to obtain several rectangular meshes. Each mesh is an element, and each element in the design domain corresponds to a design variable. All variables in the design domain constitute a variable field.

[0034] Optionally, for any element within the design domain, the pseudo-density of that element can be calculated using the variables and volumes of elements within the target region centered on that element. As an example, the elements within the design domain can be determined based on the following formula. i ( i =1, 2, 3, ... n d ; n d The pseudo-density (which is the total number of elements within the design domain):

[0035] in, It is a unit i The pseudo-density; It is a unit i Corresponding density filtering function; variable field It is a storage unit i Corresponding variables ; It is a unit j The coordinate vector of the geometric center point; It is a unit j Volume; Based on units i A set of units within the central target area. Is with unit i Corresponding unit j The weights.

[0036] unit i It refers to the first one within the design domain i Each unit, similarly, unit j Refers to a set of units The first in j Units.

[0037] As an example, in two-dimensional topology optimization, in terms of elements... i The target area centered on can be in units i A circular area centered on the unit, or... i The rectangular area centered on it.

[0038] As an example, if it is three-dimensional topology optimization, in terms of elements i The target area centered on can be in units i A spherical region centered on the unit, or... i The central cuboid or cube region.

[0039] The value of is equivalent to a unit. j With unit i The distance between them, that is, the unit j With unit i The smaller the distance between them, The larger the value, the more the unit j With unit i The greater the distance between them, The smaller the value, the better.

[0040] As an example, when the target area centered on unit i is a circular or spherical region, it can be determined by the following formula. and : (2) (3) in, It is the preset filter radius.

[0041] The above example merely illustrates one implementation method for obtaining the pseudo-density of each element within the design domain. This application can also employ other methods to obtain the pseudo-density of each element within the design domain, for example, by element... i The target area centered on can be in units i An elliptical region centered on the center, or a region of other shapes. The value of can be calculated in other ways.

[0042] Step S102: With the goal of minimizing the maximum displacement among the displacements of each node in the first specified region of the target structure, optimize the values ​​of the variable field in the design domain under multiple constraints; the nodes in the first specified region include at least the vertices of each element in the first specified region.

[0043] In a two-dimensional topology optimization scenario, if each cell is a rectangular mesh, then a cell has 4 vertices and 4 edges, and thus can have 4 nodes; or, a cell can have 8 nodes, including 4 vertices and the midpoints of 4 edges. Assuming there are B cells in the first specified region, since adjacent cells in the first specified region have the same vertices and edges, the number of nodes in the first specified region is less than 4B or less than 8B.

[0044] In a 3D topology optimization scenario, if each cell is a cuboid or cube mesh, then a cell has 8 vertices and 12 edges, and thus can have 8 nodes; alternatively, a cell can have 20 nodes, including 8 vertices and the midpoints of the 12 edges. Assuming there are B cells in the first specified region, since adjacent cells in the first specified region have the same vertices and edges, the number of nodes in the first specified region is less than 8B or less than 20B.

[0045] The displacement of each node within the first designated region is determined based on the pseudo-density of each element within the design domain, the temperature-related material properties of each element within the design domain, and the relationship between the material properties and temperature.

[0046] The above-mentioned constraints may include: When a heat flux is applied to a non-design domain of the target structure, the maximum temperature of each node in the second specified region of the target structure is less than or equal to a temperature threshold. The second specified region and the first specified region can be two independent regions, or the second specified region and the first specified region can be the same region, or the second specified region and the first specified region can have partially overlapping areas.

[0047] The weighted sum of the volumes of all elements within the design domain is less than or equal to the volume threshold, which is the product of the volume fraction threshold and the volume of the design domain.

[0048] The variables in the variable field are greater than zero and less than or equal to 1.

[0049] The optimization problem described above can be represented by the following mathematical model: find

[0050] minimize

[0051] subject to

[0052] Where, vector This represents a vector of design variables. yes An element, representing the first i Design variables for each unit. It is the first i The pseudo-density of each unit is filtered by the pseudo-density filtering function. Calculated. It represents the total number of designable elements. It is the set of nodes that minimizes displacement (i.e., the set of nodes within the first specified region). The nodes in the node set that minimize the displacement displacement, This represents the maximum displacement of the nodes in the node set that minimizes displacement. It is the set of nodes constrained by temperature (i.e., the set of nodes within the second specified region). Nodes in the node set representing temperature constraints l temperature, This represents the maximum temperature of the nodes in the node set that are subject to temperature constraints. This indicates the temperature threshold. It is the first i The volume of each unit. This is the allowed volume fraction threshold, as an example. . It is the total volume of all units within the design domain.

[0053] As an example, The initial value is 0.4.

[0054] Node set with minimized displacement Displacement of each node in It is determined based on the pseudo-density of each element within the design domain, the temperature-dependent material properties of each element within the design domain, and the relationship between material properties and temperature. Specifically, the node set for minimizing displacement can be determined using the fundamental equations of heat conduction and elasticity problems, based on the pseudo-density of each element within the design domain, and the temperature-dependent material properties of each element within the design domain, as well as the relationship between material properties and temperature. Displacement of each node in .

[0055] The structural topology optimization method provided in this application takes into account temperature-related material properties during the topology optimization process, thereby optimizing the topology configuration of the structure working under a large temperature gradient, so that the optimized topology is suitable for environments with large temperature gradients.

[0056] In an optional embodiment, the above-mentioned temperature-related material properties include: thermal conductivity Young's modulus E Poisson's ratio v and coefficient of linear expansion .

[0057] Table 1 shows the values ​​of the above-mentioned material-related properties of the alloy material GH4099 provided in the embodiments of this application at discrete temperatures.

[0058] Table 1

[0059] In an optional embodiment, a flowchart illustrating the above-described method for determining the displacement of each node within a first specified region based on the pseudo-density of each element within the design domain, the temperature-related material properties of each element within the design domain, and the correlation between material properties and temperature is shown below. Figure 3 As shown, it may include: Step S301: Solve the fundamental equations of the heat conduction problem to obtain the temperature of each node in the target structure. The fundamental equations of the heat conduction problem are: (4) in: (6) This is a temperature vector consisting of the temperatures of all nodes in the target structure. P For thermal load; Representation unit e The temperature, which depends on the unit e The temperature of each node is calculated. Representation unit e The thermal conductivity matrix; Indicates the number of units in the target structure; V e Representation unit e Volume; Representation unit e The gradient matrix of the shape function; T, as a superscript, denotes the matrix transpose operation; Representation unit e The thermal conductivity coefficient, which is determined by the thermal conductivity of... The first material interpolation process is performed to obtain the result. Representation unit e Solid materials at a temperature of Thermal conductivity coefficient at that time; Is with Column vectors of the same dimension are only related to the cell. e The element values ​​corresponding to each node are set to Other elements are set to zero. For unit e The number of nodes. Among them, thermal load. P It utilizes the finite element method theory, based on heat flux. q Calculated.

[0060] Solid materials refer to raw materials that have not undergone interpolation calculations.

[0061] Optionally, the fundamental equations of the heat conduction problem can be solved using the Newton-Raphson (NR) iterative method (i.e., using the Newton-Raphson iterative method for finite element analysis of heat conduction to obtain the temperature field). Specifically, The fundamental equations for the heat conduction problem can be rewritten in the following residual form: (7) Assume the initial solution is T (0) The initial solution can be manually defined or randomly generated. k The solution for the NR iteration is T (k) , then the firstk+ Solution of 1 NR iteration T (k+1) The calculation formula is: (8) in, This is called the temperature field correction. (For calculation...) , for the k+ Residual of 1 NR iteration step ,use exist T (k) Approximating the first-order Taylor formula within the neighborhood, we obtain: (9) Setting the first-order Taylor formula on the right side of equation (8) to 0, we can obtain the following equation: (10) By solving equation (10), we can obtain And then calculate .

[0062] Repeat the NR iteration until the residual is found. Once the given error range is reached, the final temperature node vector can be obtained. In other words, residuals The temperature node vector calculated when the given error range is reached. The elements in the equation represent the temperatures of the nodes in the target structure.

[0063] For any given unit, the temperature of that unit can be calculated using the temperatures of each node of that unit, as shown in formula (6). The temperature of that unit can be the average of the temperatures of each node of that unit.

[0064] The relationship between thermal conductivity and temperature can be calculated using a pre-established first functional relationship, obtained by fitting a function to the thermal conductivity at different temperatures. The functional relationship between thermal conductivity and temperature can be fitted using a polynomial in the following format:

[0065] in, This represents the number of terms (i.e., coefficients) in a polynomial. c (number of items), superscript It is an identifier used to identify the physical quantity of thermal conductivity.

[0066] The process of function fitting involves determining the number of... Sum of coefficients The fitting process can be performed using the least squares method or other methods. This application does not limit the fitting method.

[0067] Taking alloy material GH4099 as an example, the first functional relationship can be a first-order polynomial, that is:

[0068] In obtaining the unit e solid material temperature Then, the temperature Substituting into formula (12), we obtain the unit. e Solid materials at a temperature of thermal conductivity at time .

[0069] Step S302: Based on the temperature of each unit, the pre-established functional relationship between the linear expansion coefficient and temperature, and the functional relationship between the elastic matrix and temperature, obtain the linear expansion coefficient and elastic matrix of the solid material of each unit.

[0070] Among them, the coefficient of linear expansion The functional relationship with temperature (denoted as the second functional relationship) can be obtained by fitting a function to the coefficient of linear expansion at different temperatures. A polynomial in the following format can be used to fit the coefficient of linear expansion. The second functional relationship with temperature:

[0071] in, This represents the number of terms (i.e., coefficients) in a polynomial. c (number of items), superscript It is an identifier used to identify the physical quantity of linear expansion coefficient.

[0072] The process of function fitting involves determining the number of... Sum of coefficients The fitting process can be performed using the least squares method or other methods. This application does not limit the fitting method.

[0073] Taking alloy material GH4099 as an example, the second functional relationship can be a quadratic polynomial, that is: (14) Elasticity matrix of each unit D The Young's modulus of this unit can be used to determine its properties. E Compared to Poisson v According to a specific calculation formula, taking the plane stress problem as an example, the elastic matrix of any element is obtained. D It can be calculated using the following formula: First, based on Young's modulus at discrete temperatures E Compared to Poisson v The elasticity matrix at discrete temperatures is calculated. , (15) Then, for discrete temperatures Polynomial fitting yields the functional relationship between the elasticity matrix and temperature (denoted as the third function relationship). The third function relationship between the elasticity matrix and temperature can be fitted using a polynomial in the following format:

[0074] in, The coefficient matrix, The superscript indicates the number of terms in the polynomial (i.e., the number of coefficient matrices). It is an identifier used to identify the physical quantity of the elasticity matrix.

[0075] In fact, the elasticity matrix It has only three independent components:

[0076] The three independent components can be fitted using polynomial functions. For specific fitting methods, refer to the fitting methods for other physical quantities to obtain the coefficient matrix. The three independent components.

[0077] Taking the alloy material GH4099 as an example, the elastic matrix The third functional relationship with temperature can also be a quadratic functional relationship, that is:

[0078] Wherein, the coefficient matrix It includes three independent components, denoted as , and .

[0079] coefficient matrix It includes three independent components, denoted as , and .

[0080] coefficient matrix It includes three independent components, denoted as , and .

[0081] By analyzing the elasticity matrix The three independent components mentioned above are fitted separately to obtain the three independent components of each coefficient matrix: The elasticity matrix can be used independent components By performing fitting, the obtained An independent component (denoted as) ), An independent component (denoted as) )and An independent component (denoted as) ).

[0082] For the elasticity matrix independent components By fitting, the obtained An independent component (denoted as) ), An independent component (denoted as) )and An independent component (denoted as) ).

[0083] For the elasticity matrix independent components By fitting, the obtained An independent component (denoted as) ), An independent component (denoted as) )and An independent component (denoted as) ).

[0084] Taking alloy material GH4099 as an example, for any unit, the temperature of the unit is substituted into formula (14) to obtain the linear expansion coefficient of the solid material of the unit, and the temperature of the unit is substituted into formula (17) to obtain the elastic matrix of the solid material of the unit.

[0085] Step S303: Based on the elasticity matrix of the solid material of each element and the stiffness matrix of the target structure. The stiffness matrix of the target structure is obtained from the calculation formula. The formula for calculating the stiffness matrix is:

[0086] in, Representation unit e The stiffness matrix; Representation unit e The strain-displacement matrix; Representation unit e The elasticity matrix, which is obtained by applying... The result is obtained by performing a second material interpolation process; This indicates that the solid material is at a temperature of The elasticity matrix at that time.

[0087] Taking alloy material GH4099 as an example, in obtaining unit e temperature Then, the unit e temperature Substituting into formula (17), we obtain the unit. e Solid materials at a temperature of Elasticity matrix at time .

[0088] Optionally, to avoid singularity in the stiffness matrix of the structure during finite element analysis, a lower bound can be set for the design variables. ,Right now:

[0089] As an example, .

[0090] Step S304: Based on the mechanical load and thermal stress load caused by the temperature field, as well as the stiffness matrix of the target structure, solve the fundamental equations of the elasticity problem to obtain the displacements of each node of the target structure. The fundamental equations of the elasticity problem are: (19) in, This represents the displacement vector formed by the displacements of each node of the target structure; Represents the preset mechanical force load vector, in order to Figure 2 Taking the structure shown as an example, if the mechanical load F1=F2=F3=50kN, then It can be obtained from F1, F2, and F3 according to the finite element theory; Indicates thermal stress load; Representation unit e Thermal stress load; , The reference temperature for material properties is... Figure 2 For example, ; It is a preset constant vector.

[0091] According to the unit e coefficient of linear expansion With temperature difference Able to calculate the unit e The amount of expansion deformation, i.e. However, this expansion deformation is a scalar and needs to be converted into a strain vector (also called a thermal strain vector) containing components in each direction to participate in matrix operations. In elasticity, the strain vector for a two-dimensional problem is a three-dimensional column vector containing the normal strain components in the x and y directions, as well as the xy shear strain; the strain vector for a three-dimensional problem is a six-dimensional column vector with normal strain components in the x, y, and z directions, as well as the xy, yz, and xz shear strains. Because for isotropic materials, the amount of thermal expansion is equal in all directions in space, and thermal strain only has normal strain and no shear strain, therefore, for a two-dimensional problem, the vector... The value can be [1 1 0] T For three-dimensional problems, vectors The value can be [1 1 1 0 0 0]. T .

[0092] By solving equation (15), the displacement vector consisting of the displacements of each node of the target structure can be obtained. .

[0093] From the displacement vector The displacements of each node within the first specified region are extracted and used to optimize the values ​​of the variable field within the design domain.

[0094] Based on the above embodiments, the mathematical model of the above optimization problem may also include formula (4) and formula (19).

[0095] In an optional embodiment, the following formula can be used to... Perform the first material interpolation process: (twenty one) in, Representation unit e The pseudo-density; This is a penalty factor.

[0096] In an optional embodiment, the following formula can be used to... Perform second material interpolation: (twenty two) in, Representation unit e The pseudo-density; , All of these are penalty factors.

[0097] In this embodiment, material interpolation is performed only on the thermal conductivity coefficient and elasticity matrix of the elements within the design domain. For elements outside the design domain, material interpolation of the thermal conductivity coefficient and elasticity matrix is ​​not performed. In other words, during the calculation process, the thermal conductivity coefficient and elasticity matrix of the elements within the design domain are based on the interpolation results, while the thermal conductivity coefficient and elasticity matrix of the elements outside the design domain retain the thermal conductivity coefficient and elasticity matrix of the solid material.

[0098] In an optional embodiment, the process of optimizing the region of the variable field within the design domain includes: Each time the displacement of each node in the first specified region is obtained, a first smooth approximation function representing the first maximum value function of the displacement of each node in the first specified region is obtained, and a second smooth approximation function representing the second maximum value function of the temperature of each node in the second specified region is obtained.

[0099] Since the maximum value function (max) is not differentiable, gradient-based optimization algorithms cannot be used. Therefore, this application employs a smooth approximation of the maximum value function. Optionally, the Kreisselmeier–Steinhauser (KS) function can be used to obtain a smooth approximation of the maximum value function.

[0100] Taking the first maximum value function representing the maximum displacement among the displacements of each node within the first specified region as an example, the formula is as follows:

[0101] The first smooth approximation function can be:

[0102] Taking the second maximum value function, which characterizes the maximum temperature of each node within the second specified region, as an example, the formula is as follows:

[0103] The second smooth approximation function can be:

[0104] in, , All are smooth approximation parameters; It is the set of nodes within the first specified region; It is a diagonal matrix, with only the diagonal elements corresponding to the target degrees of freedom of the selected nodes set to 1, and the rest set to 0; It is the set of nodes within the second specified region; This serves as the upper bound of the temperature constraint. The node temperature... use Normalization is used to avoid data overflow during the calculation process.

[0105] Assuming there are 100 nodes in the first specified region, and each node has two degrees of freedom in two directions: x and y, then... For a 200 A column vector of 1s, where the diagonal elements of the diagonal matrix are set to either 1 or 0, allows each node to choose one or two degrees of freedom. The specific degree of freedom chosen depends on the actual needs.

[0106] The first sensitivity of the first smooth approximation function and the second sensitivity of the second smooth approximation function are derived using the adjoint method.

[0107] Optionally, one implementation of deriving the first sensitivity of the first smooth approximation function using the adjoint method can be: The first sensitivity of the first smooth approximation function is derived using the following formula:

[0108] Wherein, the adjoint vector and The following two adjoint equations are obtained: (27) in,

[0109] Formula (27) is solved by a solver.

[0110] In the above formula , , Both are asymmetric matrices resulting from the introduction of temperature-dependent material properties. In formula (28) It is composed of units e The vector formed by the temperatures of each node. In formula (29) It is composed of units e The vector formed by the displacements of each node.

[0111] Optionally, one implementation of deriving the second sensitivity of the second smooth approximation function using the adjoint method can be: The second sensitivity of the second smooth approximation function is derived using the following formula:

[0112] Wherein, the adjoint vector The following adjoint equations were obtained by solving them using a solver:

[0113] Optionally, the mature PARDISO solver can be used to solve the asymmetric adjoint matrix equations introduced by the use of TDMPs (i.e., Equations (27) and (34)) to obtain the first and second sensitivities.

[0114] The variables of each unit within the design domain are updated based on the first and second sensitivities.

[0115] The design variables for the next iteration within the design domain can be obtained using gradient optimization algorithms, based on the first and second sensitivities.

[0116] Repeat the above steps to continuously optimize and iterate. When the number of iterations reaches a preset number (e.g., 200 times), or the change in the objective function value of a preset number of consecutive optimization iterations is less than 0.1%, and all constraints are met, the optimization is terminated.

[0117] To avoid prematurely getting trapped in local solutions during optimization iterations and thus achieve better optimization results in most cases, in an optional embodiment, the penalty factor is gradually increased during the optimization of the variable field values ​​within the design domain. Optional: After each preset number of iterations, the penalty factor is increased. The value of , up to the penalty factor. The first preset value has been reached.

[0118] As an example, the first preset number of times is 10. Of course, the first preset number of times can also be other values, and no specific restrictions are made here.

[0119] As an example, the following update strategy can be used for the penalty factor. Update: Each update, the updated penalty factor The value of is the penalty factor before the update. Twice the value of, that is . Indicates the first k+ Penalty factor before 1 update The value of , Indicates the first k+ Penalty Factor after 1 Update The value of .

[0120] As an example, the first preset value is 32. Of course, the first preset value can also be other values, and no specific restrictions are made here.

[0121] Each pair of penalty factors Perform an update, and after a second preset number of iterations, increase the penalty factor. The value of , up to the penalty factor. The second preset value is reached; the number of times the second preset value is less than the number of times the first preset value is reached.

[0122] In this embodiment of the application, the penalty factor and penalty factor The updates are not simultaneous, but staggered. As an example, the second preset number of times is 5. Of course, it can also be any other value less than the first preset number of times; this application does not impose any specific limitations.

[0123] As an example, the following update strategy can be used for the penalty factor. Update: Each update, the updated penalty factor The value of is the penalty factor before the update. Twice the value of, that is . Indicates the first k+ Penalty factor before 1 update The value of , Indicates the first k+ Penalty Factor after 1 Update The value of .

[0124] As an example, the second preset value is 32. Of course, the second preset value can also be other values, which are not specifically limited here. The second preset value can be the same as or different from the first preset value.

[0125] When the penalty factor After reaching the first preset value, and after a third preset number of iterations, the penalty factor will be... Increase to the third preset value.

[0126] The third preset number of times can be the same as or different from the first preset number of times.

[0127] As an example, the penalty factor , and The initial values ​​of all are set to 1.

[0128] Optionally, the third preset value can be 2.

[0129] By updating different penalty factors at staggered times, the impact of parameter changes on the optimization process can be reduced.

[0130] In an optional embodiment, a relaxation strategy is employed for temperature constraints during the optimization of the values ​​of the variable field within the design domain.

[0131] At the start of optimization, the temperature threshold is relaxed to a larger value (denoted as ). During the optimization process, the temperature threshold was adjusted from... Gradually decrease to the fourth preset value Optional, The maximum short-term operating temperature of the selected material.

[0132] Optionally, the temperature threshold value can be decreased after every fourth preset number of iterations until the temperature threshold value reaches the fourth preset value. .

[0133] After each of the fourth preset number of iterations, the decrease in the temperature threshold value is... for:

[0134] As an example, .certainly, Other values ​​are also possible, but no specific restrictions are made here.

[0135] Another implementation flowchart of the structural topology optimization method provided in this application is shown below. Figure 4 As shown, it may include: Step S401: Based on the mechanical load, thermal load (or heat flux), and displacement boundary (i.e., the fixed position of the given structure, for example) of the structure... Figure 2 A finite element model of a given structure is established by defining the left edge of the rectangular plate that is clamped and fixed, and the temperature boundary (i.e., the temperature threshold), and defining the design domain and non-design domain.

[0136] Step S402: Based on the finite element model of the given structure, define the design variables, element pseudo-density, objective function and constraint function, and establish the mathematical model of the optimization problem.

[0137] Step S403: Initialize design variables and enter the optimization iteration.

[0138] The optimization iterative process includes: Step S404: Filter the design variables to obtain the element pseudo density.

[0139] Step S405: Based on the element pseudo-density, use the material interpolation model to calculate the temperature-related thermal conductivity coefficient of each element in the current optimization iteration step.

[0140] Step S406: Perform finite element analysis of heat conduction using the Newton-Raphson iterative method to obtain the temperature field.

[0141] Step S407: Based on the temperature field and material interpolation model, calculate the Young's modulus, Poisson's ratio and linear expansion coefficient of each element in the current optimization iteration step, and then calculate the stiffness matrix and thermal stress load vector.

[0142] Step S408: Perform finite element analysis of elasticity based on mechanical load to obtain the displacement field.

[0143] Step S409: Calculate the target and constraint function values, and then calculate the sensitivity of the design variables corresponding to the target and constraint functions.

[0144] Step S410: Solve the optimization problem using a gradient optimization algorithm.

[0145] Step S411: Determine whether convergence has occurred. If yes, end the process; otherwise, proceed to step S412.

[0146] Step S412: Update the design variables and return to step S404.

[0147] like Figure 5 As shown, this application provides four temperature constraints for the same structure. (Right now Four optimization results were obtained by taking four values ​​(as shown in Table 2). Different temperature constraints are defined as different Cases, denoted as Case1, Case2, Case3, and Case4, respectively. Figure 5 The Case ref in the figure represents the optimization result without temperature constraints. The horizontal axis represents the maximum temperature of each node in the second specified region, and the vertical axis represents the maximum displacement of each node in the first specified region.

[0148] like Figure 6 As shown, this application provides an embodiment based on... Figure 5 The figure shows the iterative curves for topology optimization under different temperature constraints. The horizontal axis represents the number of iterations, the left vertical axis represents the smoothed approximation function value of the maximum displacement among the displacements of each node in the first specified region during the iteration process, and the right vertical axis represents the maximum temperature of each node in the second specified region during the iteration process.

[0149] Table 2 shows that... Figure 5 The maximum displacement in the first specified region obtained by optimization with and without temperature constraints and with different upper limits of temperature constraints is shown. Maximum temperature in the second specified area Examples.

[0150] Table 2

[0151] As shown above, given different upper limits of temperature constraints, the optimization process reduces the structural load-bearing capacity (i.e., the structure's resistance to deformation under load) to varying degrees to meet the temperature constraints. Furthermore, the topology optimization method of this application exhibits excellent convergence, even for conditions like... Even with such strict temperature constraints, convergence is successful, yielding the desired optimization results.

[0152] Corresponding to the method embodiments, this application also provides a structural topology optimization device, such as... Figure 7 The diagram shown is a structural topology optimization device provided in an embodiment of this application, which may include: Pseudo-density acquisition module 701 and optimization module 702; wherein, The pseudo-density acquisition module 701 is used to obtain the pseudo-density of each element in the design domain based on the variable field of the design domain of the target structure. Different variables in the variable field correspond to different elements in the design domain. The pseudo-density is used to describe whether the corresponding element is void. The optimization module 702 is used to optimize the values ​​of the variable field in the design domain under multiple constraints, with the goal of minimizing the maximum displacement among the displacements of each node in the first specified region of the target structure; the nodes in the first specified region include at least the vertices of each element in the first specified region. The displacement of each node within the first designated area is determined based on the pseudo density of each element within the design domain, the temperature-related material properties of each element within the design domain, and the correlation between the material properties and temperature. The multiple constraints include: When a heat flux is applied within the non-design domain of the target structure, the maximum temperature of each node in the second specified region of the target structure is less than or equal to a temperature threshold. The weighted sum of the volumes of all units within the design domain is less than or equal to a volume threshold, which is the product of a volume fraction threshold and the volume of the design domain. The variables in the variable field are greater than zero and less than or equal to 1.

[0153] The structural topology optimization device provided in this application takes into account temperature-related material properties during the topology optimization process, thereby optimizing the topology configuration of the structure working under a large temperature gradient, so that the optimized topology is suitable for environments with large temperature gradients.

[0154] In an optional embodiment, the temperature-related material properties include: thermal conductivity, Young's modulus, Poisson's ratio, and coefficient of linear expansion.

[0155] In an optional embodiment, the optimization module 702 determines the displacement of each node in the first specified region based on the pseudo density of each element within the design domain, the temperature-related material properties of each element within the design domain, and the correlation between the material properties and temperature. This process includes: The fundamental equations for the problem of heat conduction The solution is performed to obtain the temperature of each node of the target structure, where: This is a temperature vector composed of the temperatures of all nodes of the target structure; P For thermal load; Representation unit e Temperature; Representation unit e The thermal conductivity matrix; Indicates the number of units in the target structure; V e Representation unit e Volume; Representation unit e The gradient matrix of the shape function; T, as a superscript, denotes the matrix transpose operation; Representation unit e The thermal conductivity coefficient, through the... The first material interpolation process is performed to obtain the result. Representation unit e Solid materials at a temperature of Thermal conductivity coefficient at that time; Is with Column vectors of the same dimension are only related to the cell. e The element values ​​corresponding to each node are set to Other elements are set to zero. For unit e The number of nodes; Based on the temperature of each unit, as well as the pre-established functional relationship between the linear expansion coefficient and temperature, and the functional relationship between the elastic matrix and temperature, the linear expansion coefficient and elastic matrix of the solid material of each unit are obtained. Based on the elasticity matrix of the solid material of each unit and the stiffness matrix of the target structure. The stiffness matrix of the target structure is obtained by calculating the formula, and the formula for calculating the stiffness matrix is ​​as follows:

[0156] in, Representation unit e The stiffness matrix; Representation unit e The strain-displacement matrix; Representation unit e The elasticity matrix, through the... The result is obtained by performing a second material interpolation process; This indicates that the solid material is at a temperature of The elasticity matrix at that time; Based on the mechanical load and the thermal stress load caused by the temperature field, as well as the stiffness matrix of the target structure, the fundamental equations of the elasticity problem are solved to obtain the displacements of each node of the target structure; the fundamental equations of the elasticity problem are:

[0157] in, This represents the displacement vector formed by the displacements of each node of the target structure; This indicates a preset mechanical load; Indicates thermal stress load; Representation unit e Thermal stress load; , This is the reference temperature for material properties; It is a preset constant vector.

[0158] In an alternative embodiment, wherein, The formula for the first material interpolation process can be expressed as:

[0159] And / or, The formula for the second material interpolation process can be expressed as:

[0160] in, Representation unit e The pseudo-density; , , All of these are penalty factors.

[0161] In an optional embodiment, the process by which the optimization module 702 optimizes the values ​​of the variable field within the design domain includes: Each time the displacement of each node in the first specified region is obtained, a first smooth approximation function representing the first maximum value function of the displacement of each node in the first specified region is obtained, and a second smooth approximation function representing the second maximum value function of the temperature of each node in the second specified region is obtained. The first smooth approximation function is:

[0162] The second smooth approximation function is:

[0163] in, , All are smooth approximation parameters; It is the set of nodes within the first specified region; It is a diagonal matrix, with only the diagonal elements corresponding to the target degrees of freedom of the selected nodes set to 1, and the rest set to 0; It is the set of nodes within the second specified region; This is the upper bound of the temperature constraint; The first sensitivity of the first smooth approximation function and the second sensitivity of the second smooth approximation function are derived using the adjoint method. The variables of each unit within the design domain are updated based on the first sensitivity and the second sensitivity.

[0164] In an optional embodiment, the optimization module 702 derives the first sensitivity of the first smooth approximation function using the adjoint method, including: The first sensitivity of the first smooth approximation function is derived using the following formula:

[0165] Wherein, the adjoint vector and The following two adjoint equations are obtained:

[0166] in, .

[0167] In an optional embodiment, the optimization module 702 employs the adjoint method to derive the second sensitivity of the second smooth approximation function, comprising: The second sensitivity of the second smooth approximation function is derived using the following formula:

[0168] Wherein, the adjoint vector The following adjoint equations were obtained by solving them using a solver:

[0169] In an optional embodiment, during the process of optimizing the values ​​of the variable field within the design domain, the optimization module 702... After each preset number of iterations, the penalty factor is increased. The value of the penalty factor is taken up to the value of the penalty factor. The first preset value has been reached; Each pair of the penalty factors An update is performed, and after a second preset number of iterations, the penalty factor is increased. The value of the penalty factor is taken up to the value of the penalty factor. The second preset value is reached; the second preset number of times is less than the first preset number of times. When the penalty factor After reaching the first preset value, and after a third preset number of iterations, the penalty factor is... Increase to the third preset value.

[0170] In an optional embodiment, during the process of optimizing the values ​​of the variable field within the design domain, the optimization module 702... After each fourth preset number of iterations, the temperature threshold value is reduced until the temperature threshold value reaches the fourth preset value.

[0171] Corresponding to the method embodiments, this application also provides an electronic device, a schematic diagram of which is shown below. Figure 8 As shown, it may include: at least one processor 1, at least one communication interface 2, at least one memory 3, and at least one communication bus 4.

[0172] In this embodiment, the number of processor 1, communication interface 2, memory 3, and communication bus 4 is at least one, and processor 1, communication interface 2, and memory 3 communicate with each other through communication bus 4.

[0173] Processor 1 may be a central processing unit (CPU), an application-specific integrated circuit (ASIC), or one or more integrated circuits configured to implement the embodiments of this application.

[0174] Memory 3 may include high-speed RAM, and may also include non-volatile memory, such as at least one disk storage device.

[0175] The memory 3 stores a program, and the processor 1 can call the program stored in the memory 3. The program is used for: The pseudo-density of each element within the design domain is obtained from the variable field of the design domain based on the target structure. Different variables in the variable field correspond to different elements of the design domain. The pseudo-density is used to describe whether the corresponding element is void. With the goal of minimizing the maximum displacement among the displacements of each node within the first specified region of the target structure, the values ​​of the variable field within the design domain are optimized under multiple constraints; the nodes within the first specified region include at least the vertices of each element within the first specified region. The displacement of each node within the first designated area is determined based on the pseudo density of each element within the design domain, the temperature-related material properties of each element within the design domain, and the correlation between the material properties and temperature. The multiple constraints include: When a heat flux is applied within the non-design domain of the target structure, the maximum temperature of each node in the second specified region of the target structure is less than or equal to a temperature threshold. The weighted sum of the volumes of all units within the design domain is less than or equal to a volume threshold, which is the product of a volume fraction threshold and the volume of the design domain. The variables in the variable field are greater than zero and less than or equal to 1.

[0176] Optionally, the refined and extended functions of the program can be found in the description above.

[0177] This application embodiment also provides a storage medium that can store a program suitable for execution by a processor, the program being used for: The pseudo-density of each element within the design domain is obtained from the variable field of the design domain based on the target structure. Different variables in the variable field correspond to different elements of the design domain. The pseudo-density is used to describe whether the corresponding element is void. With the goal of minimizing the maximum displacement among the displacements of each node within the first specified region of the target structure, the values ​​of the variable field within the design domain are optimized under multiple constraints; the nodes within the first specified region include at least the vertices of each element within the first specified region. The displacement of each node within the first designated area is determined based on the pseudo density of each element within the design domain, the temperature-related material properties of each element within the design domain, and the correlation between the material properties and temperature. The multiple constraints include: When a heat flux is applied within the non-design domain of the target structure, the maximum temperature of each node in the second specified region of the target structure is less than or equal to a temperature threshold. The weighted sum of the volumes of all units within the design domain is less than or equal to a volume threshold, which is the product of a volume fraction threshold and the volume of the design domain. The variables in the variable field are greater than zero and less than or equal to 1.

[0178] Optionally, the refined and extended functions of the program can be found in the description above.

[0179] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0180] In the several embodiments provided in this application, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. Furthermore, the couplings or direct couplings or communication connections shown or discussed may be indirect couplings or communication connections through interfaces, devices, or units, and may be electrical, mechanical, or other forms.

[0181] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0182] In addition, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.

[0183] It should be understood that in the embodiments of this application, the claims, various embodiments, and features can be combined with each other to solve the aforementioned technical problems.

[0184] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0185] The above description of the disclosed embodiments enables those skilled in the art to make or use this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A structural topology optimization method, characterized in that, The method includes: The pseudo-density of each element within the design domain is obtained from the variable field of the design domain based on the target structure. Different variables in the variable field correspond to different elements of the design domain. The pseudo-density is used to describe whether the corresponding element is void. With the goal of minimizing the maximum displacement among the displacements of each node within the first specified region of the target structure, the values ​​of the variable field within the design domain are optimized under multiple constraints; the nodes within the first specified region include at least the vertices of each element within the first specified region. The displacement of each node within the first designated area is determined based on the pseudo density of each element within the design domain, the temperature-related material properties of each element within the design domain, and the correlation between the material properties and temperature. The multiple constraints include: When a heat flux is applied within the non-design domain of the target structure, the maximum temperature of each node in the second specified region of the target structure is less than or equal to a temperature threshold. The weighted sum of the volumes of all units within the design domain is less than or equal to a volume threshold, which is the product of a volume fraction threshold and the volume of the design domain. The variables in the variable field are greater than zero and less than or equal to 1; The process of optimizing the values ​​of the variable field within the design domain includes: Each time the displacement of each node in the first specified region is obtained, a first smooth approximation function representing the first maximum value function of the displacement of each node in the first specified region is obtained, and a second smooth approximation function representing the second maximum value function of the temperature of each node in the second specified region is obtained. The first smooth approximation function is: The second smooth approximation function is: in, , All are smooth approximation parameters; It is the set of nodes within the first specified region; It is a diagonal matrix, with only the diagonal elements corresponding to the target degrees of freedom of the selected nodes set to 1, and the rest set to 0; This represents the displacement vector formed by the displacements of each node of the target structure; It is the set of nodes within the second specified region; This is the upper bound of the temperature constraint; For node temperature; The adjoint method is used to derive the first sensitivity of the first smooth approximation function and the second sensitivity of the second smooth approximation function; the process of deriving the first sensitivity of the first smooth approximation function using the adjoint method includes: The first sensitivity of the first smooth approximation function is derived using the following formula: Wherein, the adjoint vector and The following two adjoint equations are obtained: in, This is a temperature vector composed of the temperatures of all nodes of the target structure; Representation unit e Temperature; Representation unit e The thermal conductivity matrix; Is with Column vectors of the same dimension are only related to the cell. e The element values ​​corresponding to each node are set to Other elements are set to zero. For unit e The number of nodes; It is composed of units e The vector formed by the displacements of each node; Representation unit e The strain-displacement matrix; The variables of each unit within the design domain are updated based on the first sensitivity and the second sensitivity.

2. The method according to claim 1, characterized in that, The temperature-related material properties include: thermal conductivity, Young's modulus, Poisson's ratio, and coefficient of linear expansion.

3. The method according to claim 2, characterized in that, The process of determining the displacement of each node in the first specified region based on the pseudo-density of each element within the design domain, the temperature-related material properties of each element within the design domain, and the correlation between the material properties and temperature includes: The fundamental equations for the problem of heat conduction The solution is performed to obtain the temperature of each node of the target structure, where: This is a temperature vector composed of the temperatures of all nodes of the target structure; P For thermal load; Representation unit e Temperature; Representation unit e The thermal conductivity matrix; Indicates the number of units in the target structure; V e Representation unit e Volume; Representation unit e The gradient matrix of the shape function; T, as a superscript, denotes the matrix transpose operation; Representation unit e The thermal conductivity coefficient, through the... The first material interpolation process is performed to obtain the result. Representation unit e Solid materials at a temperature of Thermal conductivity coefficient at that time; Is with Column vectors of the same dimension are only related to the cell. e The element values ​​corresponding to each node are set to Other elements are set to zero. For unit e The number of nodes; Based on the temperature of each unit, as well as the pre-established functional relationship between the linear expansion coefficient and temperature, and the functional relationship between the elastic matrix and temperature, the linear expansion coefficient and elastic matrix of the solid material of each unit are obtained. Based on the elasticity matrix of the solid material of each unit and the stiffness matrix of the target structure. The stiffness matrix of the target structure is obtained by calculating the formula, and the formula for calculating the stiffness matrix is ​​as follows: in, Representation unit e The stiffness matrix; Representation unit e The strain-displacement matrix; Representation unit e The elasticity matrix, through the... The result is obtained by performing a second material interpolation process; This indicates that the solid material is at a temperature of The elasticity matrix at that time; Based on the mechanical load and the thermal stress load caused by the temperature field, as well as the stiffness matrix of the target structure, the fundamental equations of the elasticity problem are solved to obtain the displacements of each node of the target structure; the fundamental equations of the elasticity problem are: in, This represents the displacement vector formed by the displacements of each node of the target structure; This indicates a preset mechanical load; Indicates thermal stress load; Representation unit e Thermal stress load; , This is the reference temperature for material properties; This is a preset constant vector.

4. The method according to claim 3, characterized in that, in, The formula for the first material interpolation process can be expressed as: And / or, The formula for the second material interpolation process can be expressed as: in, Representation unit e The pseudo-density; , , All of these are penalty factors.

5. The method according to claim 1, characterized in that, The process of deriving the second sensitivity of the second smooth approximation function using the adjoint method includes: The second sensitivity of the second smooth approximation function is derived using the following formula: Wherein, the adjoint vector The following adjoint equations were obtained by solving them using a solver: 。 6. The method according to claim 4, characterized in that, During the process of optimizing the values ​​of the variable field within the design domain, After each preset number of iterations, the penalty factor is increased. The value of the penalty factor is taken up to the value of the penalty factor. The first preset value has been reached; Each pair of the penalty factors An update is performed, and after a second preset number of iterations, the penalty factor is increased. The value of the penalty factor is taken up to the value of the penalty factor. The second preset value is reached; the second preset number of times is less than the first preset number of times. When the penalty factor After reaching the first preset value, and after a third preset number of iterations, the penalty factor is... Increase to the third preset value.

7. The method according to claim 1, characterized in that, During the process of optimizing the values ​​of the variable field within the design domain, After each fourth preset number of iterations, the temperature threshold value is reduced until the temperature threshold value reaches the fourth preset value.

8. A structural topology optimization device, characterized in that, The device includes: The pseudo-density acquisition module is used to obtain the pseudo-density of each element in the design domain based on the variable field of the design domain of the target structure. Different variables in the variable field correspond to different elements in the design domain. The pseudo-density is used to describe whether the corresponding element is void. The optimization module is used to optimize the values ​​of the variable field in the design domain under multiple constraints, with the goal of minimizing the maximum displacement among the displacements of each node in the first specified region of the target structure; the nodes in the first specified region include at least the vertices of each element in the first specified region. The displacement of each node within the first designated area is determined based on the pseudo density of each element within the design domain, the temperature-related material properties of each element within the design domain, and the correlation between the material properties and temperature. The multiple constraints include: When a heat flux is applied within the non-design domain of the target structure, the maximum temperature of each node in the second specified region of the target structure is less than or equal to a temperature threshold. The weighted sum of the volumes of all units within the design domain is less than or equal to a volume threshold, which is the product of a volume fraction threshold and the volume of the design domain. The variables in the variable field are greater than zero and less than or equal to 1; The process of optimizing the values ​​of the variable field within the design domain includes: Each time the displacement of each node in the first specified region is obtained, a first smooth approximation function representing the first maximum value function of the displacement of each node in the first specified region is obtained, and a second smooth approximation function representing the second maximum value function of the temperature of each node in the second specified region is obtained. The first smooth approximation function is: The second smooth approximation function is: in, , All are smooth approximation parameters; It is the set of nodes within the first specified region; It is a diagonal matrix, with only the diagonal elements corresponding to the target degrees of freedom of the selected nodes set to 1, and the rest set to 0; This represents the displacement vector formed by the displacements of each node of the target structure; It is the set of nodes within the second specified region; This is the upper bound of the temperature constraint; For node temperature; The adjoint method is used to derive the first sensitivity of the first smooth approximation function and the second sensitivity of the second smooth approximation function; the process of deriving the first sensitivity of the first smooth approximation function using the adjoint method includes: The first sensitivity of the first smooth approximation function is derived using the following formula: Wherein, the adjoint vector and The following two adjoint equations are obtained: in, This is a temperature vector composed of the temperatures of all nodes of the target structure; Representation unit e Temperature; Representation unit e The thermal conductivity matrix; Is with Column vectors of the same dimension are only related to the cell. e The element values ​​corresponding to each node are set to Other elements are set to zero. For unit e The number of nodes; It is composed of units e The vector formed by the displacements of each node; Representation unit e The strain-displacement matrix; The variables of each unit within the design domain are updated based on the first sensitivity and the second sensitivity.

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