Thermoelastic coupling multi-objective topological optimization design method and system for gradient TPMS lattice structure

Abstract

The invention provides a thermoelastic coupling multi-objective topological optimization design method and system for a gradient TPMS lattice structure, and the method and system comprise the steps: firstly building an equivalent performance prediction model of a TPMS lattice unit cell, and building a multi-objective topological optimization model on the basis; the method is suitable for the design problem of the gradient TPMS lattice structure needing to comprehensively consider thermal management and mechanical bearing capacity. According to the method, a four-corner clamped cube calculation model is considered, a gradient TPMS lattice structure design with excellent performance and reasonable material distribution is obtained through optimization, and the bearing and heat transfer performance of the structure is greatly improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of structural optimization design, and relates to a thermal-elastic coupling multi-objective topology optimization design method and system for a gradient TPMS lattice structure. BACKGROUND

[0002] The lattice structure has a periodic configuration and high designability, can significantly improve specific strength, specific stiffness, and thermal and bearing performance while maintaining lightness, can meet the severe requirements of major engineering equipment, and is widely used in the fields of machinery, aerospace and shipbuilding, etc. The maturity of additive manufacturing technology breaks through the limitations of traditional processes on complex geometry forming, and provides a new way for the engineering application and multi-objective optimization of the lattice structure. Therefore, systematically studying the multi-performance coupling mechanism and topology optimization design method of the lattice structure has important theoretical significance and engineering value.

[0003] At present, the lattice structure is mainly divided into three types of truss type, honeycomb type and curved surface type. Among them, the curved surface type structure represented by three-periodic minimal surface (TPMS) has a continuous smooth appearance and a high surface area to volume ratio, and excellent bearing and heat transfer performance. The gradient TPMS structure can realize directional regulation of performance through morphological gradient change, ensure strength and stiffness, meet the multi-functional requirements of heat transfer, and has broad application prospects in the fields of structural bearing, energy absorption and thermal management. The topology optimization method can realize flexible customized design by reasonably distributing materials in the design domain. The design of gradient TPMS based on the topology optimization method has become a research hotspot, however, the research on the topology optimization of gradient TPMS considering bearing and heat transfer performance is still relatively insufficient. SUMMARY

[0004] In view of the design problem of the gradient TPMS lattice structure needing to consider bearing and heat transfer performance, the application provides a novel thermal-elastic coupling multi-objective topology optimization design method for the gradient TPMS lattice structure. The method establishes an equivalent performance prediction model of the TPMS lattice unit cell for the thermal-elastic coupling problem of the gradient TPMS lattice structure, and constructs the relationship between the geometric size of the TPMS lattice unit cell and the equivalent performance. On this basis, a multi-objective topology optimization model is further constructed. The application is suitable for the design problem of the gradient TPMS lattice structure needing to consider thermal management and mechanical bearing capacity.

[0005] In order to achieve the above purpose, the technical scheme adopted by the application comprises: A thermal-elastic coupling multi-objective topology optimization design method for a gradient TPMS lattice structure, the design method comprising the steps of: first, based on the mathematical expression of several common TPMS curved surfaces, adjusting the offset amount C in the expression to construct a gradient TPMS unit cell data set with thickness varying with position. Second, based on the obtained gradient TPMS unit cell data set, calculating the equivalent performance of the gradient TPMS unit cell with different offset amountsC corresponding TPMS unit cell volume , and then calculate the unit cell volume fraction , and use the Monte Carlo method to fit the TPMS unit cell volume fraction and the offset C , construct the TPMS unit cell volume fraction fitting model, and establish the gradient TPMS unit cell geometric parameter-volume fraction dataset. Third, for different volume fractions of the TPMS lattice unit cell, based on the homogenization method, the equivalent performance parameters , , and of the TPMS lattice unit cell are calculated, and the relationship between the volume fraction and the equivalent performance parameters , , and is fitted by a polynomial to construct the gradient TPMS lattice structure equivalent performance prediction model. Fourth, according to the design requirements, the optimization design domain of the structure is set and the grid is divided, each grid is filled with a TPMS unit cell, and according to the established equivalent performance prediction model, the design variable is defined as the set of volume fractions of the TPMS unit cell filled in each grid element. Fifth, the density of the design variable is filtered to obtain the physical density . Sixth, according to the design requirements, considering the optimization objectives related to bearing and heat transfer, considering several constraints, a thermal-elastic coupled multi-objective topology optimization model considering bearing and heat transfer performance is established. Seventh, according to the established optimization model, the sensitivity of the objective function and the constraint function is derived to obtain the sensitivity information of the objective function and the constraint function. Eighth, according to the sensitivity information of the objective function and the constraint function, the design variable is iteratively updated using the gradient optimization algorithm. Ninth, according to the iteration cycle step number, it is judged whether it is converged or not, if it is not converged, the cycle is repeated, if it is converged, the cycle is exited, and the volume fraction distribution of the gradient TPMS lattice structure is obtained. Finally, according to the obtained volume fraction distribution information and the constructed TPMS unit cell volume fraction fitting model, the TPMS unit cell with corresponding geometric size is filled into the corresponding finite element grid, and the control point method is used to realize the geometric smooth connection of the gradient TPMS structure, and the gradient TPMS lattice structure design is obtained.

[0006] Some embodiments of the present application provide a thermal-elastic coupled multi-objective topology optimization design system for a gradient TPMS lattice structure, which includes a processor and a memory, the memory executes computer readable program code, and the processor is configured to run the computer readable program code to implement the above method.

[0007] The beneficial effects of the present application include: for the gradient TPMS lattice structure design problem which needs to balance the bearing and heat transfer performance, the present application provides a novel thermal-elastic coupling multi-objective topology optimization design method of gradient TPMS lattice structure. By establishing the unit cell equivalent performance prediction model of gradient TPMS lattice structure, the complex gradient TPMS lattice structure design is converted into equivalent performance parameters, which provides theoretical support for the gradient TPMS lattice structure design; a multi-objective topology optimization model considering thermal-elastic coupling problem is constructed, and the multifunctional gradient TPMS lattice structure design considering the bearing and heat transfer performance requirements is realized. The present application is suitable for the gradient TPMS lattice structure design problem which needs to consider the thermal management and mechanical bearing capacity. BRIEF DESCRIPTION OF DRAWINGS

[0008] Figure 1 It is a common TPMS surface geometry diagram in step S1 of the thermal-elastic coupling multi-objective topology optimization design method of the gradient TPMS lattice structure of the present application.

[0009] Figure 2 It is a three-dimensional geometric model of a common TPMS unit cell in step S1 of the thermal-elastic coupling multi-objective topology optimization design method of the gradient TPMS lattice structure of the present application.

[0010] Figure 3 It is an example of gradient TPMS structure geometric smooth connection based on the control point method in step S10 of the thermal-elastic coupling multi-objective topology optimization design method of the gradient TPMS lattice structure of the present application.

[0011] Figure 4 It is a schematic diagram of a four-corner fixed support cube model in a specific embodiment of the method of the present application.

[0012] Figure 5 It is a flowchart of the thermal-elastic coupling multi-objective topology optimization method of the gradient TPMS lattice structure according to the embodiment of the present application.

[0013] Figure 6 It is a schematic diagram of the volume fraction distribution of the gradient TPMS lattice structure in a specific embodiment of the thermal-elastic coupling multi-objective topology optimization design method of the gradient TPMS lattice structure of the present application.

[0014] Figure 7 It is a schematic diagram of the gradient TPMS lattice structure design in a specific embodiment of the thermal-elastic coupling multi-objective topology optimization design method of the gradient TPMS lattice structure of the present application.

[0015] Figure 8 It is a schematic diagram of the mathematical expression of a typical TPMS.

[0016] Figure 9This is a schematic diagram of the fitting function curve of the bias and volume fraction of a common TPMS unit cell.

[0017] Figure 10 This is a schematic diagram of the equivalent performance fitting function for a common TPMS unit cell. Detailed Implementation

[0018] The specific embodiments of the present invention are described in detail below with reference to the technical solutions and accompanying drawings.

[0019] The thermoelastic coupling multi-objective topology optimization design method for gradient TPMS lattice structures according to the present invention includes, for example: Figure 5 As shown, the following steps can be taken: S1: First, based on the mathematical expression of the selected TPMS, for example... Figure 8 The document lists several common mathematical expressions for TPMS, and adjusts the surface offset in these expressions. C Bias value C， Construct a gradient TPMS cell dataset with thickness varying with location. The mathematical expressions for common TPMS surfaces are: (1) in, Let be the position vector in Euclidean space. The first in reciprocal space Unit vector, For amplitude, For wavelength, For phase, Let be the surface offset. From equation (1), a first-order approximation can be derived to obtain mathematical representations of several typical TPMS surfaces, such as... Figure 8 As shown, the corresponding geometric shape is as follows Figure 1 As shown. Among them, Figure 1 Part (a) represents the geometric schematic diagram of the P-type TPMS surface, part (b) represents the geometric schematic diagram of the G-type TPMS surface, part (c) represents the geometric schematic diagram of the D-type TPMS surface, and part (d) represents the geometric schematic diagram of the I-WP type TPMS surface.

[0020] bias Control the shell thickness and adjust the offset. By treating these values ​​as functions of coordinates (x, y, z), a gradient TPMS cell dataset showing thickness variations with position can be constructed. Common 3D geometric models of TPMS cells are shown below. Figure 2 As shown. Among them, Figure 2The (a) part shows a three-dimensional geometric model of a P-type TPMS unit cell, the (b) part shows a three-dimensional geometric model of a G-type TPMS unit cell, the (c) part shows a three-dimensional geometric model of a D-type TPMS unit cell, the (d) part shows a three-dimensional geometric model of an I-WP-type TPMS unit cell, and the (e) part shows a three-dimensional geometric model of a PP-type TPMS unit cell.

[0021] S2: Based on the gradient TPMS unit cell data set obtained in step S1, the volume fraction of the TPMS unit cell is calculated under different bias amounts C The corresponding TPMS unit cell volume , and then the volume fraction of the TPMS unit cell is calculated The expression of the volume fraction of the TPMS unit cell is: (2) Wherein, is the volume of the TPMS unit cell, is the volume of the external contour envelope cube of the TPMS.

[0022] The Monte Carlo method is used to fit the volume fraction of the TPMS unit cell with the bias amount C , a volume fraction fitting model of the TPMS unit cell is constructed, and a gradient TPMS unit cell geometric size-volume fraction data set is constructed. The fitting function curves of the bias amount C and the volume fraction of several common TPMS unit cells are shown in Figure 9 .

[0023] S3: Based on the gradient TPMS unit cell geometric size-volume fraction data set obtained in step S2, the equivalent performance parameters of the TPMS unit cell are calculated based on the progressive homogenization method , , and , and the relationship between the volume fraction and the equivalent performance parameters , , , and is fitted by a polynomial to construct an equivalent performance prediction model of the TPMS lattice structure. Among them, , , and are the components of the equivalent elastic matrix D H of the TPMS unit cell, is the component of the equivalent heat conduction matrix C H of the TPMS unit cell, and the relationship is as follows: (3) (4) The fitting function of the equivalent performance of several common TPMS unit cells is as follows:Figure 10 are shown.

[0024] S4: Set the optimization design domain of the structure equivalent performance prediction model according to the design requirements and divide the finite element mesh, each finite element mesh unit, simply referred to as a mesh unit, is filled with a TPMS unit cell, and a design variable is defined The current volume fraction of the TPMS unit cell filled in each mesh unit .

[0025] (5) Wherein, is the number of TPMS unit cells, which is equal to the number of discrete mesh units. When the volume fraction is 1, it represents a solid, and is taken as When the volume fraction is 0, it represents a hole, and is taken as the intermediate value, which corresponds to the area filled by the gradient TPMS unit cell. For example, the interior of the structure model can be set as the optimization design domain, and 540 meshes (30x30x6) are divided, each mesh unit is filled with a TPMS unit cell, and a design variable is defined The volume fraction of the TPMS unit cell filled in each mesh unit .

[0026] S5: According to the current design variable obtained in step S4, density filtering is performed to obtain the physical density of each mesh unit: (6) Wherein, is the set of physical densities of each mesh unit, is the physical density of each mesh unit, which can also be regarded as the component of the physical density . The physical density of any mesh unit e can be calculated by the density filtering method.

[0027] Density filtering is to make the density value of the mesh unit be affected by both itself and the density of the adjacent mesh unit, so as to avoid the "checkerboard" phenomenon. In the density filtering process, a weight is usually introduced to determine the influence of the adjacent mesh unit.

[0028] (7) Wherein, is the distance between the center points of the mesh unit and the mesh unit , is the filtering radius.

[0029] The density filtering formula is: (8) where, is the set of neighborhood grid cells with a radius of as the center, is the set of neighborhood grid cells with a radius of is the volume of grid cell . Thus, the physical density of each grid cell is determined by the density of all cells within the nearby circular domain, avoiding numerical problems such as the "checkerboard phenomenon".

[0030] S6: Based on the design variables in step S4 and the physical density obtained in step S5, set the initial configuration according to the design requirements, consider the optimization objectives related to load bearing and heat transfer, consider several constraints such as volume constraints, local displacement constraints, and establish a thermal-elastic coupled multi-objective topology optimization model considering load bearing and heat transfer performance. The optimization problem can be expressed as: (9) where, is the design variable, is the TPMS cell volume fraction of each grid cell, N is the total number of grid cells; is the objective function; is the total stiffness matrix of the structure, is the node displacement field, is the load vector; is the total thermal stiffness matrix of the structure, is the node temperature field, is the thermal load vector; is the constraint function, is the number of constraint functions, N g is the total number of constraint functions, which is determined by the design requirements; and are the lower and upper limits of the design variable, respectively.

[0031] Total load is expressed as: (10) where is the mechanical load, obtained from known conditions; is the thermal stress load, which can be expressed as: (11) where, is the area of grid cell e , , is the thermal expansion coefficient of the material, =[1 11 0 0 0] T , is the initial temperature of the center point of the mesh element, is the temperature of the center point of the mesh element, which is obtained by interpolating the node temperatures of the mesh element and the shape functions of the mesh element.

[0032] Objective function and constraint function There are performance indicators related to the thermoelastic problem, such as structural compliance, structural thermal compliance, maximum deformation, etc., and both are functions of the physical density of the mesh element.

[0033] S7: According to the optimization model in step S6, the sensitivity of the objective function and the constraint function is derived to obtain the sensitivity information of the objective function and the sensitivity information of the constraint function . Since the objective function and the constraint function are functions of the physical density of the mesh element, the sensitivity information of the objective function and the sensitivity information of the constraint function need to be obtained through the chain rule, and the formula is: Where, (12) (13) Where, is the derivative of the physical density with respect to the design variable , which can be obtained by differentiating the density filtering formula in S5.

[0034] S8: According to the sensitivity information of the objective function and the sensitivity information of the constraint function obtained in step S7, use the gradient optimization algorithm to iteratively update the design variable to obtain a new design variable , and enter the next optimization cycle.

[0035] S9: Repeat steps S4 to S7, and judge whether the optimization is converged according to the number of cycles. If the specified number of cycles is reached, the optimization is ended, and the volume fraction distribution of the TPMS point array structure is obtained according to the design variable ; otherwise, proceed to step S8.

[0036] ​S10: According to the volume fraction distribution information obtained in step S9 and the TPMS unit cell volume fraction fitting model constructed in step S2, the TPMS unit cell with corresponding geometric size is filled into the corresponding grid unit, and the geometric smooth connection of the gradient TPMS structure is realized by using the control point method to obtain the gradient TPMS lattice structure design. The mathematical expression of the gradient TPMS lattice structure obtained by using the control point method is as follows: (14) wherein, is an implicit function of the mixed structure composed of all unit cells, is an implicit function of the i-th unit cell, e is the total number of unit cells, is a transition parameter between substructures, is a point coordinate, is a transition position between substructures, that is, a control point.

[0037] An example of realizing geometric smooth connection of the gradient TPMS structure by using the control point method is shown in FIG. 4. Figure 3 In the example, four control points are used to realize geometric smooth connection of the four TPMS unit cells in the X and Y directions. In the example, X1 is a control point of the upper left corner D-type unit cell and the upper right corner G-type unit cell, that is, a transition position of the D-type and G-type unit cells. Similarly, X2 is a control point of the lower left corner G-type unit cell and the lower right corner P-type unit cell, Y1 is a control point of the upper right corner G-type unit cell and the lower right corner P-type unit cell, and Y2 is a control point of the upper left corner D-type unit cell and the lower left corner G-type unit cell.

[0038] Figure 4 A four-corner clamped cube calculation model is described, wherein the model size is , a uniform heat source is applied to the whole model, the bottom four nodes are clamped, a concentrated force F of 1 N is applied to the bottom midpoint, the temperature T of the center region of the upper surface is constrained to 0 K, and the remaining surfaces are adiabatic surfaces, Figure 5 is an implementation flowchart of the method.

[0039] S1: Based on the mathematical expressions of the selected several TPMS curved surfaces in Figure 8 , the bias amount C in the expressions is adjusted to construct a gradient TPMS unit cell data set with thickness varying with position. The three-dimensional geometric models of several common TPMS unit cells are shown in Figure 8 .

[0040] S2: According to the gradient TPMS unit cell data set obtained in step S1, the volume of the TPMS unit cell corresponding to different bias amounts C is calculated, and then the unit cell volume fraction is calculated.and the volume fraction of TPMS unit cell is fitted by Monte Carlo method and the volume fraction of TPMS unit cell is fitted by Monte Carlo method C and the volume fraction of TPMS unit cell is fitted by Monte Carlo method C and the volume fraction of TPMS unit cell is fitted by Monte Carlo method and the volume fraction of TPMS unit cell is fitted by Monte Carlo method Figure 9 and the volume fraction of TPMS unit cell is fitted by Monte Carlo method and the volume fraction of TPMS unit cell is fitted by Monte Carlo method

[0041] S3: Based on the gradient TPMS unit cell geometry size-volume fraction data set obtained in step S2, the equivalent performance parameters of the TPMS unit cell are calculated by the progressive homogenization method , , and and the relationship between the volume fraction of TPMS unit cell and the equivalent performance parameters of TPMS unit cell is fitted by a polynomial function , , and and the relationship between the volume fraction of TPMS unit cell and the equivalent performance parameters of TPMS unit cell is fitted by a polynomial function Figure 10 and the relationship between the volume fraction of TPMS unit cell and the equivalent performance parameters of TPMS unit cell is fitted by a polynomial function

[0042] S4: According to the design requirements, the interior of the four-side fixed cube model is set as the optimization design domain, and a total of 540 grids (30x30x6) are divided, each grid unit is filled with a TPMS unit cell, and the design variable is defined as the set of volume fractions of TPMS unit cells filled in each grid unit .

[0043] S5: According to the current design variable obtained in step S4, density filtering is performed to obtain the physical density of each grid unit.

[0044] S6: According to the design variable in step S4 and the physical density obtained in step S5, according to the design requirements, the initial configuration is set as a uniform TPMS lattice structure, and the pp type TPMS unit cell is filled. The weighted combination of structural compliance and thermal compliance is taken as the optimization objective, and the total volume of the material is constrained to ensure that the total volume of the structure remains unchanged during the optimization process, and a thermal-elastic coupled multi-objective topology optimization model considering the bearing and heat transfer performance is established. The optimization problem can be expressed as: (15) wherein and represent the structural compliance and the thermal compliance, respectively and are the normalization coefficients, which take the values corresponding to the initial design. Represents the linear weighting coefficients. The larger the value, the more the optimization focuses on stiffness; For volume constraint functions, Represents the total integral of the structure. To indicate volume constraints, this embodiment sets... .

[0045] Accordingly, the initial structure was set as a uniform TPMS lattice unit cell with a volume fraction of 0.3.

[0046] S7: Based on the optimization model in step S6, derive the sensitivity of the objective function and constraint function to obtain the objective function. Sensitivity information and constraint functions Sensitivity information The objective function applies to any mesh element. e physical density Sensitivity for: (16) in, For grid cells e displacement, Represents grid cells e The equivalent elasticity matrix is ​​derived from the mesh elements. e equivalent parameters , , Assembled Represents grid cells e Equivalent heat conduction matrix Assembled; For grid cells e The strain-displacement matrix, For grid cells e The thermal strain-temperature matrix.

[0047] Chain rule terms introduced by density filtering Sensitivity to volume constraints The derivation has been provided by numerous documents and will not be repeated here.

[0048] S8: Based on the objective function sensitivity information obtained in step S7 and constraint function sensitivity information Gradient optimization algorithm is used for design variables Perform iterative updates to obtain new design variables. Then, proceed to the next optimization cycle.

[0049] S9: repeat steps S4 to S7, and determine whether the optimization converges according to the number of cycles. If the specified number of cycles is reached, the optimization ends, and the design variable obtain the volume fraction distribution of the gradient TPMS lattice structure; otherwise, proceed to step S8. In this example, the specified number of cycles is set to 50 steps.

[0050] S10: according to the volume fraction distribution information obtained in step S9 and the volume fraction fitting model of the TPMS unit cell constructed in step S2, fill the TPMS unit cell with corresponding geometric dimensions into the corresponding finite element grid element, and use the control point method to realize the geometric smooth connection of the gradient TPMS structure, to obtain the gradient TPMS lattice structure design.

[0051] Figure 6 and Figure 7 The volume fraction distribution of the gradient TPMS lattice structure and the gradient TPMS lattice design of this embodiment are shown in Figs. 8 and 9, respectively. In Figs. 8 and 9, Figure 6 only the grid elements with a volume fraction greater than 0.5 are shown. As can be seen, the high-volume fraction TPMS is concentrated near the temperature constraint region and is connected to the four hinge points, enhancing the heat transfer performance near the temperature constraint region while improving the load-bearing performance of the structure, meeting the design requirements.

[0052] To intuitively show the improvement of the structure's load-bearing and heat transfer performance by the present application, this embodiment compares the performance of the optimized gradient TPMS lattice structure with that of the conventional uniform TPMS lattice structure, where the volume fraction is 30% of the total volume of the model. Compared with the uniform design, the compliance of the optimized gradient TPMS structure is reduced by 80.57%, and the thermal compliance is reduced by 75.11%. Thus, the present application can significantly improve the load-bearing and heat transfer performance of the TPMS lattice structure.

[0053] The essence of the present application is to propose a gradient TPMS lattice structure topology optimization algorithm for thermoelastic coupling problems, establish an equivalent performance prediction model of the TPMS unit cell, and use a topology optimization method to design a gradient TPMS lattice structure, thereby greatly improving the load-bearing and heat transfer performance of the structure. This method can effectively overcome the many limitations of traditional methods and stably and efficiently design structures with superior performance and reasonable material distribution.

[0054] Modifying the load-bearing and heat transfer related objective functions of the optimization problems described in the foregoing embodiments, changing the optimization method, or equivalently replacing part of the material interpolation model does not deviate the essence of the corresponding method and scheme from the scope of the methods and schemes of the embodiments of the present application.

[0055] It should be understood that the method of the present application can be implemented by a computer system, which can be referred to as a thermally elastic coupled multi-objective topology optimization design system of gradient TPMS lattice structure, which can be any computer system, for example, including a processor and a memory, the memory executing computer readable program code, the processor being configured to run the computer readable program code to implement the above method.

[0056] In addition to implementing the system provided by the present application and each device, module, unit thereof in pure computer readable program code, the system provided by the present application and each device, module, unit thereof can also be implemented in the form of logic gates, switches, application specific integrated circuits, programmable logic controllers and embedded microcontrollers, etc. by logically programming the method steps to achieve the same functions. Therefore, the system provided by the present application and each device, module, unit thereof can be considered as a hardware component, and the devices, modules, units included therein for implementing various functions can also be considered as structures within the hardware component; the devices, modules, units for implementing various functions can also be considered as both software modules implementing methods and structures within hardware components.

[0057] The above-described embodiments only express the implementation manners of the present application, and cannot be understood as a limitation on the scope of the patent of the present application. It should be noted that, for those skilled in the art, without departing from the concept of the present application, a number of modifications and improvements can be made, which are all within the protection scope of the present application.

Claims

1. A thermoelastic coupling multi-objective topology optimization design method for a gradient TPMS lattice structure, characterized in that, Including the following steps: S1, based on the mathematical expressions of multiple TPMS surfaces, adjust the bias C in the mathematical expressions to construct a gradient TPMS cell dataset with thickness varying with position; S2, based on the obtained gradient TPMS cell dataset, calculate the TPMS cell volume corresponding to different biases C. Then the unit cell volume fraction can be calculated. The Monte Carlo method was used to fit the unit cell volume fraction. To understand the relationship with the bias C, a volume fraction fitting model for TPMS cells is constructed, and a gradient TPMS cell geometric parameters-volume fraction dataset is established, which includes TPMS lattice cells with different volume fractions. S3, for different volume fractions The equivalent performance parameters of the TPMS lattice unit cell were calculated based on the progressive homogenization method, and the volume fraction was fitted using a polynomial. Based on the relationship between the equivalent performance parameters, an equivalent performance prediction model for the gradient TPMS lattice structure is constructed. S4. Based on the design requirements, define the optimization design domain of the structure and divide it into meshes. Each mesh element is filled with a TPMS unit cell. Based on the equivalent performance prediction model, define the design variables. TPMS unit cell volume fraction for filling each grid cell A set; S5, for design variables Density filtering is performed to obtain the physical density of each grid cell. ; S6, based on the physical density In addition to design requirements, optimization objectives related to load-bearing and heat transfer are considered, constraints are taken into account, and a thermoelastic coupling multi-objective topology optimization model considering load-bearing and heat transfer performance is established. S7. Based on the optimization model, the sensitivity of its objective function and constraint function is derived to obtain the sensitivity information of the objective function and the sensitivity information of the constraint function. S8. Based on the sensitivity information of the objective function and the sensitivity information of the constraint function, a gradient optimization algorithm is used to optimize the design variables. Perform iterative updates; S9, determine whether the iteration has converged based on the number of iteration steps. If it has converged, exit the loop and obtain the volume fraction distribution of the gradient TPMS lattice structure. S10, based on the volume fraction distribution and the constructed TPMS unit cell volume fraction fitting model, fill the corresponding geometric size TPMS unit cells into the corresponding grid cells, and use the control point method to achieve geometrically smooth connection of the gradient TPMS structure, thereby obtaining the design of the gradient TPMS lattice structure.

2. The thermoelastic coupling multi-objective topology optimization design method for gradient TPMS lattice structures according to claim 1, wherein: If convergence is not achieved, repeat loop S4 to S7 until S8 determines convergence.

3. The thermoelastic coupling multi-objective topology optimization design method for gradient TPMS lattice structures according to claim 1, wherein: The equivalent performance parameter is: , , and ,in, Represents the main diagonal component of the equivalent elasticity matrix of a TPMS unit cell; Represents the off-diagonal components in the equivalent elasticity matrix of a TPMS unit cell; This represents the shear component in the equivalent elasticity matrix of a TPMS unit cell; This represents the main diagonal component of the equivalent heat conduction matrix of a TPMS unit cell.

4. The thermoelastic coupling multi-objective topology optimization design method for gradient TPMS lattice structures according to claim 3. The feature is that: the TPMS unit cell equivalent elastic matrix Represented as 。 5. The thermoelastic coupling multi-objective topology optimization design method for gradient TPMS lattice structures according to claim 3, The feature is that: the TPMS unit cell equivalent heat conduction matrix Represented as: 。 6. A thermoelastic coupling multi-objective topology optimization design system for gradient TPMS lattice structures, characterized in that, It includes a processor and a memory, the memory executing computer-readable program code, and the processor being configured to run the computer-readable program code to implement the method of any one of claims 1 to 5.

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