Thermoelastic coupled multi-objective topology optimization design method and system of gradient TPMS lattice structure

Abstract

The application provides a thermal-elastic coupling multi-objective topology optimization design method and system for a gradient TPMS lattice structure, which firstly establishes an equivalent performance prediction model of a TPMS lattice unit cell, and on the basis, a multi-objective topology optimization model is constructed, which is suitable for a gradient TPMS lattice structure design problem needing to comprehensively consider thermal management and mechanical bearing capacity. The method considers a four-corner fixed support cubic calculation model, and through optimization, a gradient TPMS lattice structure design with superior performance and reasonable material distribution is obtained, 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 light weight, can meet the stringent 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, providing a new way for the engineering application and multi-objective optimization of the lattice structure. Therefore, it has important theoretical significance and engineering value to systematically study the multi-performance coupling mechanism and topology optimization design method of the lattice structure.

[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 lacking. 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:

[0006] A thermal-elastic coupling multi-objective topology optimization design method for a gradient TPMS lattice structure, the design method comprising the following steps: first, based on the mathematical expression of several common TPMS curved surfaces, adjusting the offset amount C, and a gradient TPMS unit cell dataset is constructed. Second, based on the obtained gradient TPMS unit cell dataset, the volume fraction of the TPMS unit cell is calculated under different biasing amounts C The corresponding TPMS unit cell volume , and the volume fraction of the TPMS unit cell is calculated under different biasing amounts , and the volume fraction of the TPMS unit cell is calculated under different biasing amounts , and the volume fraction of the TPMS unit cell is calculated under different biasing amounts C , and the volume fraction of the TPMS unit cell is calculated under different biasing amounts , and the volume fraction of the TPMS unit cell is calculated under different biasing amounts , , , and , and the volume fraction of the TPMS unit cell is calculated under different biasing amounts , and the volume fraction of the TPMS unit cell is calculated under different biasing amounts , and the volume fraction of the TPMS unit cell is calculated under different biasing amounts , and the volume fraction of the TPMS unit cell is calculated under different biasing amounts , and the volume fraction of the TPMS unit cell is calculated under different biasing amounts , and the volume fraction of the TPMS unit cell is calculated under different biasing amounts , and the volume fraction of the TPMS unit cell is calculated under different biasing amounts , and the volume fraction of the TPMS unit cell is calculated under different biasing amounts , and the volume fraction of the TPMS unit cell is calculated under different biasing amounts , and the volume fraction of the TPMS unit cell is calculated under different biasing amounts , and the volume fraction of the TPMS unit cell is calculated under different biasing amounts

[0007] Some embodiments of the present application provide a thermal-elastic coupled multi-objective topology optimization design system for a gradient TPMS lattice structure, comprising a processor and a memory, the memory executing computer readable program code, the processor configured to run the computer readable program code to implement the above method.

[0008] The beneficial effects of the present application include: for the design problem of gradient TPMS lattice structure which needs to balance the bearing and heat transfer performance, the present application provides a novel thermal-elastic coupled multi-objective topology optimization design method for 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 design of gradient TPMS lattice structure; a multi-objective topology optimization model considering thermal-elastic coupling problem is constructed, which realizes the multifunctional gradient TPMS lattice structure design considering the bearing and heat transfer performance requirements. The present application is suitable for the design problem of gradient TPMS lattice structure which needs to consider the heat management and mechanical bearing capacity. BRIEF DESCRIPTION OF DRAWINGS

[0009] Figure 1 It is a common TPMS curved surface geometric diagram in step S1 of the thermal-elastic coupled multi-objective topology optimization design method for gradient TPMS lattice structure of the present application.

[0010] Figure 2 It is a three-dimensional geometric model of common TPMS unit cell in step S1 of the thermal-elastic coupled multi-objective topology optimization design method for gradient TPMS lattice structure of the present application.

[0011] Figure 3 It is an example of gradient TPMS structure geometric smooth connection based on control point method in step S10 of the thermal-elastic coupled multi-objective topology optimization design method for gradient TPMS lattice structure of the present application.

[0012] 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.

[0013] Figure 5 It is a flowchart of the thermal-elastic coupled multi-objective topology optimization method for gradient TPMS lattice structure according to an embodiment of the present application.

[0014] Figure 6 It is a schematic diagram of the volume fraction distribution of gradient TPMS lattice structure in a specific embodiment of the thermal-elastic coupled multi-objective topology optimization design method for gradient TPMS lattice structure of the present application.

[0015] Figure 7It is a gradient TPMS lattice structure design schematic diagram in the embodiment of the thermal-elastic coupling multi-objective topology optimization design method of the gradient TPMS lattice structure of the application.

[0016] Figure 8 It is a schematic diagram of the mathematical expression of a typical TPMS.

[0017] Figure 9 It is a schematic diagram of the fitting function curve of the bias and volume fraction of a common TPMS unit cell.

[0018] Figure 10 It is a schematic diagram of the equivalent performance fitting function of a common TPMS unit cell. DETAILED DESCRIPTION

[0019] The specific embodiments of the application will be described in detail below in combination with the technical solutions and the accompanying drawings.

[0020] The thermal-elastic coupling multi-objective topology optimization design method of the gradient TPMS lattice structure according to the application comprises, as shown in Figure 5 , the following steps:

[0021] S1: First, based on the mathematical expression of the selected TPMS, for example, the mathematical expressions of several common TPMS listed in Figure 8 , adjust the surface bias C , simply bias, in the mathematical expression. C， Construct a gradient TPMS unit cell data set with varying thickness. The mathematical expression of the common TPMS surface is:

[0022] (1)

[0023] wherein, is a position vector in the Euclidean space, is the th unit vector in the reciprocal space, is the amplitude, is the wavelength, is the phase, is the surface bias. By first-order approximation derivation from equation (1), the mathematical expressions of several typical TPMS surfaces can be obtained, as shown in Figure 8 , and the corresponding geometric shapes are shown in Figure 1 . Among them, Figure 1 part (a) of which represents a P-type TPMS surface geometric schematic diagram, part (b) represents a G-type TPMS surface geometric schematic diagram, part (c) represents a D-type TPMS surface geometric schematic diagram, and part (d) represents an I-WP-type TPMS surface geometric schematic diagram.

[0024] bias Control the housing 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 2 (a) represents the three-dimensional geometric model of the P-type TPMS unit cell, (b) represents the three-dimensional geometric model of the G-type TPMS unit cell, (c) represents the three-dimensional geometric model of the D-type TPMS unit cell, (d) represents the three-dimensional geometric model of the I-WP type TPMS unit cell, and (e) represents the three-dimensional geometric model of the PP type TPMS unit cell.

[0025] S2: Based on the gradient TPMS cell dataset obtained in step S1, calculate different biases. C Corresponding TPMS single cell volume Then the TPMS unit cell volume fraction was calculated. The expression for TPMS unit cell volume fraction is:

[0026] (2)

[0027] in, This refers to the volume of a TPMS unit cell. Let be the volume of the outer contour envelope cube of TPMS.

[0028] Monte Carlo method was used to fit the TPMS single cell volume fraction. With bias C To understand the relationship between volume fraction and TPMS unit cell, a volume fraction fitting model is constructed, and a gradient TPMS unit cell geometry-volume fraction dataset is built. The biases of several common TPMS units are also discussed. C With volume fraction The fitted function curve is as follows Figure 9 As shown.

[0029] S3: Based on the gradient TPMS unit cell geometry-volume fraction dataset obtained in step S2, calculate its equivalent performance parameters using the asymptotic homogenization method. , ,and And a polynomial fitting of the volume fraction was used. With equivalent performance parameters , , and Based on the relationship between these factors, an equivalent performance prediction model for the TPMS lattice structure is constructed. Among these factors, , and The equivalent elasticity matrix D of a TPMS unit cell is shown below. H The amount, The equivalent heat conduction matrix C of a TPMS unit cell H The components are related as follows:

[0030] (3)

[0031] (4)

[0032] Equivalent performance fitting functions for several common TPMS unit cells are as follows: Figure 10 As shown.

[0033] S4: Based on the design requirements, define the optimization design domain of the structural equivalent performance prediction model and divide it into finite element meshes. Each finite element mesh element, referred to as a mesh element, is filled with a TPMS unit cell, and design variables are defined. The current volume fraction of TPMS unit cells used to fill each grid cell. A set of.

[0034] (5)

[0035] Where is the number of TPMS unit cells, which is equal to the number of discrete mesh elements. When the volume fraction... Time represents an entity, taken as The time represents a hole, and the median value corresponds to the region filled by gradient TPMS unit cells. For example, the interior of the structural model can be set as the optimization design domain, divided into 540 grids (30×30×6), with each grid cell filled with a TPMS unit cell, and design variables defined. TPMS unit cell volume fraction for filling each grid cell A set of.

[0036] S5: Based on the design variables obtained in step S4 Density filtering is performed to obtain the physical density of each grid cell. :

[0037] (6)

[0038] in, It is the set of physical densities of each grid cell. The physical density of each grid cell can also be considered as physical density. The components. Arbitrary mesh element. e The physical density can be calculated using the density filtering method.

[0039] Density filtering avoids the "checkerboard" effect by making the density value of a grid cell simultaneously influenced by the density of its own cells and those of its neighboring cells. A weight is typically introduced during density filtering. to determine the influence of neighboring grid cells.

[0040] (7)

[0041] where, is the grid cell and the grid cell center point, is the filtering radius.

[0042] The density filtering formula is:

[0043] (8)

[0044] where, is the set of neighborhood grid cells with the grid cell as the center, is the filtering radius, is the volume of the grid cell . Thus, the physical density of each grid cell is determined by the density of all cells within the circular domain near the cell, avoiding numerical problems such as "checkerboard phenomenon".

[0045] S6: According to 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 constraint, local displacement constraint, 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:

[0046] (9)

[0047] where, is the design variable, is the TPMS unit 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 limit and upper limit of the design variable, respectively.

[0048] Total load is expressed as:

[0049] (10)

[0050] wherein is the mechanical load, which is obtained from known conditions; is the thermal stress load, which can be expressed as:

[0051] (11)

[0052] wherein, is the area of the grid element e , , is the thermal expansion coefficient of the material, =[1 1 1 0 0 0] T , is the initial temperature of the grid element center point, is the temperature of the grid element center point, which is obtained by interpolating the grid element node temperature and the grid element shape function.

[0053] Objective function and constraint function There are performance indicators related to the problem of thermoelasticity, such as structural compliance, structural thermal compliance, maximum deformation, etc., and both are functions of the physical density of the grid element.

[0054] S7: According to the optimization model in step S6, the sensitivity of the objective function and the constraint function is derived, and the sensitivity information of the objective function and the sensitivity information of the constraint function are obtained. Since the objective function and the constraint function are functions of the physical density of the grid 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:

[0055] (12)

[0056] (13)

[0057] wherein, is the derivative of the physical density with respect to the design variable , which can be obtained by derivation according to the density filtering formula in S5.

[0058] ​​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.

[0059] S9: Repeat steps S4 to S7, and determine whether the optimization has converged based on the number of iterations. If the specified number of iterations is reached, the optimization ends, based on the design variables. Obtain the gradient TPMS lattice structure volume fraction distribution; otherwise, proceed to step S8.

[0060] S10: Based on the volume fraction distribution information obtained in step S9 and the TPMS unit cell volume fraction fitting model constructed in step S2, TPMS unit cells of corresponding geometric dimensions are filled into the corresponding mesh elements, and the control point method is used to achieve geometrically smooth connections of the gradient TPMS structure, thus obtaining the gradient TPMS lattice structure design. The mathematical expression of the gradient TPMS lattice structure obtained using the control point method is as follows:

[0061] (14)

[0062] in, For the implicit function of the hybrid structure composed of all unit cells, For the first e Implicit functions of a single cell The total number of cells. These are transition parameters between substructures. Here are the coordinates of each point. These are the transition points between substructures, i.e., control points.

[0063] An example of implementing geometrically smooth connections in gradient TPMS structures using the control point method is as follows: Figure 3 As shown in the example, four control points are used to achieve a geometrically smooth connection between four TPMS units in the X and Y directions. X1 is the control point between the top-left D-type unit and the top-right G-type unit, representing the transition between the two. Similarly, X2 is the control point between the bottom-left G-type unit and the bottom-right P-type unit, Y1 is the control point between the top-right G-type unit and the bottom-right P-type unit, and Y2 is the control point between the top-left D-type unit and the bottom-left G-type unit.

[0064] Figure 4 This describes a computational model of a cube with fixed corners, where the model dimensions are... A uniform heat source is applied to the entire model. The bottom surface is fixed at four nodes, and a concentrated force F of 1 N is applied at the midpoint of the bottom surface. The temperature T is constrained to 0 K in the central region of the upper surface, and the remaining surfaces are adiabatic.Figure 5 is the flow chart of the method.

[0065] S1: Based on Figure 8 selected several TPMS surface mathematical expression of the expression in the offset C , the construction of the thickness of the gradient TPMS unit cell data set. Several common TPMS unit cell three-dimensional geometric model as Figure 8 shown.

[0066] S2: According to the gradient TPMS unit cell data set obtained in step S1, the volume of the TPMS unit cell corresponding to the different offset C , , and then calculate the volume fraction of the unit cell , and the Monte Carlo method fitting TPMS unit cell volume fraction and offset C relationship, the volume fraction fitting model of TPMS unit cell is constructed, and the geometric parameter-volume fraction data set of gradient TPMS unit cell is established. The fitting function curve mathematical expression of the offset C and volume fraction of common TPMS unit cell as shown in Figure 9 .

[0067] S3: According to the geometric size-volume fraction data set of gradient TPMS unit cell obtained in step S2, the equivalent performance parameters , , and are calculated based on the method of progressive homogenization, and the relationship between volume fraction and equivalent performance parameters , and is fitted by polynomial to construct the equivalent performance prediction model of TPMS lattice structure. The equivalent performance fitting function of several common TPMS unit cell as shown in Figure 10 .

[0068] S4: According to the design requirements, set the four-side fixed cube model inside the optimization design domain, a total of 540 grids (30x30x6), each grid unit is filled with a TPMS unit cell, and the design variable is defined as the set of volume fraction of TPMS unit cell filled in each grid unit .

[0069] S5: According to the current design variable obtained in step S4, the density filtering is carried out to obtain the physical density of each grid unit .

[0070] S6: Based on the design variables in step S4 and the physical density obtained in step S5, and according to the design requirements, the initial configuration is set as a uniform TPMS lattice structure, and pp-type TPMS unit cells are used for filling. The structural compliance and thermal compliance are weighted and combined as optimization objectives, while constraints are imposed on the total material volume to ensure that the total structural volume remains unchanged during the optimization process. A thermoelastic coupled multi-objective topology optimization model considering load-bearing and heat transfer performance is established. The optimization problem can be expressed as:

[0071] (15)

[0072] in, and These represent structural compliance and thermal compliance, respectively. and Its normalization coefficient is taken as the corresponding value in 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... .

[0073] Accordingly, the initial structure was set as a uniform TPMS lattice unit cell with a volume fraction of 0.3.

[0074] 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:

[0075] (16)

[0076] 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 cellse a strain-displacement matrix, a thermal strain-temperature matrix for the grid cell e a thermal strain-temperature matrix for the grid cell.

[0077] density filter introduced chain rule terms and volume constraint sensitivities have been provided by a large number of literature, here will not be repeated.

[0078] S8: the objective function sensitivity information obtained according to step S7 and constraint function sensitivity information , using gradient optimization algorithm to iterative update design variable , get new design variable , into the next round of optimization cycle.

[0079] S9: repeat steps S4 to S7, and judge whether the optimization is converged according to the cycle number. If the specified cycle number is reached, the optimization is ended, and the gradient TPMS point array structure volume fraction distribution is obtained according to the design variable ; otherwise, step S8 is performed. In this example, the specified cycle number is set to 50 steps.

[0080] S10: according to the volume fraction distribution information obtained in step S9 and the TPMS unit volume fraction fitting model constructed in step S2, fill the TPMS unit corresponding to the geometric size into the corresponding finite element grid cell, and realize the geometric smooth connection of the gradient TPMS structure using the control point method to obtain the gradient TPMS point array structure design.

[0081] Figure 6 and Figure 7 respectively give the gradient TPMS point array structure volume fraction distribution and the gradient TPMS point array design of this embodiment. Among them, Figure 6 only the grid cell with volume fraction greater than 0.5 is shown. It can be seen that the high volume fraction TPMS is concentrated near the temperature constraint area and connected with the four hinge points, which enhances the heat transfer performance near the temperature constraint area and improves the carrying capacity of the structure, meeting the design requirements.

[0082] In order to intuitively reflect the improvement of the structure carrying capacity and heat transfer performance of the present application, this embodiment compares the performance of the optimized gradient TPMS point array structure and the traditional uniform TPMS point array structure, wherein the volume fraction is 30% of the total volume of the model. Compared with the uniform design, the flexibility of the optimized gradient TPMS structure is reduced by 80.57%, and the thermal flexibility is reduced by 75.11%. Therefore, the present application can significantly improve the carrying capacity and heat transfer performance of the TPMS point array structure.

[0083] 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 realize the design of the gradient TPMS lattice structure by using the topology optimization method, so as to greatly improve the structure bearing and heat transfer performance. This method can effectively overcome the many limitations of traditional methods and can stably and efficiently design structures with superior performance and reasonable material distribution.

[0084] The modification of the bearing and heat transfer related objective function of the optimization problem described in the foregoing embodiments, the change of the optimization method, or the equivalent replacement of part of the material interpolation model does not deviate from the essence of the corresponding method and scheme, and does not deviate from the scope of the method and scheme of the embodiments of the present application.

[0085] 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 thermal-elastic coupling 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.

[0086] 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 realized 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 function. 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 the method and structures within the hardware component.

[0087] The above-described embodiments only express the implementation of the present application, but cannot be interpreted as limiting the scope of the present patent, and 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 scope of the present application.

Claims

1. A thermo-elastic coupled multi-objective topology optimization design method of a gradient TPMS lattice structure, characterized in that, The method comprises the steps of: S1, constructing a gradient TPMS unit cell data set with a thickness varying with position by adjusting a bias C in a mathematical expression of a plurality of TPMS surfaces; S2, calculating the volume of the TPMS unit cell corresponding to different bias amounts C based on the obtained gradient TPMS unit cell data set , and then calculating the volume fraction of the unit cell , and fitting the volume fraction of the unit cell with the bias amount C by using the Monte Carlo method , constructing a volume fraction fitting model of the TPMS unit cell, and establishing a geometric parameter-volume fraction data set of the gradient TPMS unit cell, wherein the data set comprises TPMS lattice unit cells with different volume fractions; S3, for different volume fractions of TPMS lattice unit, the equivalent performance parameters are calculated based on the method of homogenization, and the relationship between the volume fraction and each of the equivalent performance parameters is fitted by a polynomial to construct an equivalent performance prediction model of the gradient TPMS lattice structure. S4, setting an optimization design domain of the structure according to design requirements and dividing a grid, each grid unit being filled with a TPMS unit cell, and defining design variables according to the equivalent performance prediction model a set of volumes of the TPMS unit cells filled for each grid unit a set of volumes of the TPMS unit cells filled for each grid unit S5, on the design variables Density filtering is performed to obtain the physical density of each grid cell ; S6, according to the physical density And design requirements, considering the optimization goal of bearing and heat transfer, considering constraints, and establishing a thermo-elastic coupling multi-objective topology optimization model considering bearing and heat transfer performance; S7, deriving sensitivity information of a target function and sensitivity information of a constraint function of the optimization model according to the optimization model; S8, using a gradient optimization algorithm to iteratively update the design variables based on the sensitivity information of the objective function and the sensitivity information of the constraint functions performing an iterative update; S9, judging whether to converge according to a loop step number of the iterative updating, and if converging, exiting the loop to obtain a volume fraction distribution of the gradient TPMS point array structure; S10, filling a TPMS unit cell with corresponding geometric dimensions to a corresponding grid unit according to the volume fraction distribution and a constructed TPMS unit cell volume fraction fitting model, and realizing geometric smooth connection of the gradient TPMS structure by using a control point method to obtain a design of the gradient TPMS point array structure.

2. The thermo-elastic coupled multi-objective topology optimization design method of gradient TPMS lattice structures of claim 1, wherein it is characterized by: If not converging, repeating the loop of S4 to S7 until S8 judges to converge.

3. The thermally elastic coupled multi-objective topology optimization design method of gradient TPMS lattice structures of claim 1, wherein it is characterized by: The equivalent performance parameters are , , and wherein, represents the main diagonal components of the TPMS unit cell equivalent elastic matrix; represents the off-diagonal components in the TPMS unit cell equivalent elastic matrix; represents the shear components in the TPMS unit cell equivalent elastic matrix; represents the main diagonal components of the TPMS unit cell equivalent thermal conduction matrix.

4. The thermo-elastic coupled multi-objective topology optimization design method of gradient TPMS lattice structures of claim 3, wherein, characterized in that: wherein, the TPMS unit cell equivalent elastic matrix is represented as 。 5. The thermal-elastic coupled multi-objective topology optimization design method of gradient TPMS lattice structures of claim 3, wherein, characterized in that: wherein, the TPMS unit cell equivalent heat conduction matrix is represented as: 。 6. A thermo-elastic coupled multi-objective topology optimization design system of a gradient TPMS lattice structure, characterized in that, The system comprises 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 method in any one of claims 1 to 5.

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