Gradient conformal dot matrix design method and system based on topological optimization density field mapping and application

Abstract

The invention provides a gradient conformal dot matrix design method and system based on topological optimization density field mapping and application, and relates to the field of structural lightweight design. The design method comprises the following steps: dividing a model into conformal hexahedral grids, wherein the size of a grid unit is set as the size of a lattice cell element; on the basis of topological optimization pretreatment calculation, density field information of grid units is extracted, and a continuous gradient TPMS lattice structure is constructed on the basis of a three-way linear interpolation method through density field mapping; extracting space coordinates of TPMS unit cells of the density field corresponding to each conformal hexahedral grid unit; all vertex coordinates of the TPMS unit cells in the local coordinate system are converted into corresponding conformal hexahedral grid unit coordinates in the overall coordinate system based on isoparametric conversion; traversing all the conformal hexahedral grid units to obtain the gradient conformal TPMS lattice structure and outputting the gradient conformal TPMS lattice structure. According to the method, the defect that the mechanical property of the structure is influenced due to incomplete and non-conformal cells during traditional dot matrix filling can be overcome.

Description

Technical Field

[0001] The present invention relates to the field of lightweight structure design and additive manufacturing, and in particular to a gradient conformal lattice design method, system and application based on topological optimization density field mapping. Background Art

[0002] The three-dimensional lattice structure is a spatial structure formed by microstructures arranged in a certain periodicity. It has many excellent mechanical properties such as high specific strength, high specific stiffness, high energy absorption and light weight. Lightweight or functional design based on the lattice structure is currently an important method for innovative design for additive manufacturing, which can quickly realize lightweight structural design that meets functional requirements.

[0003] However, at present, there are the following difficulties in the filling design of lattice structures: first, the existing design is to replace the whole or part of the structure to be filled with a lattice structure. The design for structures with relatively regular appearance is relatively simple, but the shape of structural parts in actual engineering usually has a curved contour. The lattice cells of fixed size will not be able to guarantee a completely complete filling, and damaged cells will appear at the boundary of the structure, which will inevitably affect the overall performance of the lattice structure; second, most of the optimization designs are for uniform periodic lattice structures, and there is a lack of optimization design for conformal lattice structures. Summary of the invention

[0004] Purpose of the invention: A gradient conformal lattice design method based on topological optimization density field mapping is proposed, a system driving the design method is also proposed, and an application of the design method is further proposed. By selecting the unit size and unit type, a conformal hexahedral mesh is generated by the sweeping method for the model to be designed and its mesh information is obtained; after determining the boundary conditions and loads, the model after the hexahedral mesh is divided is subjected to topological optimization pre-processing calculations, and the density field information of the mesh unit is extracted from the results; based on the density field information, a continuous density field is calculated by a three-way linear interpolation method, thereby constructing a continuous gradient TPMS lattice structure; for each conformal hexahedral mesh unit, the spatial coordinates of all vertices of the TPMS unit cell corresponding to the density field are extracted; based on isoparametric transformation, all vertex coordinates of the TPMS unit cell located in the local coordinate system are transformed to the corresponding conformal hexahedral mesh unit coordinates located in the global coordinate system; all conformal hexahedral mesh units are traversed to obtain the gradient conformal TPMS lattice structure and output it. A gradient conformal lattice filling method for structural parts with curved contours is obtained, which can solve the shortcomings of traditional lattice filling that affects the mechanical properties of the structure due to incomplete and non-conformal cells.

[0005] In a first aspect of the present invention, a gradient conformal lattice design method based on topological optimization density field mapping is proposed, and the steps are as follows:

[0006] Divide the original model to be designed into conformal hexahedral meshes;

[0007] Performing topology optimization pre-processing calculation on the divided conformal hexahedral mesh to extract density field information of the mesh unit;

[0008] According to the density field information, a gradient TPMS lattice structure is constructed by a three-way linear interpolation method, and the gradient value of the lattice cell is equal to the density value of the hexahedral grid unit;

[0009] The spatial coordinates of the nodes of the conformal hexahedral grid unit are extracted respectively, and the density field information of the unit cell corresponding to the gradient TPMS lattice structure is determined;

[0010] Extract the spatial coordinates of the TPMS unit cell corresponding to the conformal hexahedral mesh unit and fill it into the conformal hexahedral mesh through isoparametric transformation;

[0011] Traverse all conformal hexahedral grid cells to obtain a gradient conformal lattice structure;

[0012] The gradient conformal lattice structure is output as a target model source file.

[0013] In order to optimize the above technical solution, the original model to be designed is divided into a conformal hexahedral mesh, which specifically includes: determining the mesh unit size, mesh unit type, and mesh generation technology. The mesh unit size is the size of the lattice unit cell to be filled. According to the requirements of the additive manufacturing process, the unit size should not be too small to avoid failure to print, and the unit size should not be too large to cause loss of model details; the mesh unit type should be an 8-node linear hexahedral unit; the mesh generation technology can choose the neutral axis algorithm in the sweep.

[0014] In order to optimize the above technical solution, the topology optimization of the divided conformal hexahedral mesh model needs to be performed. The elastic modulus E of the material used in the structure needs to be determined. c , Poisson's ratio υ, density ρ, structural boundary conditions, load loading, topology optimization algorithm, convergence criteria, optimization objectives and constraints, topology optimization problem based on the minimum strain energy criterion, its mathematical model of topology optimization can be described as follows:

[0015] find:ρ=[ρ1,ρ2,…,ρ i ,…,ρ n ] T

[0016] minimize:

[0017] subject to:KU(ρ)=F

[0018]

[0019] 0≤ρ min ≤ρ i ≤ρ max ≤1

[0020] Among them, the objective function C represents the structural strain energy, and the minimum strain energy is the optimization target, that is, the maximum stiffness; U(ρ) represents the node displacement vector, which is obtained by solving the finite element equilibrium equation KU(ρ)=F, and K represents the overall stiffness matrix; n represents the number of discrete hexahedral elements in the topology optimization design domain, and ρ is the normalized density field of each hexahedral element; V * represents the volume limit of the material in the topology optimization design domain, v = [v1, v2, …, v i ,v n ] T is the volume vector of each hexahedral unit, ρ min and ρ max Respectively represent the lower and upper limits of the hexahedral unit density field. In the numerical implementation, the optimization problem is solved by the OC algorithm, and the sensitivity derived from the adjoint method is used as the input condition. Finally, the hexahedral unit density field ρ is output at the optimal solution. fin .

[0021] In order to optimize the above technical solution, a continuous gradient TPMS lattice density field is constructed through three-way linear interpolation. The principle is to infer the value of any point in the bounding box through the information of the eight known vertices of the bounding box of the overall lattice structure. The steps are to perform linear interpolation in the x, y, and z directions respectively. Specifically, assuming that the information of the eight vertices of the function f from P1, P2 to P8 is known, to solve the value of point P in the space, linear interpolation can be performed along the x direction first, and the function value of R1 can be obtained using P1 and P2. Similarly, the values ​​of R2, R3, and R4 can be obtained; then, based on the solution results of R1, R2, R3, and R4, linear interpolation can be performed along the y direction to obtain the function values ​​of O1 and O2; finally, linear interpolation is performed along the z direction using O1 and O2 to obtain the result of the unknown point P. The specific formula is as follows:

[0022]

[0023] In the formula, x represents point R i The x-axis coordinate, x 2i Indicates point P 2i The x-axis coordinate of 2i-1 Indicates point P 2i-1 The x-axis coordinate of point O j The y-axis coordinate, y 2j Indicates point R 2j The y-axis coordinate of 2j-1 Indicates point R 2j-1 The y-axis coordinate of point P k The z-axis coordinate, z2k Indicates point O 2k The z-axis coordinate of 2k-1 Indicates point O 2k-1 The z-axis coordinate of .

[0024] In order to optimize the above technical solution, the density field information of the TPMS unit cell corresponding to the conformal hexahedral grid unit is extracted. Assuming that the number of gradient TPMS lattice structures in the x, y, and z directions is a, b, and c respectively, and the resolution of the generated TPMS lattice is n, the index of the density information corresponding to the i+1th unit cell in the gradient TPMS lattice density field information is:

[0025] [n*i:n*(i+1)+1,0:n+1,0:n+1]i<a

[0026] [n*(ia):n*(i–a+1)+1,n:2n+1,0:n+1]a≤i<2a

[0027] …

[0028] [n*(i–(b–1)*a):n*(i–(b–1)*a+1)+1,(b–1)*n:b*n+1,0:n+1](b–1)*a≤i<b*a

[0029] [n*(i–b*a):n*(i–b*a+1)+1,0:n+1,n:2n+1]b*a≤i<(b+1)*a

[0030] [n*(i–(b+1)*a):n*(i–(b+1)*a+1)+1,n:2n+1,n:2n+1](b+1)*a≤i<(b+2)*a

[0031] …

[0032] [n*(i–(2b–1)*a):n*(i–(2b–1)*a+1)+1,(b–1)*n:b*n+1,n:2n+1](2b-1)*a≤i<2b*a

[0033] [n*(i–2b*a):n*(i–2b*a+1)+1,0:n+1,2n:3n+1]2b*a≤i<(2b+1)*a

[0034] [n*(i–(2b+1)*a):n*(i–(2b+1)*a+1)+1,n:2n+1,2n:3n+1](2b+1)*a≤i<(2b+2)*a

[0035] …

[0036] [n*(i–(3b–1)*a):n*(i–(3b–1)*a+1)+1,(b–1)*n:b*n+1,2n:3n+1](3b–1)*a≤i<3b*a

[0037] …

[0038] [n*(i–(cb–1)*a):n*(i–(cb–1)*a+1)+1,(b–1)*n:b*n+1,(c–1)*n:c*n+1](cb–1)*a≤i<cb*a

[0039] The TPMS unit cell corresponding to the above conformal hexahedral grid unit is a grid model generated by the Marching cube algorithm. The coordinates (x, y, z) of its grid vertices in the local coordinate system of the lattice unit cell model are transformed into coordinates (X, Y, Z) in the global coordinate system of the model to be filled by means of isoparametric transformation of control points. The eight control points of the lattice unit cell are the eight vertices of the cube bounding box, which are calculated in the following way:

[0040]

[0041] in, are the spatial coordinates of the i-th control point in the three directions of the local coordinate system of the lattice unit cell model, all of which are not 0. are respectively the spatial coordinates of the ith node of the conformal hexahedral mesh unit in three directions in the global coordinate system of the model to be filled;

[0042] All vertices in the lattice unit cell model are traversed to complete the filling of the lattice unit cell model in a conformal hexahedral grid unit.

[0043] The second aspect of the present invention proposes to construct the gradient conformal lattice design method based on topology optimization density field mapping disclosed in the first aspect into a complete design system, which includes:

[0044] A first calculation module is used to divide the original model to be designed into conformal hexahedral meshes;

[0045] A second calculation module is used to perform topology optimization pre-processing calculation on the divided conformal hexahedral mesh and extract density field information of the mesh unit;

[0046] A third calculation module is used to construct a gradient TPMS lattice structure by a three-way linear interpolation method according to the density field information, wherein the gradient value of the lattice cell is equal to the density value of the hexahedral grid cell;

[0047] The fourth calculation module is used to extract the spatial coordinates of the nodes of the conformal hexahedral grid unit respectively, and determine the density field information of the unit cell corresponding to the gradient TPMS lattice structure;

[0048] A fifth calculation module is used to extract the spatial coordinates of the TPMS unit cell corresponding to the conformal hexahedral grid unit and fill it into the conformal hexahedral grid through isoparametric transformation;

[0049] A loop module, used for traversing all conformal hexahedral grid units, repeatedly driving the second calculation module, the third calculation module, the fourth calculation module, and the fifth calculation module to obtain a gradient conformal lattice structure;

[0050] An output module is used to output the gradient conformal lattice structure as a target model source file.

[0051] As a third aspect of the present invention, the application of the gradient conformal lattice design method based on topology optimization density field mapping disclosed in the above embodiment to the generation of computer three-dimensional modeling is proposed. The verified three-dimensional lattice model is output as a target model source file for subsequent industrial design and manufacturing.

[0052] Beneficial effects: The present invention innovatively proposes a gradient conformal lattice design concept based on topological optimization. The optimal structural density field information is obtained by topological optimization of the original model to be filled, and the model to be filled is discretely meshed. Any lattice unit cell can be conformally filled through isoparametric transformation, which is not restricted by the geometric shape of the lattice unit cell. It effectively solves the shortcomings of traditional design, such as the incomplete unit cells that reduce structural performance and the lack of optimization design methods for conformal lattice structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 Flow chart of the gradient conformal lattice design method in this embodiment.

[0054] Figure 2 Schematic diagram of boundary conditions and load loading during the structural topology optimization process after being divided into conformal hexahedral meshes.

[0055] Figure 3 Infographic of the density field for the best structure for topology optimization.

[0056] Figure 4 This is the schematic diagram of three-way linear interpolation.

[0057] Figure 5 Schematic diagram of the geometric representation of a gradient conformal lattice design based on topology optimization density field mapping. DETAILED DESCRIPTION

[0058] In the following description, a large number of specific details are provided to provide a more thorough understanding of the present invention. However, it is apparent to those skilled in the art that the present invention can be implemented without one or more of these details. In other examples, in order to avoid confusion with the present invention, some technical features known in the art are not described.

[0059] The present invention provides a gradient conformal lattice design method based on topological optimization density field mapping, the process is shown in Figure 1 As shown, the steps are as follows:

[0060] S1: Divide the original model to be designed into a conformal hexahedral grid, and the grid unit size is the size of the unit cell of the lattice to be filled;

[0061] Constructing a conformal hexahedral mesh includes determining the mesh unit size, mesh unit type, and mesh generation technology. The mesh unit size is the size of the lattice unit cell to be filled. According to the additive manufacturing process requirements, the unit size should not be too small to avoid failure to print, nor should it be too large to cause loss of model details. The mesh unit type should be an 8-node linear hexahedral unit. The mesh generation technology can select the neutral axis algorithm in the sweep.

[0062] S2: Perform topology optimization pre-processing calculations on the divided conformal hexahedral mesh model to extract the density field information of the mesh cells;

[0063] To perform topological optimization on the filled structure with a conformal hexahedral mesh, it is necessary to determine the elastic modulus E of the material used in the structure. c , Poisson's ratio υ, density ρ, structural boundary conditions, load loading, topology optimization algorithm, convergence criteria, optimization objectives and constraints, topology optimization problem based on the minimum strain energy criterion, its mathematical model of topology optimization can be described as follows:

[0064] find:ρ=[ρ1,ρ2,…,ρ i ,…,ρ n ] T

[0065] minimize:

[0066] subject to:KU(ρ)=F

[0067]

[0068] 0≤ρ min ≤ρ i ≤ρ max ≤1

[0069] Among them, the objective function C represents the structural strain energy, and the minimum strain energy is the optimization target, that is, the maximum stiffness; U(ρ) represents the node displacement vector, which is obtained by solving the finite element equilibrium equation KU(ρ)=F, and K represents the overall stiffness matrix; n represents the number of discrete hexahedral elements in the topology optimization design domain, and ρ is the normalized density field of each hexahedral element; V * represents the volume limit of the material in the topology optimization design domain, v = [v1, v2, …, v i ,v n ] T is the volume vector of each hexahedral unit, ρ min and ρ max Respectively represent the lower and upper limits of the hexahedral unit density field. In the numerical implementation, the optimization problem is solved by the OC algorithm, and the sensitivity derived from the adjoint method is used as the input condition. Finally, the hexahedral unit density field ρ is output at the optimal solution. fin .

[0070] S3: Based on the density field information, a gradient TPMS lattice structure is constructed by a three-way linear interpolation method, and the gradient value of the lattice cell is equal to the density value of the hexahedral grid cell;

[0071] Based on the obtained hexahedral density field information, a continuous gradient TPMS lattice density field is constructed through three-way linear interpolation. The principle is to infer the value of any point in the bounding box through the information of the eight known vertices of the bounding box of the overall lattice structure. The steps are to perform linear interpolation along the x, y, and z directions respectively. Specifically, assuming that the information of the eight vertices of the function f from P1, P2 to P8 is known, to solve the value of point P in the space, linear interpolation can be performed along the x direction first, and the function value of R1 can be obtained using P1 and P2. Similarly, the values ​​of R2, R3, and R4 can be obtained; then, based on the solution results of R1, R2, R3, and R4, linear interpolation can be performed along the y direction to obtain the function values ​​of O1 and O2; finally, linear interpolation is performed along the z direction using O1 and O2 to obtain the result of the unknown point P. The specific formula is as follows:

[0072]

[0073] The surface implicit equations of the TPMS lattice include but are not limited to the following categories:

[0074] P-type lattice surface equation:

[0075] f P (x,y,z)=cosX+cosY+cosZ-0.51(cosXcosY+cosXcosY+cosYcosZ)-t

[0076] G-type lattice surface equation:

[0077] f G(c,y,z)=sinXcosY+sinYcosZ+sinZcosX-t

[0078] D-type lattice surface equation:

[0079] f D (x,y,z)=sinXsinYsinZ+sinXcosYcosZ+cosXsinYcosZ+cosXcosYsinZ-t

[0080] IWP type lattice surface equation:

[0081] f IWP (x,y,z)=cosXcosY+cosXcosZ+cosYcosZ-0.51(cos2X+cos2Y+cos2Z)-t

[0082] Among them, X = 2πx / L, Y = 2πy / L, Z = 2πz / L, L controls the lattice unit size, and the relative density of the lattice structure is controlled by the level set constant t. x, y, and z are the three axial coordinates in the Cartesian coordinate system.

[0083] S4: extracting the spatial coordinates of the nodes of the conformal hexahedral grid unit respectively, and determining the density field information of the unit cell corresponding to the gradient TPMS lattice structure;

[0084] Based on the conformal hexahedral mesh model divided in S1, the unit information and node information can be obtained. Then, based on the continuous gradient TPMS lattice density field, the density field information of the TPMS unit cell corresponding to the conformal hexahedral mesh unit is extracted. Assuming that the number of gradient TPMS lattice structures in the x, y, and z directions is a, b, and c, respectively, and the resolution of the generated TPMS lattice is n, the index of the density information corresponding to the i+1th unit cell in the gradient TPMS lattice density field information is:

[0085] [n*i:n*(i+1)+1,0:n+1,0:n+1] i<a[n*(ia):n*(i–a+1)+1,n:2n+1,0:n+1] a≤i<2a…

[0086] [n*(i–(b–1)*a):n*(i–(b–1)*a+1)+1,(b–1)*n:b*n+1,0:n+1] (b–1)*a≤i<b*a[n*(i–b*a):n*(i–b*a+1)+1,0:n+1,n:2n+1] b*a≤i<(b+1)*a[n*(i–(b+1)*a):n*(i–(b+1)*a+1)+1,n:2n+1,n:2n+1] (b+1)*a≤i<(b+2)*a…

[0087] [n*(i–(2b–1)*a):n*(i–(2b–1)*a+1)+1,(b–1)*n:b*n+1,n:2n+1] (2b-1)*a≤i<2b*a[n*(i–2b*a):n*(i–2b*a+1)+1,0:n+1,2n:3n+1] 2b*a≤i<(2b+1)*a[n*(i–(2b+1)*a):n*(i–(2b+1)*a+1)+1,n:2n+1,2n:3n+1] (2b+1)*a≤i<(2b+2)*a…

[0088] [n*(i–(3b–1)*a):n*(i–(3b–1)*a+1)+1,(b–1)*n:b*n+1,2n:3n+1](3b–1)*a≤i<3b*a…

[0089] [n*(i–(cb–1)*a):n*(i–(cb–1)*a+1)+1,(b–1)*n:b*n+1,(c–1)*n:c*n+1](cb–1)*a≤i<cb*a

[0090] S5: extracting the spatial coordinates of the TPMS unit cell corresponding to the conformal hexahedral mesh unit, and filling it into the conformal hexahedral mesh through isoparametric transformation;

[0091] The TPMS unit cell corresponding to the conformal hexahedral grid unit is a grid model generated by the Marching cube algorithm. The coordinates (x, y, z) of its grid vertices in the local coordinate system of the lattice unit cell model are transformed into coordinates (X, Y, Z) in the global coordinate system of the model to be filled by means of isoparametric transformation of control points. The eight control points of the lattice unit cell are the eight vertices of the cube bounding box, which are calculated in the following way:

[0092]

[0093] in, are respectively the spatial coordinates of the i-th control point in three directions in the local coordinate system of the lattice unit cell model, and none of them is 0. are respectively the spatial coordinates of the ith node of the conformal hexahedral mesh unit in three directions in the global coordinate system of the model to be filled;

[0094] Traversing all vertices in the lattice unit cell model to complete filling of the lattice unit cell model in a conformal hexahedral grid unit;

[0095] S6: Traversing all conformal hexahedral grid units, thus completing the design of the gradient conformal lattice structure of the model to be filled.

[0096] S7: Output the gradient conformal lattice structure based on topology optimization obtained in S6 and store it as an STL file for subsequent additive manufacturing.

[0097] Example 1

[0098] As described in the background technology, traditional lattice filling often results in incomplete unit cells in structural parts with curved contours, affecting overall performance, and lacks optimization methods for conformal lattices. In order to solve the above problems, an embodiment of the present invention provides a gradient conformal lattice design method based on topological optimization density field mapping, such as Figure 1 As shown, Figure 1 It is a flow chart of the present invention.

[0099] Specifically: The present invention is explained below by taking the gradient conformal P lattice optimization design for a curved sandwich shell structure as an example.

[0100] S1-S2: For the model bounding box size of 100mm*20mm*50mm, select a hexahedral mesh with a unit size of 5, and select an 8-node linear hexahedral unit as the mesh unit type; the mesh generation technology selects the neutral axis algorithm in the sweep. Topology optimization is carried out on the original model; the elastic modulus E of the material used is 2004.99MPa, the Poisson's ratio υ is 0.41, and the density ρ is 1.39e-9g / mm 3 , the bottom surface of the structure is completely fixed, and the top is subjected to a vertical concentrated force F = 100N. Figure 2 The objective function of topology optimization is set to minimize the strain energy, the volume constraint is set to 25%, the minimum density is set to 10%, the maximum density is set to 70%, and the delta criterion of the objective function is set to 0.001. The optimal structural density field information distribution diagram after optimization iteration is shown in Figure 3 shown.

[0101] S3-S4: In this example, a=25, b=4, c=4, n=50. Based on the obtained density field information, a continuous density field is constructed by three-way linear interpolation. The principle is as follows: Figure 4 As shown, it is a three-dimensional array with a shape of [1250, 200, 200]. A continuous gradient P-type lattice structure is generated by the Marching Cube algorithm. The density field information of the unit cell in the gradient P-type lattice corresponding to the unit numbered 1 in the conformal hexahedral mesh is: [0:51, 0:51, 0:51].

[0102] S5-S7: For the unit with the conformal hexahedral mesh number 1, extract its unit node sequence and spatial coordinates. Through its corresponding unit cell density field information, the spatial coordinates of all vertices of the P-type lattice unit cell can be extracted. Its eight control points are the eight vertices of the unit cell bounding box. Through the formula of isoparametric transformation, all vertices of the unit cell can be transformed from the local coordinate system to the overall coordinate system of the structure to be filled, thus completing the conformal lattice filling of a unit. By traversing all conformal hexahedral mesh units, the gradient conformal lattice filling design for the entire model to be filled can be completed. Since the generated P-type lattice is a grid structure, the final output gradient conformal lattice is also a grid structure, which can be easily exported to STL format for subsequent additive manufacturing operations. The geometric diagram of the operation process is shown below. Figure 5 shown.

[0103] In industrial applications, the gradient conformal lattice design method based on topological optimization density field mapping disclosed above can be connected to the three-dimensional lattice model generation system in the form of software code; the verified three-dimensional lattice model is used as the target model, and the preset processing requirements are added to complete the manufacturing. The specific design process is not described here. The above is only a feasible application scenario proposed, and it is not to be interpreted as an application limitation of the technical solution of the present invention.

[0104] As described above, although the present invention has been shown and described with reference to specific preferred embodiments, it should not be construed as limiting the present invention itself. Various changes may be made to it in form and detail without departing from the spirit and scope of the present invention as defined in the appended claims.

Claims

1. A gradient conformal lattice design method based on topological optimization density field mapping, characterized in that: The steps include: Divide the original model to be designed into conformal hexahedral meshes; Performing topology optimization pre-processing calculation on the divided conformal hexahedral mesh to extract density field information of the mesh unit; According to the density field information, a gradient TPMS lattice structure is constructed by a three-way linear interpolation method, and the gradient value of the lattice cell is equal to the density value of the hexahedral grid unit; The spatial coordinates of the nodes of the conformal hexahedral grid unit are extracted respectively, and the density field information of the unit cell corresponding to the gradient TPMS lattice structure is determined; Extract the spatial coordinates of the TPMS unit cell corresponding to the conformal hexahedral mesh unit and fill it into the conformal hexahedral mesh through isoparametric transformation; Traverse all conformal hexahedral grid cells to obtain a gradient conformal lattice structure; The gradient conformal lattice structure is output as a target model source file.

2. The gradient conformal lattice design method based on topological optimization density field mapping according to claim 1 is characterized in that: The original model to be designed is divided into a conformal hexahedral mesh using a neutral axis algorithm, in which: The size of the grid unit is the size of the unit cell of the lattice to be filled; The type of mesh element is eight-node linear hexahedral element.

3. The gradient conformal lattice design method based on topological optimization density field mapping according to claim 1 is characterized in that: The topology optimization pre-processing calculation is performed on the divided conformal hexahedral mesh to extract the density field information of the mesh unit. The mathematical model of topology optimization is described as follows: Wherein, the objective function C represents the structural strain energy, and the minimum strain energy is taken as the optimization target, that is, the maximum stiffness; U(ρ) represents the node displacement vector, which is obtained by solving the finite element equilibrium equation KU(ρ)=F, and K represents the overall stiffness matrix; n represents the number of discrete hexahedral elements in the topology optimization design domain, and ρ is the normalized density field of each hexahedral element; V * represents the volume limit of the material in the topology optimization design domain, v = [v1, v2, …, v i ,v n ] T is the volume vector of each hexahedral unit, ρ min and ρ max They represent the lower and upper limits of the density field of the hexahedral unit respectively.

4. The gradient conformal lattice design method based on topological optimization density field mapping according to claim 1, characterized in that: The method of constructing the gradient TPMS lattice structure by three-way linear interpolation specifically includes: The value of any point P in the bounding box is inferred through the information of the eight known vertices P1, P2, P3, P4, P5, P6, P7, and P8 of the overall lattice structure bounding box.

5. The gradient conformal lattice design method based on topological optimization density field mapping according to claim 4 is characterized in that: The method of constructing the gradient TPMS lattice structure by three-way linear interpolation specifically includes: Perform linear interpolation along the x direction and use the known vertices P1 and P2 to obtain the values ​​of R1, R2, R3, and R4: Based on the solution results of R1, R2, R3 and R4, linear interpolation is performed along the y direction to obtain the function values ​​of O1 and O2: Use O1 and O2 to perform linear interpolation along the z direction to obtain the result of the unknown point P: In the formula, x represents point R i The x-axis coordinate, x 2i Indicates point P 2i The x-axis coordinate of 2i-1 Indicates point P 2i-1 The x-axis coordinate of y represents point O j The y-axis coordinate, y 2j Indicates point R 2j The y-axis coordinate of 2j-1 Indicates point R 2j-1 The y-axis coordinate of z represents point P k The z-axis coordinate, z 2k Indicates point O 2k The z-axis coordinate of 2k-1 Indicates point O 2k-1 The z-axis coordinate of .

6. The gradient conformal lattice design method based on topological optimization density field mapping according to claim 1, characterized in that: The step of extracting the spatial coordinates of the TPMS unit cell corresponding to the conformal hexahedral grid unit specifically includes: The coordinates (x, y, z) of the mesh vertices of the conformal hexahedral mesh unit in the local coordinate system of the lattice unit cell model are transformed into the coordinates (X, Y, Z) in the global coordinate system of the model to be filled by means of isoparametric transformation of the control points. The eight control points of the lattice unit cell are the eight vertices of the cube bounding box, which are calculated in the following way: In the formula, are the spatial coordinates of the i-th control point in three directions in the local coordinate system of the lattice unit cell model, all of which are not 0; are respectively the spatial coordinates of the i-th node of the conformal hexahedral mesh unit in three directions in the global coordinate system of the model to be filled.

7. The gradient conformal lattice design method based on topology optimization density field mapping according to any one of claims 1 to 6, wherein the design process thereof is constructed as a complete design system, wherein the design system comprises: A first calculation module is used to divide the original model to be designed into conformal hexahedral meshes; A second calculation module is used to perform topology optimization pre-processing calculation on the divided conformal hexahedral mesh and extract density field information of the mesh unit; A third calculation module is used to construct a gradient TPMS lattice structure by a three-way linear interpolation method according to the density field information, wherein the gradient value of the lattice cell is equal to the density value of the hexahedral grid cell; The fourth calculation module is used to extract the spatial coordinates of the nodes of the conformal hexahedral grid unit respectively, and determine the density field information of the unit cell corresponding to the gradient TPMS lattice structure; A fifth calculation module is used to extract the spatial coordinates of the TPMS unit cell corresponding to the conformal hexahedral grid unit and fill it into the conformal hexahedral grid through isoparametric transformation; A loop module, used for traversing all conformal hexahedral grid units, repeatedly driving the second calculation module, the third calculation module, the fourth calculation module, and the fifth calculation module to obtain a gradient conformal lattice structure; An output module is used to output the gradient conformal lattice structure as a target model source file.

8. Application of the gradient conformal lattice design method based on topology optimization density field mapping in generating computer three-dimensional modeling according to any one of claims 1 to 6; characterized in that: The verified 3D lattice model is output as the target model source file for subsequent industrial design and manufacturing.

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