Gradient conformal lattice design method, system and application based on topology optimization density field mapping

Abstract

The present invention provides a gradient conformal lattice design method, system, and application based on topology optimization density field mapping, which relates to the field of structural lightweight design. The design method includes: dividing the model into conformal hexahedral grids, with the grid unit size set to the size of the lattice cell; extracting the density field information of the grid cell based on topology optimization pre-processing calculations, and constructing a continuous gradient TPMS lattice structure based on a three-way linear interpolation method through density field mapping; extracting the spatial coordinates of the TPMS unit cell corresponding to the density field for each conformal hexahedral grid cell; transforming all vertex coordinates of the TPMS unit cell in the local coordinate system to the corresponding conformal hexahedral grid unit coordinates in the global coordinate system based on isoparametric transformation; traversing all conformal hexahedral grid cells to obtain and output the gradient conformal TPMS lattice structure. This method can solve the shortcomings of traditional lattice filling, which affects the mechanical properties of the structure due to incomplete and non-conformal cells.

Description

Technical Field

[0001] The present invention relates to the fields of structural lightweight 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] A three-dimensional lattice structure is a spatial structure composed of microstructures arranged in a certain periodic pattern. 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 lattice structures is currently an important method for innovative design in additive manufacturing, and 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 replaces the entire or part of the structure to be filled with a lattice structure. The design for structures with a relatively regular appearance is relatively simple, but in actual engineering, the appearance of structural parts usually has a curved contour. The lattice cells of fixed size will not guarantee exactly 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 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: To propose a gradient conformal lattice design method based on topology optimization density field mapping, a system to drive the design method, and further an application of the design method. 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 topology 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 the three-way linear interpolation method to construct 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 the isoparametric transformation, the coordinates of all vertices 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 was obtained, which can solve the shortcomings of traditional lattice filling that affect 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, comprising the following steps:

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

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

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

[0009] The spatial coordinates of the conformal hexahedral grid unit nodes 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 grid unit and fill it into the conformal hexahedral grid 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] To optimize the above technical solution, the original model to be designed is divided into a conformal hexahedral mesh. Specifically, the mesh element size, mesh element type, and mesh generation technique are determined. The mesh element size is the size of the lattice unit cell to be filled. Due to the requirements of the additive manufacturing process, the element size should not be too small to prevent printing, nor too large to cause loss of model details. The mesh element type is preferably an 8-node linear hexahedral element. The neutral axis algorithm in the sweeping method can be used as the mesh generation technique.

[0014] In order to optimize the above technical solution, the topology optimization of the divided conformal hexahedral mesh model is carried out, and 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] Wherein, the objective function C represents the structural strain energy, and the optimization goal is to minimize the strain energy, i.e., maximize the 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 In numerical implementation, the optimization problem is solved by OC algorithm, and the sensitivity derived from the adjoint method is used as input condition. Finally, the hexahedral cell 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 at P1, P2 to P8 is known, to solve the value of point P in the space, linear interpolation can be performed first along the x direction, 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 can be 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] Where x represents point R i The x-axis coordinate, x 2i Represents point P 2i The x-axis coordinate of 2i-1 Represents 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] 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 through the control point isoparametric transformation. The eight control points of the lattice unit cell are the eight vertices of the cube bounding box, which are calculated as follows:

[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 the spatial coordinates of the i-th node of the conformal hexahedral mesh element 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 a conformal hexahedral grid;

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

[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 conformal hexahedral grid unit nodes and determine the density field information of the unit cell corresponding to the gradient TPMS lattice structure;

[0048] The 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, configured to traverse all conformal hexahedral grid cells and repeatedly drive 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 gradient conformal lattice design method based on topology optimization density field mapping disclosed in the above-mentioned embodiments is applied to the generation of computer-generated three-dimensional modeling. 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 topology optimization. By performing topological optimization on the original model to be filled, the optimal structural density field information is obtained, 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 Flowchart of the gradient conformal lattice design method in this embodiment.

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

[0055] Figure 3 Density field infographic of the optimal structure for topology optimization.

[0056] Figure 4 This is the principle 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, numerous specific details are provided to provide a more thorough understanding of the present invention. However, it will be apparent to those skilled in the art that the present invention may be practiced without one or more of these details. In other instances, certain technical features well known in the art have not been described to avoid confusion with the present invention.

[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 lattice unit cell to be filled;

[0061] Constructing a conformal hexahedral mesh involves properly determining the mesh element size, mesh element type, and mesh generation technology. The mesh element size is the size of the lattice unit cell to be filled. Due to additive manufacturing process requirements, the element size should not be too small to prevent printing, nor too large to cause loss of model details. The mesh element type should be 8-node linear hexahedral elements. The neutral axis algorithm in the sweeping method can be used as the mesh generation technology.

[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] Wherein, the objective function C represents the structural strain energy, and the optimization goal is to minimize the strain energy, i.e., maximize the 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 In numerical implementation, the optimization problem is solved by OC algorithm, and the sensitivity derived from the adjoint method is used as input condition. Finally, the hexahedral cell 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. 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, we can first perform linear interpolation along the x direction, and use P1 and P2 to obtain the function value of R1. Similarly, we can obtain the values ​​of R2, R3, and R4. Then, based on the solution results of R1, R2, R3, and R4, we can perform linear interpolation along the y direction to obtain the function values ​​of O1 and O2. Finally, we can use O1 and O2 to perform linear interpolation along the z direction 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: extract the spatial coordinates of the conformal hexahedral grid unit nodes respectively, and determine 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: 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;

[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 the coordinates (X, Y, Z) in the global coordinate system of the model to be filled through the control point isoparametric transformation. The eight control points of the lattice unit cell are the eight vertices of the cube bounding box, which are calculated as follows:

[0092]

[0093] in, are 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 the spatial coordinates of the i-th node of the conformal hexahedral mesh element 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: Traverse all conformal hexahedral grid cells, 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 mentioned in the background technology, traditional lattice filling often has shortcomings such as incomplete unit cells in structural parts with curved contours, affecting overall performance, and lacking optimization methods for conformal lattices. In order to solve the above problems, the 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 Flowchart of the present invention.

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

[0100] S1-S2: For a model bounding box size of 100mm*20mm*50mm, a hexahedral mesh with an element size of 5 and an 8-node linear hexahedral element type was selected. The swept neutral axis algorithm was used as the mesh generation technique. Topology optimization was performed on the original model. The material used had an elastic modulus E of 2004.99MPa, a Poisson's ratio υ of 0.41, and a density ρ of 1.39e-9g / mm2. 3 , the bottom surface of the structure is completely fixed, and the top is subjected to a vertical downward concentrated force F = 100N, such as Figure 2 As shown. 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 number 1 of the conformal hexahedral grid 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 of 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 as follows: Figure 5 shown.

[0103] In industrial applications, the gradient conformal lattice design method based on topology optimization density field mapping disclosed above can be integrated into a 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 preset processing requirements are added to complete the manufacturing. The specific design process is not detailed here. The above is only a feasible application scenario proposed and is not to be construed as limiting the application 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 topology optimization density field mapping, characterized by: The steps include: Divide the original model to be designed into a conformal hexahedral mesh; A topology optimization pre-processing calculation is performed on the divided conformal hexahedral mesh to extract the density field information of the mesh cells. The mathematical model of topology optimization is described as follows: Where, the objective function C represents the structural strain energy, and the minimum strain energy is the optimization target, that is, the maximum stiffness; Represents the node displacement vector, by solving the finite element equilibrium equation get, represents the overall stiffness matrix; n represents the number of discrete hexahedral elements in the topology optimization design domain, is the normalized density field of each hexahedral unit; represents the volume limit of the material in the topology optimization design domain, is the volume vector of each hexahedral unit, and They represent the lower and upper limits of the density field of the hexahedral unit respectively; According to the density field information, a gradient TPMS lattice structure is constructed by a three-way linear interpolation method, where the gradient value of the lattice cell is equal to the density value of the hexahedral grid cell, specifically including: 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; along x Perform linear interpolation in the 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, along y Perform linear interpolation in the direction to obtain the function values ​​of O1 and O2: Use O1 and O2 along z Do linear interpolation in the direction to get the result of the unknown point P: In the formula, x represents the point The x-axis coordinate, Indicates a point The x-axis coordinate of Indicates a point The x-axis coordinate of y represents the point The y-axis coordinate, Indicates a point The y-axis coordinate of Indicates a point The y-axis coordinate of z represents a point The z-axis coordinate of Indicates a point The z-axis coordinate of Indicates a point The z-axis coordinate of The spatial coordinates of the conformal hexahedral grid unit nodes 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 grid unit and fill it into the conformal hexahedral grid 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 topology 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 the neutral axis algorithm. In the conformal hexahedral mesh: The size of the grid cell is the size of the lattice unit cell to be filled; The mesh element type is eight-node linear hexahedral element.

3. The gradient conformal lattice design method based on topology optimization density field mapping according to claim 1, characterized in that: The extracting of 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 as follows: Where, 、 、 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 i-th node of the conformal hexahedral mesh unit in three directions in the global coordinate system of the model to be filled.

4. The gradient conformal lattice design method based on topology optimization density field mapping according to any one of claims 1 to 3, wherein the design process thereof is constructed as a complete design system, the design system comprising: A first calculation module is used to divide the original model to be designed into a conformal hexahedral grid; A second calculation module is used to perform topology optimization pre-processing calculations on the divided conformal hexahedral mesh and extract density field information of the mesh cells; 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 conformal hexahedral grid unit nodes and determine the density field information of the unit cell corresponding to the gradient TPMS lattice structure; The 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, configured to traverse all conformal hexahedral grid cells and repeatedly drive 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.

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

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