Multi-scale design methods, systems and applications based on the fusion of heterogeneous lattice geometry continuity and strain energy drive

Abstract

The present invention provides a multi-scale design method, system, and application for heterogeneous lattice geometric continuity fusion and strain energy drive, relating to the fields of structural lightweight design and additive manufacturing. The method comprises: establishing a three-dimensional lattice model and numerically calculating its lattice structure to obtain discrete values ​​related to the mechanical properties of the lattice structure and density; meshing and topologically optimizing the three-dimensional lattice model according to voxel units of predetermined size, outputting the unit node displacement field and voxel unit density field; calculating the strain energy value at each lattice unit node to obtain the lattice cell configuration distribution field; performing geometric continuity fusion optimization on the heterogeneous cell boundary portion of the lattice structure based on the lattice cell configuration field and the density field after voxel unit interpolation, and then outputting a three-dimensional lattice model; and performing additive manufacturing using the three-dimensional lattice model as the input model. This method can achieve an orderly and adaptive distribution of the TPMS lattice configuration and its relative density within the design domain, obtaining a high-rigidity heterogeneous fusion lattice, which can be applied to additive manufacturing.

Description

Technical Field

[0001] The present invention relates to the field of lightweight structural design and additive manufacturing, and in particular to a multi-scale design method, system and application that integrates heterogeneous lattice geometric continuity and is driven by strain energy. Background Art

[0002] Triple Periodic Minimal Surfaces (TPMS) lattice structures possess numerous excellent mechanical properties, including high specific strength, high specific stiffness, high energy absorption, and lightweight. They are also easily parametrically designed and can effectively avoid stress concentration, leading to their widespread application in aerospace, biomedicine, and other fields. Advances in additive manufacturing technology have provided a greater design space for TPMS lattices. Heterogeneous fusion lattices can fully leverage the functional advantages of different TPMS lattice configurations, facilitating the integrated material and functional design of lattice structures under service conditions.

[0003] However, the current optimization design of heterogeneous fusion lattices has the following defects: first, the basis for the lattice configuration distribution mostly comes from prior results, and the lattice relative density distribution lacks orderly design criteria; second, there is a lack of universal and efficient lattice multi-scale design methods, which makes it difficult to achieve coordinated optimization of density field and configuration field, and unable to give full play to the performance advantages of lattice materials in limited space, limiting the in-depth application of lightweight lattice structures in major projects.

[0004] To this end, it is necessary to propose an optimization scheme for heterogeneous fusion lattices to achieve adaptive distribution of TPMS configurations and their relative densities within the design domain, and obtain high-rigidity heterogeneous fusion lattices for application in subsequent industrial design, production and manufacturing, and other links. Summary of the Invention

[0005] Purpose of the invention: To propose a multi-scale design method that integrates the geometric continuity of heterogeneous lattices and is driven by strain energy, and further propose an application of this design method, which can realize the adaptive distribution of TPMS configurations and their relative densities within the design domain, establish a complete cross-scale lightweight design process of micro-lattice materials and macro-service structures, obtain high-rigidity heterogeneous fusion lattices, and thus better solve the above-mentioned problems existing in the prior art.

[0006] First, a multi-scale design method based on the fusion of heterogeneous lattice geometric continuity and strain energy drive is proposed. The steps are as follows:

[0007] Step 1: Establish a TPMS three-dimensional lattice model and perform numerical calculations on its lattice structure to obtain discrete values ​​related to the mechanical properties of the lattice structure and density;

[0008] Step 2: Meshing the TPMS three-dimensional lattice model according to voxel units of a predetermined size; topologically optimizing the TPMS three-dimensional lattice model, and outputting a unit node displacement field and a voxel unit density field;

[0009] Step 3: Calculate the strain energy value at each lattice unit node based on the unit node displacement field and the voxel unit density field, take the maximum value of the strain energy of each lattice unit under different TPMS lattice types, and obtain the lattice cell configuration distribution field;

[0010] Step 4: Based on the voxel unit density field and the lattice cell configuration distribution field, the heterogeneous cell boundary portion of the TPMS 3D lattice model is fused and optimized, and then the TPMS 3D lattice model is output and verified;

[0011] Step 5: Output the verified three-dimensional lattice model as a target model source file.

[0012] In a further embodiment of the first aspect, the TPMS three-dimensional lattice model is established by an implicit function, and the expression is as follows:

[0013] P-type lattice surface equation:

[0014] f p (x,y,z)=cosX+cosY+cosZ-0.51(cosXcosY+cosYcosZ+cosZcosX)-t

[0015] IWP type lattice surface equation:

[0016] f iwp (x,y,z)=cosXcosY+cosXcosZ+cosYcosZ-0.51(cos2X+cos2Y+cos2Z)-t

[0017] D-type lattice surface equation:

[0018] f D (x,y,z)=sinXsinYsinZ+sinXcosYcosZ+cosXsinYcosZ+cosXcosYsinZ-t

[0019] G-type lattice surface equation:

[0020] f G (x,y,z)=sinXcosY+sinYcosZ+sinZcosX-t

[0021] Where X = 2πx / L, Y = 2πy / L, Z = 2πz / L, L represents the unit size of the lattice structure, and the relative density change 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.

[0022] In a further embodiment of the first aspect, in step 1, the TPMS three-dimensional lattice model is numerically calculated to obtain discrete values ​​associated with the mechanical properties of the lattice structure and the density, as follows:

[0023] The constitutive elastic matrix D of the lattice material is expressed as:

[0024]

[0025] Set one of the strain components to unit strain. In this case, the stiffness coefficient in the elastic matrix is ​​equal to one of the stress components:

[0026]

[0027] In the finite element analysis of given periodic boundary conditions, the lattice structure belongs to the cubic system, and C 11 =C 22 =C 33 、C 12 =C 23 =C 31 、C 44 =C 55 =C 66 , parameters are obtained by applying unit strain;

[0028] After obtaining the corresponding value, the TPMS lattice stiffness coefficient A fourth-order polynomial fitting is performed between ρ and density ρ, and the formula is as follows:

[0029]

[0030] In a further embodiment of the first aspect, step 2 specifically includes:

[0031] Step 2.1, divide the TPMS 3D lattice model into a hexahedral grid with voxel units of a predetermined size. The voxel unit size is the same as the lattice unit size, and the voxel unit index is circularly marked in the XYZ direction;

[0032] Step 2.2: Perform topology optimization on the TPMS three-dimensional lattice model. The optimization objective equation is as follows:

[0033] find:ρ=[ρ1,ρ2,…,ρ i ,…,ρ n ] T

[0034] minimize:c(ρ,U)=F T U(ρ)

[0035] subject to:KU(ρ)=F

[0036]

[0037] 0≤ρ min ≤ρ i ≤ρ max ≤1

[0038] Where, the objective function c(ρ,U) represents the structural flexibility, and the optimization goal is to minimize flexibility, i.e., maximize stiffness; F T is the node force vector, U(ρ) represents the node displacement vector, which is obtained by solving the finite element equilibrium equation KU(ρ)=F, where F is determined by the load conditions and the boundary conditions will limit the displacement of some units; K represents the overall stiffness matrix, which is obtained by the unit stiffness matrix k i Assembled; n represents the number of units in the topology optimization design domain, ρ is the density field of each voxel unit; V * Indicates that the volume limit of the material in the topology optimization design domain is set to 0.3; v = [v1, v2, …, v i ,v n ] T is the volume vector of each voxel unit, ρ min and ρ max Respectively represent the lower and upper limits of the voxel unit density field;

[0039] Step 2.3: Output the unit node displacement field and voxel unit density field.

[0040] In a further embodiment of the first aspect, step 3 specifically includes:

[0041] Step 3.1: Based on the elastic matrix D of the TPMS lattice i Calculate the effective stiffness matrix k of the element i :

[0042]

[0043] Where, Ω e Represents the design domain unit; B T represents the transpose of the element strain matrix;

[0044] Get the unit node displacement u e , the strain energy w at the lattice unit node is calculated by the following formula i :

[0045]

[0046] Where u e Represents the unit node displacement matrix; Represents the unit node displacement transposed matrix;

[0047] Step 3.2: Select the lattice with maximum strain energy based on the voxel unit density field and unit node displacement field obtained by the SIMP method, obtain the lattice cell configuration distribution field, and calculate the maximum strain energy of each unit under different TPMS lattice types.

[0048] In a further embodiment of the first aspect, the elastic matrix D of the TPMS dot matrix i The expression is as follows:

[0049]

[0050] M=1,2,3,4

[0051] Where, Where M refers to the index number of the TPMS type, and i refers to the index of the corresponding voxel unit; C ij,TPMs (ρ i ) represents the value of the stiffness coefficient at the corresponding density of the TPMS dot matrix.

[0052] In a further embodiment of the first aspect, step 4 specifically includes:

[0053] Step 4.1: According to the voxel unit density field and the lattice cell configuration distribution field, based on the Gaussian radial basis function, the density enhancement factors of the six directions under each index of the lattice structure are calculated.

[0054] The specific calculation method is: first determine whether the adjacent unit is a heterogeneous lattice. If it is a heterogeneous lattice, add the corresponding density factor enhancement function in the transition boundary direction, and adjust the corresponding value according to the properties of the lattice itself. The basic density factor boundary enhancement equation in a single x direction can be expressed as:

[0055]

[0056] Where, d + and d _ is the density factor of the TPMS lattice on the inner and outer sides of the transition interface. Its mathematical form is the same as the Sigmoid function, which ensures that the density factor can accurately act on the transition boundary. + and C - represents the amplitude function of the density factor, and its value is related to the relative density of the two adjacent units; p represents the constant that controls the width of the density factor; X intersec represents the coordinates of discrete points at the transition interface in the design domain.

[0057] The amplitude constant of each TPMS cell is C p =12, C IWP =4 and C G =C D =1, the density factor scope width coefficient is p p =0.3, p IWP =0.4, p G =0.8 and p D = 1. Based on the above formula, the density factor can be applied to the three-dimensional direction of the lattice structure, combined with the Gaussian radial basis equation, to obtain the final formula based on density factor enhancement:

[0058]

[0059] Fusion hance =Fusion+u + d x+ +v + d y+ +w + d z+ +u - d x- +v - d y- +w - d z-

[0060] Where Fusion is the final fusion structure, TPMS is the implicit equation corresponding to the TPMS type, and x center 、y center 、z center Indicates the coordinates of the center point of each unit, k is the control factor of the transition interval, u, v, w depend on the adjacency relationship of the cell along the x, y, and z directions. If the adjacent unit is a heterogeneous lattice, it is set to True and the optimization in this direction is performed. Otherwise, the adjacent surface density optimization is not used. d + and d - are the density factors in the corresponding directions in the above formula respectively;

[0061] Step 4.2: Perform finite element simulation of the single configuration gradient structure and the heterogeneous fusion gradient structure, conduct performance comparison and verification, and finally output the verified three-dimensional lattice model.

[0062] As a second aspect of the present invention, it is proposed to construct the heterogeneous lattice geometric continuity fusion and strain energy-driven multi-scale design method disclosed in the first aspect into a complete computing system, which includes three computing units and a model output unit. Specifically, it includes:

[0063] The first calculation unit is used to establish a TPMS three-dimensional lattice model and perform numerical calculations on its lattice structure to obtain discrete values ​​associated with the mechanical properties of the lattice structure and density;

[0064] a second computing unit, configured to mesh the TPMS three-dimensional lattice model according to voxel units of a predetermined size; perform topology optimization on the TPMS three-dimensional lattice model, and output a unit node displacement field and a voxel unit density field;

[0065] A third calculation unit is used to calculate the strain energy value at each lattice unit node according to the unit node displacement field and the voxel unit density field, and take the maximum value of the strain energy of each lattice unit under different TPMS lattice types to obtain the lattice cell configuration distribution field;

[0066] The model output unit is used to perform heterogeneous fusion of the lattice structure based on the voxel unit density field and the lattice cell configuration distribution field, output a three-dimensional lattice model and verify it.

[0067] As a third aspect of the present invention, the heterogeneous fusion lattice multi-scale design method disclosed in the above embodiment is applied to the generation of computer 3D modeling. The verified 3D lattice model is output as a target model source file for subsequent industrial design and manufacturing.

[0068] The present invention has the following beneficial effects: the multi-scale design method of heterogeneous lattice geometric continuity fusion and strain energy drive proposed in the present invention has certain universality in application in the method of optimizing the mechanical properties of three-dimensional model entities. The degree of freedom of design can be expanded through lattice structure homogenization calculation, and the adaptive distribution and transition boundary optimization of TPMS configuration and relative density within the design domain can be realized. The method has a relatively complete theoretical basis, establishes a complete cross-scale lightweight design process of detailed lattice materials and macroscopic service structures, and effectively realizes the optimization of structural mechanical properties. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 This is a flow chart of the multi-scale design method of the present invention that integrates heterogeneous lattice geometric continuity and is driven by strain energy.

[0070] Figure 2 Schematic diagram of the application of boundary conditions in finite element simulation.

[0071] Figure 3 This is a graph showing the relationship between the TPMS structural stiffness coefficient and relative density.

[0072] Figure 4 Flowchart for cell selection based on strain energy for TPMS structure.

[0073] Figure 5The figure shows the comparison of finite element simulation results and performance parameters before and after TPMS structure optimization. DETAILED DESCRIPTION

[0074] 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 are not described to avoid confusion with the present invention.

[0075] The present invention provides a multi-scale design method for heterogeneous lattice geometric continuity fusion and strain energy drive, the process is shown in Figure 1 As shown, the steps are as follows:

[0076] Step 1: Establish four types of TPMS three-dimensional lattice models and set independent numbers for the cells of each type of lattice structure;

[0077] The parameters that need to be determined for the TPMS lattice structure include the type of lattice structure, overall scale, unit size, and relative density. The implicit equation for the TPMS lattice structure surface is as follows:

[0078] P-type lattice surface equation:

[0079] f p (x,y,z)=cosX+cosY+cosZ-0.51(cosXcosY+cosYcosZ+cosZcosX)-t

[0080] IWP type lattice surface equation:

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

[0082] D-type lattice surface equation:

[0083] f D (x,y,z)=sinXsinYsinZ+sinXcosYcosZ+cosXsinYcosZ+cosXcosYsinZ-t

[0084] G-type lattice surface equation:

[0085] f G (x,y,z)=sinXcosY+sinYcosZ+sinZcosX-t

[0086] Among them, X = 2πx / L, Y = 2πy / L, Z = 2πz / L, L represents the unit size of the lattice structure, and the relative density change 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.

[0087] Each type of lattice structure unit is assigned a number, the form of which includes but is not limited to Arabic numerals, English letters and their permutations and combinations. The unit number of each type of TPMS lattice structure is unique, and the number of numbers depends on the number of lattice unit types in the heterogeneous fusion lattice (i.e., the number of types of TPMS lattice structures of lattice units in the heterogeneous fusion lattice).

[0088] After obtaining the corresponding value, the TPMS lattice stiffness coefficient A fourth-order polynomial fitting is performed between the density and the equation is as follows:

[0089]

[0090] The relationship between TPMS structural stiffness coefficient and relative density is shown in the figure Figure 3 shown.

[0091] Step 2: Calculate the unit space coordinate matrix of the lattice unit according to the lattice scale and unit size of the lattice structure determined in step 1, and use this to perform structural topology optimization to obtain the voxel unit density field and unit node displacement field.

[0092] The specific process includes the following:

[0093] The principle of calculating the unit space coordinate matrix of the lattice unit based on the lattice scale and unit size is as follows: the TPMS lattice structure is a periodic structure obtained by the TPMS lattice unit array. If the center point of the lattice structure is the origin (0, 0, 0), then under a certain lattice scale and lattice unit size, the center coordinates of each TPMS lattice unit that constitutes the TPMS lattice structure can be calculated. The result of the calculation is the unit space coordinate matrix, and the center coordinates reflect the spatial position of the TPMS lattice unit in the TPMS lattice structure.

[0094] The specific calculation process is as follows:

[0095] First calculate the center coordinates of the lattice unit using the following formula:

[0096]

[0097] Among them, (x i ,y j ,z k) is the center coordinate of the lattice unit in the design domain, i, j and k represent the spatial index of the current lattice unit in the x, y and z directions respectively (for example, i represents the i-th lattice unit in the x direction of the lattice structure), numx, numy and numz represent the number of lattice units in the x, y and z directions respectively, and L represents the unit size of the lattice structure;

[0098] Then, the unit space coordinate matrix is ​​calculated by the following formula:

[0099]

[0100] where ele[(x i ,y j ,z k )] is the unit space coordinate matrix, k=1,2,3,... represents each value of k,ele[(x i ,y j ,z k )] all correspond to all elements on the right side of the above formula, for example, k=2, then ele[(x i ,y j ,z k )] includes all elements on the right side of the above formula k Corresponding to the value of z2.

[0101] Based on the spatial coordinate matrix of the center point of the lattice unit, the cantilever beam structure is used as the optimized component and the voxel unit is divided. The voxel unit size corresponds to the unit size L of the lattice structure mentioned above. After applying the boundary conditions and load conditions (such as Figure 2 ), perform topology optimization, and the specific optimization objective equation is as follows:

[0102] find:ρ=[ρ1,ρ2,…,ρ i ,…,ρ n ] T

[0103] minimize:c(ρ,U)=F T U(ρ)

[0104] subject to:KU(ρ)=F

[0105]

[0106] 0≤ρ min ≤ρ i ≤ρ max ≤1

[0107] Among them, the objective function c(ρ,U) represents the structural flexibility, and the optimization goal is to minimize flexibility, that is, maximize stiffness; F Tis the node force vector, U(ρ) represents the node displacement vector, which is obtained by solving the finite element equilibrium equation KU(ρ)=F, where F is determined by the load conditions and the boundary conditions will limit the displacement of some units; K represents the overall stiffness matrix, which is obtained by the unit stiffness matrix k i Assembled; n represents the number of units in the topology optimization design domain, ρ is the density field of each voxel unit; V * The volume limit of the material in the topology optimization design domain is set to 0.3, v = [v1, v2, …, v i ,v n ] T is the volume vector of each voxel unit, ρ min and ρ max Represent the lower and upper limits of the voxel density field respectively. After the topology optimization is completed, the corresponding voxel density field can be obtained, that is, each voxel unit is found in the topology optimization objective equation: ρ=[ρ1,ρ2,…,ρ i ,…ρ n ] T The optimal solution obtained by the search also requires the unit node displacement generated by the structure under the load condition. Similarly, KU(ρ)=F can be used for calculation in the topology optimization process. Since F is the load, that is, the known item, and the stiffness matrix K is obtained through the unit stiffness matrix k i Calculation yields:

[0108]

[0109] Among them, B is the unit strain matrix, D i is the unit elastic matrix, and the specific calculation method is as follows:

[0110] For a certain voxel domain after SIMP topology optimization, the unit strain matrix B is a constant matrix, which is obtained by the shape function N i Calculation yields:

[0111]

[0112] ξ, η, ζ are the coordinates of the natural coordinate system, ξ i ,η i ,ζ i is the normal parameter in the natural coordinate system, in which the voxel unit size is defined to realize the transformation between the natural coordinate system and the global coordinate system, and the unit strain matrix B can be obtained:

[0113]

[0114] The constitutive elastic matrix D of the lattice material can be expressed as:

[0115] In the numerical implementation step, one of the strain components is set to unit strain, and the other five are set to 0, as shown in the following formula. At this time, the stiffness coefficient in the elastic matrix is ​​equal to one of the stress components, which can be calculated by extracting the support reaction force of the corresponding surface through finite element calculation. According to the equation σ = εD, we can get:

[0116]

[0117] In the finite element analysis given periodic boundary conditions, the voxel unit is used, whose properties are similar to those of the cubic crystal system, and C 11 =C 22 =C 33 、C 12 =C 23 =C 31 、C 44 =C 55 =C 66 , and C 11 and C 12 The unit normal strain (e.g. ε 11 =1) to obtain C 44 Then, the unit shear strain (e.g. 12 =1) to obtain.

[0118] The above calculation can be used to solve U(ρ) and obtain the unit node displacement field.

[0119] Step 3: Based on the voxel unit density field and unit node displacement field determined in step 2, calculate the strain energy value of each unit of the corresponding TPMS lattice type, and select the type according to the maximum strain energy criterion. The selection process is shown in Figure 4 , including the following specific processes:

[0120] According to the unit strain energy calculation formula, the unit node displacement u is obtained e After that, the strain energy can be calculated by the following formula:

[0121]

[0122] At this time, the element stiffness matrix k i It needs to be changed according to different TPMS dot matrix types, that is, the elastic matrix D of different TPMS dot matrix structures i The TPMS lattice is a cubic crystal system, and the elastic matrix calculation method of the voxel unit can be similar to that of the voxel unit, which can be obtained:

[0123]

[0124] M=1,2,3,4

[0125] The above formula The M in it refers to the index number of the TPMS type, and i refers to the index of the corresponding voxel unit.

[0126] According to the node displacement of each unit, the strain energy of each unit at the corresponding density of different TPMS lattice types is calculated. M is the TPMS dot matrix type index, compare them and take the maximum value And record the TPMS dot matrix type number under each unit.

[0127] Step 4: Based on the unit TPMS lattice type determined in step 3, a three-dimensional lattice heterogeneous fusion multi-scale design model is constructed, and the effectiveness of the method is verified through finite element simulation.

[0128] The specific process includes the following:

[0129] According to the coordinates of the unit center point determined in step 2, the coordinates of the cell center can be calculated from the corresponding unit. First, the coordinates of the two diagonal vertices of the unit (x max ,y max ,z max )、(x min ,y min ,z min ) Then calculate the center point using the following formula:

[0130] x center =(x max -x min ) / 2

[0131] y center =(y max -y min ) / 2

[0132] z center =(z max -z min ) / 2

[0133] Based on the obtained voxel unit density field and lattice cell configuration distribution field, the density enhancement factors in six directions under each index of the lattice structure are calculated based on the Gaussian radial basis function.

[0134] First, determine whether the adjacent unit is a heterogeneous lattice. If it is a heterogeneous lattice, add the corresponding density factor enhancement function in the transition boundary direction and adjust the corresponding value according to the properties of the lattice itself. The basic density factor boundary enhancement equation in a single x direction can be expressed as:

[0135]

[0136] The amplitude constant of each TPMS cell is C P =12, CIWP =4 and C G =C D =1, the density factor scope width coefficient is p p =0.3, p IWP =0.4, p G =0.8 and p D = 1. Based on the above formula, the density factor can be applied to the three-dimensional direction of the lattice structure, combined with the Gaussian radial basis equation, to obtain the final formula based on density factor enhancement:

[0137]

[0138] Fusion hance =Fusion+u + d x+ +v + d y+ +w + d z+ +u - d x- +v - d y- +w - d z-

[0139] Based on the above equations, a three-dimensional lattice model is constructed, and finite element simulations of single-configuration gradient structures and heterogeneous fusion gradient structures are performed to conduct performance comparison and verification, and finally the verified three-dimensional lattice model is output.

[0140] Step 5: Use the verified 3D lattice model as the target model for subsequent industrial design and manufacturing.

[0141] In industrial applications, an additive manufacturing device can be connected to a 3D lattice model generation system. The verified 3D lattice model is used as a target model and imported into the additive manufacturing device. Preset processing requirements are then added, and the additive manufacturing device then executes the additive manufacturing process based on the target model's configuration and processing requirements. The additive manufacturing process is as described in the above embodiment and will not be further described here. The above is only one possible application scenario and is not to be construed as limiting the application of the technical solution of the present invention.

[0142] After completing the heterogeneous fusion, the obtained heterogeneous fusion structure was compared with the density gradient structure under a single configuration by finite element simulation. Four different structures, namely P lattice gradient, IWP lattice gradient, P-IWP heterogeneous fusion (unoptimized) and P-IWP heterogeneous fusion (optimized), were compared. Figure 5Finite element simulation results for four structures are presented. As can be seen from the data in the table below, the structures obtained after interface optimization exhibit improved structural stiffness, increasing by 20.5% compared to the gradient P and 39.6% compared to the gradient IWP. Furthermore, the structural stiffness of the P-IWP lattice after boundary optimization increased by 21.2% compared to the pre-optimization model, and the relative density was closer to the target value, further verifying the effectiveness and necessity of the proposed interface optimization design method.

[0143] 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 multi-scale design method based on the fusion of heterogeneous lattice geometric continuity and strain energy drive, characterized by: The steps include: Step 1: Establish a TPMS three-dimensional lattice model and perform numerical calculations on its lattice structure to obtain discrete values ​​related to the mechanical properties of the lattice structure and density; Step 2: Meshing the TPMS three-dimensional lattice model according to voxel units of a predetermined size; topologically optimizing the TPMS three-dimensional lattice model, and outputting a unit node displacement field and a voxel unit density field; Step 3: Calculate the strain energy value at each lattice unit node based on the unit node displacement field and the voxel unit density field, take the maximum value of the strain energy of each lattice unit under different TPMS lattice types, and obtain the lattice cell configuration distribution field; Step 4: Based on the voxel unit density field and the lattice cell configuration distribution field, perform geometric continuity fusion optimization on the heterogeneous cell boundary part of the TPMS 3D lattice model, then output the TPMS 3D lattice model and verify it; Step 5: Output the verified three-dimensional lattice model as a target model source file.

2. The multi-scale design method of heterogeneous lattice geometric continuity fusion and strain energy drive according to claim 1 is characterized in that: The TPMS three-dimensional lattice model is established by an implicit function, and the expression is as follows: P-type lattice surface equation: f p (x,y,z)=cosX+cosY+cosZ-0.51(cosXcosY+cosYcosZ+cosZcosX)-t IWP type lattice surface equation: f iwp (x,y,z)=cosXcosY+cosXcosZ+cosYcosZ-0.51(cos2X+cos2Y+cos2Z)-t D-type lattice surface equation: f D (x,y,z)=sinXsinYsinZ+sinXcosYcosZ+cosXsinYcosZ+cosXcosYsinZ-t G-type lattice surface equation: f G (x,y,z)=sinXcosY+sinYcosZ+sinZcosX-t Where X = 2πx / L, Y = 2πy / L, Z = 2πz / L, L represents the unit size of the lattice structure, and the relative density change 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.

3. The multi-scale design method of heterogeneous lattice geometric continuity fusion and strain energy drive according to claim 1 is characterized in that: In step 1, the TPMS three-dimensional lattice model is numerically calculated to obtain discrete values ​​related to the mechanical properties of the lattice structure and density, as follows: The constitutive elastic matrix D of the lattice material is expressed as: Set one of the strain components to unit strain. In this case, the stiffness coefficient in the elastic matrix is ​​equal to one of the stress components: In the finite element analysis of given periodic boundary conditions, the lattice structure belongs to the cubic system, and C 11 =C 22 =C 33 、C 12 =C 23 =C 31 、C 44 =C 55 =C 66 , parameters are obtained by applying unit strain; After obtaining the corresponding value, the TPMS lattice stiffness coefficient A fourth-order polynomial fitting is performed between ρ and density ρ, and the formula is as follows:

4. The multi-scale design method of heterogeneous lattice geometric continuity fusion and strain energy drive according to claim 1 is characterized in that: Step 2 specifically includes: Step 2.1, divide the TPMS 3D lattice model into a hexahedral grid with voxel units of a predetermined size. The voxel unit size is the same as the lattice unit size, and the voxel unit index is circularly marked in the XYZ direction; Step 2.2: Perform topology optimization on the TPMS three-dimensional lattice model. The optimization objective equation is as follows: find:ρ=[ρ1,ρ2,…,ρ i ,…,r n ] T minimize:c(ρ,U)=F T U(p) subject to:KU(ρ)=F 0≤ρ min ≤ρ i ≤ρ max ≤1 Where, the objective function c(ρ,U) represents the structural flexibility, and the optimization goal is to minimize flexibility, i.e., maximize stiffness; F T is the node force vector, U(ρ) represents the node displacement vector, which is obtained by solving the finite element equilibrium equation KU(ρ)=F, where F is determined by the load conditions and the boundary conditions will limit the displacement of some units; K represents the overall stiffness matrix, which is obtained by the unit stiffness matrix k i Assembled; n represents the number of units in the topology optimization design domain, ρ is the density field of each voxel unit; V * Indicates that the volume limit of the material in the topology optimization design domain is set to 0.3; v = [v1, v2, …, v i ,v n ] T is the volume vector of each voxel unit, ρ min and ρ max Respectively represent the lower and upper limits of the voxel unit density field; Step 2.3: Output the unit node displacement field and voxel unit density field.

5. The multi-scale design method of heterogeneous lattice geometric continuity fusion and strain energy drive according to claim 4 is characterized in that: Step 3 specifically includes: Step 3.1: Based on the elastic matrix D of the TPMS lattice i Calculate the effective stiffness matrix k of the element i : Where, Ω e Represents the design domain unit; B T represents the transpose of the element strain matrix; Get the unit node displacement u e , the strain energy w at the lattice unit node is calculated by the following formula i : Where u e Represents the unit node displacement matrix; Represents the unit node displacement transposed matrix; Step 3.2: Select the lattice with maximum strain energy based on the voxel unit density field and unit node displacement field obtained by the SIMP method, obtain the lattice cell configuration distribution field, and calculate the maximum strain energy of each unit under different TPMS lattice types.

6. The multi-scale design method of heterogeneous lattice geometric continuity fusion and strain energy drive according to claim 5 is characterized in that: The elastic matrix D of the TPMS lattice i The expression is as follows: Where, Where M refers to the index number of the TPMS type, and i refers to the index of the corresponding voxel unit; C ij,TPMS (ρ i ) represents the value of the stiffness coefficient at the corresponding density of the TPMS dot matrix.

7. The multi-scale design method of heterogeneous lattice geometric continuity fusion and strain energy drive according to claim 5 is characterized in that: Step 4 specifically includes: Step 4.1, based on the voxel unit density field and the lattice cell configuration distribution field, calculate the density enhancement factors of six directions at each index of the lattice structure based on the Gaussian radial basis function; The specific calculation method is as follows: first determine whether the adjacent unit is a heterogeneous lattice. If it is a heterogeneous lattice, add the corresponding density factor enhancement function in the transition boundary direction, and adjust the corresponding value according to the properties of the lattice itself; the basic density factor boundary enhancement equation in a single x direction is expressed as: Where, d + and d - is the density factor of the TPMS lattice inside and outside the transition interface; C + and C - represents the amplitude function of the density factor, and its value is related to the relative density of the two adjacent units; p represents the constant that controls the width of the density factor; X intersec represents the coordinates of discrete points at the transition interface in the design domain; The amplitude constant of each TPMS cell is C P =12, C IWP =4 and C G =C D =1, the density factor scope width coefficient is p p =0.3, p IWP =0.4, p G =0.8 and p D =1; Based on the above formula, the density factor is applied to the three-dimensional direction of the lattice structure, combined with the Gaussian radial basis equation, and the final formula based on density factor enhancement is obtained: Fusion hance =Fusion+u + d x+ +v + d y+ +w + d z+ +u - d x- +v - d y- +w - d z- Where Fusion is the final fusion structure, TPMS is the implicit equation corresponding to the TPMS type, and x center 、y center 、z center Indicates the coordinates of the center point of each unit, k is the control factor of the transition interval, u, v, w depend on the adjacency relationship of the cell along the x, y, and z directions. If the adjacent unit is a heterogeneous lattice, it is set to True and the optimization in this direction is performed. Otherwise, the adjacent surface density optimization is not used. d + and d - are the density factors in the corresponding directions in the above formula respectively; Step 4.2: Perform finite element simulation of the single configuration gradient structure and the heterogeneous fusion gradient structure, conduct performance comparison and verification, and finally output the verified three-dimensional lattice model.

8. The multi-scale design method for heterogeneous lattice geometric continuity fusion and strain energy drive according to any one of claims 1 to 7, wherein the design process is constructed as a complete computing system, including three computing units and a model output unit, characterized in that: include: The first calculation unit is used to establish a TPMS three-dimensional lattice model and perform numerical calculations on its lattice units to obtain discrete values ​​associated with the mechanical properties of the lattice structure and density; a second computing unit, configured to mesh the TPMS three-dimensional lattice model according to voxel units of a predetermined size; Perform topology optimization on the TPMS 3D lattice model and output the unit node displacement field and voxel unit density field; A third calculation unit is used to calculate the strain energy value at each lattice unit node according to the unit node displacement field and the voxel unit density field, and take the maximum value of the strain energy of each lattice unit under different TPMS lattice types to obtain the lattice cell configuration distribution field; The model output unit is used to fuse and optimize the heterogeneous cell boundary part of the TPMS three-dimensional lattice model based on the voxel unit density field and the lattice cell configuration distribution field, output the three-dimensional lattice model and verify it.

9. Application of the multi-scale design method for heterogeneous lattice geometric continuity fusion and strain energy drive in generating computer three-dimensional modeling according to any one of claims 1 to 7; 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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