A bi-scale optimization design method of multi-configuration lattice structure

Abstract

The application provides a double-scale optimization design method of a multi-configuration lattice structure, which adopts a topology optimization based on a variable volume rate method and an integer programming model based on a digital coding unit library in macro and micro scales respectively, and adopts an RBF neural network to connect the macro and micro optimization problems; the macro determines the optimal volume rate of each unit in the lattice structure so as to minimize the overall structure flexibility, and the micro determines the optimal configuration of each unit so as to minimize the unit strain energy. The multi-configuration lattice obtained through the optimization design has significant advantages, compared with the traditional single-configuration lattice structure, and can ensure that a lower flexibility and a larger stiffness design result is obtained under the same material consumption, and meanwhile, the multi-configuration lattice unit can effectively adapt to the stress state of different regions in the macro structure and effectively reduce the stress concentration phenomenon. The method is suitable for any load working condition, and can realize the performance requirements of light weight, high strength, uniform stress and convenience for 3D printing of the lattice structure.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of lattice structure design and optimization, and particularly relates to a double-scale optimization design method of a multi-configuration lattice structure BACKGROUND

[0002] Traditional lattice structures are mainly obtained by periodic array of TPMS units or truss units. TPMS units have higher heat exchange efficiency due to larger specific surface area, but the curved shell characteristics of TPMS weaken the structural stiffness and cause in-plane buckling; truss units are simple to manufacture and have clear force transmission path, but the traditional lattice structure arranged by single truss unit array cannot effectively strengthen the core stress area, and the single type of truss unit causes local stress concentration and damage of internal nodes.

[0003] Compared with traditional single-configuration lattice structures, multi-configuration lattice structures have stronger programmability. By adjusting the unit configuration and volume fraction, the overall structure can have stronger stiffness under the same material consumption, and the impact resistance and energy dissipation characteristics are improved. Therefore, in recent years, multi-configuration lattice structures have been widely used in mechanical parts, vehicle body structures and other fields, especially in the field of aerospace vehicle manufacturing, which has higher requirements for lightweight and high strength performance. The double-scale optimization design of multi-configuration lattice structure can significantly reduce the weight of aerospace structures and improve the mechanical properties.

[0004] 3D printing technology, also known as additive manufacturing, is a rapid prototyping technology. This technology first creates a digital model file, then uses metal powder or hot melt plastic, and finally generates a physical structure through layer-by-layer printing by a 3D printer. In addition, photopolymerization technology is also an important method of 3D printing, which uses photosensitive resin to solidify under ultraviolet light. These technologies are widely used in industrial design, civil engineering and construction, vehicle engineering, aerospace, biomedical engineering, gun manufacturing and other fields.

[0005] The purpose of the present application is to provide a double-scale optimization design method of a multi-configuration lattice structure to overcome the problems of existing lattice structures.

[0006] The present application can be implemented by the following technical solutions:

[0007] (1) A hybrid combination of the initial module is generated by means of combinatorics and undirected graph structure to generate a digital coding unit library, and the truss lattice unit in the digital coding unit library has general characteristics.

[0008] (2) According to the general characteristics of the truss lattice unit, the form and basic parameters of the unit are determined, and the elastic tensor data of the unit is calculated by using the energy homogenization theory, and the RBF neural network proxy model is established combining the basic parameters and elastic tensor data of the unit.

[0009] (3) According to the RBFNN agent model, the sensitivity theory calculation formula of the macroscopic topology optimization problem is established, the variable volume rate method is used to carry out the topology optimization design at the macroscopic scale, and the optimal volume rate of each micro point array unit is determined.

[0010] (4) According to the optimal volume rate optimization result of the micro point array unit, considering the volume rate constraint, the integer programming design of the micro point array unit configuration is carried out based on the digital coding unit library, so as to determine the final multi-configuration point array structure form.

[0011] (5) The stl model of the optimization design result is uploaded to the 3D printer, and is printed as a whole.

[0012] The beneficial effects of the application are:

[0013] The design method provided can be used in the design of point array structures under any load working condition, such as mechanical parts, spacecraft sandwich plates, or biomedical human implant structures.

[0014] The design method provided clearly shows that the structure formed after the double-scale optimization has the general characteristics of the truss point array structure, the volume rate of each micro truss point array unit can be obtained in the macroscopic topology optimization process, and the material distribution mode that maximizes the overall stiffness of the structure is determined.

[0015] The multi-configuration point array structure formed has the following advantages: compared with the traditional structure, it realizes high lightweight design, reduces stress concentration, and has good structural stiffness performance.

[0016] The multi-configuration point array structure formed has the following characteristics: the overall structure is composed of six types of truss point array units, the rod size of the truss point array unit in the maximum tensile area at the bottom is increased to ensure the overall bearing capacity, and additional space diagonal basic truss modules are added to the center shear area on both sides, which can effectively prevent local shear failure. BRIEF DESCRIPTION OF DRAWINGS

[0017] In order to further illustrate the flow of the application and the characteristics of each embodiment, a more specific description of each embodiment of the application will be presented with reference to the accompanying drawings. It should be considered that these drawings only depict typical embodiments of the application, and therefore should not be considered as limiting the scope thereof.

[0018] Figure 1 The flow chart of the double-scale topology optimization design of the point array structure of the embodiment of the application.

[0019] Figure 2 The combination example diagram of the A-H eight basic truss modules and units of the embodiment of the application.

[0020] Figure 3 The compliance convergence curve diagram in the optimization process under three-point bending load of the embodiment of the application.

[0021] Figure 4 Structure change process diagram for different stages in the optimization process of the embodiment of the present application.

[0022] Figure 5 Mechanical test diagram of the optimization design result of the multi-configuration lattice structure of the embodiment of the present application and the traditional lattice structure.

[0023] Figure 6 Comparison diagram of the optimization design result of the multi-configuration lattice structure of the embodiment of the present application and the experimental result of the traditional lattice structure.

[0024] Figure 7 Physical diagram of the multi-configuration lattice structure formed by 3D printing of the embodiment of the present application.

[0025] Figure 8 Diagram of the truss lattice unit contained in the optimization result of the multi-configuration lattice structure of the embodiment of the present application. DETAILED DESCRIPTION

[0026] In order to make the purpose and technical scheme of the present application clearer and more understandable, the present application will be further described in detail below with reference to the drawings. A double-scale optimization design method of a multi-configuration lattice structure includes the following steps:

[0027] A double-scale optimization design method of a multi-configuration lattice structure includes the following steps:

[0028] Step one, generate a digital coding unit library by hybrid combination of a pre-defined initial module with the aid of combinatorial mathematics and undirected graph structure, and determine that the truss lattice unit in the digital coding unit library has general characteristics;

[0029] Step two, determine the form and basic parameters x of the unit according to the general characteristics of the truss lattice unit, and calculate the elastic tensor D data of the unit by using the energy homogenization theory, and establish a RBF neural network surrogate model combining the basic parameters of the unit and the elastic tensor data;

[0030] Step three, establish a sensitivity theory calculation formula of the macroscopic topology optimization problem according to the RBF neural network surrogate model, carry out topology optimization design at the macroscopic scale based on the variable volume fraction method, and determine the optimal volume fraction of each micro-lattice unit;

[0031] Step four, consider the volume fraction constraint based on the optimal volume fraction optimization result of the micro-lattice unit, carry out integer programming design of the micro-lattice unit configuration based on the digital coding unit library, and thus determine the final multi-configuration lattice structure form;

[0032] Step five, upload the model of the optimization design result to a 3D printer, and print it into a whole.

[0033] Further, the designed multi-configuration lattice structure contains a plurality of different configuration lattice units, which are derived from a predefined digital coding unit library, and step one specifically includes:

[0034] (1) Determine the geometric shape of the n basic components represented by the letter elements, and record their node coordinates and node numbers of the rod ends;

[0035] (2) Exhaust all letter combination structures of the basic components using combinatorics,

[0036]

[0037] Where Num=255 represents all possible combinations in the digital coding unit library; n=8 is the number of basic components; k is the number of basic components contained in the lattice unit generated by hybrid combination;

[0038] (3) Introducing 0-1 Boolean values to quantify the presence of each basic component in the combination, thereby generating an n-bit binary code X representing each possible cell combination;

[0039] (4) Determine the module code X with more than one connected component by the adjacency matrix of the undirected graph G, and eliminate it from the digital coding unit library, so as to ensure that the cell is conducive to the internal connection of the lattice structure,

[0040]

[0041] V(G)={v1,v2,v3,...,v n}

[0042] E(G)={(v1,v2),(v1,v3),...,(v i ,v j )}

[0043] In the formula, G is an undirected graph; V is the set of vertices; E is the set of edges, an unordered binary geometry composed of elements in V.

[0044] Further, step two specifically includes:

[0045] (1) Calculate the elastic tensor D data and volume rate V vol

[0046]

[0047] In the formula, u is the unit displacement corresponding to the specified unit strain field, k e is the unit stiffness matrix, Ω is the total volume of the unit cell of the lattice structure, VLC is the three-dimensional logical matrix of the combined voxel model, and nx ,n y ,n z is the number of voxels in x, y, z direction;

[0048] (2) Establish RBF neural network surrogate model combined with basic parameters of binding unit and elastic tensor data

[0049]

[0050] where x = [x1, x2,..., x8, p e ] is the input vector, c i = [c i1 , c i2 ,..., c i9 ] is the center vector of the i-th radial basis function, is the width parameter of the radial basis function, w ij is the weight of the i-th hidden layer neuron to the j-th output layer neuron, b j is the bias of the j-th output layer neuron.

[0051] Further, step three specifically includes:

[0052] (1) Establish a theoretical model of macroscopic optimization design problem;

[0053] Find: p = {p e ,..., p N}

[0054] Minimize:

[0055] Subject to:

[0056] : KU = F

[0057] : 0 < p min ≤ p ≤ p max e = 1,..., N

[0058] where is the overall stiffness matrix of the lattice structure, C is the compliance of the lattice structure, U and F are the overall displacement vector and load vector of the lattice structure respectively, K is the overall stiffness matrix of the lattice structure, determined by the type and volume fraction of the unit cell, p is the volume fraction vector of all unit cells, p min and p max are the minimum and maximum volume fractions of the unit cell respectively, and η is the volume fraction of the lattice structure, V e and V mrespectively the volume of the hexahedral element and the lattice structure filled with unit cells, N is the number of all unit cells in the lattice structure, which is also equal to the number of hexahedral meshes in the finite element, u e and k e are respectively the displacement vector and the stiffness matrix of the unit cell;

[0059] (2) The solution of the macroscopic optimization design problem is performed, and in the solution process, the density field p is iterated until convergence through the optimization criterion method. The sensitivity analysis required in the iteration process is as follows:

[0060]

[0061] Where C e is the compliance of the e-th element at the macroscopic scale, B is a geometric matrix of an 8-node hexahedral element, Ω e is the element domain.

[0062] Further, step four specifically includes:

[0063] (1) Considering the volume fraction constraint, an integer programming design model of micro-lattice unit configuration based on a digital coded unit library is established as follows:

[0064] Find: x = {x1,...,x8}

[0065] Minimize:

[0066] Subject to: D e (x) ε e = σ e

[0067] : V vol = p e

[0068] : x i = 0 or 1 i = 1,...,8

[0069] In the formula, x is the code, V e is the volume of the unit cell, σ e = D e Bu e is the stress vector at the center of the unit cell is the corresponding strain vector;

[0070] (2) For the integer programming design model of micro-lattice unit configuration, an implicit enumeration method is used to traverse the coded unit library for solving.

[0071] Further, step five specifically includes the following sub-steps:

[0072] (1) Based on the modular code X and rod radius r of each lattice unit obtained from the optimization design results, perform Rhino parametric reconstruction and export it as an STL model;

[0073] (2) Use Cura slicing software to generate the G code for the corresponding STL model;

[0074] (3) Import the G code into the fused deposition modeling 3D printer to manufacture the design results. Select PLA as the printing material, set the printing temperature to 200℃, the platform temperature to 60℃, the layer height to 0.2mm, the printing speed to 50mm / s, and the infill density to 100%.

[0075] 1. For example Figure 1 The overall process for dual-scale optimization of multi-configuration lattice results is divided into six steps: preprocessing, macro-topology optimization, micro-integer programming selection, secondary topology optimization to fine-tune cell volume, and post-processing of optimization results.

[0076] 2. Determine the candidate truss lattice element library types, and perform hybrid combinations by selecting 8 basic truss parts from A to H. An example of the given combinations is... Figure 2 As shown.

[0077] 3. Figure 3 The optimization example of the flexibility change process of a simply supported beam under a concentrated load at the top mid-span shows that as macro-topology optimization and micro-integer programming are continuously carried out, the flexibility of the overall structure is continuously reduced, ultimately minimizing the flexibility and maximizing the stiffness of the overall structure.

[0078] 4. Figure 4 The three structures in the middle are the key stages of the dual-scale optimization process. Structure 1 is the initial uniform lattice structure, structure 2 is the variable density lattice structure after macroscopic topology optimization, and structure 3 is the final optimization result after integer programming selection.

[0079] 5. Figure 5 The experimental study process for three lattice structures is presented, including a uniform lattice structure 1, a variable-density lattice structure 2, and a multi-configuration lattice structure 3. The experimental results are as follows: Figure 6 As shown, the initial stiffness and ultimate strength of the multi-morphic lattice structure 3 are 44.24% and 47.70% higher than those of the single-morphic variable density lattice structure 2, respectively.

[0080] An example based on a dual-scale optimization design method for multi-configuration lattice structures, such as... Figure 7 As shown, its structural dimensions are length × width × height = 20 × 2 × 8 cm. In the 3D printing stage, photopolymerization was used. The structure contains six different lattice structures and their parametric codes X are shown below. Figure 8The above description is only the preferred embodiment of the present application, it should be pointed out that for ordinary skilled in the art, without departing from the principles of the present application, can also make several improvements and refinements, these improvements and refinements should also be considered as the protection scope of the present application.

Claims

1. A method for bi-scale optimization design of a multi-configuration lattice structure, characterized in that, The method comprises the following steps: Step one, hybrid combination of pre-defined initial modules by means of combinatorics and undirected graph structure to generate a digital coding unit library, and determining that the truss lattice unit in the digital coding unit library has general characteristics; Step two, determining the form and basic parameter x of the unit according to the general characteristics of the truss lattice unit, and calculating the elastic tensor D data of the unit by means of energy homogenization theory, and combining the basic parameters and the elastic tensor data of the unit to establish an RBF neural network proxy model; Step three, establishing a sensitivity theoretical calculation formula of the macroscopic topology optimization problem according to the RBF neural network proxy model, and carrying out topology optimization design at a macroscopic scale based on the variable volume fraction method to determine the optimal volume fraction of each micro-lattice unit; Step four, according to the optimal volume fraction optimization result of the micro-lattice unit, considering the volume fraction constraint, carrying out integer programming design of the micro-lattice unit configuration based on the digital coding unit library, so as to determine the final multi-configuration lattice structure form; Step five, uploading the model of the optimization design result to a 3D printer, and printing the model as a whole.

2. The method of claim 1, wherein, The designed multi-configuration lattice structure contains a plurality of lattice units with different configurations, which are derived from the pre-defined digital coding unit library, and step one specifically comprises: (1) determining the geometric shapes of n basic components represented by letter elements, and recording the node coordinates and node numbers of the rod ends of the basic components; (2) using combinatorics to exhaust all letter combination structures of the basic components, Wherein Num=255 represents all possible combinations in the digital coding unit library; n=8 is the number of basic components; k is the number of basic components contained in the lattice unit generated by hybrid combination; (3) introducing 0-1 Boolean values to quantify the existence of each basic component in the combination, thereby generating an n-bit binary code X representing each possible unit cell combination; (4) judging the module code X with more than one connected component by the adjacency matrix of the undirected graph G, and eliminating it from the digital coding unit library, so as to ensure that the unit cell is conducive to the internal connection of the lattice structure, V(G) = {v1, v2, v3,..., v n} E(G) = {(vi, v2), (vi, v3),..., (vi, vn)}. i j}​ Wherein G is an undirected graph; V is a set of vertices; E is a set of edges, an unordered binary geometry composed of elements in V.

3. The method of claim 1, wherein, Step two specifically comprises: (1) The elastic tensor D data and the volume fraction V of the unit are calculated by using the energy homogenization theory vol In the formula is the unit displacement corresponding to the prescribed unit test strain field, k e is the unit stiffness matrix, Ω is the total volume of the unit cell of the lattice structure, VLC is a three-dimensional logical matrix of the combined voxel model, n x ,n y ,n z is the number of voxels in the x, y, z directions; (2) combining the basic parameters and the elastic tensor data of the unit to establish an RBF neural network proxy model where x = [x1, x2,..., x8, p e ] is the input vector, c i = [c i1 , c i2 ,..., c i9 ] is the center vector of the i-th radial basis function, is the width parameter of the radial basis function, w ij is the weight from the i-th hidden layer neuron to the j-th output layer neuron, b j is the bias of the j-th output layer neuron.

4. The method of claim 1, wherein, Step three specifically comprises: (1) establishing a theoretical model of macroscopic optimization design problem; Find: ρ = {ρ e ,...,ρ N} Subject to: :KU=F :0 < p min :0 < p max e = 1,..., N wherein K is the global stiffness matrix of the lattice structure, C is the compliance of the lattice structure, U and F are the global displacement vector and load vector of the lattice structure, respectively, K is the global stiffness matrix of the lattice structure, determined by the type and volume fraction of the unit cells, p is the volume fraction vector of all unit cells, p min and p max are the minimum and maximum volume fraction of the unit cells, respectively, η is the volume fraction of the lattice structure, V e and V m are the volume of the hexahedral element filled with unit cells and the lattice structure, respectively, N is the number of all unit cells in the lattice structure, which is also equal to the number of hexahedral meshes in the finite element, u e and k e are the displacement vector and stiffness matrix of the unit cell, respectively; (2) solving the macroscopic optimization design problem, in the solving process, the density field ρ is iterated by the optimization criterion method until convergence, and the sensitivity analysis required in the iteration process is as follows: where C e is the compliance of the e-th element at the macro-scale, B is a geometry matrix of an 8-node hexahedral element, Ω e is the element domain.

5. The method of claim 1, wherein, Step four specifically comprises: (1) considering the volume fraction constraint, and establishing an integer programming design model of the micro-lattice unit configuration based on the digital coding unit library as follows: Find:x={x1,...,x8} Minimize: Subject to: e (x)ε e =σ e :V vol = p e x i = 0 or 1 i = 1,..., 8 where x is the code, V e is the cell volume, σ e = D e Bu e is the cell center stress vector is the corresponding strain vector; (2) for the integer programming design model of the micro-lattice unit configuration, implicit enumeration method is used to traverse the coding unit library for solving.

6. The method of claim 1, wherein, Step five specifically comprises the following sub-steps: (1) According to the modular encoding X and the radius r of each lattice unit obtained from the optimization design results, Rhino parameterization reconstruction is carried out and stl model is exported; (2) Cura slicing software is used to generate G code corresponding to the stl model; (3) The G code is imported into the fused deposition modeling 3D printer to manufacture the design results, PLA is selected as the printing material, the printing temperature is set to 200℃, the platform temperature is set to 60℃, the layer height is set to 0.2mm, the printing speed is set to 50mm / s, and the filling density is set to 100%.

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