Dual-scale optimization design method for multi-configuration lattice structure

Abstract

The invention provides a dual-scale optimization design method of a multi-configuration lattice structure, which comprises the following steps of: respectively adopting topological optimization based on a variable volume rate method and an integer programming model based on a digital coding unit library at a macroscopic scale and a microscopic scale, and connecting a macroscopic optimization problem and a microscopic optimization problem by adopting an RBF (Radial Basis Function) neural network; macroscopically determining the optimal volume ratio of each unit in the lattice structure to minimize the flexibility of the whole structure, and microscopically determining the optimal configuration of each unit to minimize the strain energy of the unit. The multi-configuration dot matrix obtained through optimization design has remarkable advantages, and compared with a traditional single-configuration dot matrix structure, it can be guaranteed that a design result with lower flexibility and higher rigidity can be obtained under the condition of the same material use amount; and meanwhile, the multi-configuration dot matrix unit can effectively adapt to stress states of different areas in the macrostructure, so that the stress concentration phenomenon is effectively reduced. The method is suitable for any load working condition, and the performance requirements of light weight, high strength, uniform stress and convenient 3D printing of the lattice structure are met.

Description

Technical field:

[0001] The present invention relates to the field of lattice structure design and optimization, and in particular to a dual-scale optimization design method for a multi-configuration lattice structure. Background technology:

[0002] The traditional lattice structure is mainly obtained by periodically arranging TPMS units or truss units. The TPMS unit has a larger specific surface area and higher heat transfer efficiency, but the curved thin shell characteristics of the TPMS will weaken the structural stiffness and cause in-plane buckling; the truss unit is easy to manufacture and has a clear force transmission path, but the traditional lattice structure with a single truss unit array cannot effectively strengthen the core stress area, and the single type of truss unit leads to local stress concentration damage at the internal node stress.

[0003] Compared with the traditional single-configuration lattice structure, the multi-configuration lattice structure has stronger programmability. By adjusting the unit configuration and volume ratio, the overall structure can have stronger rigidity under the same material, and improve impact resistance and energy consumption characteristics. Therefore, it has been widely used in mechanical parts, body structures and other fields in recent years. Especially in the field of aerospace aircraft manufacturing, the requirements for lightweight and high-strength performance are more stringent. The dual-scale optimization design of the multi-configuration lattice structure can significantly reduce the weight of the aerospace structure 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, and then uses metal powder or hot-melt plastic to print layer by layer through a 3D printer to finally generate a physical structure. In addition, photocuring technology is also an important method of 3D printing, which uses photosensitive resin to cure and shape under ultraviolet light. These technologies are now widely used in many fields such as industrial design, civil engineering and construction, vehicle engineering, aerospace, biomedicine, and firearms manufacturing.

[0005] The purpose of the present invention is to overcome the problems existing in the existing lattice structure and to provide a dual-scale optimization design method for a multi-configuration lattice structure.

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

[0007] (1) By means of combinatorial mathematics and undirected graph structure, the predefined initial modules are hybridized to generate a digital coding unit library, and it is determined that the truss lattice units in the digital coding unit library have 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 using the energy homogenization theory. The RBF neural network proxy model is established by combining the basic parameters of the unit and the elastic tensor data.

[0009] (3) Based on the RBFNN proxy model, a sensitivity theory calculation formula for the macroscopic topology optimization problem is established. The macroscopic-scale topology optimization design is carried out based on the variable volume ratio method to determine the optimal volume ratio of each microscopic array unit.

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

[0011] (5) Upload the stl model of the optimized design result to the 3D printer and print it as a whole.

[0012] The beneficial effects of the present invention are:

[0013] The provided design method can be used in the design of lattice structures under arbitrary loading conditions, such as mechanical parts, spacecraft sandwich panels, or biomedical human implant structures.

[0014] The provided design method clarifies that the structure formed after dual-scale optimization has the general characteristics of a truss lattice structure. The volume ratio of each microscopic truss lattice unit can be obtained during the macroscopic topology optimization process, and the material distribution pattern that maximizes the overall stiffness of the structure is determined.

[0015] The formed multi-configuration lattice structure has the following advantages: compared with the traditional structure, it can achieve highly lightweight design, reduce structural stress concentration, and have good structural stiffness performance.

[0016] The formed multi-configuration lattice structure has the following characteristics: the overall structure is composed of truss lattice units of 6 configurations, the rod size of the truss lattice unit in the bottom maximum tension area is increased to ensure the overall bearing capacity, and additional spatial diagonal basic truss modules are added to the central shear areas on both sides, which can effectively prevent local shear failure. Description of the drawings:

[0017] In order to further clarify the process of the present invention and the features of each embodiment, a more specific description of each embodiment of the present invention will be presented with reference to the accompanying drawings. It should be understood that these drawings are only typical embodiments of the present invention and are not to be considered as limiting the scope thereof.

[0018] Figure 1 This is a dual-scale topology optimization design flow chart of the lattice structure of an embodiment of the present invention.

[0019] Figure 2 This is an example diagram of A to H8 basic truss modules and unit combinations according to an embodiment of the present invention.

[0020] Figure 3 It is a flexibility convergence curve diagram during the optimization process under three-point bending load of an embodiment of the present invention.

[0021] Figure 4 It is a diagram of the structural changes at different stages during the optimization process of an embodiment of the present invention.

[0022] Figure 5 It is a mechanical test diagram of the optimized design result of the multi-configuration lattice structure of an embodiment of the present invention and a traditional lattice structure.

[0023] Figure 6 It is a comparison chart of the optimized design results of the multi-configuration lattice structure of the embodiment of the present invention and the experimental results of the traditional lattice structure.

[0024] Figure 7 This is a physical picture of a multi-configuration lattice structure formed by 3D printing according to an embodiment of the present invention.

[0025] Figure 8 It is a truss lattice unit diagram included in the multi-configuration lattice structure optimization result of an embodiment of the present invention. Specific implementation method:

[0026] In order to make the purpose and technical solution of the present invention more clear, the present invention is further described in detail below with reference to the accompanying drawings. A dual-scale optimization design method for a multi-configuration lattice structure comprises the following steps:

[0027] A dual-scale optimization design method for a multi-configuration lattice structure comprises the following steps:

[0028] Step 1, using combinatorial mathematics and undirected graph structure to perform hybrid combination of predefined initial modules to generate a digital coding unit library, and determining that the truss lattice units in the digital coding unit library have general characteristics;

[0029] Step 2: According to the general characteristics of the truss lattice unit, the unit form and basic parameters x are determined, and the elastic tensor D data of the unit is calculated using the energy homogenization theory, and the RBF neural network proxy model is established by combining the basic parameters of the unit and the elastic tensor data;

[0030] Step 3: Based on the RBF neural network proxy model, a sensitivity theory calculation formula for the macroscopic topology optimization problem is established, and the macroscopic topology optimization design is carried out based on the variable volume rate method to determine the optimal volume rate of each microscopic array unit;

[0031] Step 4: According to the optimal volume rate optimization result of the micro-array unit, considering the volume rate constraint, the integer programming design of the micro-array unit configuration is carried out based on the digital coding unit library to determine the final multi-configuration lattice structure form;

[0032] Step 5: Upload the optimized design model to the 3D printer and print it as a whole.

[0033] Furthermore, the designed multi-configuration lattice structure includes lattice units of multiple different configurations, and these lattice units are derived from a predefined digital coding unit library. Step 1 specifically includes:

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

[0035] (2) Using combinatorial mathematics to exhaust the letter combination structures of all basic components,

[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 cell generated by the 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 to represent each possible cell combination;

[0039] (4) The module code X with a connected component greater than 1 is determined through the adjacency matrix of the undirected graph G and removed from the digital coding unit library, thereby ensuring that the unit cell contributes 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] Where G is an undirected graph; V is the set of vertices; E is the set of edges, an unordered binary geometry consisting of the elements in V.

[0044] Furthermore, step 2 specifically includes:

[0045] (1) Using the energy homogenization theory to calculate the elastic tensor D data and volume fraction V of the unit vol

[0046]

[0047] In the formula is the unit displacement corresponding to the specified 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 the three-dimensional logic matrix of the combined voxel model, nx ,n y ,n z is the number of voxels in the x, y, and z directions;

[0048] (2) Establishing the RBF neural network proxy model by combining the basic unit parameters and elastic tensor data

[0049]

[0050] where x=[x1,x2,...,x8,ρ e ] is the input vector, c i =[c i1 ,c i2 ,...,c i9 ] is the center vector of the ith 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 jth output layer neuron.

[0051] Furthermore, step three specifically includes:

[0052] (1) Establish a theoretical model for macro optimization design problems;

[0053] Find:ρ={ρ e ,...,ρ N}

[0054] Minimize:

[0055] Subject to:

[0056] :KU=F

[0057] :0<ρ min ≤ρ≤ρ max e=1,...,N

[0058] in 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, which is determined by the type and volume rate of the unit cell, ρ is the volume rate vector of all unit cells, ρ min and ρ max are the minimum and maximum volume rates of the unit cell, η is the volume rate of the lattice structure, V e and V mare the volume of the hexahedral unit filled with unit cells and the lattice structure, N is the number of all units 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;

[0059] (2) Solve the macro optimization design problem. In the solution process, the density field ρ is iterated by the optimization criterion method until convergence. The sensitivity analysis required in the iterative process is shown in the following formula:

[0060]

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

[0062] Furthermore, step four specifically includes:

[0063] (1) Considering the volume rate constraint, an integer programming design model for micro-array unit configuration based on the digital coding unit library is established as shown in the following formula:

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

[0065] Minimize:

[0066] Subject to:D e (x)ε e =σ e

[0067] :V vol =ρ e

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

[0069] In the formula, x is the code, V e is the unit cell volume, 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 the micro-array unit configuration, an implicit enumeration method is used to traverse the coding unit library to solve it.

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

[0072] (1) According to the modular code X and rod radius r of each lattice unit obtained from the optimization design results, Rhino parametric reconstruction is performed and exported as an STL model;

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

[0074] (3) The G code was imported into a fused deposition modeling 3D printer to manufacture the design results. PLA was selected as the printing material, and the printing temperature was set to 200°C, the platform temperature to 60°C, the layer height to 0.2 mm, the printing speed to 50 mm / s, and the filling density to 100%.

[0075] 1. If Figure 1 The overall dual-scale optimization process for multi-configuration lattice results is divided into six processes: pre-processing, macro topology optimization, micro integer programming selection, secondary topology optimization fine-tuning of unit volume and post-processing of optimization results.

[0076] 2. Determine the candidate truss lattice unit library type, and select 8 basic truss parts A to H for hybrid combination. The combination example is given as Figure 2 shown.

[0077] 3. Figure 3 This is the flexibility change process of the optimization example of a simply supported beam under a concentrated load in the top span. With the continuous progress of macro-topology optimization and micro-integer programming selection, the flexibility of the overall structure continues to decrease, ultimately minimizing the flexibility of the overall structure and maximizing the stiffness.

[0078] 4. Figure 4 The figure shows three structures in 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 research process of three lattice structures is demonstrated, including uniform lattice structure 1, variable density lattice structure 2 and multi-configuration lattice structure 3. The experimental results are shown in Figure 6 As shown, the initial stiffness and ultimate strength of the multi-morphological lattice structure 3 are 44.24% and 47.70% higher than those of the single-morphological variable-density lattice structure 2, respectively.

[0080] An embodiment formed based on a dual-scale optimization design method of a multi-configuration lattice structure, such as Figure 7 As shown in Figure 1, the structural dimensions are length × width × height = 20 × 2 × 8 cm. In the 3D printing stage, the selected material is photocuring. The 6 different lattice structures contained in the structure and their parameterized codes X are shown in Figure 1. Figure 8The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be considered as the protection scope of the present invention.

Claims

1. A dual-scale optimization design method for a multi-configuration lattice structure, characterized in that: The following steps are involved: Step 1, using combinatorial mathematics and undirected graph structure to perform hybrid combination of predefined initial modules to generate a digital coding unit library, and determining that the truss lattice units in the digital coding unit library have general characteristics; Step 2: According to the general characteristics of the truss lattice unit, the unit form and basic parameters x are determined, and the elastic tensor D data of the unit is calculated using the energy homogenization theory, and the RBF neural network proxy model is established by combining the basic parameters of the unit and the elastic tensor data; Step 3: Based on the RBF neural network proxy model, a sensitivity theory calculation formula for the macroscopic topology optimization problem is established, and the macroscopic topology optimization design is carried out based on the variable volume rate method to determine the optimal volume rate of each microscopic array unit; Step 4: According to the optimal volume rate optimization result of the micro-array unit, considering the volume rate constraint, the integer programming design of the micro-array unit configuration is carried out based on the digital coding unit library to determine the final multi-configuration lattice structure form; Step 5: Upload the optimized design model to the 3D printer and print it as a whole.

2. The dual-scale optimization design method for a multi-configuration lattice structure according to claim 1, characterized in that: The designed multi-configuration lattice structure contains lattice units of various configurations, and these lattice units are derived from a predefined digital coding unit library. Step 1 specifically includes: (1) Determine the geometric shapes of n basic components represented by letter elements and record their node coordinates and the node numbers at the ends of the rods; (2) Using combinatorial mathematics to exhaust the letter combination structures of all basic components, 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 cell generated by the hybrid combination; (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 to represent each possible cell combination; (4) The module code X with a connected component greater than 1 is determined through the adjacency matrix of the undirected graph G and removed from the digital coding unit library, thereby ensuring that the unit cell contributes to the internal connection of the lattice structure. V(G)={v1,v2,v3,...,v n } E(G)={(v1,v2),(v1,v3),...,(v i ,v j )} Where G is an undirected graph; V is the set of vertices; E is the set of edges, an unordered binary geometry consisting of the elements in V.

3. The dual-scale optimization design method for a multi-configuration lattice structure according to claim 1, characterized in that: Step 2 specifically includes: (1) Using the energy homogenization theory to calculate the elastic tensor D data and volume fraction V of the unit vol In the formula is the unit displacement corresponding to the specified 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 the three-dimensional logic matrix of the combined voxel model, n x ,n y ,n z is the number of voxels in the x, y, and z directions; (2) Establishing the RBF neural network proxy model by combining the basic unit parameters and elastic tensor data where x=[x1,x2,...,x8,ρ e ] is the input vector, c i =[c i1 ,c i2 ,...,c i9 ] is the center vector of the ith 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 jth output layer neuron.

4. The dual-scale optimization design method for a multi-configuration lattice structure according to claim 1, characterized in that: Step three specifically includes: (1) Establish a theoretical model for macro optimization design problems; Find:ρ={ρ e ,...,r N } Subject to: :KU=F :0<ρ min ≤ρ≤ρ max e=1,...,N in 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, which is determined by the type and volume rate of the unit cell, ρ is the volume rate vector of all unit cells, ρ min and ρ max are the minimum and maximum volume rates of the unit cell, η is the volume rate of the lattice structure, V e and V m are the volume of the hexahedral unit filled with unit cells and the lattice structure, N is the number of all units 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) Solve the macro optimization design problem. In the solution process, the density field ρ is iterated by the optimization criterion method until convergence. The sensitivity analysis required in the iterative process is shown in the following formula: Among them C e is the compliance of the e-th unit at the macroscopic scale, B is a geometric matrix of 8-node hexahedral elements, Ω e is the element domain.

5. The dual-scale optimization design method for a multi-configuration lattice structure according to claim 1, characterized in that: Step 4 specifically includes: (1) Considering the volume rate constraint, an integer programming design model for micro-array unit configuration based on the digital coding unit library is established as shown in the following formula: Find:x={x1,...,x8} Minimize: Subject to:D e (x)ε e =σ e :V vol =ρ e :x i =0or 1i=1,...,8 In the formula, x is the code, V e is the unit cell volume, σ e =D e Bu e is the stress vector at the center of the unit cell is the corresponding strain vector; (2) For the integer programming design model of the micro-array unit configuration, an implicit enumeration method is used to traverse the coding unit library to solve it.

6. The dual-scale optimization design method for a multi-configuration lattice structure according to claim 1, characterized in that: Step 5 specifically includes the following sub-steps: (1) According to the modular code X and rod radius r of each lattice unit obtained from the optimization design results, Rhino parametric reconstruction is performed and exported as an STL model; (2) Use Cura slicing software to generate the G code corresponding to the STL model; (3) The G code was imported into a fused deposition modeling 3D printer to manufacture the design results. PLA was selected as the printing material, and the printing temperature was set to 200°C, the platform temperature to 60°C, the layer height to 0.2 mm, the printing speed to 50 mm / s, and the filling density to 100%.

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