Data-driven enhanced lattice structure multi-scale topology optimization design method

Abstract

The application discloses a data-driven enhanced lattice structure multi-scale topological optimization design method. The application firstly establishes a macroscopic structure mechanics model based on multiple parameters; secondly, optimizes density-based topological design to realize lightweight and mechanical performance improvement of the macroscopic structure; thirdly, combines the macroscopic structure mechanics model to calculate the equivalent modulus distribution and the principal stress distribution of the optimal design structure; then, based on the equivalent modulus distribution and the principal stress distribution, a mechanics performance homogenization calculation method of the lattice unit cell is established; then, the lattice unit cell dataset is constructed; subsequently, a deep neural network model is constructed, the constructed lattice unit cell dataset is taken as a training sample, and a mapping relationship between macroscopic design parameters and the unit cell type and the mesoscopic size is established; finally, the trained deep neural network model is used to calculate the mesoscopic unit cell distribution, and multi-scale topological optimization design of the lattice structure is realized. The application can effectively improve the multi-scale topological optimization calculation efficiency of the lattice structure.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of material structure optimization design, and particularly relates to a data-driven enhanced lattice structure multi-scale topology optimization design method. BACKGROUND

[0002] Lattice structure has gradually become a research hotspot in the fields of aerospace, automobile and biomedicine due to its characteristics of realizing the collaborative design of lightweight and functionalization. By designing the morphology and size of the lattice unit cell structure, the mechanical properties and functional characteristics (heat insulation, shock absorption, noise reduction, etc.) of the lattice structure can be effectively adjusted. Combined with the current rapid development of additive manufacturing technology, the manufacturing and application of complex lightweight functional lattice structures can be realized. However, the efficient multi-scale design of lattice structure is still a difficult problem to be solved.

[0003] Multi-scale topology optimization design of structure is an effective way to realize the lightweight of lattice structure. In recent years, multi-scale topology optimization of lattice structure is realized by optimizing the relative density and cell type combination of lattice structure, so as to improve the stiffness, strength and buckling resistance of the structure. However, in multi-scale optimization calculation, the rapid and accurate realization of the internal micro-lattice cell feature design of the structure is a key link.

[0004] Numerous studies have explored the method of directly taking the size parameters of the microstructure as design variables in the optimization process. This method is usually limited to density distribution calculation and cannot effectively control the distribution of cell types. Another way is to optimize the calculation through discrete material design method, that is, different types of cell materials are selected as candidate materials, and the mechanical properties of the materials are calculated by normalized linear superposition in the optimization calculation. In addition, there is a method of dividing the multi-scale optimization calculation process into two steps, namely macro-scale and micro-scale, and optimizing them respectively. After the macroscopic topology optimization is calculated for the material distribution, the micro-scale is calculated based on the homogenization method according to the equivalent material properties to obtain the corresponding cell distribution result. This method is suitable for the design of three-period minimal surface (TPMS) porous structure, but the above methods all have the problems of multiple design variables and high optimization calculation complexity.

[0005] In summary, constructing an efficient lattice structure multi-scale design method, realizing the free distribution of multiple types of cells, and maximizing the mechanical properties of the structure are the key problems of lattice structure multi-scale optimization method applied to engineering practice. At present, macroscopic topology optimization based on data-driven is one of the effective ways to quickly generate optimal topological configuration under complex load and boundary conditions. However, there are still three numerical method problems for lattice structure multi-scale topology optimization design: 1) multi-dimensional characterization method of mechanical properties of lattice cell and the performance variation law of single cell; 2) fast mapping method of macroscopic mechanical properties and microscopic lattice cell; 3) multi-scale topology optimization design combining macroscopic optimal topological configuration and data-driven method. The above problems limit the full excavation of efficient multi-scale topology optimization design method of lattice structure. SUMMARY

[0006] In view of the problems in the prior art, the application provides a data-driven enhanced lattice structure multi-scale topology optimization method, which aims to improve the calculation efficiency of lightweight lattice structure multi-scale topology optimization design in the process of structure lightweight design in the fields of aviation, automobiles and biomedicine, and maximize the mechanical properties of the structure by combining the dual capabilities of deep learning and structure topology optimization method.

[0007] To achieve the above purpose, the following technical solutions are adopted in the application, and the specific implementation steps are as follows:

[0008] S1: A macroscopic structure mechanical model is established based on multiple parameters, and the deformation and principal stress mechanical response of the macroscopic structure are analyzed;

[0009] S2: Topology optimization design based on density is carried out to realize the lightweight and performance improvement of the macroscopic structure;

[0010] S3: The equivalent modulus distribution and principal stress distribution of the optimal design structure are calculated in combination with the macroscopic structure mechanical model;

[0011] S4: A mechanical performance homogenization calculation method of lattice cell is established, the macroscopic equivalent Young's modulus distribution law of multiple lattice cells under any mesoscopic size is analyzed, and the bearing characteristics are obtained;

[0012] S5: A lattice cell data set is constructed, and the equivalent Young's modulus and Poisson's ratio performance parameters of different cell types, mesoscopic sizes and material parameters are calculated by the mechanical performance homogenization method of lattice cell to provide a training data set for neural network training;

[0013] S6: A deep neural network model is constructed, the constructed lattice cell data set is taken as a training sample, and the mapping relationship between macroscopic design parameters and cell types and mesoscopic sizes is established;

[0014] S7: Based on the topology results optimized in S2 and the equivalent modulus distribution and principal stress distribution calculated in S3, the trained deep neural network model is used to intelligently calculate the micro-cell distribution and realize the multi-scale topology optimization design of the lattice structure.

[0015] The beneficial effects of this invention are:

[0016] First, this invention effectively improves the computational efficiency of multi-scale topology optimization for lattice structures. Through a homogenization calculation method, it calculates and collects a large amount of mechanical performance data from lattice unit cells, analyzing the performance variation patterns. This invention utilizes a large-scale lattice unit cell performance dataset to train a DNN prediction model, and then uses the DNN model to achieve online design of lattice structures, significantly improving the computational efficiency of multi-scale topology optimization. This is beneficial for rapidly fabricating high-performance, lightweight lattice structures using additive manufacturing. Therefore, this invention can be widely applied to the design and manufacture of high-performance aerospace structures, significantly improving the mechanical properties of structures, such as stiffness and strength.

[0017] Secondly, this invention, based on a data-driven approach, enables the combined design of multiple types of unit cells. In the unit cell homogenization calculation, the mechanical properties of different unit cell types are analyzed based on Young's modulus, classifying them into tensile-dominant and bending-dominant types. Combining this with DNN methods effectively learns the load-bearing characteristics of different unit cell types. In conducting data-driven fine-scale lattice optimization design, the fine-scale design of the lattice structure is performed based on the stress state of the macroscopic topology design, achieving a fine-scale combination of different unit cells. Ultimately, this fully explores the mechanical load-bearing characteristics of the lattice structure, realizing intelligent design of the lattice structure.

[0018] Finally, this invention enables lightweight structural design based on multi-scale topology optimization of lattice structures. By combining topology optimization methods and deep learning methods, it achieves efficient multi-scale optimization design of lattice structures, maximizing structural load-bearing capacity while further improving material utilization through microstructure analysis. The multi-scale optimized structure of this invention can effectively achieve lightweight design for equipment in aerospace, new energy vehicles, and biomedical devices, thereby maximizing the service performance of the equipment. Attached Figure Description

[0019] Figure 1 This invention provides a schematic flowchart of a data-driven enhanced multi-scale topology optimization design method for lattice structures.

[0020] Figure 2 Geometric models of four types of unit cell structures for training neural networks are provided in embodiments of the present invention;

[0021] Figure 3 This is a schematic diagram of the MBB beam structure provided in an embodiment of the present invention;

[0022] Figure 4 This is a diagram showing the macroscopic topology optimization density distribution results provided in an embodiment of the present invention;

[0023] Figure 5 for Figure 4 The optimized result image;

[0024] Figure 6 The stress distribution diagram corresponding to the optimal macroscopic topology provided in the embodiments of the present invention;

[0025] Figure 7 This is a diagram showing the updated macroscopic equivalent modulus distribution based on stress distribution, provided in an embodiment of the present invention.

[0026] Figure 8 The stress distribution diagram corresponding to the final macroscopic topology provided in the embodiments of the present invention;

[0027] Figure 9 The optimized design results of lattice structures composed of single-type, two-type, and four-type unit cells provided in the embodiments of the present invention;

[0028] Figure 10 The results show the structural flexibility comparison of the optimal design result of this invention. Detailed Implementation

[0029] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0030] like Figure 1 As shown, this application provides a multi-scale topology optimization design method for driven enhancement lattice structures, comprising the following steps:

[0031] S1: Establish a macroscopic mechanical analysis model of the target design structure, and analyze the mechanical response of the target structure, such as deformation and principal stress, based on the geometric configuration, operating conditions and material parameters of the structure.

[0032] Furthermore, the implementation of S1 includes:

[0033] S11: A mechanical model of the target structure is established using structural mechanics analysis theory. This can be achieved through finite element method or isogeometric method. This application uses the finite element method as an example:

[0034] First, the geometric model is discretized into several elements by mesh generation, and the stiffness matrix K of each element is calculated using the finite element method.e The stiffness matrix of the unit is calculated according to the strain-displacement relationship meeting the deformation coordination and the stress-strain relationship describing the material constitution, combined with the Gauss integral method, and the calculation formula is as follows:

[0035]

[0036] In the formula, B is the strain-displacement matrix meeting the deformation coordination relationship, D is the stress-strain relationship matrix, J is the Jacobian matrix of the conversion of the physical coordinates to the natural coordinates, , , are the coordinates corresponding to the x, y, and z axes in the natural coordinate system, respectively.

[0037] Second, the function relationship of the material properties with respect to the macroscopic density is constructed. Taking the density-based topology optimization method as an example, the elastic modulus of the material in each unit can be calculated by the following formula:

[0038]

[0039] In the formula, is the relative density of the unit, is the interpolation lower limit of the elastic modulus, and is usually less than , is the true elastic modulus of the material, and p is the interpolation penalty factor (usually p=3).

[0040] S12: Mechanical analysis of the macroscopic structure and principal stress calculation. Based on the method in S11, the structure stiffness matrix and the external load vector can be assembled according to the node degrees of freedom, so as to obtain the balance equation, and the formula is as follows:

[0041]

[0042] Further, the structure displacement vector is obtained by solving the balance equation.

[0043] Further, according to the displacement vector, the principal stress tensor of each unit inside the structure can be calculated, and the calculation formula is as follows:

[0044]

[0045] In the formula, (i,j=1,2,3) represents the stress acting on the plane perpendicular to the axis along the axis.

[0046] ​Furthermore, the principal stresses can be calculated by solving the following eigenvalue equations:

[0047]

[0048] In the formula, The amplitude of the principal stress, This corresponds to the direction of the principal stress.

[0049] S2: Improve density-based topology optimization methods to achieve structural topology design at the macroscopic level, optimize structural mechanical performance while reducing structural weight;

[0050] Furthermore, step S2 is implemented in the following ways:

[0051] S21: Construct a topology optimization model for the macroscopic structure, taking density-based topology optimization as an example, focusing on cell density. Displacement of each node The structural optimization model is established using these as design variables, and the calculation formula is as follows:

[0052] ,

[0053] ,

[0054] , ,

[0055] ,

[0056] In the formula, the objective function U represents the compliance of the structure, and U is the displacement vector of each node in the discrete structure. Let be the displacement vector of each node within element e. and These are the global stiffness matrix and the stiffness matrix within element e, respectively. For external loads, Due to material volume constraints, This is the upper limit of the allowable volume of the material. and These represent the volume within the design domain and the volume within element e, respectively. This represents the total number of discrete structural units. This represents the total number of degrees of freedom within the structure.

[0057] Among them, volume constraints Constraint on optimal design results ( The corresponding design domain The total internal material volume is less than the upper limit of the required material. The calculation formula is as follows:

[0058] .

[0059] Further, the balance equation in the constraint Guarantee the design results meet the balance condition of U in each iteration process.

[0060] S22: Calculate the sensitivity of the objective function and the constraint, the sensitivity of the structural compliance with respect to each unit density The sensitivity is calculated as follows:

[0061]

[0062] Further, in the embodiment of the application, the sensitivity calculation of the volume constraint is completed by the following method:

[0063]

[0064] S23: For the solution of the topology optimization problem, it can be solved by global convergence moving asymptote method (GCMMA), and the solution will get the optimal density distribution result in the structure And the displacement result of each node. The optimal density distribution Will be an important basis for subsequent mesostructure topology optimization.

[0065] S3: Combined with the mechanical model in S1, calculate the equivalent modulus distribution result and principal stress distribution in the optimal design structure and other mechanical responses;

[0066] Further, the implementation of the step S3 includes:

[0067] S31: According to the Obtained in S23, solve the material elastic modulus In each unit, further can calculate the structure stiffness matrix Corresponding to the optimal result, so as to analyze the displacement and stress state of the macroscopic optimal design result. The analysis result will be the basis for constructing the meso-cell.

[0068] S32: Since the meso-cell can exhibit different bearing characteristics, it is necessary to calculate the corresponding equivalent material properties According to the stress state of each unit on the basis of macroscopic topology optimization design. There are many ways to calculate the equivalent material properties, here take Gibson-Ashby model as an example, the calculation formula is as follows:

[0069]

[0070] In the formula, The elastic modulus of the matrix material of the lattice structure With For a given constant, the value in the tensile state and the bending state is different, so that the same In different stress states, different .

[0071] S33: According to the equivalent material properties of each unit calculated in S32 Again, calculate the principal stress of each unit under a given working condition, and the result is used as the basis for the design of the meso-cell distribution.

[0072] S4: Develop a homogenization calculation method for the mechanical properties of lattice cells, realize the distribution law of the macroscopic equivalent Young's modulus of a variety of different lattice cells under any mesoscopic size parameters, and subdivide the load-bearing characteristics of different types of lattice cells according to the law characteristics, such as distinguishing between bending resistance, shear resistance, and tensile resistance.

[0073] Further, the implementation of step S4 includes:

[0074] S41: Use a voxel-based homogenization method to calculate the equivalent elastic modulus of the cell.

[0075] Further, the homogenized constitutive matrix can be calculated by the following formula:

[0076]

[0077] In the formula, is the homogenized material constitutive matrix, denotes the total volume of the representative volume element (RVE), denotes the volume of the discrete element within the RVE, represents a 6*6 unit matrix, U e and B e represent the displacement matrix and strain-displacement matrix of each element, respectively, C e is the element constitutive matrix, which is calculated as follows:

[0078]

[0079] In the formula, λ represents the first Lame parameter, and μ represents the second Lame parameter. λ and μ can be calculated by the Young's modulus E and the Poisson's ratio v, respectively:

[0080]

[0081] Further, the stiffness matrix k e of each discrete element in the representative volume element and the element load vector f e i are calculated:

[0082]

[0083]

[0084] wherein, (i=1…6) represent different macroscopic strain states, which are specifically represented by strain vectors:

[0085]

[0086] ,

[0087] Further, in the embodiments of the present application, the unit stiffness matrix k e and the unit load vector f e i The global stiffness matrix K and the global load vector F are calculated i The global displacement vector U is calculated i The calculation formula is as follows:

[0088]

[0089] Further, in the embodiments of the present application, the global displacement vector U i The symmetric homogenization constitutive matrix is calculated:

[0090]

[0091] wherein, U e 0(i) is the unit displacement of the i-th unit strain obtained from the strain vector, U e (i) is the corresponding local unit displacement of U i obtained from the unit stiffness matrix and the unit load vector, and the symmetric homogenization compliance matrix S ij H can be obtained by performing an inverse operation on the symmetric homogenization constitutive matrix C ij H The calculation process is as follows:

[0092]

[0093] In the embodiments of the present application, since the unit cell involved in the present application has cubic symmetry, the Young's modulus and Poisson's ratio corresponding to the unit cell along each coordinate axis direction can be obtained, which are respectively represented as:

[0094]

[0095] wherein, , , represent the Young's modulus along the x-axis, y-axis and z-axis directions, which are obtained by inverting the diagonal elements of S ij H Specifically, since the unit cell has cubic symmetry, the Young's modulus obtained along the three axial directions is the same, that is, , and then the Poisson's ratio is calculated.

[0096] S42: Calculate the equivalent elastic modulus of different types of unit cells.

[0097] As shown in Figure 2 , in the embodiments of the present application, different types of unit cell structures are selected, and the equivalent modulus and Poisson's ratio of the unit cell are calculated by the method in S41, and the distribution rule of the elastic modulus along different directions is analyzed. According to the distribution rule of the elastic modulus along different directions, the unit cells are divided into unit cell types mainly bearing tensile load and bending load (named as tensile dominant type and bending dominant type in the following), and the analysis results can be used for selecting the unit cells in the multi-scale optimization design. According to the principal stress analysis results of the structure, the unit cell type is selected, and in the embodiments of the present application:

[0098] (1) When the principal stress direction is located in the range of [0, 22]U[68, 90], the region mainly bears tensile stress and compressive stress, and should be used for the unit cell type dominated by tension. The principal stress direction in this interval should preferentially select the corresponding unit cell type to ensure stronger bearing capacity. For example: the modulus of the simple cubic unit cell in the direction of [0, 10]U[80, 90] is relatively large, so the simple cubic unit cell should be selected when the principal stress direction is in this interval. Similarly, since the modulus of the isotruss type unit cell is large in the range of [10, 22]U[68, 80], the isotruss unit cell type is selected when the principal stress direction is in this range.

[0099] (2) When the principal stress direction is located in the range of [22, 68], the region mainly resists bending deformation, and according to the elastic modulus distribution characteristics, the unit cell type with larger modulus in this interval is preferentially selected, for example: select from octet unit cell and body-centered cubic unit cell. When the principal stress direction is located in the range of [22, 38]U[52, 68], the octet unit cell is selected, and when the angle range is [38, 52], the body-centered cubic unit cell is selected.

[0100] S5: Construct the performance data set of the lattice unit cell, calculate the equivalent Young's modulus, Poisson's ratio and other performance parameters under different lattice unit cell types, mesoscopic sizes and material parameters, and calculate a large number of data samples as the training data set of the deep neural network;

[0101] In the embodiment of the present application, according to the method in the S4, the data results of the Young's modulus, the Poisson's ratio, and the optimal principal stress direction of the different densities, sizes, and material parameters of the plurality of unit cells screened out in the S42 are calculated, a performance data set corresponding to the lattice unit cell is constructed, the data content is arranged into a csv file, and the csv file is used for subsequent training of the neural network.

[0102] S6: Constructing a deep neural network model, designing input parameters and output parameters of the model, training the neural network model by using the lattice unit cell data set constructed in the S5, so that the neural network model reaches a preset accuracy standard, and establishing a mapping relationship between relative density and stress state and the unit cell type and the mesoscopic size;

[0103] Further, the implementation mode of the S6 includes:

[0104] S61: A deep neural network (DNN) is used to establish a mapping of the mechanical properties of the material to the geometric characteristics of the unit cell. The deep neural network model is composed of an input layer, an output layer, and several hidden layers. The input layer receives the original data and transmits the original data to the hidden layer. Each layer of the hidden layer is composed of a plurality of neurons. Each neuron performs a nonlinear transformation on the weighted sum of the outputs of the previous layer. The parameters of each layer are updated according to the forward propagation and the error back propagation. Finally, the output layer generates the final result according to the task type. In the deep neural network model, the input variables are: the Young's modulus, the Poisson's ratio, the principal stress direction of the unit cell, the size, and the material. The output is: the lattice unit cell type and the size of the unit cell support structure.

[0105] In the embodiment of the present application, in order to model the nonlinear relationship between the input data and the output data, a rectified linear unit (ReLU) activation function is used, and the specific function is represented as:

[0106]

[0107] S62: Neural network model training. In the embodiment of the present application, for the error in the model, a gradient descent-based method is used for back propagation, the weight and bias data of each layer are adjusted, and the input layer is returned in turn. Once the network output error is reduced to an acceptable threshold or the preset training number of rounds is reached, the training process stops. The loss function selection in the training process is an important way to ensure the effect of the model. Taking the mean square error (MSE) as an example, the MSE calculation formula is as follows:

[0108]

[0109] In the formula, y true represents the true value of each sample, y pred represents the predicted value, and N represents the total data amount.

[0110] Further, the accuracy of the model can be calculated by the following formula:

[0111]

[0112] wherein N represents the number of samples, d represents the output dimension of each sample, represents the model prediction value of the i-th sample and the j-th output dimension, represents the true label value of the i-th sample and the j-th output dimension, and threshold represents a relative error threshold, wherein the threshold is 0.05 in the present application, is an indicator function, which is 1 when the condition is met, and 0 otherwise.

[0113] Further, the Adam optimizer is used to adaptively update the parameters in the embodiments of the present application, and the learning rate is dynamically adjusted by combining the ReduceLROnPlateau method, and the loss is monitored after each training round. If the loss does not improve within a certain number of training rounds, the learning rate is reduced by a decay factor, and the expression is as follows:

[0114]

[0115] wherein η t represents the learning rate of the t-th round (epoch), η t-1 represents the learning rate of the t-1-th round, a represents the learning rate decay factor, η min is the minimum learning rate allowed, and P is the number of waiting periods that trigger the learning rate decay. In the training process, a is 0.3, η min is 0, and P is 5 periods.

[0116] Therefore, the neural network trained by the above method can be used to construct the mapping relationship between the mechanical properties and the geometric features of the unit cell. A mesoscopic unit cell proxy model is provided for multi-scale topological optimization design.

[0117] S7: Based on the topological optimization method constructed in S2, the macroscopic optimal topological optimization calculation result is calculated, and the principal stress state of the local region is calculated in the method of S3. The unit density distribution, equivalent elastic modulus, Poisson's ratio and the corresponding stress state corresponding to the optimal design result are used as input variables, and the DNN network corresponding to the macroscopic material properties and the unit cell result trained in S6 is used to select the corresponding unit cell for each local region and predict the corresponding mesoscopic structure size. The lattice unit cells corresponding to each unit position are assembled to form an optimal multi-scale lattice structure design result. The deep neural network model trained in S6 is used to intelligently calculate the mesoscopic unit cell distribution for the macroscopic optimal topological structure, and the multi-scale topological optimization design of the lattice structure is realized.

[0118] To clearly illustrate the present invention, the following detailed description is provided in conjunction with specific embodiments:

[0119] like Figure 3 As shown in the embodiment of this application, the structure to be optimized is a three-dimensional MBB beam structure. The multi-scale topology optimization design method proposed in this application is used to optimize the distribution of mesoscopic unit cells within the design domain of the lattice structure, thereby improving the overall stiffness of the structure. The design domain is a symmetrical structure, so half of it is taken. The left end face is a boundary condition symmetrical with respect to the yz plane, the lower right is a simple boundary, and the left symmetrical plane is distributed with a uniformly distributed load in the z direction.

[0120] Furthermore, according to the method of this application, macroscopic structural topology optimization is performed on the design region of the structure. For example... Figure 4 As shown, red areas represent regions with relatively high density, and blue areas represent regions with relatively low density. To effectively represent areas with high density distribution, the embodiment uses... Partial removal, the result is as follows Figure 5 As shown. Further stress analysis is performed on the optimal design results, as follows: Figure 6 As shown. The stress state of each element is determined based on the principal stress calculation results. The equivalent elastic modulus parameter for each element is calculated using different parameters corresponding to the tensile / bending states in the Gibson-ashby model. The material distribution is as follows. Figure 7 As shown. Based on the updated material parameter distribution, the stress distribution, which approximates the true state, is calculated again. The von Mises stress distribution results are as follows. Figure 8 As shown. This completes the density and stress calculations corresponding to the macroscopic topology optimization. In the fine-grained matrix design, these parameters are used as input variables, and a trained DNN model is used to predict the corresponding unit cell structure for each cell.

[0121] In the embodiments of this application, if the optimal matrix structure is constructed using only a single-cell structure, the corresponding result is as follows: Figure 9 As shown in (a), if the optimal matrix structure is constructed using two forms of unit cell structure, the corresponding results are as follows: Figure 9 As shown in (b), the optimal lattice structure was constructed using four unit cell configurations, and the results are as follows. Figure 9 As shown in (c). Furthermore, the overall structural stiffness of the corresponding results is as follows: Figure 10 As shown in the figure, comparison reveals that multi-scale optimization calculations can improve the stiffness of the macroscopically optimized topology structure; the stiffness is further improved when using two and four different unit cell designs for the optimal lattice structure. This demonstrates that the present invention, by considering the structural stress state and selecting the corresponding optimal unit cell during the topology optimization process of the lattice structure, can effectively improve the overall performance of the structure. Furthermore, this embodiment proves the feasibility and effectiveness of the enhanced multi-scale topology optimization design method for lattice structures driven by material properties and stress state data.

[0122] In summary, the data-driven enhanced lattice structure multi-scale topology optimization design method proposed by the present application is used to solve the efficient multi-scale topology optimization design problem of lattice structure. Since the traditional multi-scale topology optimization method needs to use the geometric characteristics of the meso-cell as the design variable or uses a multi-step optimization design method to realize the optimal design from the macro to the micro, the calculation complexity is high, and it is only suitable for multi-scale topology optimization calculation of limited cell types. In view of the above problems, the present application proposes to use a data-driven method to realize the multi-scale optimization design method from the macro design to the micro structure, to construct the mapping relationship between the mechanical properties of the cell and the type and micro size of the cell through a deep neural network (DNN), thereby realizing the online design of the micro structure and improving the calculation efficiency of the multi-scale optimization design; in addition, in the micro structure design, the type of the optimal cell is selected according to the stress state of the local region, so as to further optimize the mechanical properties of the macro structure in the micro lattice structure design.

[0123] Those skilled in the art will easily understand that the above description is only a preferred embodiment of the present application, and is not intended to limit the present application, and any modifications, equivalent replacements and improvements made within the spirit and principles of the present application shall be included in the protection scope of the present application.

Claims

1. A data-driven enhanced lattice structure multi-scale topology optimization design method, characterized in that, Includes the following steps: S1: Establish a macroscopic structural mechanics model based on multiple parameters to analyze the deformation and principal stress mechanical response of the macroscopic structure; S2: Conduct density-based topology optimization design to achieve lightweighting and improved mechanical performance of the macroscopic structure; S3: Based on the macroscopic structural mechanics model, calculate the equivalent modulus distribution and principal stress distribution of the optimal design structure; S4: Establish a method for uniformizing the mechanical properties of lattice unit cells, analyze the distribution law of macroscopic equivalent Young's modulus of various lattice unit cells under arbitrary microscale, and obtain their load-bearing characteristics; S5: Construct a lattice unit cell dataset. Calculate the equivalent Young's modulus and Poisson's ratio performance parameters under different unit cell types, microstructures, and material parameters using the mechanical property homogenization method of lattice unit cells, providing a training dataset for neural network training. S6: Construct a deep neural network model, using the constructed lattice unit cell dataset as training samples, and establish a mapping relationship between macroscopic design parameters and unit cell type and microscopic size; S7: Based on the topology results optimized in S2 and the equivalent modulus distribution and principal stress distribution calculated in S3, the trained deep neural network model is used to intelligently calculate the micro-cell distribution and realize the multi-scale topology optimization design of the lattice structure.

2. The data-driven enhanced lattice structure multi-scale topology optimization design method of claim 1, wherein, S1 includes the following steps: Macroscopic structural mechanics models are established using structural mechanics analysis theory, including finite element or isogeometric methods; Establish a functional relationship between material properties and macroscopic density; When using the finite element method, the geometric model is discretized into several elements by meshing. Based on the strain-displacement relationship and the material constitutive relation, the stiffness matrix of each element is calculated using Gaussian integral.

3. The data-driven enhanced lattice structure multi-scale topology optimization design method of claim 2, wherein, Establishing a macroscopic structural mechanics model using the finite element method includes the following steps: By assembling the structural stiffness matrix and external load vector through nodal degrees of freedom, a global stiffness matrix and load vector are formed. The equilibrium equations are established using the global stiffness moment and load vector described above. Solve the equilibrium equations to perform mechanical analysis, and calculate the structural deformation and principal stresses.

4. The data-driven enhanced lattice structure multi-scale topology optimization design method of claim 1, wherein, S2 includes the following steps: A density-based topology optimization model is used to construct a topology optimization model for the macroscopic structure, with element density and node displacement as design variables. Calculate the sensitivity of structural compliance to the unit density and the sensitivity of volume constraints; The topology optimization problem is solved by using the globally convergent moving asymptote method to obtain the optimal density distribution and the displacement results of each node.

5. The data-driven enhanced lattice structure multi-scale topology optimization design method of claim 4, wherein, S3 includes the following steps: Based on the optimal density distribution, the elastic modulus of the material in each unit is solved, the optimal structural stiffness matrix is ​​calculated, and the displacement and stress state of the macroscopic optimal design are analyzed, providing a basis for the construction of the microscopic unit cell. Based on the macroscopic topology optimization results, the corresponding equivalent material properties are calculated using the Gibson-Ashby model according to the stress state of each element. Based on the equivalent material properties, update the principal stresses of each element under a given working condition.

6. The data-driven enhanced lattice structure multi-scale topology optimization design method of claim 1, wherein, S4 includes the following steps: The equivalent elastic modulus of a single cell was calculated using a voxel-based homogenization method. Calculate the equivalent elastic modulus of unit cells for different types; Analyze the differences in equivalent modulus of different unit cells at relative densities.

7. The data-driven enhanced lattice structure multi-scale topology optimization design method of claim 6, wherein, The calculation of the equivalent elastic modulus of a single cell based on the voxel homogenization method includes: In a given different macroscopic strain state, the stiffness matrix and the load vector of each discrete unit in the representative volume element are calculated; By assembling the unit stiffness matrix and the unit load vector, the global stiffness matrix and the load vector are constructed, and the global displacement vector is solved; Combined with the global displacement vector, the equivalent stiffness tensor in the representative volume element is calculated to obtain the symmetric homogenization constitutive matrix; The symmetric homogenization compliance matrix is obtained by inverting the homogenization constitutive matrix; By using the cubic symmetry of the unit cell, the Young's modulus and Poisson's ratio are obtained by inverting the diagonal elements of the symmetric homogenization compliance matrix; Based on the directional distribution characteristics of the equivalent elastic modulus, the unit cell is divided into two types of tensile dominant type and bending dominant type, and the unit cell type selection is carried out through the principal stress direction interval.

8. The data-driven enhanced lattice structure multi-scale topology optimization design method of claim 1, wherein, The S5 comprises: A large number of sample data of the screened unit cell under different mesoscopic sizes and material parameters are calculated by using the unit cell equivalent modulus calculation method, and a deep neural network training data set is constructed.

9. The data-driven enhanced lattice structure multi-scale topology optimization design method of claim 1, wherein, The S6 comprises: A deep neural network model is used to establish the mapping of the mechanical properties of the material to the geometric characteristics of the unit cell; Based on the deep neural network model training, the weights and biases are updated by gradient descent back propagation, the MSE is used as the loss function to evaluate the error, the Adam optimizer and the dynamic learning rate adjustment strategy are combined, the training is stopped when the error is up to standard or the training round is exhausted, and the accuracy is calculated through a preset threshold.

10. The data-driven enhanced lattice structure multi-scale topology optimization design method of claim 1, wherein, The S7 comprises: The density, equivalent elastic modulus and corresponding principal stress direction of each unit obtained in S3 are used as input variables of the deep neural network, and the corresponding lattice unit of each unit is predicted by using the deep neural network model trained in S6; the lattice unit corresponding to the position of each unit is assembled to form the optimal multi-scale lattice structure design result, and the data-driven enhanced lattice structure multi-scale topology optimization design is realized.

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