Multi-scale topological optimization method and equipment for TPMS lattice structure
By using a cross-modal knowledge distillation network and a multi-objective optimization model, the performance prediction and geometric transition problems in the design of TPMS lattice structures were solved, achieving efficient stiffness optimization and additive manufacturing compatibility, and improving the design quality of TPMS lattice structures.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- HUAZHONG UNIV OF SCI & TECH
- Filing Date
- 2025-12-24
- Publication Date
- 2026-04-17
AI Technical Summary
Existing TPMS lattice structure design methods have shortcomings in performance prediction, type distribution optimization, and geometric transition, making it difficult to maximize stiffness, achieve geometric continuity, and achieve compatibility with additive manufacturing, leading to manufacturing defects and performance degradation.
A cross-modal knowledge distillation network is used to learn the cross-modal fusion relationship between geometric and parametric modes of TPMS type. Combined with a multi-objective optimization model and a weighted mixing strategy, high-precision prediction of equivalent elastic tensor and geometrically smooth transition connection are achieved, ensuring stiffness optimization and spatial continuity.
It achieves a balance between high-precision performance prediction and computational efficiency, ensures the physical feasibility of type distribution and compatibility with additive manufacturing, reduces design constraints, and improves material utilization and structural continuity.
Smart Images
Figure CN121885035A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the technical field of structural topology optimization, and more specifically, relates to a multi-scale topology optimization method and device for TPMS lattice structures. Background Technology
[0002] With the increasing demand for high-performance lightweight structures in aerospace, biomedicine, and other fields, Tri-Period Minimal Surface (TPMS) lattice structures have attracted widespread attention due to their excellent mechanical properties, thermal conductivity, and biocompatibility. TPMS lattice structures are a class of periodic porous materials described by implicit functions, including various configurations such as Primitive, Gyroid, and Diamond. Each configuration can be further divided into net and sheet types, with different volume fraction ranges and mechanical properties. The development of additive manufacturing technology has provided a feasible approach for the fabrication of TPMS lattice structures, especially processes such as powder bed melting and photopolymerization, which can achieve high-precision molding of complex three-dimensional geometries. In TPMS lattice structure design, it is necessary to simultaneously optimize the volume fraction distribution and type distribution of the structure to achieve objectives such as maximizing stiffness. However, existing TPMS lattice structure design methods have many shortcomings in performance prediction, type distribution optimization, and geometric transition. Traditional performance prediction methods construct homogenized databases and use polynomial fitting, but the fitting accuracy is relatively low, making it difficult to accurately capture the nonlinear mapping relationships between different TPMS types. When employing deep learning methods, neural networks based solely on scalar parameters cannot fully represent complex 3D geometric topology information. While 3D convolutional networks that directly process voxel geometry offer high accuracy, they suffer from low computational efficiency and high storage requirements, making them impractical for large-scale prediction scenarios. Regarding type distribution optimization, traditional greedy strategies only consider maximizing the stiffness of individual elements, resulting in numerous discontinuous interfaces, leading to geometric discontinuities, stress concentrations, manufacturing defects, and printing failures. Clustering-based methods require manual partitioning of material regions, relying on engineer experience and incurring significant stiffness losses. Global optimization methods such as genetic algorithms are computationally expensive, highly parameter-sensitive, and difficult to scale to large-scale meshes. These methods do not consider the compatibility constraints between density and configuration, failing to guarantee the physical feasibility of TPMS type selection and additive manufacturing printability. In terms of geometric transitions, traditional function blending methods require large transition regions, resulting in low material utilization, limited design freedom, and deviations from topology optimization results. Gaussian weight-based blending methods struggle to precisely control weight allocation in 3D space and do not consider the compatibility between volume fraction and TPMS configuration. Methods based on latent spatial interpolation suffer from connectivity issues, are prone to failure at low volume fractions, and are computationally expensive. Since adjacent elements using different TPMS types may have completely mismatched topologies at their interface, direct splicing can result in geometric tears or isolated material blocks at the boundaries, leading to additive manufacturing failures, deterioration of mechanical properties, and invalid 3D model files.
[0003] Therefore, there is an urgent need for a multi-scale topology optimization method for TPMS lattice structures that integrates efficient performance prediction, intelligent optimization of type distribution, and smooth geometric transition, so as to realize the whole-process design from topology optimization results to additive manufacturing, while taking into account both the maximization of structural stiffness and the requirements of additive manufacturing process. Summary of the Invention
[0004] To address the aforementioned deficiencies or improvement needs of existing technologies, this invention provides a multi-scale topology optimization method and device for TPMS lattice structures, which aims to solve the problem that existing optimization methods struggle to achieve geometrically smooth transition connections.
[0005] To achieve the above objectives, according to one aspect of the present invention, a multi-scale topology optimization method for a TPMS lattice structure is provided, comprising the following steps: (1) The teacher network of the cross-modal knowledge distillation network learns the cross-modal fusion relationship between the geometric mode and the parametric mode of the TPMS type, and then distills the cross-modal fusion relationship to the student network. The student network is used to predict the equivalent elastic tensor of each unit in the optimization region under all candidate TPMS types. All the equivalent elastic tensors obtained form a candidate performance matrix. (2) Based on the candidate performance matrix, the density field and displacement field of the structure to be optimized, a multi-objective optimization model including stiffness maximization and spatial continuity is constructed, and then the type field is obtained based on the multi-objective optimization model; the multi-objective optimization model introduces density and configuration compatibility constraints; (3) Density interpolation is performed on the density field, and then type boundary detection is performed on the type field at the point level. Then density interpolation is performed on the non-boundary points to calculate the non-boundary point distance field value. After calculating the type weights for the boundary points, the obtained type weights are processed by a weighted mixing strategy to obtain the boundary point distance field. The boundary point distance field is compensated by the degree of mixing adaptive compensation to obtain the boundary point distance field value. Based on the non-boundary point distance field value and the boundary point distance field value, a three-dimensional topological configuration that can be directly used for additive manufacturing is obtained.
[0006] Furthermore, topology optimization is performed on the structure to be optimized to obtain the density field and displacement field. The topology optimization adopts the minimization of compliance as the optimization objective, and the optimization objective is:
[0007] In the formula, the constraint condition is: , , ,in For the relative density of the unit cell, Let be the nodal displacement vector. For the overall stiffness matrix, For load vector, Due to volume constraints, The total number of units; Volume fraction per unit; The minimum volume fraction for a single unit; This represents the maximum volume fraction of a single unit.
[0008] Furthermore, based on the substrate parameters and load boundary conditions, the density distribution is iteratively solved using the solid isotropic penalty microstructure method to obtain the optimal density field and displacement field.
[0009] Furthermore, parameterized modeling and voxelization were performed on various TPMS configurations under different volume fractions to obtain voxel models. The voxel models were homogenized to obtain the equivalent elastic tensor of each sample. The TPMS type number, volume fraction, voxel model and equivalent elastic tensor constituted a homogenized dataset. A cross-modal knowledge distillation network was trained based on the homogenized dataset.
[0010] Furthermore, a weighted combination of prediction loss and distillation loss was used to train the student network; the mean squared error loss function was used to train the teacher network.
[0011] Furthermore, during the student network training phase, the capacity of the student network's parametric modal encoder is expanded to twice that of the teacher network. The total loss function is a weighted combination of the prediction loss and the distillation loss, and the corresponding expression is:
[0012] In the formula, To predict losses, This is due to distillation losses; For distillation weight.
[0013] Furthermore, the mathematical expression for the objective function of the multi-objective optimization model is:
[0014] The first term is the maximization of total strain energy. Representation unit Using TPMS type Strain energy at time, As a decision variable, when Time representation unit Select type ,otherwise The second term is a spatial continuity penalty. Representation unit The set of six neighboring units is penalized when neighboring units are of different types. To penalize weights; the multi-objective optimization model must satisfy three constraints, including: Uniqueness constraint: , Integer constraints: , And density and configuration compatibility constraints: , In the formula, This represents the total number of units in the design area. The total number of TPMS types; The minimum volume fraction for a single unit; Let be the density value of the i-th cell; The maximum volume fraction of a single unit; This represents the lower limit of density for the net configuration; This represents the upper limit of the density for sheet configurations.
[0015] Furthermore, the formula for allocating type weights is as follows:
[0016]
[0017] in, and These represent the weights of the current type and the neighboring types, respectively. This is the distance from the current point to the type boundary; This represents the width of the transition area.
[0018] The present invention also provides a multi-scale topology optimization system for TPMS lattice structures. The system includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to perform the multi-scale topology optimization method for TPMS lattice structures as described above.
[0019] The present invention also provides a computer-readable storage medium storing machine-executable instructions, which, when invoked and executed by a processor, cause the processor to implement the multi-scale topology optimization method for the TPMS lattice structure as described above.
[0020] In summary, compared with the prior art, the multi-scale topology optimization method and device for TPMS lattice structures provided by this invention have the following advantages: 1. This invention constructs an optimization objective that includes maximizing stiffness and penalizing spatial continuity, while introducing density and configuration compatibility constraints, which significantly improves spatial continuity while ensuring stiffness optimization; based on a weighted composite distance field and an overall compensation mechanism, it realizes a smooth transition connection between arbitrary TPMS configurations, and can connect unit cell pairs with large volume fractions and structural differences.
[0021] 2. By constructing a cross-modal knowledge distillation network, the teacher network integrates geometric and parametric modes to learn cross-modal collaborative relationships, while the student network learns the transformation from parametric to geometric modes through knowledge distillation. High-precision prediction of the equivalent elastic tensor can be achieved with only parametric mode input, which has the dual advantages of high prediction accuracy and high inference efficiency.
[0022] 3. The requirement for transition regions is significantly reduced by combining point-level boundary detection with linear weights, which greatly preserves the original physical properties of the TPMS structure. It also supports the connection of a single TPMS configuration with multiple different types of TPMS configurations on different surfaces, reducing the design limitations of TPMS types.
[0023] 4. This invention supports multiple candidate TPMS configurations, covering various net and sheet configurations, and greatly expands the design space of lattice structures. Attached Figure Description
[0024] Figure 1 This is a flowchart of a multi-scale topology optimization method for a TPMS lattice structure provided in an embodiment of the present invention; Figure 2(a) is a three-dimensional schematic diagram of the first example three-dimensional cantilever beam structure, Figure 2(b) is the density field obtained by the topology optimization result based on the SIMP method for the first example, and Figure 2(c) is the displacement field obtained by the topology optimization result based on the SIMP method for the first example. Figure 3 This is a schematic diagram of the voxel model of 12 TPMS configurations, including net configurations (D, F, G, I, P, S) and sheet configurations (D, F, G, I, P, S). Figure 4 This is a schematic diagram of the framework of a cross-modal knowledge distillation network, showing the network framework of the Teacher network and the Student network, as well as the principle of knowledge distillation. Figure 5(a) is a scatter plot of the prediction results of the Teacher network on the test set, and Figure 5(b) is a scatter plot of the prediction results of the Student network on the test set. Figure 6 This is the first example of a TPMS type distribution diagram obtained based on a constrained optimization algorithm; Figure 7 This is a schematic diagram illustrating the core principle of the geometric smooth transition algorithm. Figure 8 (a), (b), and (c) in the image are detailed renderings of the transition area between some TPMS configuration combinations in the first example. Figure 9 In the diagrams (a) and (b), the STL model results obtained by the first example using the geometric smooth transition algorithm are shown. Figure 10 This is a 3D schematic diagram of the second example MBB beam structure; Figures 11(a) and 11(b) show the density field obtained by topology optimization based on the SIMP method and the distribution map of example TPMS type obtained by constraint optimization algorithm, respectively, for the second example. Figure 12 This is a schematic diagram of the STL model result obtained through the geometric smooth transition algorithm in the second example. Detailed Implementation
[0025] 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.
[0026] This invention provides a multi-scale topology optimization method for TPMS lattice structures. The topology optimization method achieves efficient and accurate prediction of TPMS performance through cross-modal knowledge distillation networks, and realizes geometrical continuity between different volume fractions and configurations through parameterized geometric filling and smooth transition connections. This provides an efficient and accurate technical approach for the optimization design of high-performance lightweight structures in aerospace, biomedical and other fields.
[0027] The topology optimization method includes the following steps: Step 1: Perform topology optimization on the structure to be optimized to obtain the density field and displacement field.
[0028] Step 2: The teacher network of the cross-modal knowledge distillation network learns the cross-modal fusion relationship between the geometric mode and the parametric mode of the TPMS type, and then distills the cross-modal fusion relationship into the student network. The student network is then used to predict the equivalent elastic tensor of each unit in the optimization region under all candidate TPMS types. All the obtained equivalent elastic tensors form a candidate performance matrix.
[0029] The student network predicts the equivalent elastic tensor based on the density field, type number, and volume fraction.
[0030] Step 3: Based on the density field, displacement field, candidate performance matrix, and constrained optimization algorithm, a multi-objective optimization model is constructed that includes stiffness maximization and spatial continuity. Then, the type field is obtained based on the multi-objective optimization model. The multi-objective optimization model introduces density and configuration compatibility constraints to ensure that the volume fraction range of the selected TPMS type matches the element density, and simultaneously achieves stiffness optimization and manufacturing performance improvement in the two-stage iterative improvement process.
[0031] Step four involves density interpolation of the density field, followed by type boundary detection at the point level for the type field. Density interpolation is then performed on non-boundary points to calculate the non-boundary point distance field value. After calculating the type weights for the boundary points, a weighted mixing strategy is used to process the obtained type weights to obtain the boundary point distance field. Adaptive compensation for the degree of mixing is then used to compensate the boundary point distance field to obtain the boundary point distance field value. Based on the non-boundary point distance field value and the boundary point distance field value, a complete 3D model that can be directly used for additive manufacturing is obtained.
[0032] Specifically, isosurfaces are extracted from the distance field values of non-boundary points and the distance field of boundary points using an isosurface extraction algorithm, thereby obtaining a three-dimensional mesh model that can be directly used for additive manufacturing.
[0033] Compared with existing TPMS lattice structure design methods, the method proposed in this invention strictly guarantees the balance between performance prediction accuracy and computational efficiency, the physical feasibility and manufacturing feasibility of type distribution, and the smoothness of geometric transition and material continuity. It has the characteristics of high-precision prediction, high-efficiency calculation, physical constraint guarantee and additive manufacturing compatibility.
[0034] Please see Figure 1 In one implementation, a multi-scale topology optimization method based on a cross-modal knowledge distillation network and a smoothly transitioning TPMS lattice structure includes the following steps: S1. Perform structural topology optimization on the design domain of the structure to be optimized: Based on the substrate parameters and load boundary conditions, iteratively solve the density distribution using the solid isotropic penalty microstructure method to obtain the optimal density field distribution and displacement field distribution, providing a mechanical basis for subsequent neural network prediction and type distribution optimization.
[0035] Topology optimization uses compliance minimization as its objective. The optimization objective is:
[0036] In the formula, the constraint condition is: , , ,in For the relative density of the unit cell, Let be the nodal displacement vector. For the overall stiffness matrix, For load vector, Due to volume constraints, The total number of elements; the topology optimization solution for the density and displacement fields is obtained using the OC optimizer and the material interpolation model in the standard SIMP method to obtain the density field of the voxel elements. and displacement field ; Volume fraction per unit; The minimum volume fraction for a single unit; This represents the maximum volume fraction of a single unit.
[0037] In one implementation, Figure 2(a) shows a three-dimensional schematic diagram of the first example, which is a three-dimensional short cantilever beam structure with a design domain size of [missing information]. Divide it into A single element is used, with its left side completely fixed and a downward concentrated load applied to the center of its right side. The volume constraint is set to 0.4, and the upper and lower limits of the element volume constraint are 0.6 and 0.1, respectively. The original density field of the topology optimization result is then obtained using the SIMP method, with the SIMP penalty factor set to 3 and the density filtering radius set to 3.5 times the element size. See Figure 2(b) for the density field distribution obtained from the topology optimization result based on the SIMP method; and Figure 2(c) for the displacement field distribution obtained from the topology optimization result.
[0038] S2, Prepare a homogenized dataset of TPMS lattice structures: Perform parameterized modeling and voxelization on various TPMS configurations at different volume fractions to obtain voxel models. Perform homogenization calculation on the voxel models to obtain the equivalent elastic tensor of each sample. The TPMS type number, volume fraction, voxel model and equivalent elastic tensor constitute the homogenized dataset.
[0039] The net configuration TPMS is sampled in the volume fraction range, and the sheet configuration TPMS is sampled in the lower volume fraction range. Each sample is generated into a voxel model through parametric modeling as the geometric mode input, and the equivalent elastic tensor after cubic symmetry simplification is obtained through homogenization calculation as the mechanical response mode output.
[0040] The equivalent elastic tensor has cubic symmetry and can be represented by three independent components:
[0041] in, , and These are three independent elastic constants, which can be obtained from the microscale by homogenization methods.
[0042] In one implementation, please refer to Figure 3The diagram shows voxel models of 12 TPMS configurations, including six net-type and six sheet-type configurations. D represents Diamond type, F represents Fischer-Koch S type, G represents Gyroid type, I represents I-WP type, P represents Primitive type, and S represents Schwarz P type. Net-type TPMS (Primitive, Gyroid, Diamond, I-WP, Fischer-Koch S, F-RD) were sampled at volume fractions ranging from 0.3 to 0.6, while sheet-type TPMS (Primitive, Gyroid, Diamond, I-WP, Fischer-Koch S, F-RD) were sampled at volume fractions ranging from 0.1 to 0.4. For each TPMS configuration, 151 samples were uniformly sampled at 0.002 intervals. Each sample was generated through parametric modeling. A high-resolution voxel model is used as the geometric modal input, and homogenization calculations are performed on each voxel model. Periodic boundary conditions are applied, and the equivalent elastic tensor is obtained by applying six independent strain modes and solving the finite element equations. The equivalent elastic tensor has 36 independent components. Since all TPMS lattice structures are cubically symmetric, the equivalent elastic tensor simplifies to three independent components (…). , , ), which serves as the mechanical response mode output.
[0043] S3, Constructing a Cross-Modal Knowledge Distillation Network: First, a teacher network containing a 3D convolutional geometric encoder and a parametric modal encoder is trained based on a homogenized dataset. The cross-modal fusion layer of the teacher network learns the synergistic relationship between geometric modalities and parametric modalities, enabling parametric modal features to learn advanced cross-modal encoding containing geometric modal information during fusion training. Subsequently, a student network that only accepts parametric modal input is constructed. The student network is trained using a weighted combination of prediction loss and distillation loss, transferring the synergistic relationship between geometric modalities and parametric modalities to the student network to achieve high-precision and lightweight prediction.
[0044] The student network comprises an expanded parametric encoder and a distillation-aligned projection layer. During the teacher network training phase, a 3D convolutional geometric encoder extracts topological features of voxel geometry through multi-layer convolution and pooling operations. The parametric modality encoder encodes discrete categorical modes and continuous parametric modes through a type embedding layer and a multilayer perceptron, respectively. The cross-modal fusion layer concatenates the geometric and parametric modes and learns their collaborative relationship through a fully connected layer. The prediction head outputs three independent components of the equivalent elastic tensor. The teacher network is trained using a mean squared error loss function until convergence. During this process, the high-level cross-modal representation from parametric modes to geometric modes is learned through the backpropagation gradient influence of the cross-modal fusion layer.
[0045] During the student network training phase, the capacity of the student network's parametric modality encoder is increased to twice that of the teacher network, providing sufficient expressive power to derive the geometric modality from the parametric modality. A projection layer is then used to reduce the dimensionality of the high-dimensional features to the teacher network's parametric modality space for distillation alignment. The total loss function is a weighted combination of the prediction loss and the distillation loss, mathematically expressed as:
[0046] Among them, predicted loss Mean squared error is used to measure the difference between student network predictions and true labels:
[0047] Distillation loss Including mean squared error and cosine similarity constraints, the parametric modal feature spaces used to align the student and teacher networks are expressed as follows:
[0048] Distillation weight A dynamic scheduling strategy is adopted. In the early stage of training, strong distillation is applied to quickly establish a foundation. In the middle stage, the transformation from autoparametric mode to geometric mode is continuously guided. In the later stage, the weights are gradually reduced until they are completely independent. In the end, the prediction accuracy of the student network surpasses that of the teacher network, while the inference speed is increased by several times and the input complexity is reduced by several orders of magnitude.
[0049] In one implementation, please refer to Figure 4 The Teacher network training phase uses a 3D convolutional geometric encoder for processing. The voxel model extracts geometric modalities through four convolutional layers (32, 64, 128, and 256 channels respectively). Simultaneously, a parametric modality encoder receives 2D parameter input (TPMS type number and volume fraction) and encodes the parametric modality through a three-layer fully connected network (64, 128, and 256 hidden layer dimensions respectively). The geometric and parametric modalities learn their synergistic relationship through a cross-modal fusion layer using feature concatenation and attention mechanisms. The fused features are then processed through a three-layer fully connected network (256, 128, and 64 hidden layer dimensions respectively) to output three equivalent elastic tensor components.
[0050] The Student network only accepts parametric modal input. Its parameter representation capability is enhanced by expanding the parametric encoder to a 5-layer fully connected network (with hidden layer dimensions of 128, 256, 512, 256, and 128 respectively). A distillation alignment projection layer is also added to project the Student network's parametric modalities into a 256-dimensional space identical to the Teacher network's fused features. The Student network training process uses a total loss function, which includes two terms: prediction loss and distillation loss. The prediction loss is the mean squared error loss, and the distillation loss includes the mean squared error and cosine similarity constraints.
[0051] Distillation weight A four-stage dynamic scheduling strategy is adopted: rounds 1 to 100 are set to 5.0 to achieve strong distillation, rounds 101 to 200 are set to 3.0 for continuous guidance, rounds 201 to 300 are set to 1.0 for mild maintenance, and rounds 301 to 400 are set to 0.0 to achieve completely independent prediction.
[0052] Please refer to Figures 5(a) and 5(b), which show the scatter plots of the prediction results of the Teacher network and the Student network on the intelligent sampling test set, respectively. The intelligent sampling test set contains 240 sample points (12 TPMS configurations, selecting the sample with the smallest prediction error within their respective effective volume fraction ranges, while also considering the uniformity of distribution). The Teacher network has an average absolute percentage error of 1.40% on the intelligent sampling test set, while the Student network, after knowledge distillation, has an average absolute percentage error reduced to 0.78%, thus surpassing the Teacher network in prediction accuracy.
[0053] S4. Based on the density field obtained from the structural topology optimization, the trained student network is used to perform batch prediction of the equivalent elastic tensor for each unit in the optimization region: For each unit, the candidate TPMS type number and the volume fraction of the unit are input respectively to obtain the equivalent elastic tensor of the unit under all candidate types. All the obtained equivalent elastic tensors form a complete candidate performance matrix.
[0054] The set of candidate TPMS types to be predicted for each cell is determined based on the density field. Cells with densities outside the effective range of TPMS are not assigned a type. Cells with densities in the medium range are allowed to choose between net and sheet configurations. Cells with densities in the high range are allowed only net configurations. Cells with densities in the low range are allowed only sheet configurations. This ensures that the volume fraction range of candidate types matches the cell density.
[0055] In one implementation, based on the density field obtained in step S1, a set of candidate TPMS types is determined for each element within the design domain according to its density value. The effective volume fraction of TPMS is set to a range of 0.1 to 0.6, and no TPMS type is assigned to elements with densities below 0.1 or above 0.6. The lower limit of the effective volume fraction is set to 0.3 for net-type configurations, and the upper limit of the effective volume fraction is set to 0.4 for sheet-type configurations. For cells with a density in the range of 0.1 to 0.3, only sheet configurations (numbered 7 to 12, including Primitive-sheet, Gyroid-sheet, Diamond-sheet, IWP-sheet, FischerKochS-sheet, and FRD-sheet) are allowed. For cells with a density in the range of 0.3 to 0.4, a total of 12 net and sheet configurations are allowed. For cells with a density in the range of 0.4 to 0.6, only net configurations (numbered 1 to 6, including Primitive-net, Gyroid-net, Diamond-net, IWP-net, FischerKochS-net, and FRD-net) are allowed.
[0056] For each candidate type of each unit, a 2D parameter vector is formed by combining the TPMS type number (1 to 12) with the corresponding unit density value, and then batch-input into the trained Student network. The Student network inference process does not require voxel model input; it obtains the three independent components of the corresponding equivalent elastic tensor simply through forward propagation of the expanded fully connected network of the Student network. , , Taking a typical working condition as an example, for an optimization region containing 1000 units, each unit predicts 12 candidate TPMS types, requiring a total of 12000 sets of equivalent elastic tensors to be predicted. The Student network has a single-sample inference time of approximately 0.005 seconds and a total prediction time of approximately 60 seconds, which is 4 times more efficient than the Teacher network (which uses 3D-CNN geometric encoding and requires 240 seconds), and more than 4000 times more efficient than the traditional numerical homogenization method (which requires 20 seconds per sample and takes approximately three days in total).
[0057] S5. Determine the TPMS type distribution based on the constraint optimization algorithm: Calculate the strain energy of each element under different TPMS types according to the density field, displacement field and candidate performance matrix. Based on the strain energy and the constraint optimization algorithm, construct a multi-objective optimization model that includes stiffness maximization and spatial continuity penalty. The multi-objective optimization model introduces density and configuration compatibility constraints to ensure that the volume fraction range of the selected type matches the element density. Then, iterative optimization is performed to balance stiffness and continuity, and finally, the type field that meets the physical feasibility and additive manufacturing requirements is output.
[0058] The multi-objective optimization model includes two terms: stiffness maximization and spatial continuity penalty. The mathematical expression of the objective function is:
[0059] The first term is the maximization of total strain energy. Representation unit Using TPMS type Strain energy at time, As a decision variable, when Time representation unit Select type ,otherwise The second term is a spatial continuity penalty. Representation unit The set of six neighboring units is penalized when neighboring units are of different types. To penalize weights, an adaptive strategy or manual specification is used to balance stiffness optimization and manufacturing performance improvement.
[0060] The multi-objective optimization model must satisfy three constraints, including: Uniqueness constraint:
[0061] Integer constraints:
[0062] And density and configuration compatibility constraints: .
[0063] Density and configuration compatibility constraints ensure the feasibility of the selected TPMS type. Cells with densities below the lower limit are not assigned any TPMS type. Cells with densities below the effective lower limit of net configuration and within the effective range of sheet configuration are only allowed to select sheet configuration. Cells with densities in the intersection of the two configurations are allowed to select any configuration. Cells with densities above the effective upper limit of sheet configuration and within the effective range of net configuration are only allowed to select net configuration. Cells with densities exceeding the upper limit are not assigned any type, ensuring geometric realizability, homogenization effectiveness, and additive manufacturing compatibility.
[0064] In the greedy initialization phase, the type with the largest strain energy is selected for each element from its candidate type set to quickly obtain a high-quality initial solution. In the iterative optimization phase, all elements are traversed. For each element, while keeping other element types unchanged, the objective function change after switching to other types in the candidate set is evaluated. If the objective function increases, the switch is accepted. Through multiple rounds of iteration until convergence, a local optimal balance between stiffness and continuity is achieved.
[0065] In one implementation, the strain energy of each element under different TPMS types is calculated based on the density field, displacement field, and candidate performance matrix obtained in step S4. For the elements... Using TPMS type First, based on the three components of the equivalent elastic tensor ( , , Construct a complete Stiffness matrix Then, the displacement gradient of the element in the topology optimization is extracted to calculate the strain vector. The formula for calculating strain energy is:
[0066] A two-stage iterative improvement algorithm is employed to solve the problem. In the greedy initialization stage, the type with the highest strain energy is selected for each element from its candidate type set, completing initialization in approximately 0.1 seconds for 400 elements. In the iterative optimization stage, all elements are traversed column-wise. For each element, while keeping other element types unchanged, the objective function change after switching to other types in the candidate set is evaluated one by one. ,like If the cell type is changed, the switch to update the cell type is accepted. After 20 iterations, the objective function change is less than 0.1%, reaching convergence. The total computation time is approximately 5 seconds. Please refer to [link / reference]. Figure 6 This shows the first example of a TPMS type distribution map obtained based on a constrained optimization algorithm.
[0067] S6 generates a manufacturable 3D model through a geometric smoothing transition algorithm: First, the density field is smoothed by trilinear interpolation. Then, at the point level, the type field is detected for type boundaries and the linear type weights based on distance are calculated. For non-boundary points, the distance field value is directly calculated using interpolated density. For boundary points, a weighted mixing strategy is adopted and adaptive compensation for the degree of mixing is introduced to ensure the connectivity of materials at the interface of different types and avoid geometric breaks. Finally, a 3D mesh model is generated through an isosurface extraction algorithm and exported in a file format that can be directly used for additive manufacturing.
[0068] Trilinear interpolation is performed on the density field to eliminate discretization artifacts and ensure continuous volume fraction variation. The distances from a point to each of the six faces of the current element are calculated. The nearest face is found, and the type of neighboring elements in that direction is checked. If the neighboring types are different and the point's distance to the boundary is... Less than the transition width threshold If a boundary point is identified, it is marked as a type boundary point, and a type weight is calculated for that boundary point. The formula for assigning type weights is as follows:
[0069]
[0070] in, and These represent the weights of the current type and the neighboring types, respectively, ensuring the boundary center ( The two types are equally weighted. The weight of the current type increases linearly with distance, reaching a maximum, while the weight of the neighboring type decreases linearly to zero.
[0071] In distance field calculations, for non-boundary points, an interpolation density lookup table is used to convert the volume fraction corresponding to the non-boundary point into the level set constant corresponding to the current type. The corresponding distance field value is calculated based on the configuration category.
[0072] For net configuration:
[0073] For sheet configuration:
[0074] in, For TPMS implicit functions at point The value at that location, is the level set constant. The net configuration generates a single-layer surface structure, and the sheet configuration generates a double-layer sandwich surface structure. The distance field values for each participating type are calculated at the boundary points. All types share the same interpolation density to ensure volume fraction conservation. The pre-calculated type weights are weighted and mixed, as expressed by:
[0075] In the formula, For type linear weights, For type At point Distance field value at that location, The number of types participating in the mixing. Then, adaptive compensation is applied based on the degree of mixing; the compensation amount is calculated using the following formula:
[0076] in, As a compensation factor, the degree of mixing term It reaches its maximum value at the boundary center and is zero in the pure type region, set to 0.36 in both examples. The final distance field value is:
[0077] A global positive offset is applied to the mixed distance field value to prevent material thinning caused by weighted mixing, thus ensuring the connectivity and geometric smoothness of the material in the transition region.
[0078] In one implementation, please refer to Figure 7 It adopts a three-layer architecture design, with the first layer being a density interpolation smoothing layer. The discrete density field is subjected to trilinear interpolation to generate A continuous density field with high resolution eliminates discretization artifacts and ensures continuous variation in volume fraction.
[0079] The second layer is a type boundary detection layer. It finds the nearest face and checks the type of its neighboring cells in that direction. If the neighboring types are different and the distance from the point to the boundary is... Less than the transition width threshold If the boundary point is marked as a type boundary point, the class weight of the boundary point is calculated.
[0080] After generating the complete range field, the Marching Cubes algorithm is used to extract the isosurface of the zero level set. A triangular mesh model is generated. Then, Laplacian smoothing is applied to the mesh in the transition region, iterated three times, to improve the surface quality of the transition region. Finally, it is exported as an STL file for use in additive manufacturing.
[0081] Please see Figure 8 In the figure, the net-type Primitive unit cell (Primitive-net, number 1) is simultaneously connected to the sheet-type Diamond unit cell (Diamond-sheet, number 9) and the sheet-type FRD unit cell (FRD-sheet, number 12) on two adjacent faces. Although the topological structures of the connection surfaces of the net-type and sheet-type are completely mismatched, and a single unit is connected to two different sheet-type configurations at the same time, the transition region still achieves a smooth connection effect with continuous material without breakage and smooth geometric shape without abrupt changes, verifying the applicability of the present invention in arbitrary TPMS type combinations and multi-directional transition scenarios.
[0082] Please see Figure 9 The overall structure presents a natural topological form, with different TPMS configurations smoothly transitioning in space, and possessing good manufacturability.
[0083] Implementation Case 2 demonstrates the topology optimization results for an MBB beam structure. Please refer to [link / reference]. Figure 10 The complete design domain size is Due to symmetry, the default boundary conditions correspond to the semi-design domain of the "MBB beam". Divide it into A single element is used, with the load applied to the upper left corner. The left edge has symmetrical boundary conditions, and the structure is horizontally supported at the lower right corner. The volume constraint is set to 0.5, the SIMP penalty factor to 3, and the density filtering radius to 3 times the element size. See Figure 11(a), which shows a clear mechanical transfer path. See Figure 11(b), which shows the TPMS type distribution diagram obtained based on the constraint optimization algorithm in a second example. Primitive-net and Diamond-net configurations are mainly allocated in the high-stress oblique member region, while Diamond-sheet and F-RD-sheet configurations are allocated in the low-stress filling region. The type distribution follows the stress-oriented principle while maintaining spatial continuity. Please refer to... Figure 12 The second example demonstrates the STL model results obtained through the geometric smooth transition algorithm. The smooth transition between different TPMS configurations ensures structural integrity and manufacturing feasibility. This case further illustrates the effectiveness and universality of the multi-scale topology optimization method for TPMS lattice structures provided by this invention under different boundary conditions and load conditions.
[0084] The present invention also provides a multi-scale topology optimization system for TPMS lattice structures. The system includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to perform the multi-scale topology optimization method for TPMS lattice structures as described above.
[0085] The present invention also provides a computer-readable storage medium storing machine-executable instructions, which, when invoked and executed by a processor, cause the processor to implement the multi-scale topology optimization method for the TPMS lattice structure as described above.
[0086] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
Claims
1. A multi-scale topology optimization method for TPMS lattice structures, characterized in that, The steps are as follows: (1) The teacher network of the cross-modal knowledge distillation network learns the cross-modal fusion relationship between the geometric mode and the parametric mode of the TPMS type, and then distills the cross-modal fusion relationship to the student network. The student network is used to predict the equivalent elastic tensor of each unit in the optimization region under all candidate TPMS types. All the equivalent elastic tensors obtained form a candidate performance matrix. (2) Based on the candidate performance matrix, the density field and displacement field of the structure to be optimized, a multi-objective optimization model including stiffness maximization and spatial continuity is constructed, and then the type field is obtained based on the multi-objective optimization model; the multi-objective optimization model introduces density and configuration compatibility constraints; (3) Density interpolation is performed on the density field, and then type boundary detection is performed on the type field at the point level. Then density interpolation is performed on the non-boundary points to calculate the non-boundary point distance field value. After calculating the type weights for the boundary points, the obtained type weights are processed by a weighted mixing strategy to obtain the boundary point distance field. The boundary point distance field is compensated by the degree of mixing adaptive compensation to obtain the boundary point distance field value. Based on the non-boundary point distance field value and the boundary point distance field value, a three-dimensional topological configuration that can be directly used for additive manufacturing is obtained.
2. The multi-scale topology optimization method for TPMS lattice structures as described in claim 1, characterized in that: Topology optimization is performed on the structure to be optimized to obtain the density and displacement fields. The optimization objective is to minimize the compliance. In the formula, the constraint condition is: , , ,in For the relative density of the unit cell, Let be the nodal displacement vector. For the overall stiffness matrix, For load vector, Due to volume constraints, The total number of units; Volume fraction per unit; The minimum volume fraction for a single unit; This represents the maximum volume fraction of a single unit.
3. The multi-scale topology optimization method for TPMS lattice structures as described in claim 2, characterized in that: Based on the substrate parameters and load boundary conditions, the density distribution is iteratively solved using the solid isotropic penalty microstructure method to obtain the optimal density field and displacement field.
4. The multi-scale topology optimization method for TPMS lattice structures as described in claim 1, characterized in that: Parametric modeling and voxelization of various TPMS configurations under different volume fractions are performed to obtain voxel models. The voxel models are homogenized to obtain the equivalent elastic tensor of each sample. The TPMS type number, volume fraction, voxel model and equivalent elastic tensor constitute a homogenized dataset. A cross-modal knowledge distillation network is trained based on the homogenized dataset.
5. The multi-scale topology optimization method for TPMS lattice structures as described in claim 1, characterized in that: The student network was trained using a weighted combination of prediction loss and distillation loss; the teacher network was trained using the mean squared error loss function.
6. The multi-scale topology optimization method for TPMS lattice structures as described in claim 5, characterized in that: During the student network training phase, the capacity of the student network's parametric modal encoder is expanded to twice that of the teacher network. The total loss function is a weighted combination of the prediction loss and the distillation loss, and the corresponding expression is: In the formula, To predict losses, This is due to distillation losses; For distillation weight.
7. The multi-scale topology optimization method for TPMS lattice structures as described in any one of claims 1-6, characterized in that: The mathematical expression for the objective function of the multi-objective optimization model is: The first term is the maximization of total strain energy. Representation unit Using TPMS type Strain energy at time, As a decision variable, when Time representation unit Select type ,otherwise The second term is a spatial continuity penalty. Representation unit The set of six neighboring units is penalized when neighboring units are of different types. To penalize weights; the multi-objective optimization model must satisfy three constraints, including: Uniqueness constraint: , Integer constraints: , And density and configuration compatibility constraints: , In the formula, This represents the total number of units in the design area. The total number of TPMS types; The minimum volume fraction for a single unit; Let be the density value of the i-th cell; The maximum volume fraction of a single unit; This represents the lower limit of density for the net configuration; This represents the upper limit of the density for sheet configurations.
8. The multi-scale topology optimization method for TPMS lattice structures as described in any one of claims 1-6, characterized in that: The formula for allocating type weights is: in, and These represent the weights of the current type and the neighboring types, respectively. This is the distance from the current point to the type boundary; This represents the width of the transition area.
9. A multi-scale topology optimization system with a TPMS lattice structure, characterized in that: The system includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it performs the multi-scale topology optimization method for the TPMS lattice structure as described in any one of claims 1-8.
10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores machine-executable instructions, which, when invoked and executed by a processor, cause the processor to implement the multi-scale topology optimization method for the TPMS lattice structure as described in any one of claims 1-8.