Reverse design and optimization method of two-dimensional deformation adjustable mechanical structure
By combining neural networks and genetic algorithms for collaborative optimization, along with finite element simulation and additive manufacturing, we have achieved efficient and accurate negative Poisson's ratio structure design. This solves the problems of long design cycles and difficult reverse design in traditional methods, and meets the complex deformation requirements of aerospace, biomedicine and other fields.
Patent Information
- Application Number
- CN202511541900.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-10-27
- Publication Date
- 2026-01-27
AI Technical Summary
Existing design methods are difficult to achieve efficient and precise control of negative Poisson's ratio structural parameters, have long design cycles and high costs, are difficult to reverse design, have poor engineering adaptability, and are difficult to meet the complex deformation requirements of aerospace, biomedicine and other fields.
By employing intelligent optimization algorithms combined with neural network proxy models, and through finite element simulation and additive manufacturing, we reverse-engineer and optimize two-dimensional deformation-adjustable mechanical structures. By utilizing the geometric feature parameters of concave, chiral, and perforated cells, we construct a multi-parameter coupled design system to achieve efficient and accurate structural design.
Significantly shorten the design cycle, improve design efficiency, achieve precise control of complex structures, adapt to personalized deformation needs in fields such as aerospace and biomedicine, and reduce engineering research and development costs.
Smart Images
Figure CN121413047A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of mechanical structure design technology, specifically a reverse design and optimization method for two-dimensional deformable and adjustable mechanical structures. Background Technology
[0002] As modern engineering technology develops towards high integration, flexibility, and multifunctionality, the demand for controllable mechanical structures is becoming increasingly urgent. Negative Poisson's ratio materials, due to their unique properties of lateral expansion under tension and lateral contraction under compression, show broad application prospects in aerospace, biomedicine, flexible electronics, and soft robotics.
[0003] Currently, typical negative Poisson's ratio cells mainly include concave structures, chiral structures, and perforated structures. Although these structures possess excellent mechanical properties and designability, existing design methods have the following shortcomings: 1) Complex parameter control: The mechanical properties of the cell are affected by the coupling of multiple parameters, and traditional trial-and-error methods are difficult to achieve precise control; 2) Low design efficiency: Relying on repeated finite element simulations, the design cycle is long and the cost is high; 3) Difficult reverse design: It is difficult to directly deduce the optimal structural parameters from the target deformation; 4) Poor engineering adaptability: The problems of structural continuity and stress concentration under complex deformation profiles have not been effectively solved.
[0004] These limitations restrict the widespread application of negative Poisson's ratio structures in practical engineering, necessitating an efficient and accurate reverse design and optimization method. Summary of the Invention
[0005] The purpose of this section is to outline some aspects of the embodiments of the present invention and to briefly describe some preferred embodiments. Simplifications or omissions may be made in this section, as well as in the abstract and title of this application, to avoid obscuring the purpose of these documents; however, such simplifications or omissions should not be construed as limiting the scope of the invention.
[0006] Therefore, the purpose of this invention is to provide a reverse design and optimization method for two-dimensional deformable and adjustable mechanical structures. Combined with intelligent optimization algorithms, it can reversely solve for the optimal design parameters that meet the target performance. Compared with traditional experience-driven methods, it can not only significantly shorten the design cycle, but also achieve more complex structural designs.
[0007] To address the aforementioned technical problems, according to one aspect of the present invention, the present invention provides the following technical solution: A reverse design and optimization method for two-dimensional deformation-adjustable mechanical structures, comprising the following steps: S1. Determine the target deformation curve and set multiple control points on the target deformation curve and their target coordinates; S2. Select a negative Poisson's ratio cell and define the geometric characteristic parameters of the negative Poisson's ratio cell. The geometric characteristic parameters can control the Poisson's ratio and elastic modulus of the cell. S3. Based on the geometric characteristic parameters of the negative Poisson's ratio cell, construct multiple sets of two-dimensional structural models with different parameter combinations, apply preset loading conditions to each two-dimensional structural model and perform finite element simulation, extract the structural deformation response data corresponding to each set of parameter combinations, and form a simulation database of cell geometric characteristic parameters and deformation response. S4. Using the geometric feature parameters in the simulation database as input and the corresponding deformation response data as output, train a neural network proxy model so that the neural network proxy model has the ability to predict the structural deformation response under given geometric feature parameters. S5. Using the error between the control point coordinates predicted by the neural network surrogate model and the target coordinates as the fitness function, the geometric feature parameters of the negative Poisson ratio cell are iteratively optimized through a genetic algorithm until the fitness function value meets the preset convergence threshold, thereby obtaining the optimal combination of geometric feature parameters. S6. Construct a two-dimensional deformation-adjustable mechanical structure based on the optimal combination of geometric feature parameters, prepare structural samples and test their deformation performance.
[0008] As a preferred embodiment of the reverse design and optimization method for a two-dimensional deformable adjustable mechanical structure described in this invention, in step S2, the negative Poisson's ratio cell is selected from one or more of the following: concave structure cell, four-ligament chiral structure cell, and perforated structure cell. As a preferred embodiment of the reverse design and optimization method for a two-dimensional deformable adjustable mechanical structure described in this invention, when the negative Poisson's ratio cell is an inwardly concave structural cell, its geometric characteristic parameters include the angle of the inclined rod. θ , crossbar length ratio β=L 1 / L , rod thickness ratio γ = t / L , length ratio of diagonal bar μ=L 2 / L ,in L The total length of the concave structural cell. L 1 represents the length of the crossbar. L 2 represents the length of the diagonal brace. t The thickness of the member; the included angle of the diagonal member. θ The value range is 60°-80°, and can be adjusted... θ The value can adjust the Poisson's ratio and elastic modulus of the concave structural cell, and its Poisson's ratio and elastic modulus satisfy:
[0009]
[0010] in,v Poisson's ratio, E For the elastic modulus, ε x and ε y The strains of the concave structure along the X and Y directions are respectively. E s It represents the elastic modulus of the concave structure cell substrate.
[0011] As a preferred embodiment of the reverse design and optimization method for a two-dimensional deformable and adjustable mechanical structure described in this invention, when the negative Poisson's ratio cell is a four-ligament chiral structure cell, its geometric characteristic parameters include the radius of the central circle. r Horizontal center distance L x Longitudinal circle center distance L y , rod thickness t , L The total length of the chiral structure cell is given by the ratio of the radius to the total length of the cell. r / L As a core control parameter, the radius ratio r / L The value range is 0.2-0.4, which can be adjusted... r / L The Poisson's ratio and elastic modulus of the chiral structural cell can be adjusted, and their Poisson's ratio and elastic modulus satisfy the following:
[0012]
[0013] in, v Poisson's ratio, E For the elastic modulus, ε x and ε y The strains of the concave structure along the X and Y directions are respectively. E s It represents the elastic modulus of the concave structure cell substrate.
[0014] As a preferred embodiment of the reverse design and optimization method for a two-dimensional deformable adjustable mechanical structure described in this invention, when the negative Poisson's ratio cell is a perforated structure cell, its geometric characteristic parameters include the porosity aspect ratio. AR=b / a Spacing ratio IS=c / L ,in a The length of the short axis of the perforation. b The length of the major axis of the perforation. c The perforation spacing, L The overall length of the perforated structure cell should be maintained during the design. L and AR Unchanged, based on spacing ratio IS As a core control parameter, the spacing ratio IS The value range is 0.1-0.3, and it can be adjusted... IS The value can adjust the Poisson's ratio and elastic modulus of the perforated structure cell.
[0015] As a preferred embodiment of the reverse design and optimization method for a two-dimensional deformable and adjustable mechanical structure described in this invention, in step S3, when constructing the two-dimensional structural model, a gradient filling strategy is adopted, specifically: the number of cells in the design area is set to 6×15, that is, 6 cells in the vertical stretching direction and 15 cells in the stretching direction, the size of a single cell is 20mm×20mm, and the overall structural size is h×L=300mm×120mm; The preset loading condition is axial tensile strain of 10%, the boundary condition is set to one end fixed and the other end displacement loading, the structural unit type is shell unit, and the dimensions of the connection between adjacent cells are kept consistent to avoid stress concentration.
[0016] As a preferred embodiment of the reverse design and optimization method for a two-dimensional deformable and adjustable mechanical structure described in this invention, in step S4, the neural network proxy model is a fully connected neural network, including an input layer, three hidden layers and an output layer. The number of neurons in the input layer is the same as the number of geometric feature parameters of the negative Poisson's ratio cells, and the number of neurons in the output layer is twice the dimension of the control point coordinates. The number of neurons in the three hidden layers are 64, 32, and 16, respectively, and the activation function is ReLU; The model was trained using the Adam optimizer with a learning rate of 0.001, a batch size of 32, and 500 training epochs. An early stopping mechanism was enabled during training, and training was terminated when the validation loss decreased by less than 0.1% for 20 consecutive epochs.
[0017] As a preferred embodiment of the reverse design and optimization method for a two-dimensional deformable adjustable mechanical structure described in this invention, in step S5, the fitness function is the root mean square error (RMSE) between the predicted coordinates of the control points and the target coordinates, and its calculation formula is as follows:
[0018] in N To control the number of points, i For control point numbers, ( h predicted ,L predicted ) represents the predicted coordinates of the control points, h target ,L target ) represents the target coordinates of the control point, and the preset convergence threshold is RMSE < 1.0; the population size of the genetic algorithm is set to 50, the crossover probability is 0.7, and the mutation probability is 0.05.
[0019] As a preferred embodiment of the reverse design and optimization method for a two-dimensional deformable adjustable mechanical structure described in this invention, in step S6, a structural sample is prepared using an additive manufacturing process, wherein the additive manufacturing process is selective laser sintering, and the material used is thermoplastic polyurethane elastomer; during the preparation process, the optimal geometric feature parameters are imported into three-dimensional modeling software to generate a structural model, and the laser sintering parameters are set as follows: layer thickness 0.1 mm, laser power 30 W, scanning speed 5.0 m / s, chamber temperature 165 °C, and the printed sample is subjected to slow cooling treatment in the chamber for 4 hours.
[0020] As a preferred embodiment of the reverse design and optimization method for a two-dimensional deformable adjustable mechanical structure described in this invention, in step S6, the deformation performance test adopts a combination of an electronic tensile testing machine and a digital image correlation system. The clamping distance of the electronic tensile testing machine is set to 320mm, the preload force is 0.5N, the tensile speed is 2mm / min, and 10% axial strain is applied. The digital image correlation system has a lens focal length of 50mm, a speckle size of 0.3mm, and a sampling rate of 5Hz. The strain calculation adopts the Green-Lagrange tensor formula. By analyzing the control point coordinates and strain distribution of the actual deformation of the sample, its consistency with the target deformation curve is verified.
[0021] Compared with the prior art, the beneficial effects of the present invention are: This invention presents a reverse design and optimization method that addresses the challenges of reverse designing irregular metamaterial structures through a collaborative optimization approach using artificial neural networks and genetic algorithms. Parametric modeling and Latin hypercube sampling overcome the instability of neural network training under small sample conditions. Furthermore, by employing finite element verification and additive manufacturing process parameter optimization, it overcomes the problems of long design cycles and lack of universality inherent in traditional trial-and-error methods, achieving efficient and accurate gradient negative Poisson's ratio structure design. Its effectiveness is verified through DIC deformation measurement.
[0022] This invention innovatively integrates three types of negative Poisson's ratio cell configurations: concave, chiral, and perforated. It establishes a design system with multiple cell types and multi-parameter coupling. By adjusting the characteristic parameters of the cells, the Poisson's ratio and elastic modulus of the structure can be precisely controlled, achieving a high degree of matching for various target deformation profiles such as parabolic, sine, linear, and combined curves. Furthermore, by employing a gradient filling strategy and geometric continuity constraints at cell connections, gradient parameter cells are arranged along the stretching direction, while maintaining uniform cell size in the vertical direction. This avoids the risk of stress concentration and ensures a smooth transition of non-uniform deformation. It can adapt to the personalized deformation needs of different fields such as aerospace variable wing structures, biomedical implantable devices, and flexible electronic stretchable circuits, significantly improving design adaptability compared to traditional methods.
[0023] This invention constructs a reverse design framework that integrates parametric modeling, surrogate models, and GA collaborative optimization. The artificial neural network surrogate model trained with multiple sets of simulation data can replace traditional finite element simulation to achieve rapid prediction of structural deformation. The time for a single performance prediction is reduced from several hours in traditional simulation to milliseconds, and the computational efficiency is improved by tens of thousands of times. Moreover, combined with the global search capability of the genetic algorithm (GA), it can automatically iteratively optimize multiple design variables without the need for manual intervention and trial and error. For typical target deformations such as sine curves, the design cycle is significantly shortened, significantly reducing the time cost of engineering research and development and meeting the needs of rapid iteration. Attached Figure Description
[0024] To more clearly illustrate the technical solutions of the embodiments of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and detailed embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein: Figure 1 This is a flowchart of a reverse design and optimization method for a two-dimensional deformable and adjustable mechanical structure according to the present invention; Figure 2 A schematic diagram illustrating the parameter definition of the concave structural cell provided by this invention; Figure 3 A schematic diagram illustrating the parameter definition of the chiral cell unit of the four ligaments provided by this invention; Figure 4 A schematic diagram illustrating the parameter definition of the perforated structure cell provided by this invention; Figure 5 A diagram showing the relationship between the mechanical properties and dimensional parameters of the concave structural cell provided by this invention; Figure 6 A graph showing the relationship between the mechanical properties and dimensional parameters of the four-ligament chiral structure cell provided by this invention; Figure 7 A diagram showing the relationship between the mechanical properties and dimensional parameters of the perforated structural cell provided by this invention; Figure 8 (a) is a schematic diagram of the gradient filling strategy for negative Poisson's ratio cells provided by the present invention. Figure 8 (b) is a schematic diagram of the concave configuration filling; Figure 9 A diagram illustrating the reverse design method based on the combination of machine learning and genetic algorithms provided by this invention; Figure 10 The training process for the concave cell configuration provided by this invention: wherein, Figure 10 (a) is the graph of the loss function. Figure 10 (b) is a comparison chart of predictions and actual results; Figure 11This invention provides a structural sample with an inwardly recessed cell configuration. Figure 12 The images provided in this invention are deformation test photos and displacement cloud maps of the concave structure sample. The left image shows the initial state of the sample, the middle image shows the state of the sample after tensioning, and the right image is the displacement field cloud map obtained through Vic-3D analysis. Detailed Implementation
[0025] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
[0026] like Figure 1 As shown, a reverse design and optimization method for a two-dimensional deformable and adjustable mechanical structure is described, with the following steps: S1. Determine the target deformation curve and set multiple control points on the target deformation curve and their target coordinates; S2. Select a negative Poisson's ratio cell and define the geometric characteristic parameters of the negative Poisson's ratio cell. The geometric characteristic parameters can adjust the Poisson's ratio and elastic modulus of the cell. In this embodiment, the negative Poisson's ratio cell is selected from one or more of the following: concave structure cell, four-ligament chiral structure cell, and perforated structure cell. like Figure 2 As shown, when the negative Poisson's ratio cell is a concave structure cell, its geometric characteristic parameters include the angle of the inclined rod. θ , crossbar length ratio β=L 1 / L , rod thickness ratio γ = t / L , length ratio of diagonal bar μ=L 2 / L ,in L The total length of the concave structural cell. L 1 represents the length of the crossbar. L 2 represents the length of the diagonal brace. t For the thickness of the rod; according to Figure 5 The relationship between the mechanical properties and dimensional parameters of the diagonal bar is shown in the figure. θ The value range is 60°-80°, and can be adjusted... θ The value can adjust the Poisson's ratio and elastic modulus of the concave structural cell, and its Poisson's ratio and elastic modulus satisfy:
[0027]
[0028] in, v Poisson's ratio, E For the elastic modulus, ε x and ε y The strains of the concave structure along the X and Y directions are respectively.E s The elastic modulus of the concave structure cell substrate; like Figure 3 As shown, when the negative Poisson's ratio cell is a four-ligament chiral structure cell, its geometric characteristic parameters include the radius of the central circle. r Horizontal center distance L x Longitudinal circle center distance L y , rod thickness t , L The total length of the chiral structure cell is given by the ratio of the radius to the total length of the cell. r / L As a core control parameter, according to Figure 6 The graph showing the relationship between mechanical properties and dimensional parameters, including the radius ratio. r / L The value range is 0.2-0.4, which can be adjusted... r / L The Poisson's ratio and elastic modulus of the chiral structural cell can be adjusted, and their Poisson's ratio and elastic modulus satisfy the following:
[0029]
[0030] in, v Poisson's ratio, E For the elastic modulus, ε x and ε y The strains of the concave structure along the X and Y directions are respectively. E s The elastic modulus of the concave structure cell substrate; like Figure 4 As shown, when the negative Poisson's ratio cell is a perforated structure cell, its geometric characteristic parameters include the porosity aspect ratio. AR=b / a Spacing ratio IS=c / L ,in a The length of the short axis of the perforation. b The length of the major axis of the perforation. c The perforation spacing, L The overall length of the perforated structure cell should be maintained during the design. L and AR Unchanged, based on spacing ratio IS As a core control parameter, according to Figure 7 The relationship between mechanical properties and dimensional parameters, the spacing ratio IS The value range is 0.1-0.3, and it can be adjusted... IS The value can adjust the Poisson's ratio and elastic modulus of the perforated structure cell; S3. Based on the geometric characteristic parameters of the negative Poisson's ratio cell, construct multiple sets of two-dimensional structural models with different parameter combinations. Apply preset loading conditions to each two-dimensional structural model and perform finite element simulation. Extract the structural deformation response data corresponding to each set of parameter combinations to form a simulation database of cell geometric characteristic parameters and deformation response. In this embodiment, when constructing the two-dimensional structural model, a gradient filling strategy is adopted. Specifically, the number of cells in the design area is set to 6×15, that is, 6 cells in the vertical stretching direction and 15 cells in the stretching direction. The size of a single cell is 20mm×20mm, and the overall structural size is h×L=300mm×120mm. The preset loading condition is axial tensile strain of 10%, the boundary condition is set to one end fixed and the other end displacement loading, the structural unit type is shell unit, and the dimensions of the connection between adjacent cells are kept consistent to avoid stress concentration. S4. Using the geometric feature parameters in the simulation database as input and the corresponding deformation response data as output, train a neural network surrogate model so that the neural network surrogate model has the ability to predict the structural deformation response under given geometric feature parameters. In this embodiment, the neural network surrogate model is a fully connected neural network, including an input layer, three hidden layers and an output layer. The number of neurons in the input layer is the same as the number of geometric feature parameters of the negative Poisson ratio cells. The number of neurons in the output layer is twice the dimension of the control point coordinates. The number of neurons in the three hidden layers are 64, 32 and 16 respectively. The activation function is ReLU. The model training uses the Adam optimizer with a learning rate of 0.001, a batch size of 32, and 500 training rounds. An early stopping mechanism is enabled during training. Training is terminated when the validation loss decreases by <0.1% for 20 consecutive rounds. S5. Using the error between the control point coordinates predicted by the neural network surrogate model and the target coordinates as the fitness function, the geometric feature parameters of the negative Poisson's ratio cell are iteratively optimized using a genetic algorithm until the fitness function value meets a preset convergence threshold, thus obtaining the optimal combination of geometric feature parameters. In this embodiment, the fitness function is the root mean square error (RMSE) between the predicted control point coordinates and the target coordinates, and its calculation formula is as follows:
[0031] in N To control the number of points, i For control point numbers, ( h predicted ,L predicted ) represents the predicted coordinates of the control points, h target ,L target) represents the target coordinates of the control point, and the preset convergence threshold is RMSE < 1.0; the population size of the genetic algorithm is set to 50, the crossover probability is 0.7, and the mutation probability is 0.05; S6. Based on the optimal combination of geometric feature parameters, a two-dimensional deformable and adjustable mechanical structure is constructed, a structural sample is prepared, and its deformation performance is tested. In this embodiment, the structural sample is prepared using an additive manufacturing process, specifically selective laser sintering (SLS), and the material used is thermoplastic polyurethane elastomer. During the preparation process, the optimal geometric feature parameters are imported into three-dimensional modeling software to generate a structural model. The laser sintering parameters are set as follows: layer thickness 0.1 mm, laser power 30 W, scanning speed 5.0 m / s, chamber temperature 165 °C. After printing, the sample undergoes a 4-hour slow cooling treatment inside the chamber. The deformation performance test uses a combination of an electronic tensile testing machine and a digital image correlation system. The clamping distance of the electronic tensile testing machine is set to 320 mm, the preload force is 0.5 N, the tensile speed is 2 mm / min, and 10% axial strain is applied. The lens focal length of the digital image correlation system is 50 mm, the speckle size is 0.3 mm, the sampling rate is 5 Hz, and the strain calculation uses the Green-Lagrange tensor formula. By analyzing the control point coordinates and strain distribution of the actual deformation of the sample, its consistency with the target deformation curve is verified.
[0032] To verify the technical effect of the reverse design and optimization method for a two-dimensional deformable and adjustable mechanical structure of the present invention, the following specific embodiment is provided: a concave configuration achieves the target deformation of a sinusoidal curve; This embodiment addresses the sinusoidal deformation requirements of flexible aerospace skins by employing concave cell configurations for the reverse design and optimization of two-dimensional mechanical structures. The specific steps are as follows: Step 1: Determine the target curve: Select a sine curve as the target deformation profile, and define 6 uniformly distributed control points on the upper boundary of the structure (to characterize the deformation accuracy). Their initial coordinates (h is the longitudinal coordinate and L is the transverse coordinate) and the target coordinates after stretching are shown in Table 1. Table 1 shows the initial coordinates and corresponding target coordinates of the six evenly distributed control points.
[0033] The axial tension is set to 10% (i.e., total longitudinal displacement of 30mm) to ensure that it matches the actual working strain of the flexible skin. Step 2: Cell selection and structural modeling: Cell selection: adopting, for example Figure 2 The concave cell shown has the following characteristic parameter: the angle between the diagonal bars. θ (Core control parameters), rod thickness t =1mm, crossbar length L 1. Length of diagonal brace L2. Cell side length L = 20mm (meets the standard unit cell size of 20mm × 20mm); according to Figure 5 The relationship between the mechanical properties and dimensional parameters shown is used to determine... θ The value range is 60°-80° (within this range) θ It exhibits a stable negative correlation with Poisson's ratio and elastic modulus, facilitating deformation control. Overall structural filling: Refer to Figure 8 (a) Fill loading illustration and Figure 8 (b) The concave filling scheme has a design area size of h×L=300mm×120mm, with 15 concave cells arranged along the longitudinal direction (tension direction) (corresponding to 15 design variables). θ 1 ~ θ 15 Six concave cells are arranged laterally; the thickness and side length of the rods at the cell connections are kept consistent to avoid stress concentration.
[0034] Parameter sampling: Initial parameters are generated using the Latin hypercube sampling method. θ Parameters (random seed set to 20240615 to ensure repeatability), sampling range 60°-80°, 15 design variables. θ 1 ~ θ 15 The initial values are: 74.0°, 68.0°, 75.6°, 73.6°, 65.2°, 78.6°, 64.0°, 70.4°, 76.4°, 62.3°, 71.3°, 66.9°, 79.7°, 72.1°, 69.0°; Step 3: Finite Element Simulation Setup (1) Software and element type: ABAQUS 6.14 was used to build the shell element model, and the element type was S4R (four-node reduced integral shell element, suitable for large deformation analysis). (2) Material parameters: TPU elastomer is selected (to meet the requirements of flexible skin), elastic modulus E s =50MPa, Poisson's ratio μ=0.4; (3) Boundary conditions: Refer to Figure 8 (a) shows the loading diagram, where all degrees of freedom at one longitudinal end (h=0mm) are constrained, and a 30mm axial displacement (10% strain) is applied to the other end (h=300mm). (4) Data extraction: 1000 randomly generated sets of data were extracted. θ Simulations were performed using parameter combinations (including the 15 initial values mentioned above). The L-coordinate and strain distribution data of the 6 control points after tension were extracted to construct a simulation database (900 sets for training and 100 sets for testing). Step 4: Building and Training the Neural Network Agent Model (ANN) (1) Model structure: Refer to Figure 9 The reverse design strategy shown constructs a fully connected neural network with 3 hidden layers: (2) Input layer: 15 neurons (corresponding to 15) θ parameter); (3) Hidden layers: 64, 32, and 16 neurons respectively, with ReLU (adaptive nonlinear mapping learning) as the activation function. (4) Output layer: 12 neurons (corresponding to the h and L coordinates of 6 control points); (5) Training parameters: The Adam optimizer was used (learning rate 0.001, β1=0.9, β2=0.999), the loss function was mean squared error (MSE), the batch size was 32, the training rounds were 500, and the early stopping mechanism was enabled (the training was terminated when the loss decreased by <0.1% for 20 consecutive rounds). (6) Training results: such as Figure 10 As shown in (a), the loss value drops to 10 after 500 training rounds. -3 The following tends to stabilize; such as Figure 10 As shown in (b), the goodness of fit between the predicted coordinates of the test set and the actual simulation coordinates is >99%, proving that the model can learn accurately. θ The mapping relationship with deformation; Step 5: Genetic Algorithm (GA) Parameter Settings (1) Population size: 50 (balancing search efficiency and diversity); (2) Genetic operations: crossover probability 0.7 (preserving superior genes), mutation probability 0.05 (avoiding local optima); (3) Fitness function: The coordinates are predicted using control points ( h predicted ,L predicted ) and target coordinates ( h target , L target The root mean square error (RMSE) of the target value is RMSE < 0.5. Step Six: Optimization and Iteration Round 1: Input Initial Information θ The parameters are as follows: ANN predicts RMSE = 2.8; GA generates 50 new parameters through crossover and mutation; in round 157, RMSE = 0.48 (meets the threshold), iteration stops, and the optimal result is obtained. θParameter combinations: 68.2°, 71.5°, 75.1°, 72.8°, 69.3°, 66.7°, 70.4°, 73.9°, 76.2°, 74.5°, 71.0°, 67.8°, 69.6°, 72.1°, 65.3°; the average deviation between the optimal parameters and the theoretical values is 2.3°, and the maximum deviation is 4.1°, which meets the design accuracy requirements. Step 7: Finite element simulation verification The best θ Import the parameters into the ABAQUS model, repeat step three of the finite element simulation settings, and obtain: The coordinates of control point L are 120.1mm, 125.3mm, 129.8mm, 125.1mm, 120.2mm, and 115.4mm. The maximum deviation from the target value is 0.6mm, and the RMSE is 0.45, proving that the optimal parameters can achieve the deformation of the sine curve. Step 8: Preparation of structural prototypes Reference Figure 11 The concave-shaped sample was prepared using selective laser sintering (EOS P396 equipment): Material: Evonik INFINAM® eTEC 6802 TPU powder (flexible, fatigue-resistant, suitable for skin requirements); Printing parameters: layer thickness 0.1mm, laser power 30W, scanning speed 5.0m / s, chamber temperature 165℃; Post-processing: After printing, the sample was left to stand in the chamber for 4 hours. The final sample size was 300.2mm × 120.3mm × 5.1mm.
[0035] Step Nine: Experimental Testing and Result Analysis In a constant temperature and humidity laboratory environment (temperature 23±1℃, humidity 50±5%), an Instron 5967 electronic universal testing machine (equipped with a 5kN sensor) was used to perform loading tests on the test specimens prepared in the above steps. The specimen clamping distance was set to 320mm, the preload force was 0.5N, and the tensile speed was controlled at 2mm / min until the target displacement was 30mm. Simultaneously, the CorrelatedSolutions VIC-3D system was used to collect deformation data (lens focal length 50mm, speckle size 0.3mm, sampling rate 5Hz). Strain calculations were performed using the Green-Lagrange tensor formula, with a sub-region size of 21×21 pixels and a step size of 7 pixels. Figure 12As shown, the deformation profile of the sample after stretching perfectly matches the sine curve. The measured data shows that the coordinates of the control point L are 120.3mm, 125.5mm, 130.1mm, 125.2mm, 120.4mm, and 115.6mm, with an average absolute error of 0.53mm and a root mean square error (RMSE) of 0.57. The strain field analysis shows that the maximum principal strain of 18.3% is concentrated in the diagonal joint area, with a deviation of less than 2.2% from the simulation prediction of 17.9%. The force-displacement curve test yielded a stiffness coefficient of 85.3N / mm, with an error of only 1.9% from the theoretical prediction of 83.7N / mm. The system verifies the effectiveness and reliability of the design method.
[0036] Although the present invention has been described above with reference to embodiments, various modifications can be made and components can be replaced with equivalents without departing from the scope of the invention. In particular, as long as there is no structural conflict, the features in the disclosed embodiments can be combined with each other in any manner. The lack of an exhaustive description of these combinations in this specification is merely for the sake of brevity and resource conservation. Therefore, the present invention is not limited to the specific embodiments disclosed herein, but includes all technical solutions falling within the scope of the claims.
Claims
1. A method for reverse design and optimization of a two-dimensional deformable and adjustable mechanical structure, characterized in that, The steps are as follows: S1. Determine the target deformation curve and set multiple control points on the target deformation curve and their target coordinates; S2. Select a negative Poisson's ratio cell and define the geometric characteristic parameters of the negative Poisson's ratio cell. The geometric characteristic parameters can control the Poisson's ratio and elastic modulus of the cell. S3. Based on the geometric characteristic parameters of the negative Poisson's ratio cell, construct multiple sets of two-dimensional structural models with different parameter combinations, apply preset loading conditions to each two-dimensional structural model and perform finite element simulation, extract the structural deformation response data corresponding to each set of parameter combinations, and form a simulation database of cell geometric characteristic parameters and deformation response. S4. Using the geometric feature parameters in the simulation database as input and the corresponding deformation response data as output, train a neural network proxy model so that the neural network proxy model has the ability to predict the structural deformation response under given geometric feature parameters. S5. Using the error between the control point coordinates predicted by the neural network surrogate model and the target coordinates as the fitness function, the geometric feature parameters of the negative Poisson ratio cell are iteratively optimized through a genetic algorithm until the fitness function value meets the preset convergence threshold, thereby obtaining the optimal combination of geometric feature parameters. S6. Construct a two-dimensional deformation-adjustable mechanical structure based on the optimal combination of geometric feature parameters, prepare structural samples and test their deformation performance.
2. The reverse design and optimization method for a two-dimensional deformable adjustable mechanical structure according to claim 1, characterized in that, In step S2, the negative Poisson's ratio cell is selected from one or more of the following: concave structure cell, four-ligament chiral structure cell, and perforated structure cell.
3. The reverse design and optimization method for a two-dimensional deformable adjustable mechanical structure according to claim 2, characterized in that, When the negative Poisson's ratio cell is a concave structure cell, its geometric characteristic parameters include the angle of the inclined rod. θ , crossbar length ratio β=L 1 / L , rod thickness ratio γ = t / L , length ratio of diagonal bar μ=L 2 / L ,in L The total length of the concave structural cell. L 1 represents the length of the crossbar. L 2 represents the length of the diagonal brace. t The thickness of the member; the included angle of the diagonal member. θ The value range is 60°-80°, and can be adjusted... θ The value can adjust the Poisson's ratio and elastic modulus of the concave structural cell, and its Poisson's ratio and elastic modulus satisfy: ; ;in, v Poisson's ratio, E For the elastic modulus, ε x and ε y The strains of the concave structure along the X and Y directions are respectively. E s It represents the elastic modulus of the concave structure cell substrate.
4. The reverse design and optimization method for a two-dimensional deformable adjustable mechanical structure according to claim 2, characterized in that, When the negative Poisson's ratio cell is a four-ligament chiral structure cell, its geometric characteristic parameters include the radius of the central circle. r Horizontal center distance L x Longitudinal circle center distance L y , rod thickness t , L The total length of the chiral structure cell is given by the ratio of the radius to the total length of the cell. r / L As a core control parameter, the radius ratio r / L The value range is 0.2-0.4, which can be adjusted... r / L The Poisson's ratio and elastic modulus of the chiral structural cell can be adjusted, and their Poisson's ratio and elastic modulus satisfy the following: ; ;in, v Poisson's ratio, E For the elastic modulus, ε x and ε y The strains of the concave structure along the X and Y directions are respectively. E s It represents the elastic modulus of the concave structure cell substrate.
5. The reverse design and optimization method for a two-dimensional deformable adjustable mechanical structure according to claim 2, characterized in that, When the negative Poisson's ratio cell is a perforated structure cell, its geometric characteristic parameters include the porosity aspect ratio. AR=b / a Spacing ratio IS=c / L ,in a The length of the short axis of the perforation. b The length of the major axis of the perforation. c The perforation spacing, L The overall length of the perforated structure cell should be maintained during the design. L and AR Unchanged, based on spacing ratio IS As a core control parameter, the spacing ratio IS The value range is 0.1-0.3, and it can be adjusted... IS The value can adjust the Poisson's ratio and elastic modulus of the perforated structure cell.
6. The reverse design and optimization method for a two-dimensional deformable adjustable mechanical structure according to claim 1, characterized in that, In step S3, when constructing the two-dimensional structural model, a gradient filling strategy is adopted, specifically: the number of cells in the design area is set to 6×15, that is, 6 cells in the vertical stretching direction and 15 cells in the stretching direction. The size of a single cell is 20mm×20mm, and the overall structural size is h×L=300mm×120mm. The preset loading condition is axial tensile strain of 10%, the boundary condition is set to one end fixed and the other end displacement loading, the structural unit type is shell unit, and the dimensions of the connection between adjacent cells are kept consistent to avoid stress concentration.
7. The reverse design and optimization method for a two-dimensional deformable adjustable mechanical structure according to claim 1, characterized in that, In step S4, the neural network proxy model is a fully connected neural network, including an input layer, three hidden layers, and an output layer; The number of neurons in the input layer is the same as the number of geometric feature parameters of the negative Poisson's ratio cells, and the number of neurons in the output layer is twice the dimension of the control point coordinates. The number of neurons in the three hidden layers are 64, 32, and 16, respectively, and the activation function is ReLU; The model was trained using the Adam optimizer with a learning rate of 0.001, a batch size of 32, and 500 training epochs. An early stopping mechanism was enabled during training, and training was terminated when the validation loss decreased by less than 0.1% for 20 consecutive epochs.
8. The reverse design and optimization method for a two-dimensional deformable adjustable mechanical structure according to claim 1, characterized in that, In step S5, the fitness function is the root mean square error (RMSE) between the predicted coordinates of the control points and the target coordinates, and its calculation formula is as follows: ;in N To control the number of points, i For control point numbers, ( h predicted ,L predicted ) represents the predicted coordinates of the control points, h target ,L target ) represents the target coordinates of the control point, and the preset convergence threshold is RMSE < 1.0; the population size of the genetic algorithm is set to 50, the crossover probability is 0.7, and the mutation probability is 0.
05.
9. The reverse design and optimization method for a two-dimensional deformable adjustable mechanical structure according to claim 1, characterized in that, In step S6, a structural sample is prepared using an additive manufacturing process, specifically selective laser sintering (SLS), and the material used is thermoplastic polyurethane elastomer. During the preparation process, the optimal geometric feature parameters are imported into 3D modeling software to generate a structural model. The laser sintering parameters are set as follows: layer thickness 0.1 mm, laser power 30 W, scanning speed 5.0 m / s, chamber temperature 165 °C. After printing, the sample undergoes a slow cooling process inside the chamber for 4 hours.
10. The reverse design and optimization method for a two-dimensional deformable adjustable mechanical structure according to claim 1, characterized in that, In step S6, the deformation performance test uses a combination of an electronic tensile testing machine and a digital image correlation system. The clamping distance of the electronic tensile testing machine is set to 320 mm, the preload force is 0.5 N, the tensile speed is 2 mm / min, and 10% axial strain is applied. The digital image correlation system has a lens focal length of 50mm, a speckle size of 0.3mm, and a sampling rate of 5Hz. The strain calculation adopts the Green-Lagrange tensor formula. By analyzing the control point coordinates and strain distribution of the actual deformation of the sample, its consistency with the target deformation curve is verified.