Quasi-zero stiffness unit cell reverse design method based on neural network and genetic algorithm

Abstract

The invention discloses a quasi-zero stiffness unit cell reverse design method based on a neural network and a genetic algorithm, and the method comprises the steps: firstly carrying out the parametric modeling of a curved beam unit cell through a non-uniform rational B-spline curve, and constructing a large-scale data set containing a curved beam geometric parameter and force-displacement response mapping relation through an automatic simulation scheme; then, a deep neural network forward prediction model is constructed, and second-level prediction from structural parameters to mechanical properties is achieved; and finally, taking the trained deep neural network model as a fitness evaluation function of a genetic algorithm, and constructing a reverse design framework. According to the method, the optimal structure parameters can be automatically generated according to the target constant force requirement, the multi-stage programmable constant force characteristic can be achieved through isomorphic or heterogeneous unit cell combination, and the design efficiency and precision of the constant force compliant mechanism are remarkably improved.

Description

Technical Field

[0001] This invention relates to the field of flexible mechanism design and mechanical metamaterials technology, specifically to a reverse design method for quasi-zero stiffness unit cells based on neural networks and genetic algorithms, which realizes an efficient reverse design method for quasi-zero stiffness unit cells with target constant force characteristics. Background Technology

[0002] In the field of microelectromechanical systems (MEMS) assembly, the requirements for reliable clamping of small, fragile components are extremely high. Compliant grippers transmit motion through the deformation of flexible components, and have advantages such as frictionless, backlash-free, and good passive compliance, making them a core component for achieving precision assembly.

[0003] Traditional constant-force compliant mechanism design heavily relies on iterative finite element analysis and the designer's expert experience. For quasi-zero stiffness structures with large nonlinear deformations, the forward design process is computationally intensive and time-consuming, and it's difficult to directly deduce structural parameters from the target mechanical properties. Furthermore, most existing constant-force mechanisms have short strokes and limited modes, making it difficult to meet the assembly adaptability requirements of multi-sized parts. Summary of the Invention

[0004] The purpose of this invention is to address the problems existing in the prior art by providing a quasi-zero stiffness unit cell reverse design method based on neural networks and genetic algorithms.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A reverse design method for quasi-zero stiffness unit cells based on neural networks and genetic algorithms includes the following steps: S1. The centerline geometry of the unit cell of the elastic curved beam is defined by NURBS curves (non-uniform rational basic-splines). The geometric description equation is constructed by setting several control points and the corresponding weight factors of the control points. S2. Establish geometric constraint functions to exclude curve shapes that do not conform to physical reality. Within the pre-defined design constraint space, randomly generate multiple sets of geometric parameter vectors for structural parameters. Use an automated simulation process to perform finite element static simulation on the three-dimensional model of the curved beam corresponding to each set of structural parameters, obtain its force-displacement response data, and construct a curved beam mapping dataset of structural parameters and mechanical response. S3. Using the geometric parameter vector as input and the corresponding force-displacement response data as output, train a deep neural network to establish a positive prediction model from structural parameters to force-displacement response. S4. Set the target constant force value and the target constant force displacement range. Embed the positive prediction model trained in step S3 into the genetic algorithm as the evaluation function of individual fitness. Use the geometric parameter vector as the chromosome of the genetic algorithm. Use the degree of approximation between the force-displacement curve predicted by the positive prediction model and the target constant force value in the target constant force displacement range as the optimization objective. Run the genetic algorithm for iterative optimization. After the genetic algorithm converges, output the optimal geometric parameter vector that makes the predicted mechanical response closest to the design objective. S5. Based on the optimal geometric parameter vector obtained in step S4, generate the corresponding NURBS curve and curved beam solid model, and connect the two identical curved beam solid models in a symmetrical arrangement to form a unit cell with the target standard zero stiffness characteristics.

[0006] This reverse design method can automatically generate optimal structural parameters based on the target constant force requirement, and can achieve multi-level programmable constant force characteristics through the combination of isomorphic or heteromorphic unit cells, which significantly improves the design efficiency and accuracy of constant force compliant mechanisms.

[0007] Furthermore, in step S1, the NURBS curve is defined by n control points, wherein the spatial positions of the first and last control points are fixed, and the horizontal and vertical coordinates of the middle n-2 control points are designable variables, and all the control points have corresponding weighting factors.

[0008] Furthermore, in step S2, the geometric constraint function is defined by the following logic: , In the formula, Represents geometric constraint functions. , , , , and These represent the first, second, third, fourth, fifth, and sixth constraints, respectively. , Used to control the NURBS curve of the curved beam within the rectangular space defined by the first and last control points. Given the range of weights for the last four control points, In It refers to curves The radius of curvature is used to ensure that a smooth curved beam can be generated without reporting sweep errors during subsequent software sweeping along this curve. Used to prevent the included angle of the lines connecting control points from being too small. Used to prevent curves from crossing themselves. ω i As a weighting factor, and respectively represent the abscissa and ordinate of the sampling data control point, and i is a natural number greater than 1.

[0009] Furthermore, in step S2, the force-displacement response data is processed by normalized stiffness, and the normalized stiffness is defined as: , In the formula, F r is the reaction force at the right end face of the curved beam, with the unit of N, the unit of Young's modulus E is MPa, and the geometric parameters b and l have the unit of mm. After conversion, the normalized stiffness K N is a dimensionless number to eliminate the influence of absolute material and dimensional quantities, and focus on the effect of geometric shape on mechanical properties.

[0010] Furthermore, in step S2, the automated simulation process uses the programming language script supporting the finite element simulation software to automatically read the sampled structural parameters (geometric parameter vector), automatically establish the three-dimensional model of the curved beam, automatically divide the element mesh, automatically apply the load and boundary conditions; automatically extract the force-displacement response data after the nonlinear static analysis, and clean the original structural parameter data to eliminate the samples with non-convergence or singular solutions.

[0011] Furthermore, the programming language script includes a template script and a main control script. The template script is used to read the CSV file containing the curve coordinate points and generate a curve sketch, establish a rectangular cross-section and sweep along the curve to generate the three-dimensional model of the solid curved beam, create an analysis step and enable the geometric nonlinear option, apply the boundary conditions, perform mesh division, submit the job and save the result file of the three-dimensional model of the curved beam to an independent folder, and finally output the end face reaction force to a new CSV file; the main control script is responsible for passing the paths of the input and output table files to the template script, and implementing multi-threaded batch scheduling, calculating the normalized stiffness data of the force-displacement response data, storing the structural parameters and normalized stiffness files of the curved beam corresponding to the numbers, and constructing a complete mapping data set of the curved beam.

[0012] Furthermore, in step S3, the deep neural network is a fully connected feedforward network with multiple hidden layers, using the ReLU activation function, and using the mean square error as the loss function for training; the forward prediction model is regarded as a nonlinear operation function, receiving the input vector from the input layer and returning the predicted value of the output vector.

[0013] Furthermore, in step S4, the fitness function is defined as: , In the formula, F 0 This refers to the target constant force value, where n and m correspond to the initial and final displacements within the target constant force range, respectively. u 1 and u 2 The numbering in the dimension of the reaction force vector. It is the prediction value of the neural network in the j-th dimension; the optimization objective is to find suitable structural parameters under constraints such that Minimum.

[0014] Furthermore, the unit cell includes isomorphic unit cells and heteromorphic unit cells. The series and / or parallel connection of the isomorphic unit cells, and the series connection of the heteromorphic unit cells, constitute different constant force units. The different constant force units are connected in series at different levels to form a multi-level quasi-zero stiffness metamaterial.

[0015] Furthermore, let the constant force value of the unit cell be... F t The constant force range is d 0 The combination configuration of series and parallel unit cells is represented digitally using matrices. The combination configuration of n isomorphic unit cells connected in series is denoted as matrix [n;1], and the constant force value is obtained. F t constant force range of lower multiples nd 0 The configuration of m isomorphic unit cells connected in parallel is denoted as matrix [1;m]. In the constant force interval... d 0 The constant force value obtained is a multiple. mF t The configuration of isomorphic unit cells arranged in i rows and j columns is denoted as matrix [i;j], which yields the multiple constant force values ​​in the multiple constant force interval. jF t ; After assembling isomorphic unit cells into constant force units with different constant force properties, p constant force units are then connected in series according to the magnitude of the constant force, where the configuration of the k-th constant force unit is as follows. There is a constant force range n k d 0 constant force value m k F t And let Then we obtain the results in the constant force interval respectively. The constant force values ​​obtained above are respectively The p-level constant force characteristic is that the length of the constant force interval is consistent and the constant force value increases step by step under continuous stroke.

[0016] Compared with existing technologies, the beneficial effects of this invention are as follows: 1. This quasi-zero stiffness unit cell reverse design method based on neural networks and genetic algorithms can overcome the problems of high computational cost, long design cycle, and reliance on expert experience in existing quasi-zero stiffness unit design methods. It can realize user input of target constant force value and displacement range, and the system automatically outputs the optimal structural parameters that meet the requirements and constructs the unit cell accordingly; 2. This reverse design method can use deep neural networks to replace time-consuming simulation calculations and combine them with genetic algorithms to search for optimal structural parameters in the entire domain, quickly generating quasi-zero stiffness structures that meet specific constant force value requirements; at the same time, this reverse design method and optimization scheme can also provide a design scheme for metamaterials that perform other functions; 3. In terms of computational efficiency, the forward prediction neural network trained using this reverse design method only requires 0.166 seconds, which greatly reduces the time cost required to calculate the fitness function when the genetic algorithm optimizes the design; 4. The introduction of the forward prediction model allows the genetic algorithm to select a larger population size and number of iterations to improve the optimization effect of the algorithm. Attached Figure Description

[0017] Figure 1 This is a schematic diagram illustrating the process of establishing the NURBS curved beam dataset in the unit cell reverse design method of this invention; Figure 2 This is a schematic diagram illustrating the influence of different material parameters on the normalized stiffness of the same curved beam according to the present invention. Figure 3 This is a schematic diagram of the ABAQUS batch processing simulation process using Python scripts according to the present invention. Figure 4 This is a schematic diagram of the deep neural network forward prediction model of the present invention; Figure 5 This is a schematic diagram of the NURBS curved beam reverse design model based on genetic algorithm and neural network of the present invention; Figure 6 This is a schematic diagram of the NURBS curve and mechanical properties obtained from the reverse design model when the expected constant force value of the curved beam is 0.20 N. Figure 7 This is a schematic diagram of the quasi-zero stiffness unit cell obtained by reverse design in this invention. Figure 8 This is a schematic diagram of the multi-level design strategy for programmable quasi-zero stiffness metamaterials of the present invention; Figure 9 This is a schematic diagram of the multi-level constant force combination strategy of the isomorphic unit cell of the present invention; Figure 10 This is a schematic diagram of the multi-level constant force combination strategy of the heterogeneous unit cell of the present invention; Figure 11 This is a schematic diagram of the statics of the quasi-zero stiffness unit cell 1 of the present invention; Figure 12 This is a schematic diagram illustrating the three-level constant force characteristic analysis of the isomorphic unit cell array of the present invention; Figure 13 This is a schematic diagram of the statics of the quasi-zero stiffness unit cells 2 and 3 of the present invention; Figure 14 This is a schematic diagram illustrating the three-level constant force characteristic analysis of heterogeneous unit cells 1, 2, and 3 connected in series according to the present invention; In the figure: 1, unit cell; 101, curved beam; 102, moving end; 103, fixed end. Detailed Implementation

[0018] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are merely some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] In the description of this invention, it should be noted that the terms "middle", "upper", "lower", "left", "right", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0020] A reverse design method for quasi-zero stiffness unit cells based on neural networks and genetic algorithms includes the following steps: S1. The centerline geometry of the elastic curved beam unit cell is defined using NURBS curves, by setting n control points. P i and the weighting factors corresponding to the control points ω i Construct the geometric description equation; S2. Establish geometric constraint functions to exclude curve shapes that do not conform to physical reality. Within the pre-defined design constraint space (the space constrained by the geometric constraint functions), randomly generate multiple sets of geometric parameter vectors for structural parameters. Use an automated simulation process to perform finite element static simulation on the three-dimensional model of the curved beam corresponding to each set of structural parameters, obtain its force-displacement response data, and construct a curved beam mapping dataset of structural parameters and mechanical response. S3. Using the geometric parameter vector as input and the corresponding force-displacement response data as output, train a deep neural network to establish a positive prediction model from structural parameters to force-displacement response. S4. Set the target constant force value and the target constant force displacement range. Embed the positive prediction model trained in step S3 into the genetic algorithm as the evaluation function of individual fitness. Use the geometric parameter vector as the chromosome of the genetic algorithm. Use the degree of approximation between the force-displacement curve predicted by the positive prediction model and the target constant force value in the target constant force displacement range as the optimization objective. Run the genetic algorithm for iterative optimization. After the genetic algorithm converges, output the optimal geometric parameter vector that makes the predicted mechanical response closest to the design objective. S5. Based on the optimal geometric parameter vector obtained in step S4, generate the corresponding NURBS curve and curved beam solid model, and connect two identical curved beam solid models in a symmetrical arrangement to form a unit cell with the target standard zero stiffness characteristic. The curved beam solid model is a solidified three-dimensional curved beam model in the computer, or it can be a physical model made by 3D printing or other methods.

[0021] This reverse design method for quasi-zero stiffness unit cells, based on neural networks and genetic algorithms, overcomes the problems of high computational cost, long design cycle, and reliance on expert experience in existing quasi-zero stiffness element design methods. It allows users to input target constant force values ​​and displacement ranges, and the system automatically outputs the optimal structural parameters that meet the requirements, constructing the unit cell accordingly. This reverse design method utilizes deep neural networks to replace time-consuming simulation calculations and combines them with genetic algorithms to search for optimal structural parameters across the entire domain, rapidly generating quasi-zero stiffness structures that meet specific constant force requirements. Furthermore, this reverse design method and optimization scheme can also provide a design solution for metamaterials performing other functions.

[0022] In terms of computational efficiency, calculating the force-displacement curves of 10,000 curved beams using the finite element method takes 40 hours, while the forward prediction neural network trained using this reverse design method only takes 0.166 seconds, significantly reducing the time cost required to calculate the fitness function during genetic algorithm optimization. The introduction of the forward prediction model allows the genetic algorithm to select a larger population size and a greater number of iterations to improve the optimization effect.

[0023] Furthermore, in step S1, the NURBS curve is defined by n control points, wherein the spatial positions of the first and last control points are fixed, and the horizontal and vertical coordinates of the middle n-2 control points are designable variables, and all the control points have corresponding weighting factors.

[0024] Furthermore, in step S2, the geometric constraint function is defined by the following logic: , In the formula, Represents geometric constraint functions. , , , , and These represent the first, second, third, fourth, fifth, and sixth constraints, respectively. , This is used to control the NURBS curve of the curved beam within a two-dimensional rectangular space defined by the first and last control points, so as to avoid its basis functions being too non-uniform. Given the range of weights for the last four control points, In It refers to curves The radius of curvature is used to ensure that a smooth curved beam can be generated without reporting sweep errors during subsequent software sweeping along this curve. Used to prevent the included angle of the lines connecting control points from being too small. Used to prevent curves from crossing themselves. ω i As a weighting factor, and Let i represent the x-coordinate and y-coordinate of the control point in the sampled data, respectively, where i is a natural number greater than 1.

[0025] Under constraints , Below, within the range , , By randomly assigning values ​​to the internal structural parameter θ, accurate to three decimal places, a specified number of distinct curves can be generated. However, the diversity of spline curves can also lead to the problem of curve self-intersection; therefore, constraints are introduced. This constraint function can effectively prevent curves from self-crossing.

[0026] Specifically, such as Figure 1 As shown, the process of establishing the NURBS curved beam mapping dataset is as follows: First, calculate the NURBS curve according to the formula based on the curve parameters. By randomly selecting values ​​for the input parameters within a certain range, multiple non-repeating and diverse NURBS curve shapes can be obtained. Store the structural parameters of the curve design and the horizontal and vertical coordinates of the corresponding points on the curve in a table file. Second, import the curve coordinate data into ABAQUS software for batch geometric nonlinear static simulation, and store the reaction force data output by each curved beam simulation. Finally, store the structural parameters of the curve and the reaction force data obtained from the simulation accordingly to obtain the curved beam mapping dataset. In this embodiment, a NURBS curve with five control points is used to define the curved beam shape, with l=15mm and h=7.5; a quadratic polynomial spline basis function is selected, i.e., the curve degree is p=2, and the open node vector is determined. . Randomly generate N = 15,000 NURBS curves, and record their variable structure parameters respectively , and extract the abscissa and ordinate of 100 points on the curve into a sequentially numbered csv table file. The three-dimensional model of the curved beam is generated by sweeping a rectangular cross-section along a spline curve. Select the cross-sectional dimensions of the curved beam as t = 1.2 mm and b = 10 mm to construct the TPU curved beam dataset. After finite element verification, the maximum stress meets the allowable requirements.

[0027] Furthermore, in step S2, the force-displacement response data is processed by normalized stiffness, and the normalized stiffness is defined as: , In the formula, F r is the reaction force at the right end face of the curved beam, with the unit of N, the unit of Young's modulus E is MPa, and the geometric parameters b and l have the unit of mm. After conversion, the normalized stiffness K N is a dimensionless number to eliminate the influence of absolute material and dimensional quantities, and focus on the effect of geometric shape on mechanical properties.

[0028] For the same three-dimensional model of the curved beam, finite element simulations of static analysis are performed with different material parameters, and the normalized stiffness is obtained as Figure 2 shown. It can be seen that different material parameters have little influence on the normalized stiffness of the same structure. The normalized stiffness can be used as the performance index of the curved beam output to more accurately reflect the influence of the curve shape on the mechanical properties of the curved beam. Subsequently, the mechanical properties can be predicted quickly according to different real material parameters.

[0029] Furthermore, in step S2, the automated simulation process uses the programming language script supporting the finite element simulation software to automatically read the sampled structure parameters (geometric parameter vectors), automatically establish the three-dimensional model of the curved beam, automatically divide the element mesh, automatically apply loads and boundary conditions; automatically extract the load-displacement data (force-displacement response data) after nonlinear static analysis, and clean the original structure parameter data (sampled sample data), and剔除 samples that do not converge or have singular solutions.

[0030] Batch simulation analysis is performed on the TPU curved beams generated by 15,000 NURBS curves. Using ABAQUS software, batch processing operations are implemented through Python scripts. The flow chart is as Figure 3As shown. Specifically, template scripts and master scripts for parametric statics simulation were written to enable batch submission and result storage of finite element tasks. The template script is used to read a CSV file containing curve coordinate points and generate a curve sketch, establish a rectangular cross-section and sweep along the curve to generate a solid 3D model of the curved beam, create an analysis step and enable the geometric nonlinearity option, apply boundary conditions, perform mesh generation, submit the job and save the 3D model result file of the curved beam to a separate folder, and finally output the end face reaction force to a new CSV file. The master script is responsible for passing the paths of the input and output table files to the template script, implementing multi-threaded batch scheduling, calculating the normalized stiffness data of the force-displacement response data, storing the structural parameters of the curved beam and the normalized stiffness file according to their corresponding numbers, and constructing a complete curved beam mapping dataset.

[0031] Furthermore, in step S3, the deep neural network is a fully connected feedforward network containing multiple hidden layers, employs the ReLU activation function, and uses mean squared error as the loss function for training; the forward prediction model is regarded as a nonlinear operation function that receives input vectors from the input layer and returns the predicted value of the output vector.

[0032] Furthermore, in step S4, the fitness function of the genetic algorithm... Defined as: , In the formula, F 0 This refers to the target constant force value, where n and m correspond to the initial and final displacements within the target constant force range, respectively. u 1 and u 2 The numbering in the dimension of the reaction force vector. It is the prediction value of the neural network in the j-th dimension; the optimization objective is to find suitable structural parameters under constraints such that Minimum.

[0033] Specifically, deep neural network positive prediction models, such as Figure 4 As shown, the forward prediction model of a deep neural network can be viewed as a non-linear computational function that receives an input vector X from the input layer and returns the predicted value of the output vector h: , The activation function chosen is ReLU, the first... l The first layer j one neuron and the previous layer of neurons The relationship can be calculated using the following expression: , , in, and Here are the network parameters, and x is the activation function. The independent variable.

[0034] Mean squared error is used as the loss function to calculate the error of the forward prediction model of the deep neural network. : , In the formula, N tr It is the number of samples in the training set. h i and y i These are the DNN numbers. i The estimated and true values ​​of each output. By finding suitable network parameters, the estimated and true values ​​can be obtained. L Minimum.

[0035] To make training more likely to find the global optimum, the data is preprocessed. This includes preprocessing the geometric parameters of the input layer. The input data is scaled using Z-score normalization. , in, These are the original geometric parameters (structural parameters) in the dataset. and The first The mean and standard deviation of each geometric parameter characteristic. It is standardized network input data.

[0036] The mechanical data of the output layer is mapped to the range [0,1] using Min-Max normalization according to the following formula. The reaction force of each data sample is obtained by uniformly sampling the force-displacement curve at equal intervals, and the corresponding displacement value is uniformly distributed in the interval [0,h].

[0037] , , in, It is the normalized stiffness of the j-th output value. It is the processed network output data. and These represent the minimum and maximum values ​​of the j-th output value in the dataset, respectively. It is the restored normalized stiffness. It is the j-th predicted value output by the network.

[0038] A DNN with four hidden layers, each containing 160 neurons, is used. The input data is 10-dimensional, and the output data is 100-dimensional, with a total of 95,140 network parameters. Backpropagation is used to calculate the gradient of the loss function with respect to the network parameters, and the Adam algorithm is used as the gradient descent optimizer. L2 regularization is introduced to constrain the network weights, and weight decay is set to reduce model complexity. An early stopping strategy is applied so that the model stops training prematurely if the training set error does not decrease after a certain number of iterations.

[0039] Using the average coefficient of determination As an indicator for evaluating the prediction accuracy of neural networks.

[0040] , in, It is the true value of the reaction force of the i-th sample in the j-th dimension, generated by the finite element method. It is the predicted reaction force value of the network at that point. This is the number of samples in the test set. It is the average of the true values ​​in the j-th dimension: , Average error of training set for: .

[0041] In the formula, It is the number of samples in the training set. err i This represents the error of the i-th sample.

[0042] A positive prediction model for the transformation from the design parameters of the curved beam to the force-displacement curve was obtained. The average coefficient of determination on the test set was 0.9913, and the average prediction error was 3.0873%. The results show that the positive prediction model can predict the mechanical properties of the curved beam well.

[0043] Furthermore, in order to solve for the structural parameters with the target mechanical response, a structural parameter inverse design model combining a forward prediction model and a genetic algorithm is adopted.

[0044] Its computational model is as follows Figure 5 As shown, for design variables For optimization, the constraint function of the genetic algorithm is the boundary condition of the design variables. In the design of NURBS curved beams with a constant force range, the optimization objective of the genetic algorithm is to minimize the mean absolute error between the reaction force value and the target constant force value within the target zero stiffness range. For the genetic algorithm part of the inverse design model, the population size is set to 1000, the crossover rate to 0.9, and the mutation rate to 0.1. The algorithm terminates after the 300th iteration to obtain the optimized solution for the design variables. The tournament selection operator is used to implement the selection operation step, and the simulated binary crossover operator is used to implement the crossover operation.

[0045] Figure 6 Demonstrates the design goal of constant force The NURBS curves of the optimal solution of the inverse design model, the predicted values ​​of the curved beam reaction force and displacement, and the curves of the finite element solution are shown for different target displacement ranges at 0.15N and 0.20N. The curve shows that the actual constant force range can cover the target constant force range, indicating that the inverse design model can generate the corresponding NURBS curve parameters based on the target constant force value and the target displacement range, and the constant force value and displacement range can be freely selected within the achievable range.

[0046] Connecting two identical curved beam models in a symmetrical arrangement creates a unit cell with zero stiffness at the target standard, such as... Figure 7 As shown, the upper part of the curved beam 101 is the movable end 102, and the lower part is the fixed end 103, which are connected to form an integral structure to form the unit cell 1.

[0047] like Figure 8 As shown, a design strategy is proposed, from NURBS curved beams to quasi-zero stiffness unit cells to multi-level constant force elements.

[0048] The unit cell includes isomorphic unit cells and heteromorphic unit cells. The series and / or parallel connection of the isomorphic unit cells, as well as the series connection of the heteromorphic unit cells, constitute different constant force units. The different constant force units are connected in series at different levels to form a multi-level quasi-zero stiffness metamaterial.

[0049] like Figure 9 As shown in (a), according to Hooke's Law, the series and parallel stiffness combination law of connected springs, when the unit cells are connected in parallel, the deformation of all the units is the same as the overall deformation, and the sum of the forces on all the units is equal to the total force, so the multiple constant force value can be obtained; when the unit cells are connected in series, the force on all the units is equal to the external force, and the sum of the deformations of all the units is equal to the overall deformation, so the multiple constant force range can be obtained.

[0050] Let the constant force value of the unit cell be... F t The constant force range is d 0The combination configuration of series and parallel unit cells is represented digitally using matrices. The combination configuration of n isomorphic unit cells connected in series is denoted as matrix [n;1], and the constant force value is obtained. F t constant force range of lower multiples nd 0 The configuration of m isomorphic unit cells connected in parallel is denoted as matrix [1;m]. In the constant force interval... d 0 The constant force value obtained is a multiple. mF t The configuration of isomorphic unit cells arranged in i rows and j columns is denoted as matrix [i;j], which yields the multiple constant force values ​​in the multiple constant force interval. jF t ; By combining isomorphic unit cells into constant force units with different constant force characteristics using the above strategies, and then connecting these constant force units in series according to the magnitude of the constant force, multi-stage constant force output characteristics can be obtained. For example... Figure 9 As shown in (b), p constant force units are connected in series, where the configuration of the k-th constant force unit is as follows: There is a constant force range n k d 0 constant force value m k F t And let Then we obtain the results in the constant force interval respectively. The constant force values ​​obtained above are respectively The p-level constant force characteristic is that the length of the constant force interval is consistent and the constant force value increases step by step under continuous stroke.

[0051] like Figure 10 As shown, by sequentially connecting quasi-zero stiffness unit cells with different constant force values, a mechanism with multi-level constant force characteristics can be constructed. Compared with the strategy of combining isomorphic unit cells, this strategy of connecting heterogeneous unit cells has the advantages of simple structure and small overall size. The force-displacement results conform to the multi-level constant force strategy of connecting heterogeneous unit cells, and the resulting constant force characteristics at each level conform to the constant force characteristics of each quasi-zero stiffness unit cell.

[0052] Figure 11-14 This is a case study of a quasi-zero stiffness unit cell designed in practice and combined into a multi-stage constant force mechanism. For Figure 11 The unit cell shown is modeled and statically analyzed using the [1,1,1; 1,2,3] configuration, and the results are as follows. Figure 12As shown. When three layers of constant force elements are connected in series, the overall displacement is the sum of the displacements of each layer. In the finite element analysis, the maximum total displacement applied to the top surface is 30 mm. The results conform to the aforementioned multi-level constant force combination law, yielding a three-level constant force characteristic with consistent constant force interval length and progressively increasing constant force value under continuous stroke.

[0053] Selecting different curved beam structures with quasi-zero stiffness unit cells 2 and 3, such as Figure 13 As shown, zero-stiffness unit cells 1, 2, and 3 are connected in series with increasing constant force values. The bottom surface of unit cell 3 is used as the fixed end, and the top surface of unit cell 2 is used as the moving end. A displacement of 30 mm is applied to the three-stage series heterogeneous unit cells. The static analysis is as follows: Figure 14 As shown.

[0054] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A reverse design method for quasi-zero stiffness unit cells based on neural networks and genetic algorithms, characterized in that, It includes the following steps: S1. Define the centerline geometric configuration of the elastic curved beam unit cell using NURBS curves, and construct a geometric description equation by setting a number of control points and the corresponding weight factors of the control points; S2. Establish a geometric constraint function to exclude curve forms that do not conform to physical reality. Within a pre-set design constraint space, randomly generate multiple geometric parameter vectors of structural parameters. Use an automated simulation process to perform finite element static simulation on the three-dimensional curved beam model corresponding to each set of structural parameters, obtain its force-displacement response data, and construct a curved beam mapping data set of structural parameters and mechanical responses; S3. Use the geometric parameter vector as the input and the corresponding force-displacement response data as the output to train a deep neural network and establish a forward prediction model from structural parameters to force-displacement responses; S4. Set a target constant force value and a target constant force displacement interval. Embed the forward prediction model trained in step S3 into a genetic algorithm as an evaluation function for individual fitness. Use the geometric parameter vector as the chromosome of the genetic algorithm, and use the approximation degree between the force-displacement curve predicted by the forward prediction model within the target constant force displacement interval and the target constant force value as the optimization goal, and run the genetic algorithm for iterative optimization. After the genetic algorithm converges, output the optimal geometric parameter vector that makes the predicted mechanical response closest to the design goal; S5. Generate the corresponding NURBS curve and curved beam solid model according to the optimal geometric parameter vector obtained in step S4, and connect two identical curved beam solid models in a symmetric layout to form a unit cell with the target zero stiffness characteristic.

2. The quasi-zero stiffness unit cell reverse design method based on neural networks and genetic algorithms according to claim 1, characterized in that, In step S1, the NURBS curve is defined by n control points, where the spatial positions of the first and last control points are fixed, and the abscissas and ordinates of the middle n - 2 control points are design variables, and all the control points have corresponding weight factors.

3. The quasi-zero stiffness unit cell reverse design method based on neural networks and genetic algorithms according to claim 1, characterized in that, In step S2, the geometric constraint function is defined by the following logic: ， In the formula, Represents geometric constraint functions. , , , , and These represent the first, second, third, fourth, fifth, and sixth constraints, respectively. , Used to control the NURBS curve of the curved beam within the rectangular space defined by the first and last control points. Given the range of weights for the last four control points, In It refers to curves The radius of curvature is used to ensure that a smooth curved beam can be generated without reporting sweep errors during subsequent software sweeping along this curve. Used to prevent the included angle of the lines connecting control points from being too small. Used to prevent curves from crossing themselves. ω i As a weighting factor, and Let i represent the x-coordinate and y-coordinate of the control point in the sampled data, respectively, where i is a natural number greater than 1.

4. The quasi-zero stiffness unit cell reverse design method based on neural networks and genetic algorithms according to claim 1, characterized in that, In step S2, the force-displacement response data is processed by normalized stiffness, and the normalized stiffness is defined as: , In the formula, F r It is the reaction force on the right end face of the curved beam, in N, and Young's modulus. E The unit is MPa, geometric parameters b and l The unit is mm, which is used to calculate the normalized stiffness. K N It is a dimensionless number, which eliminates the influence of absolute material and size dimensions and focuses on the effect of geometry on mechanical properties.

5. The quasi-zero stiffness unit cell reverse design method based on neural networks and genetic algorithms according to claim 1, characterized in that, In step S2, the automated simulation process uses the programming language script supporting the finite element simulation software to automatically read the sampled structural parameters, automatically establish the three-dimensional curved beam model, automatically divide the unit mesh, automatically apply loads and boundary conditions; automatically extract the force-displacement response data after nonlinear static analysis, and clean the original structural parameter data to eliminate samples that do not converge or have singular solutions.

6. The quasi-zero stiffness unit cell reverse design method based on neural networks and genetic algorithms according to claim 5, characterized in that, The programming language script includes a template script and a main control script. The template script is used to read a CSV file containing curve coordinate points and generate a curve sketch, establish a rectangular cross-section and sweep along the curve to generate a solid 3D model of the curved beam, create an analysis step and enable the geometric nonlinearity option, apply boundary conditions, perform mesh generation, submit the job and save the 3D model result file of the curved beam to a separate folder, and finally output the end face reaction force to a new CSV file. The main control script is responsible for passing the paths of the input and output table files to the template script, implementing multi-threaded batch scheduling, calculating the normalized stiffness data of the force-displacement response data, storing the structural parameters of the curved beam and the normalized stiffness file according to their corresponding numbers, and constructing a complete curved beam mapping dataset.

7. The quasi-zero stiffness unit cell reverse design method based on neural networks and genetic algorithms according to claim 1, characterized in that, In step S3, the deep neural network is a fully connected feedforward network containing multiple hidden layers, which uses the ReLU activation function and the mean squared error as the loss function for training; the forward prediction model is regarded as a non-linear operation function that receives the input vector from the input layer and returns the predicted value of the output vector.

8. The quasi-zero stiffness unit cell reverse design method based on neural networks and genetic algorithms according to claim 1, characterized in that, In step S4, the fitness function of the genetic algorithm Defined as: ， In the formula, F 0 This refers to the target constant force value, where n and m correspond to the initial and final displacements within the target constant force range, respectively. u 1 and u 2 The numbering in the dimension of the reaction force vector. It is the prediction value of the neural network in the j-th dimension; the optimization objective is to find suitable structural parameters under constraints such that Minimum.

9. The quasi-zero stiffness unit cell reverse design method based on neural networks and genetic algorithms according to claim 1, characterized in that, The unit cell includes isomorphic unit cells and heteromorphic unit cells. The series and / or parallel connection of the isomorphic unit cells, as well as the series connection of the heteromorphic unit cells, constitute different constant force units. The different constant force units are connected in series at different levels to form a multi-level quasi-zero stiffness metamaterial.

10. The quasi-zero stiffness unit cell reverse design method based on neural networks and genetic algorithms according to claim 9, characterized in that, Let the constant force value of the unit cell be... F t The constant force range is d 0 The combination configuration of series and parallel unit cells is represented digitally using matrices. The combination configuration of n isomorphic unit cells connected in series is denoted as matrix [n;1], and the constant force value is obtained. F t constant force range of lower multiples nd 0 The configuration of m isomorphic unit cells connected in parallel is denoted as matrix [1;m]. In the constant force interval... d 0 The constant force value obtained is a multiple. mF t The configuration of isomorphic unit cells arranged in i rows and j columns is denoted as matrix [i;j], which yields the multiple constant force values ​​in the multiple constant force interval. jF t ; After assembling isomorphic unit cells into constant force units with different constant force properties, p constant force units are then connected in series according to the magnitude of the constant force, where the configuration of the k-th constant force unit is as follows. , There is a constant force range n k d 0 constant force value m k F t And let Then we obtain the results in the constant force interval respectively. The constant force values ​​obtained above are respectively The p-level constant force characteristic is that the length of the constant force interval is consistent and the constant force value increases step by step under continuous stroke.

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