Dot matrix metamaterial design method based on fast restart intelligent algorithm

Abstract

The present application relates to a kind of lattice metamaterial design method based on fast restart intelligent algorithm, the present application proposes the improved ESPSO algorithm based on fast restart strategy, realizes the efficient solution of lattice metamaterial multidimensional design variable.Periodically refreshes the optimization process of algorithm using fast restart strategy, avoids the risk of algorithm falling into local convergence, ensures that algorithm can explore design space more in detail, fully to obtain global optimal solution, in the premise of guaranteeing in same running number, the solution obtained by improved ESPSO algorithm can be more optimal.For the design of lattice metamaterial under complex service conditions, the present application uses improved ESPSO intelligent algorithm to realize the independent design of all rod diameters in lattice metamaterial cell, and allows lattice rod to delete and increase, significantly improves the design flexibility of lattice metamaterial, fully expands the design space of lattice metamaterial, improves the mechanical properties of lattice metamaterial.

Description

Technical Field

[0001] This invention relates to a method for designing lattice metamaterials, and in particular to a method for designing lattice metamaterials based on a fast restart intelligent algorithm. Background Technology

[0002] Lattices are high-porosity materials composed of unit cells made up of rods arranged periodically in space. They possess superior mechanical advantages such as light weight, high specific strength / stiffness, and high impact energy absorption rate, as well as excellent multifunctional properties such as thermal insulation, sound insulation, vibration reduction, and biocompatibility. They have extremely important application value in many fields such as aerospace, marine, automotive, defense, and biomedicine. Currently, most lattice metamaterial configuration designs are based on experiments or empirical improvements, making it difficult to obtain innovative lattice configurations. Research on the mechanical properties of lattice metamaterials mainly focuses on their inherent mechanical properties, with less consideration given to optimizing the mechanical properties of lattice metamaterials under complex service conditions. This results in the underutilization of the design space of lattice metamaterials, severely restricting the improvement of their mechanical properties. Intelligent optimization algorithms have advantages such as simple principles, convenient implementation, and easy convergence to the global optimum. They have wide applications in complex optimization problems (minimization) and are very suitable for finding free configuration optimizations of lattice metamaterials under complex service conditions.

[0003] For the optimized design of lattice metamaterials, some related research has been conducted by those skilled in the art. For example, reference 1, "S.Wang, Y.Ma, Z.Deng, Stretching-dominated truss lattice materials: Elastic anisotropy evaluation, control, and design, Composite Structures, 2022, 298:116004," proposes an analytical homogenization formula that treats lattice geometric parameters, matrix material properties, and load direction as independent variables, achieving anisotropic design of tension-dominated lattice materials. However, this method does not further optimize the configuration of lattice materials to fully explore the design space and realize the material's potential. Reference 2: "L.Bai C.Gong X.Chen J.Zheng J.Yang K.Li Y.Sun Heterogeneous compressive responses of additively manufactured Ti-6Al-4V lattice structures by varying geometric parameters of cells, International Journal of Mechanical Sciences, 2022, 214:106922." This paper designs lattice materials with different morphologies and relative densities by adjusting the geometric parameters of the lattice unit cells to obtain customized mechanical properties. However, this method does not consider the lattice material configuration design under actual service conditions, and cannot fully utilize the material potential to improve the structural mechanical properties. Reference 3: "Maurizi M,Gao C,Berto F.Inverse design of truss latticematerials with superior buckling resistance.npj Computational Materials, 2022,8(1):247." This paper proposes an assembly-based lattice material design method based on deep learning and genetic algorithms, which obtains lattice materials with excellent buckling resistance by assembling lattice unit cells with different configurations. However, this method does not consider the optimization of the unit cell configuration of the lattice material, and all members in the lattice unit cell have the same diameter, which limits the design space of the lattice material and cannot fully improve the structural mechanical properties.

[0004] This invention addresses the challenge of designing high-performance lattice metamaterials under complex service conditions. Based on an approximate model-assisted particle swarm optimization (ESPSO) algorithm, it proposes an intelligent optimization design method for lattice metamaterials with free configurations. This method targets the mechanical properties of lattice materials under complex service conditions. By independently optimizing the geometric parameters of each component of the lattice metamaterial, and selectively removing lattice components with low load-bearing efficiency during the optimization process, it fully explores the lattice design space, obtaining innovative designs for the lattice metamaterial configuration to maximize its mechanical properties. Furthermore, to address the risk of the ESPSO algorithm getting stuck in local convergence, this invention employs a fast restart strategy to periodically refresh the optimization process of the intelligent algorithm, proposing an improved ESPSO algorithm to ensure that the algorithm can explore the design space more thoroughly and fully to obtain the global optimum, while guaranteeing the stability and efficiency of the algorithm's iterative convergence process. Summary of the Invention

[0005] To address the above problems, this invention provides a lattice metamaterial design method based on a fast restart intelligent algorithm.

[0006] The present invention adopts the following technical solution:

[0007] A design method for lattice metamaterials based on a fast restart intelligent algorithm includes the following steps:

[0008] Step 1: The lattice structure consists of periodically repeating lattice metamaterial unit cells, which are selected as the objects to be optimized. The lattice metamaterial unit cells to be optimized are constructed by connecting predefined nodes using rods. Each lattice rod consists of a cylinder and two spheres at its ends. The geometry of the cylinder and spheres is described using explicit topological functions based on level sets, thus achieving an explicit geometric description of the lattice rods. The rods are then used to connect the predefined nodes, forming the initial design of the lattice metamaterial unit cell.

[0009] The explicit topological description model of the lattice rod based on level sets is as follows:

[0010]

[0011] in

[0012] φ(x)=max(φ c (x,y,z),φ s1 (x,y,z),φ s2 (x,y,z)),

[0013] φ c (x,y,z)=min(φ c1 (x,y,z),φ c2 (x,y,z)),

[0014] φ c1 (x,y,z)=(L / 2) 2 -(cosθ·L d ) 2 ,φ c2 (x,y,z)=(t / 2) 2 -(sinθ·L d ) 2 ,

[0015]

[0016]

[0017]

[0018] φ s1 (x,y,z)=(t / 2) 2 -(x-x1) 2 +(y-y1) 2 +(z-z1) 2 ,

[0019] φ s2 (x,y,z)=(t / 2) 2 -(x-x2) 2 +(y-y2) 2 +(z-z2) 2

[0020] In the formula, The Ω represents the spatial design domain of the lattice metamaterial, and the Ω represents the solid region where the rod-like part is located. Let φ be the boundary of the bar structure. The lattice bar consists of a cylinder and two spheres, with horizontal set functions φ and φ', respectively. c (x,y,z), φ c1 (x,y,z), φ c2 (x, y, z); the centers of the ends of the cylinder are (x1, y1, z1) and (x2, y2, z2), and are also the centers of the two spheres, that is, the diameter t of the cylinder is equal to the diameter of the two spheres. (x0, y0, z0) and L are the coordinates of the center point of the cylinder and the length of the rod, respectively.

[0021] Step 2: Taking the minimization of the overall flexibility of the lattice structure under complex service conditions as the optimization objective, establish a mathematical optimization model with the diameters of each member of the lattice metamaterial unit cell as design variables:

[0022] Find: t = (t1, t2, ..., t j ),j=1,2,...,D

[0023] Minimize: C(t) = F T U = U T KU

[0024] Subjectto:G(t)=V(t)-fV0≤0,

[0025] F = KU,

[0026] 0≤t min ≤t j ≤t max .

[0027] Where t1, t2, ..., t j Let be the diameter of the different members to be determined, D be the total number of members, C be the overall flexibility of the lattice structure, F be the total load matrix, U be the total displacement matrix under load, K be the overall stiffness matrix of the lattice structure, G be the volume ratio constraint of the lattice structure, V(t) and V0 be the material region volume and design domain volume of the lattice unit cell, respectively, f be the given material volume ratio, and t be the design domain volume. min and t max These are the upper and lower limits of the rod diameter;

[0028] Step 3: Use the improved ESPSO algorithm to find the optimal diameter for each member. The specific steps are as follows:

[0029] Step 3.1: Generate an initial population. Each particle in the population has D dimensions. The position of the particle in each dimension represents the possible diameter of a rod. There are a total of D dimensions representing the possible diameters of all rods.

[0030] Step 3.2: Use Radial Basis Function (RBF) to establish the global and local approximation models in the particle swarm optimization algorithm. The global approximation model is built based on all evaluated particle points in the entire design space, while the local approximation model is built in the neighborhood of the particle.

[0031] Step 3.3: Update the velocity and position of the particles using the following strategy to obtain the optimal position of the particles, and delete particles whose rod diameter is smaller than a preset threshold during the optimization process to obtain the optimal position of the particles in this iteration.

[0032]

[0033] xid (t+1)= xid (t)+ vid (t+1)

[0034] in

[0035]

[0036] d represents the d-th dimension of the optimization problem, v i (t)=[v i1 (t),v i2 (t),...,v id [(t)] and x i (t)=[x i1 (t),x i2 (t),...,x id [(t)] represents the velocity and position of the i-th particle in the t-th iteration, respectively. i (t)=[p i1 (t),p i2 (t),...,p id [(t)] represents the historical best position reached by the i-th particle of an individual. g (t)=[p g1 (t),p g2 (t),...,p gd [(t)] is the global optimal position for all particles. X is the predicted response value of a global RBF model constructed from all particles in the design space; Gbest It is its optimal value point in the entire design space, that is, the global optimal position. It is composed of particle p i (t) The predicted response of the local RBF model composed of particles in the neighborhood; X Nbest It is the optimal value point in its neighborhood, that is, the local optimum position. Particle p i (t) The position is updated by tracking these two optimal values. r1 and r2 are two random numbers uniformly distributed in the range [0,1]; c1 and c2 are acceleration factors, usually with values ​​greater than zero. Where φ = c1 + c2. Usually φ is greater than 4, so c1 and c2 are each 2.05. k is a constant in the range [0,1], usually with a value of 0.729;

[0037] Step 3.4: Determine if the maximum number of iterations has been reached. If yes, proceed to the next step; otherwise, update the population using the optimal particle position obtained in this iteration and repeat Step 3.1.

[0038] Step 3.5: Output the optimal position of the particle obtained in the last iteration, and obtain the optimal diameter value of each rod corresponding to the optimal particle.

[0039] Furthermore, in step 3.1, for the global approximation model, the number of sample points is consistent with the pre-determined number of particle swarms, which is generally set to 30; for the local approximation model, the number of sample points is generally set to be greater than 5D.

[0040] Furthermore, in step 3.4, the maximum number of iterations is 3 or more.

[0041] Compared with the prior art, the present invention, by adopting the above technical solution, has the following advantages:

[0042] 1. The technical solution provided by this invention proposes a novel free-configuration lattice metamaterial design method compared with existing lattice metamaterial design methods. Specifically, it realizes the independent design of the diameter of all rods within the lattice unit cell and allows the removal of rods with low load-bearing efficiency within the lattice unit cell, thereby improving the design flexibility of lattice metamaterials, expanding the design space of lattice metamaterials, and thus fully enhancing the mechanical properties of lattice metamaterials.

[0043] 2. This invention achieves explicit description and precise control of the geometric configuration of lattice metamaterials by employing an explicit topological geometric description function based on level sets, and ensures the smoothness and clarity of the geometric boundaries of the lattice metamaterials.

[0044] 3. This invention proposes an improved ESPSO algorithm based on a fast restart strategy, achieving efficient solutions for multidimensional design variables of lattice metamaterials. While maintaining the same number of runs, the new approach yields a better solution. In other words, to obtain the same optimal solution, the new method requires fewer iterations. Because the fast restart strategy periodically refreshes the algorithm's optimization process, it avoids the risk of intelligent optimization algorithms getting stuck in local convergence, ensuring that the algorithm can explore the design space more thoroughly and fully to obtain the global optimum, while also guaranteeing the stability and efficiency of the iterative convergence process.

[0045] 4. This invention provides a free-configuration lattice metamaterial design method based on a fast restart intelligent algorithm. This method not only optimizes the geometric parameters of each member within the lattice metamaterial but also allows for the deletion and addition of lattice members, enabling free design of lattice metamaterial configurations for complex service conditions. Compared to traditional lattice material design, this method significantly expands the design space of lattice materials, fully utilizes the material's potential, and effectively improves the mechanical properties of lattice materials while reducing structural weight.

[0046] The present invention will now be described in detail with reference to the accompanying drawings and embodiments. Attached Figure Description

[0047] Figure 1 Figure (a) shows a schematic diagram of the design domain of the four-point support structure, and Figure (b) shows a schematic diagram of the initial design configuration of the lattice unit cell.

[0048] Figure 2 Figure (a) shows the initial design schematic of the lattice unit cell, and Figure (b) shows the optimal design structure.

[0049] Figure 3Figure (a) shows the initial design of the lattice unit cell and its elastic modulus surface plot; Figure (b) shows the optimal design of the lattice unit cell and its elastic modulus surface plot.

[0050] Figure 4 A schematic diagram of the optimal 3×3×3 periodic arrangement of lattice unit cells;

[0051] Figure 5 A schematic diagram of the optimal 3×3×3 periodic arrangement of lattice unit cells;

[0052] Figure 6 A schematic diagram of the final lattice design for a four-point support structure;

[0053] Figure 7 This is a flowchart of the method of the present invention. Detailed Implementation

[0054] The principles and features of the present invention are described below with reference to the accompanying drawings. The examples given are only for explaining the present invention and are not intended to limit the scope of the present invention.

[0055] The principles and features of the present invention are described below with reference to the accompanying drawings. The embodiments are illustrated using a four-point support structure. The examples given are only for explaining the present invention and are not intended to limit the scope of the present invention.

[0056] To achieve the above objectives, according to the present invention, a method for designing free-configuration lattice metamaterials based on a fast restart intelligent algorithm is provided, the method comprising the following steps:

[0057] (a) The lattice metamaterial unit cell to be optimized is constructed by connecting predefined nodes with rods. Each rod consists of a cylinder and spheres at its two ends. The spheres ensure a perfect connection between the two rods at the nodes. The geometry of the cylinder and the two spheres is described using an explicit geometric topological function based on level sets. First, the design domain of the 3D lattice unit cell to be optimized is discretized into a finite element mesh. The coordinates of the finite element mesh nodes represent the positions of the nodes in space. A four-dimensional level set function is formed by defining level set values ​​on the nodes within the 3D lattice design domain. The level set values ​​represent the minimum distance from the node to the structural boundary. The zero isosurface of the four-dimensional level set function is the structural boundary of the 3D lattice. Unlike the traditional method of defining level set functions using free functions or radial basis functions, this invention defines level set functions using mathematical relationships between spheres and cylinders with explicit mathematical relations. This achieves an explicit description of the structural geometric boundary of the 3D lattice, enabling precise control of the structural geometric features by adjusting the level set function parameters. Subsequently, the predefined nodes are connected using the described rods to form the initial design of the three-dimensional lattice unit cell.

[0058] (b) Taking the lattice structure under complex service conditions as the optimization object, the lattice structure is discretized into several periodic lattice unit cells. First, the equivalent elastic tensor of the three-dimensional lattice unit cell is calculated using the homogenization method, and the element stiffness matrix of the lattice unit cell is further calculated. Then, the global stiffness matrix of the entire lattice structure is obtained by assembling the element stiffness matrix of the lattice unit cells, and the overall flexibility of the entire lattice structure is obtained by finite element analysis. Subsequently, with the given material volume ratio of the lattice unit cell as a constraint, the optimization objective is to minimize the overall flexibility of the lattice structure under complex service conditions. A mathematical optimization model is established with the diameter of each member of the lattice unit cell as the design variable.

[0059] (c) The improved ESPSO algorithm is used to efficiently solve the mathematical optimization model in step (b), and the globally optimal particle is the optimal solution of the model. First, the initial particle swarm size of the ESPSO algorithm is set, which is generally five times the number of design variables, and the fitness of each particle is evaluated. At the same time, the deletion threshold of the design variables is set.

[0060] Secondly, the velocity and position of the particles are updated using the optimal solution information of the global and local approximation models, and particles smaller than the deletion threshold are assigned 0. Then, the volume fraction of the lattice structure is calculated based on the optimal particles found by the algorithm to see if it meets the volume ratio constraint. If it does, the compliance of the lattice structure is calculated by optimizing the model. If it does not meet the constraint, a better particle is searched again.

[0061] Finally, a restart strategy is used to periodically refresh the algorithm optimization process, so that the optimal particle from the previous optimization becomes the initial particle for the next optimization. This ensures a more thorough exploration of the design space to obtain the global optimal solution, ultimately resulting in a performance-optimized multi-parameter lattice structure.

[0062] As a further preferred embodiment, in step (a), taking a three-dimensional lattice unit cell as an example, the explicit topological description model of the lattice rods based on the level set is as follows:

[0063]

[0064] in

[0065] φ(x)=max(φ c (x,y,z),φ s1 (x,y,z),φ s2 (x,y,z)),

[0066] φ c (x,y,z)=min(φ c1 (x,y,z),φ c2 (x,y,z)),

[0067] φ c1(x,y,z)=(L / 2) 2 -(cosθ·L d ) 2 ,φ c2 (x,y,z)=(t / 2) 2 -(sinθ·L d ) 2 ,

[0068]

[0069] φ s1 (x,y,z)=(t / 2) 2 -(x-x1) 2 +(y-y1) 2 +(z-z1) 2 ,

[0070] φ s2 (x,y,z)=(t / 2) 2 -(x-x2) 2 +(y-y2) 2 +(z-z2) 2

[0071] In the formula, The Ω represents the spatial design domain of the lattice metamaterial, and the Ω represents the solid region where the rod-like part is located. Let φ be the boundary of the bar structure. The lattice bar consists of a cylinder and two spheres, with horizontal set functions φ and φ', respectively. c (x,y,z), φ c1 (x,y,z), φ c2 (x, y, z); the centers of the ends of the cylinder are (x1, y1, z1) and (x2, y2, z2) respectively, and are also the centers of the two spheres, i.e., the diameter of the cylinder. t It equals the diameter of the two spheres. (x0, y0, z0) and L are the coordinates of the center point of the cylinder and the length of the rod, respectively.

[0072] As a further preferred embodiment, in step (b), the formula for calculating the equivalent elastic tensor of the lattice unit cell using the homogenization method can be expressed as:

[0073]

[0074] Where |Y| represents the volume of the lattice unit cell, and i,j,k,l=1,2,3,...,d is the spatial dimension of the design problem. This represents the initial unit test strain, which in a three-dimensional problem contains six independent unit strains, namely (1,0,0,0,0,0). T (0,1,0,0,0,0) T(0,0,1,0,0,0) T (0,0,0,1,0,0) T (0,0,0,0,1,0) T (0,0,0,0,0,1) T . The unknown strain field is generated within the lattice unit cell after the initial element test strain field is applied, and can be obtained by solving the following linear elastic equilibrium equation:

[0075]

[0076] In the formula, ν i It is a virtual displacement field. It represents the kinematically permissible displacement space under periodic boundary conditions.

[0077] After obtaining the equivalent elastic tensor of the unit cell, the element stiffness matrix k of the lattice unit cell is... e The following formula can be used for calculation:

[0078]

[0079] Among them, Ω m Let be the domain of the m-th finite element, Ne be the total number of finite elements, and B be the strain-displacement matrix.

[0080] The global stiffness matrix K of the lattice structure can be obtained by assembling the element stiffness matrix, as shown in the following equation:

[0081]

[0082] After obtaining the overall stiffness matrix, the displacement field of the lattice structure can be obtained by solving the equilibrium equations of the lattice structure, and the overall compliance value of the lattice structure can be further calculated.

[0083] F = KU

[0084] C = F T U = U T KU

[0085] As a further preferred embodiment, in step (b), the geometric description parameters of the lattice unit cell are used as design variables, the given material usage is used as a constraint, and the overall compliance of the lattice structure is minimized as the objective function. The optimization mathematical model is constructed as shown in the following equation:

[0086] Find: t = (t1, t2, ..., t j ),j=1,2,...,D

[0087] Minimize: C(t) = F T U = U TKU

[0088] Subjectto:G(t)=V(t)-fV0≤0,

[0089] F = KU,

[0090] 0≤t min ≤t j ≤t max .

[0091] Where t1, t2, ..., t j Let be the diameter of the different members to be determined, D be the total number of members, C be the overall flexibility of the lattice structure, F be the total load matrix, U be the total displacement matrix under load, K be the overall stiffness matrix of the lattice structure, G be the volume ratio constraint of the lattice structure, V(t) and V0 be the material region volume and design domain volume of the lattice unit cell, respectively, f be the given material volume ratio, and t be the design domain volume. min and t max These are the upper and lower limits of the rod diameter;

[0092] As a further preferred embodiment, in step (c), the ESPSO algorithm is used to find the optimal diameter value for each member of the three-dimensional lattice unit cell. By introducing the BRF approximation model, global and local approximation models in the particle swarm optimization algorithm are established. The global approximation model is constructed based on all evaluated particle points throughout the entire design space, while the local approximation model is constructed within the neighborhood regions of the particles. The RBF model used in this invention is defined as follows: assuming there are n sample points x1, x2, ..., x... n ∈R D Their responses are f(x1), f(x2), ... f(x) n If n are n samples, then the RBF approximation model established from these n sample points can be expressed as:

[0093]

[0094] Where Φ i (·) represents the i-th basis function, ||·|| is the Euclidean norm, and λ i Let φ(r) be the weight coefficient of the i-th basis function. This paper uses the cubic basis function: φ(r) = r 3 Furthermore, p(x) is a first-order polynomial: b T x+a. To establish an accurate global and local approximation model, for the global approximation model, the number of sample points is consistent with the pre-determined particle swarm number, which is generally set to 30; for the local approximation model, the number of sample points is generally set to be greater than 5D, where D is the number of design variables.

[0095] To further improve the optimization efficiency of the approximate model cooperative PSO algorithm, a new strategy is adopted in the ESPSO algorithm to update the particle velocity, and the update method is as follows:

[0096]

[0097] xid (t+1)= xid (t)+ vid (t+1)

[0098] in

[0099]

[0100] d is the d-th dimension of the optimization problem, v i (t)=[v i1 (t),v i2 (t),...,v id [(t)] and x i (t)=[x i1 (t),x i2 (t),...,x id [(t)] represents the velocity and position of the i-th particle in the t-th iteration, respectively. i (t)=[p i1 (t),p i2 (t),...,p id [(t)] represents the historical best position reached by the i-th particle of an individual. g (t)=[p g1 (t),p g2 (t),...,p gd [(t)] is the global optimal position for all particles. X is the predicted response value of a global RBF model constructed from all particles in the design space; Gbest It is its optimal value point in the entire design space, that is, the global optimal position. It is composed of particle p i (t) The predicted response of the local RBF model composed of particles in the neighborhood; X Nbest It is the optimal value point in its neighborhood, that is, the local optimum position. Particle p i (t) The position is updated by tracking these two optimal values. r1 and r2 are two random numbers uniformly distributed in the range [0,1]; c1 and c2 are acceleration factors, usually with values ​​greater than zero. Where φ = c1 + c2. Usually φ is greater than 4, so c1 and c2 are each 2.05. k is a constant in the range [0,1], usually with a value of 0.729.

[0101] To further expand the design space of the lattice unit cell and unleash the material's potential, the ESPSO algorithm allows the removal of lattice members with low load-bearing efficiency during the optimization process, thereby improving the mechanical performance of the lattice structure. Simultaneously, to address the risk of the ESPSO algorithm easily getting trapped in local convergence, this invention employs a fast restart strategy to periodically refresh the intelligent algorithm's optimization process. This ensures that multiple iterations of the optimization algorithm are achieved under the same computational cost, allowing the algorithm to explore the design space more thoroughly to obtain the globally optimal solution.

[0102] 1) Deletion Strategy: As the optimization process progresses, the main load-bearing members will gradually thicken, while the secondary load-bearing members will gradually thin. If a member's load is too low, i.e., its load-bearing efficiency is too low, its diameter t should be 0, indicating that the member is deleted to improve material utilization and enhance lattice mechanical properties. Specifically, during the optimization process, when t is less than a set threshold, i.e., t... n <t min (Deletion threshold), then t n The diameter is assigned a value of 0, meaning the nth member is deleted. Deletion threshold t min It is generally set as the minimum structural size allowed during the manufacturing process or the minimum mesh size of the precise FEA.

[0103] 2) Restart Strategy: Particle swarm optimization (PSO) algorithms based on surrogate models enable the entire population to evolve from disordered to ordered evolution by sharing particle information. However, due to the influence of the transition to the optimal solution, it is prone to getting trapped in local convergence. Without a suitable mechanism, it is impossible to escape the local trap, resulting in a lack of diversity in results and even a lack of high-quality solutions. To address this, this invention proposes an improved algorithm based on a restart strategy to avoid the algorithm getting trapped in local convergence. Once the population gets trapped in local convergence, the restart mechanism redistributes the population particles in space and guides them to search for better solutions in the global region based on the previously found optimal solution.

[0104] The above description provides examples of the preferred embodiments of the present invention. Parts not detailed herein are common knowledge to those skilled in the art. The scope of protection of the present invention is determined by the claims. Any equivalent modifications based on the technical teachings of the present invention are also within the scope of protection of the present invention.

Claims

1. A method for designing lattice metamaterials based on a fast restart intelligent algorithm, characterized in that, Includes the following steps: Step 1: Establish a lattice structure model. The lattice structure consists of periodically repeating lattice metamaterial unit cells. Take the lattice metamaterial unit cell as the object to be optimized. The lattice metamaterial unit cell to be optimized is a lattice rod formed by connecting predefined nodes through rods. The lattice rod consists of a cylinder and two spheres located at its two ends. The geometry of the cylinder and spheres is described by an explicit topological function based on level sets to realize the explicit geometric description of the lattice rod. The rods are used to connect the predefined nodes to form the initial design of the lattice metamaterial unit cell. The explicit topological description model of the lattice rod based on level sets is as follows: in φ(x)=max(φ c (x,y,z),φ s1 (x,y,z),φ s2 (x,y,z)), ϕ c (x,y,z)=min(φ c1 (x,y,z),φ c2 (x,y,z)), φ c1 (x,y,z)=(L / 2) 2 -(cosθ·L d ) 2 ,φ c2 (x,y,z)=(t / 2) 2 -(sinθ·L d ) 2 , d x2 =x2-x0,d y2 =y2-y0,d z2 =z2-z0,d x =x-x0,d y =y-y0,d z =z-z0, ϕ s1 (x,y,z)=(t / 2) 2 -(x-x1) 2 +(y-y1) 2 +(z-z1) 2 , ϕ s2 (x,y,z)=(t / 2) 2 -(x-x2) 2 +(y-y2) 2 +(z-z2) 2 In the formula, The Ω represents the spatial design domain of the lattice metamaterial, and the Ω represents the solid region where the rod-like part is located. The boundary of the bar structure; the lattice bar consists of a cylinder and two spheres, with their horizontal set functions φ and φ, respectively. c (x,y,z), φ c1 (x,y,z), φ c2 (x,y,z); the centers of the ends of the cylinder are (x1,y1,z1) and (x2,y2,z2), and are also the centers of the two spheres, that is, the diameter t of the cylinder is equal to the diameter of the two spheres; (x0,y0,z0) and L are the coordinates of the center point of the cylinder and the length of the rod, respectively; Step 2: Taking the minimization of the overall flexibility of the lattice structure under complex service conditions as the optimization objective, establish a mathematical optimization model with the diameters of each member of the lattice metamaterial unit cell as design variables: Find:t=(t1,t2,...,t j ),j=1,2,...,D Minimize:C(t)=F T U=U T KU Subjectto:G(t)=V(t)-fV0≤0, F = KU, 0≤t min ≤t j ≤t max . Where t1, t2, ..., t j Let be the diameter of the different members to be determined, D be the total number of members, C be the overall flexibility of the lattice structure, F be the total load matrix, U be the total displacement matrix under load, K be the overall stiffness matrix of the lattice structure, G be the volume ratio constraint of the lattice structure, V(t) and V0 be the material region volume and design domain volume of the lattice unit cell, respectively, f be the given material volume ratio, and t be the design domain volume. min and t max These are the upper and lower limits of the rod diameter; Step 3: Use the improved ESPSO algorithm to find the optimal diameter for each member. The specific steps are as follows: Step 3.1: Generate an initial population. Each particle in the population has D dimensions. The position of the particle in each dimension represents the possible diameter of a rod. There are a total of D dimensions representing the possible diameters of all rods. Step 3.2: Use radial basis functions to establish the global RBF model and local RBF model in the particle swarm optimization algorithm. The global RBF model is built based on all evaluated particle points in the entire design space, while the local RBF model is built in the neighborhood of the particle. Step 3.3: Update the velocity and position of the particles using the following strategy to obtain the optimal position of the particles, and delete particles whose rod diameter is smaller than a preset threshold during the optimization process to obtain the optimal position of the particles in this iteration. xid (t+1)= xid (t)+ vid (t+1) in d represents the d-th dimension of the optimization problem, v i (t)=[v i1 (t),v i2 (t),...,v id [(t)] and x i (t)=[x i1 (t),x i2 (t),...,x id [(t)] represents the velocity and position of the i-th particle in the t-th iteration; p i (t)=[p i1 (t),p i2 (t),...,p id [(t)] is the historical best position reached by the i-th particle; p g (t)=[p g1 (t),p g2 (t),...,p gd [(t)] is the global optimal position of all particles; X is the predicted response value of a global RBF model constructed from all particles in the design space; Gbest It is its optimal value point in the entire design space, that is, the globally optimal position; It is composed of particle p i (t) The predicted response of the local RBF model composed of particles in the neighborhood; X Nbest It is its optimal value point in the neighborhood, that is, its local optimal position; particle p i (t) The position is updated by tracking the two optimal values; r1 and r2 are two random numbers uniformly distributed in the range [0,1]; c1 and c2 are acceleration factors; where φ = c1 + c2; Step 3.4: Determine if the maximum number of iterations has been reached. If yes, proceed to the next step; otherwise, update the population using the optimal particle position obtained in this iteration and repeat Step 3.

1. Step 3.5: Output the optimal position of the particle obtained in the last iteration, and obtain the optimal diameter value of each rod corresponding to the optimal particle.

2. The lattice metamaterial design method based on a fast restart intelligent algorithm according to claim 1, characterized in that, In step 3.1, for the global approximation model, the number of sample points is consistent with the pre-determined number of particle swarms; for the local approximation model, the number of sample points is generally set to be greater than 5D.

3. The lattice metamaterial design method based on a fast restart intelligent algorithm according to claim 1, characterized in that, In step 3.4, the maximum number of restarts is 3 or more.

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