CN-121031157-B - Topology optimization method and system for accurately and efficiently regulating structural deformation characteristics

CN121031157BCN 121031157 BCN121031157 BCN 121031157BCN-121031157-B

Abstract

The invention belongs to the field of structural optimization design, and particularly discloses a topological optimization method and a topological optimization system for accurately and efficiently regulating and controlling structural deformation characteristics, wherein the topological optimization method comprises the steps of carrying out finite element mesh subdivision on a structure to be optimized with spring deformation characteristics, and defining design variables corresponding to meshes; determining total strain energy constraint of a structure according to a spring stiffness coefficient and maximum deformation, establishing a first topological optimization model with the aim of minimizing the total volume of the structure, performing topological optimization based on the first topological optimization model to obtain the structure configuration and the total volume of the structure, setting the upper limit of the total volume constraint of the structure according to the total volume, constructing the total volume constraint of the structure, simultaneously taking the total strain energy constraint of the structure of the first topological optimization model as the aim of minimizing the p norm of local deformation errors caused by external force, establishing a second topological optimization model, and performing topological optimization based on the second topological optimization model to obtain the final structure configuration. The invention has the advantages of strong universality, multiple functions, accuracy and high efficiency.

Inventors

LI HAO
YANG BO
JIA SHUNTIAN
MA ZHAOXIN
LIN KEXIN
GAO LIANG

Assignees

华中科技大学

Dates

Publication Date: 20260505
Application Date: 20250717

Claims (8)

1. A topology optimization method for accurately and efficiently regulating structural deformation characteristics is characterized by comprising the following steps: Performing finite element meshing on a structure to be optimized with spring deformation characteristics, and defining design variables corresponding to meshes; Obtaining expected total strain energy of the structure according to the required spring stiffness coefficient and maximum deformation, determining total strain energy constraint of the structure, and establishing a first topological optimization model with the aim of minimizing the total volume of the structure; performing topology optimization based on the first topology optimization model to obtain a structural configuration and total volume thereof ; Based on total volume Setting the upper limit of the total volume constraint of the structure Constructing a total volume constraint of the structure, and simultaneously, constructing a second topological optimization model by taking the p norm of the local deformation error under the action of external force as a target along the total strain energy constraint of the structure of the first topological optimization model; Performing topology optimization based on the second topology optimization model to obtain a final structure configuration; The first topology optimization model is expressed as: In the formula, To design the number of finite element meshes within a domain, 、、 Respectively designing variables, physical variables and volumes corresponding to the ith grid; Is an objective function, namely the total volume of the structure; in the form of a finite element equilibrium equation, Is an array of the external force and is provided with a plurality of external force lines, In order to make the node be in the displacement array, Is a structural overall stiffness matrix; As a function of the total strain energy constraint of the structure, In order to provide a spring stiffness coefficient, Is the maximum deformation; the second topology optimization model is expressed as: In the formula, A set of local area mesh node numbers for external forces to act on, Is a collection Inner first The displacement in the direction of the external force of the individual nodes, An even number greater than 1; As a function of the object to be processed, Is a constraint function of the total volume of the structure.
2. The topological optimization method for precisely and efficiently regulating structural deformation characteristics according to claim 1, wherein for an external force array The external force direction is only parallel to a certain direction in a three-dimensional space Cartesian coordinate system, and all node forces in the array are equal, and the requirements are satisfied: In the formula, A degree-of-freedom numbering array representing the action of external forces, Representing the array Is provided for the length of (a), Representing the array Corresponding node forces.
3. The topological optimization method for accurately and efficiently regulating and controlling the deformation characteristics of the structure according to claim 1, wherein the design variables are pseudo-densities, and the design variables are subjected to density filtering and projection to obtain physical variables which truly reflect the presence or absence of materials in the grid.
4. A method for topologically optimizing the deformation characteristics of a precisely and efficiently tuned structure as claimed in claim 3, wherein a spherical filter or a cylindrical filter is used for density filtering and a Heaviside step function is used for projection.
5. The topological optimization method for precisely and efficiently regulating structural deformation characteristics according to claim 1, wherein the method is based on total volume Setting the upper limit of the total volume constraint of the structure The calculation formula is: In the formula, In order to be a volumetric quantization error, To round up operators.
6. The topology optimization method for precisely and efficiently regulating and controlling structural deformation characteristics according to claim 1, wherein topology optimization is performed based on a first topology optimization model/a second topology optimization model, comprising the steps of: And (3) carrying out finite element analysis on the structure to obtain a displacement field, then calculating the sensitivity of the target and the constraint function relative to the design variable, updating the design variable by adopting a gradient-based optimization algorithm, and repeating the process until the convergence condition is met to obtain the structure configuration.
7. The topological optimization method for precisely and efficiently regulating and controlling the deformation characteristics of a structure according to any one of claims 1 to 6, wherein the structure to be optimized having the spring deformation characteristics is a spring, a leaf spring, a reed or an integrated elastic supporting device.
8. A topology optimization system for precisely and efficiently regulating structural deformation characteristics, comprising a processor for executing the topology optimization method for precisely and efficiently regulating structural deformation characteristics according to any one of claims 1-7.

Description

Topology optimization method and system for accurately and efficiently regulating structural deformation characteristics Technical Field The invention belongs to the field of structural optimization design, and particularly relates to a topological optimization method and a topological optimization system for accurately and efficiently regulating structural deformation characteristics. Background Topology optimization is used as a front edge structure design method based on advanced mathematical algorithm, and aims to search the optimal distribution of materials in space so as to maximize the performances of structural rigidity, frequency and the like or minimize the performances of deformation, quality and the like. The method is widely applied to various fields of aerospace, automobile manufacturing, biomedicine, consumer electronics and the like, can remarkably improve the product performance, can effectively reduce the weight and the cost, and shows great application advantages. In flexible mechanism design, topological optimization can generate a configuration with maximum output displacement, and in maximum displacement constraint or minimization problem, the flexibility and rigidity requirements are effectively balanced. However, aiming at the structural optimization design problems of leaf springs, reeds, integrated elastic supporting devices and the like with spring deformation characteristics, the problems are difficult to directly solve by adopting the method, the current research is limited to the traditional parameter optimization method, and the innovative design of the topological configuration is fresh and has deep exploration. Therefore, the research of the topological optimization method for regulating and controlling the deformation characteristics of the spring is developed, and the method has important significance for breaking through the limit of empirical design, digging a lightweight and high-performance structural model and pushing the integrated design of the flexible mechanism and the elastic element, can fill the gap of the theoretical and application research in the field, and has great engineering application value for improving the performances of precise instruments, buffer equipment and the like. In the research field of deformation characteristics of a regulating structure, most of the existing related methods have obvious defects. Much research heretofore has focused on the topology optimization design of flexible mechanisms to create a configuration with maximum output displacement, but it is difficult to achieve precise regulation of the ratio of external force to maximum deformation in a particular region (i.e., spring stiffness coefficient). And the external force action part and the output displacement part are generally distributed on two sides of the structure, which limits the application of the structure in the structure with the spring deformation characteristic. In addition, a small number of researches disclose topological optimization methods for structure maximum displacement constraint or maximum displacement minimization, but the topological optimization methods can generally only control the maximum deformation (displacement) of a structure not to exceed a specific value, and are difficult to accurately regulate and control the ratio relation between external force and the maximum deformation of a specific area, and the problem of uniform distribution of the maximum deformation cannot be solved. For the traditional spiral spring with fixed modeling, the methods such as parameter optimization and the like are enough to realize performance improvement, but for the structures such as plate springs, reeds, integrated elastic supporting devices and the like, the limitation of parameter optimization technology is large, and no topology optimization method aiming at the problems exists at present. Therefore, it is needed to develop a topology optimization method capable of accurately and efficiently regulating and controlling the deformation characteristics of springs, so as to break the limitation of the traditional design method and obtain a novel topology configuration with better performance. Disclosure of Invention Aiming at the defects or improvement demands of the prior art, the invention provides a topology optimization method and a system for accurately and efficiently regulating and controlling the deformation characteristics of a structure, and aims to realize accurate and efficient topology optimization of the structure with the spring deformation characteristics. In order to achieve the above object, according to an aspect of the present invention, a topology optimization method for accurately and efficiently controlling deformation characteristics of a structure is provided, including the following steps: Performing finite element meshing on a structure to be optimized with spring deformation characteristics, and defining design variables correspon