CN-116151062-B - Multi-constraint geometric nonlinear level set topology optimization method, equipment and medium

Abstract

The application discloses a multi-constraint geometric nonlinear level set topology optimization method, equipment and medium, which are used for solving the problem that the level set method of the current linear condition is difficult to perform good optimization on the large deformation condition of a member to be optimized. The method comprises the steps of dividing a design domain corresponding to a member to be optimized into a plurality of finite element units, establishing a corresponding level set radial basis function based on volume constraint, introducing a displacement constraint item and a frequency constraint item according to the relation between the unit strain increment and the node displacement increment of the finite element units, expanding a Lagrange function, calculating to obtain a unit thermal load and an overall thermal load according to nonlinear unit unbalanced force, and performing topological optimization on the design domain based on the expanded Lagrange function and the overall thermal load of the member to be optimized at a set temperature. The application considers displacement constraint and frequency constraint under non-linearity, is suitable for the member to be optimized under the condition of large deformation, and can achieve the optimal topological result.

Inventors

• XU AN
• WANG SUJUN
• ZHAO RUOHONG
• FU JIYANG
• WU JIURONG

Assignees

• 广州大学

Dates

Publication Date

20260512

Application Date

20221215

Claims (8)

1. 1. A multi-constraint geometric nonlinear level set topology optimization method, comprising: Dividing a design domain corresponding to a member to be optimized into a plurality of finite element units, and establishing a corresponding level set radial basis function based on volume constraint; Determining an incremental strain matrix corresponding to the unit strain increment and the node displacement increment according to the virtual work equation of the finite element unit; Obtaining a unit balance equation according to the virtual work equation and the incremental strain matrix; based on the unit balance equation, adopting an increment column method to represent the relationship between the unit stress increment and the strain increment, and determining the relationship between the unit strain increment and the node displacement increment; Introducing a displacement constraint term and a frequency constraint term according to the relation between the unit strain increment and the node displacement increment of the finite element unit, and expanding the Lagrangian function; calculating to obtain a unit thermal load and an overall thermal load according to the nonlinear unit unbalanced force; Performing topological optimization on the design domain based on the expanded Lagrangian function and the overall thermal load of the member to be optimized at the set temperature; The expanding the Lagrangian function specifically comprises: Decomposing the incremental strain matrix to obtain a first matrix irrelevant to node displacement and a second matrix relevant to node displacement; and determining a unit stiffness equation in an increment form according to the first matrix, the second matrix and the relation between the unit strain increment and the node displacement increment, and obtaining an overall increment equation.
2. 2. The method of claim 1, wherein the finite element elements comprise holes and mesh nodes; the establishing a corresponding level set radial basis function based on volume constraint specifically comprises the following steps: according to the distance between the hole and the grid node, combining a two-dimensional multiple spline basis function to establish a level set radial basis function; based on the condition of the unique solution of the level set radial basis function interpolation, constraint is carried out on the generalized expansion coefficient in the level set radial basis function, and the level set radial basis function is updated according to the boundary constraint condition; and establishing a volume constraint model based on the updated level set radial basis function to obtain a level set radial basis function based on volume constraint.
3. 3. The method according to claim 1, wherein the introducing a displacement constraint term and a frequency constraint term expands a lagrangian function, specifically comprising: introducing a displacement constraint term comprising a displacement Lagrangian multiplier and a displacement increment; Introducing a frequency constraint term comprising a frequency Lagrangian multiplier and a frequency increment; an extended Lagrangian function is determined that is comprised of an objective function, a volume constraint term, the displacement constraint term, and a frequency constraint term.
4. 4. The method according to claim 1, wherein the calculating the cell thermal load and the overall thermal load based on the nonlinear cell imbalance force comprises: determining a temperature initial strain; in the calculation of nonlinear cell imbalance forces, determining cell thermal loads according to the overall cell node forces, the overall internal forces of the structure and the temperature initial strain; Adding the unit thermal loads to obtain an overall thermal load.
5. 5. The method according to claim 1, wherein the member to be optimized is a deformed structure having a degree of deformability exceeding a preset threshold.
6. 6. The method of claim 5, wherein the method further comprises: and setting corresponding displacement limit and frequency limit according to the allowable deformable range of the scene to which the deformation structure is applied.
7. 7. A multi-constraint geometrically nonlinear level set topology optimization device, comprising: A memory, a processor and a computer program stored on the memory and executable on the processor, which when executed by the processor performs the method steps of: Dividing a design domain corresponding to a member to be optimized into a plurality of finite element units, and establishing a corresponding level set radial basis function based on volume constraint; Determining an incremental strain matrix corresponding to the unit strain increment and the node displacement increment according to the virtual work equation of the finite element unit; Obtaining a unit balance equation according to the virtual work equation and the incremental strain matrix; based on the unit balance equation, adopting an increment column method to represent the relationship between the unit stress increment and the strain increment, and determining the relationship between the unit strain increment and the node displacement increment; Introducing a displacement constraint term and a frequency constraint term according to the relation between the unit strain increment and the node displacement increment of the finite element unit, and expanding the Lagrangian function; calculating to obtain a unit thermal load and an overall thermal load according to the nonlinear unit unbalanced force; Performing topological optimization on the design domain based on the expanded Lagrangian function and the overall thermal load of the member to be optimized at the set temperature; The expanding the Lagrangian function specifically comprises: Decomposing the incremental strain matrix to obtain a first matrix irrelevant to node displacement and a second matrix relevant to node displacement; and determining a unit stiffness equation in an increment form according to the first matrix, the second matrix and the relation between the unit strain increment and the node displacement increment, and obtaining an overall increment equation.
8. 8. A computer storage medium storing computer executable instructions, the computer executable instructions configured to: Dividing a design domain corresponding to a member to be optimized into a plurality of finite element units, and establishing a corresponding level set radial basis function based on volume constraint; Determining an incremental strain matrix corresponding to the unit strain increment and the node displacement increment according to the virtual work equation of the finite element unit; Obtaining a unit balance equation according to the virtual work equation and the incremental strain matrix; based on the unit balance equation, adopting an increment column method to represent the relationship between the unit stress increment and the strain increment, and determining the relationship between the unit strain increment and the node displacement increment; Introducing a displacement constraint term and a frequency constraint term according to the relation between the unit strain increment and the node displacement increment of the finite element unit, and expanding the Lagrangian function; calculating to obtain a unit thermal load and an overall thermal load according to the nonlinear unit unbalanced force; Performing topological optimization on the design domain based on the expanded Lagrangian function and the overall thermal load of the member to be optimized at the set temperature; The expanding the Lagrangian function specifically comprises: Decomposing the incremental strain matrix to obtain a first matrix irrelevant to node displacement and a second matrix relevant to node displacement; and determining a unit stiffness equation in an increment form according to the first matrix, the second matrix and the relation between the unit strain increment and the node displacement increment, and obtaining an overall increment equation.

Description

Multi-constraint geometric nonlinear level set topology optimization method, equipment and medium Technical Field The application relates to the technical field of topology optimization, in particular to a multi-constraint geometrical nonlinear level set topology optimization method, equipment and medium. Background The Level Set (Level Set) method is one of the main centralized topology optimization methods at present, and has the main advantages that the boundary of an optimization result is smooth, and compared with the optimization results of a variable density (SIMP) method, a Bi-directional evolution (Bi-directional Evolutionary Structural Optimization, BESO) method and the like, the Level Set method can avoid the problem of boundary jaggy or checkerboard phenomenon. The current level set method generally takes the flexibility of the structure as an objective function under the linear condition and takes the volume fraction of the structure as a constraint condition. Wherein the volume fraction represents the ratio of the volume of the optimized solid material to the volume of the original design domain. However, in practical engineering, the member to be optimized is inevitably subjected to large deformation, namely, geometric nonlinearity, which cannot be considered by the level set method of the current linear condition, and the problem of non-ideal optimization results is caused. Disclosure of Invention The embodiment of the application provides a multi-constraint geometric nonlinear level set topology optimization method, equipment and medium, which are used for solving the problem that the level set method of the current linear condition is difficult to perform good optimization on the large deformation condition of a member to be optimized. The embodiment of the application provides a multi-constraint geometrical nonlinear level set topology optimization method, which comprises the following steps: Dividing a design domain corresponding to a member to be optimized into a plurality of finite element units, and establishing a corresponding level set radial basis function based on volume constraint; Introducing a displacement constraint term and a frequency constraint term according to the relation between the unit strain increment and the node displacement increment of the finite element unit, and expanding the Lagrangian function; calculating to obtain a unit thermal load and an overall thermal load according to the nonlinear unit unbalanced force; And performing topological optimization on the design domain based on the expanded Lagrangian function and the overall thermal load of the member to be optimized at the set temperature. In one example, the finite element unit comprises holes and grid nodes, the establishing of the corresponding level set radial basis function based on volume constraint specifically comprises the steps of combining a two-dimensional multiple spline basis function according to the distance between the holes and the grid nodes, establishing the level set radial basis function, interpolating a unique solution based on the level set radial basis function, constraining generalized expansion coefficients in the level set radial basis function, updating the level set radial basis function according to boundary constraint conditions, and establishing a volume constraint model based on the updated level set radial basis function to obtain the level set radial basis function based on the volume constraint. In one example, before the displacement constraint item and the frequency constraint item are introduced according to the relation between the unit strain increment and the node displacement increment of the finite element unit, the method further comprises the steps of determining an increment strain matrix corresponding to the unit strain increment and the node displacement increment according to a virtual work equation of the finite element unit, obtaining a unit balance equation according to the virtual work equation and the increment strain matrix, expressing the relation between the unit stress increment and the node displacement increment by adopting an increment column method based on the unit balance equation, and determining the relation between the unit strain increment and the node displacement increment. In one example, according to the relation between the unit strain increment and the node displacement increment of the finite element unit, a displacement constraint item and a frequency constraint item are introduced to expand the Lagrange function, and the Lagrange function specifically comprises the steps of decomposing the increment strain matrix to obtain a first matrix irrelevant to the node displacement and a second matrix relevant to the node displacement, determining a unit stiffness equation in an increment form according to the first matrix and the second matrix and the relation between the unit strain increment and the node displacement increment, and