Efficient structure frequency response topological optimization method

Abstract

The invention belongs to the technical field related to structure topological optimization design, and discloses an efficient structure frequency response topological optimization method. The method comprises the following steps that: (1) decoupling two coupling variables including time and space in a standard level set function in a dynamic model of which the structure is to be optimized, and meanwhile, expressing the level set function related to time as a matrix product form; (2) converting a partial differential equation of the time-related level set function into an ordinary differential equation so as to obtain a new linear system, and solving to obtain the time-related level set function; (3) carrying out finite element analysis on a macrostructure so as to calculate a target function and a constraint function of a structure optimization problem; and (4) calculating the sensitivity, which relates to a design variable of the target function and the constraint function obtained in the (3), and judging whether the target function is convergent or not after the design variable is updated. By use of the method, a discrete wavelet transform technology is adopted to carry out recompression on an interpolation matrix, efficiency is improved, and cost is lowered.

Description

technical field [0001] The invention belongs to the related technical field of structural topology optimization design, and more specifically relates to an efficient structural frequency response topology optimization method. Background technique [0002] The boundary description technology based on level set has unique characteristics, such as smooth and clear boundary shape, and can conveniently and flexibly describe its topology and shape changes through boundary fusion and splitting. Since the level set function has no explicit analytical solution, the entire design domain needs to be discretized with a rectangular grid, and the finite difference method is used to solve the level set equation, so there are many defects when the traditional level set method is applied to structural topology optimization problems. There are many problems in the topological shape optimization of the traditional level set method. For example, the step size of the upwind difference scheme for...

AI Technical Summary

Problems solved by technology

There are many problems in the topological shape optimization of the traditional level set method. For example, the step size of the upwind difference scheme for solving the Hamilton-Jacobi partial differential equation is limited by the Courant-Friedrichs-Lewy (CFL) condition, the solution speed is slow, and the optimization efficiency is not high; the topological shape optimization In the process, it is necessary to continuously perform time-consuming periodic initialization of the level set function to ensure the accuracy and numerical stability of the solution; the evolution of the structure boundary must be realized by solving the Hamilton-Jacobi partial differential equation, which cannot be the same as the mature and efficient optimization in the field of optimization. Combination of algorithms (such as optimization criterion method, mathematical programming method, etc.)

Therefore, the numerical problems of the discrete calculation of the traditional level set function have seriously affected the advantages of the level set method in the application of structural optimization.

[0003] In addition, for structural dynamics optimization design problems, structural dynamics topology optimization mainly includes eigenvalue topology optimization and frequency response topology optimization, and structural frequency response topology optimization is usually more difficult

First of all, the frequency response optimization problem has the characteristics of highly nonlinear and non-convex objective function, which reduces the stability and convergence of the optimization process; secondly, it is difficult to solve the frequency response sensitivity, which involves the sensitivity analysis of frequency and mode shape at the same time; , the solution of the finite element equilibrium equation for the vibration problem is complex

These difficulties lead to the slow development of structural frequency response topology optimization, and relatively few research results. At present, most of the research in this field is the dynamic response optimization under single frequency excitation. In practical applications, such as rocket, missile radar, tracker and other servo Systems, aerospace precision equipment, automotive shock and noise reduction structures and systems, etc. are usually excited by frequency bands within a certain bandwidth. This type of structural frequency response optimization problem further increases the difficulty of solving: on the one hand, structural optimization design needs to avoid A frequency band range to avoid resonance. During the optimization process, when the natural frequency of the structure falls into the target frequency band range, multiple corresponding peaks may be generated, which affects the stability of the iteration. On the other hand, the objective function of the topology optimization of the structural response under frequency band excitation is an integral form , which means that when Gaussian integration and other methods are used for numerical processing, complex vibration equations must be solved many times, which is inefficient and greatly increases the calculation cost. When the problem scale is large, it is easy to lead to optimization failure.

Images