Structural topology optimization method based on material field reduction stage expansion

Abstract

The invention discloses a structure topology optimization method based on material field reduction series expansion, and solves the problem of low calculation efficiency caused by too many design variables and need of relative density or sensitivity filtering measures in traditional density method topology optimization. The method comprises the following steps: a bounded material field consideringcorrelation is defined; a spectral decomposition method is adopted to perform transform to obtain a linear combination of a series of undetermined coefficients, the undetermined coefficients are usedas design variables, an optimization model is constructed based on a unit density interpolation model, a gradient class or non-gradient class optimization algorithm is adopted to solve a topologicaloptimization problem, and then a topological configuration with a clear boundary is obtained efficiently. According to the method, the number of design variables in density method topology optimization can be greatly reduced, and meanwhile, the method has the natural advantage of completely avoiding grid dependence and chessboard format problems. The method also inherits the advantages of simple density method form, convenience in engineering popularization and the like, the optimization solving speed is high, and the research and development efficiency of the innovative topological design ofthe complex equipment structure can be ensured.

Description

technical field [0001] The invention belongs to the field of lightweight design of machinery and aerospace engineering equipment, and relates to a structural topology optimization method based on material field series expansion. Background technique [0002] Currently, the mainstream methods for topology optimization of continuum structures include: variable density method, level set method and (two-way) progressive optimization method. Among them, the variable density method is widely used in the innovative topology optimization design of mechanical and aerospace engineering structures because of its simple model and easy implementation, and is integrated in many optimization design commercial software. The variable density method converts the 0-1 discrete variable topology optimization problem into an optimization problem with continuous values ​​of design variables by introducing and penalizing the relative density of intermediate materials between 0 and 1, and through a ...

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Problems solved by technology

[0003] Aiming at the shortcomings of the traditional density method in dealing with large-scale and complex structure topology optimization problems with too many design variables, the present invention provides a topology optimization design method for greatly reducing the scale of design variables, which can greatly reduce the density method topology optimization. The number of design variables in , improves the optimization solution efficiency, and at the same time has the natural advantage of completely avoiding grid dependence and checkerboard format problems

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