Multi-Scale Structure Optimization Design Based on Eigenvalue Analysis

SUN Guomin; ZHANG Xiaozhong; SUN Yanhua

doi:10.21656/1000-0887.390207

Volume 40 Issue 6

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SUN Guomin, ZHANG Xiaozhong, SUN Yanhua. Multi-Scale Structure Optimization Design Based on Eigenvalue Analysis[J]. Applied Mathematics and Mechanics, 2019, 40(6): 630-640. doi: 10.21656/1000-0887.390207

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Multi-Scale Structure Optimization Design Based on Eigenvalue Analysis

doi: 10.21656/1000-0887.390207

School of Civil and Architectural Engineering, Guizhou University of Engineering Science, Bijie, Guizhou 551700, P.R.China

Received Date: 2018-07-24
Rev Recd Date: 2019-04-18
Publish Date: 2019-06-01

Abstract

Abstract

A multi-scale structure optimization method was proposed based on eigenvlue analysis, to find the macrostructure and microstructure of maximum macro stiffness under the worst load. The constraint that the Euclidian norm of the uncertain load is 1 was introduced, the structural compliance was calculated according to the Rayleigh-Ritz theorem, and the compliance was transformed to a symmetric matrix with the same dimensions as the local load vector. In this way, the compliance minimization problem under the worst load was transformed to the minimum problem of the maximum eigenvalue of the symmetric matrix. Moreover, the worst load case was determined with the eigenvector corresponding to the maximum eigenvalue of the matrix. Several numerical experiments demonstrated the validity of the proposed method, and illustrated the reasonability of the macro topological structure and the micro material distribution. The proposed multi-scale optimization method has virtues of iterative stability and rapid convergence. The update of the density function in the topological optimization was performed based on sensitivity analysis and the method of moving asymptotes (MMA).
- optimum structural design,
- multi-scale,
- macrostructure,
- micro material,
- eigenvalue analysis

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References

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