# Topology optimization for worst load conditions based on the eigenvalue analysis of an aggregated linear system

Akihiro Takezawa, Satoru Nii, Mitsuru Kitamura, Nozomu Kogiso

64 被引用数 (Scopus)

## 抄録

This paper proposes a topology optimization for a linear elasticity design problem subjected to an uncertain load. The design problem is formulated to minimize a robust compliance that is defined as the maximum compliance induced by the worst load case of an uncertain load set. Since the robust compliance can be formulated as the scalar product of the uncertain input load and output displacement vectors, the idea of "aggregation" used in the field of control is introduced to assess the value of the robust compliance. The aggregation solution technique provides the direct relationship between the uncertain input load and output displacement, as a small linear system composed of these vectors and the reduced size of a symmetric matrix, in the context of a discretized linear elasticity problem, using the finite element method. Introducing the constraint that the Euclidean norm of the uncertain load set is fixed, the robust compliance minimization problem is formulated as the minimization of the maximum eigenvalue of the aggregated symmetric matrix according to the Rayleigh-Ritz theorem for symmetric matrices. Moreover, the worst load case is easily established as the eigenvector corresponding to the maximum eigenvalue of the matrix. The proposed structural optimization method is implemented using topology optimization and the method of moving asymptotes (MMA). The numerical examples provided illustrate mechanically reasonable structures and establish the worst load cases corresponding to these optimal structures.

本文言語 English 2268-2281 14 Computer Methods in Applied Mechanics and Engineering 200 25-28 https://doi.org/10.1016/j.cma.2011.03.008 Published - 2011 6 15 はい

## ASJC Scopus subject areas

• 計算力学
• 材料力学
• 機械工学
• 物理学および天文学（全般）
• コンピュータ サイエンスの応用

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