J1202-1-3 統合・簡易化された線形システムの固有値解析に基づくロバストトポロジー最適化([J1202-1]解析・設計の高度化・最適化I)

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This paper proposes a robust topology optimization method for a linear elasticity design problem subjected to an uncertain load. The robust design problem is formulated to minimize a robust compliance that is defined as the maximum compliance for the worst load case of an uncertain load set. Since the robust compliance can be formulated the scalar product of the uncertain input load and output displacement, the idea of "aggregation" used in the field of control research is introduced to evaluate the value of the robust compliance under the uncertainty of input load. Aggregation is to represent the direct relationship between the uncertain input load and output displacement by 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. According to the Rayleigh-Ritz theorem for symmetric matrices, the robust compliance minimization problem is formulated as the minimization problem of the maximum eigenvalue of the aggregated symmetric matrix when Euclidean norm of the uncertain load set is fixed.
一般社団法人日本機械学会の論文
2010-09-04