TY - JOUR

T1 - Robust topology optimization based on an aggregated linear system and eigenvalue analysis

AU - Nit, Satom

AU - Takezawa, Akihiro

AU - Kitamura, Mitsum

AU - Kogiso, Nozomu

N1 - Copyright:
Copyright 2012 Elsevier B.V., All rights reserved.

PY - 2011

Y1 - 2011

N2 - 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 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 research is introduced to evaluate the value of the robust compliance. The aggregation is applied to provide the direct relationship between the uncertain input load and output displacement using a small linear system composed of these vectors and the itduced size of a symmetric matrix in the context of a discretized linear elasticity problem using the finite element method. The robust compliance minimization problem is formulated as the minimization of the maximum eigenvalue of the aggregated symmetric matrix subject to the constraint that the Euclidean norm of the uncertain load set is fixed. Moreover, the worst load case is easily established as the eigenvector corresponding to the maximum eigenvalue of the matrix. The proposed robust stmctural optimization method is implemented using the topology optimization method, sensitivity analysis and the method of moving asymptotes (MN/IA). The numerical examples provided illustrate mechanically itasonable stmctures and establish the worst load cases corresponding to these optimal structuits.

AB - 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 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 research is introduced to evaluate the value of the robust compliance. The aggregation is applied to provide the direct relationship between the uncertain input load and output displacement using a small linear system composed of these vectors and the itduced size of a symmetric matrix in the context of a discretized linear elasticity problem using the finite element method. The robust compliance minimization problem is formulated as the minimization of the maximum eigenvalue of the aggregated symmetric matrix subject to the constraint that the Euclidean norm of the uncertain load set is fixed. Moreover, the worst load case is easily established as the eigenvector corresponding to the maximum eigenvalue of the matrix. The proposed robust stmctural optimization method is implemented using the topology optimization method, sensitivity analysis and the method of moving asymptotes (MN/IA). The numerical examples provided illustrate mechanically itasonable stmctures and establish the worst load cases corresponding to these optimal structuits.

KW - Eigenvalue Analysis

KW - Finite Element Method

KW - Robust Design

KW - Sensitivity Analysis

KW - Topology Optimization

KW - Worst Case Design

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M3 - Article

AN - SCOPUS:84856447265

SN - 0387-5008

VL - 77

SP - 472

EP - 482

JO - Nihon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A

JF - Nihon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A

IS - 775

ER -