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This paper presents a numerical analysis technique for application to shape optimization problems of linear elastic structures subject to multiple loading conditions. The problems dealt with here are a mean compliance minimization problem in relation to individual load cases and a fully stressed design problem. The proposed technique is based on the traction method which analyzes the domain variation. A shape optimization system was developed and applied to fundamental problems in two and three dimensions. The computed results confirmed the validity and usefulness of the proposed technique.

In this paper we present a numerical shape optimization method of continua for solving min-max problems and identification problems. The min-max shape optimization problems involve minimization of maximum stress or maximum displacement; the shape identification problems involve the determination of shapes that achieve a given desired stress distribution or displacement distribution. Each problem is formulated and sensitivity functions are derived using the Lagrangian multiplier method and the material derivative method. The traction method, which is a shape optimization method, is employed to find the optimal domain variation that reduces the objective functional. The proposed numerical analysis method makes it possible to design optimal structures for maximizing strength and rigidity and for controlling stress and displacement distributions. Examples of computed results are presented to show the validity and practical utility of the proposed method.