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In this paper, we present a numerical solution to shape optimization problems in automotive shell structural designs subject to a strength constraint. Using the proposed method, the optimal shape can be obtained without any parameterization of design variables. With the aim of reducing the weight, a volume minimization problem subject to a von Mises stress constraint is formulated as a distributed-parameter shape optimization problem, or a non-parametric shape optimization problem. It is assumed that the design domain is varied in the tangential direction to the surface to maintain the curvatures of the initial shape. The shape gradient function and the optimality conditions are theoretically derived for this problem using the material derivative method, Lagrange multiplier method and the adjoint variable method. The traction method we have proposed earlier is applied to determine the smooth domain variation that minimizes the objective functional.

This paper describes the shape optimization analysis of solid structures such as chassis components of a car, where the shape optimization problems of linearly elastic structures are treated to improve strength or to reduce weight of solid structures. The optimization method used here is the growth-strain method, and the shape optimization system is developed based on this method. The growth-strain method, which modifies a shape by generating bulk strain, was previously proposed for analysis of the uniform-strength shape. The generation law of the bulk strain is given as a function of a distributed parameter to be uniformed, such as von Mises stress. Two improved generation laws are presented. The first law makes the distributed parameter uniform while controlling the structural volume to a target value. The second law makes the distributed parameter uniform while controlling the maximum value of the distributed parameter to a target value.

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.