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This paper presents a free-form optimization method for achieving a desired stiffness in the shape design of automotive sheet metal structures. A squared error norm of displacements at loaded points is introduced as an objective functional in the formulation of a distributed-parameter shape identification problem. The shape gradient function theoretically derived for this problem is applied to the non-parametric free-form optimization method for shells that was developed by one of the authors. With this method, an optimal arbitrarily formed shell, or a shell with optimal curvature distribution can be obtained without any shape parameterization. The calculated results show the effectiveness and the practical utility of the proposed method for controlling stiffness when designing sheet metal structures.

This paper presents a shape optimization method for the rigidity design of sheet metal structures under multiple loading conditions with the aim of weight reduction. In order to maintain the curvatures of the given initial shape, it is assumed that the design domain is varied in the in-plane direction. Using compliance as an index of the rigidity, a volume minimization problem subjected to multiple rigidity constraints is formulated as a non-parametric shape optimization problem. The shape gradient function and the optimality conditions are theoretically derived for this problem. The traction method is applied to determine the smooth in-plane domain variation that minimizes the objective functional. The calculated results of fundamental design examples and actual automotive chassis components will show the effectiveness and practical utility of the proposed method in solving shape optimization problems of sheet metal structures.