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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.

In this paper, we present a parameter-free, or a node-based optimization method for finding the smooth optimal free-form of automotive shell structures, including global and local curvature distributions such as beads or embossed ribs. The design problems dealt with in this paper involve a stiffness problem. Stiffness is maximized using the compliance as an objective functional. The optimum design problem is formulated as a distributed-parameter, or non-parametric, shape optimization problem under the assumptions that the shell is varied in the normal direction to the surface and the thickness is constant. The shape gradient function and the optimality conditions are then theoretically derived. The optimum free-form, or optimal curvature distribution, is determined by applying the derived shape gradient function in the normal direction to the shell surface as pseudo external forces to vary the surface and to minimize the objective functional.