A Non-parametric Free-form Optimization Method for Controlling the Stiffness of Automotive Sheet Metal Structures

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.