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Thin-walled structures such as shells and folded plates are extensively used in various industrial products. In this paper, a free-form optimization method is presented that is aimed at giving a function to thin-walled structures. As a concrete target, a method to achieve a desired deformation, or to control a static deformed shape to a desired one, is proposed for the design of linear elastic shell structures. As an objective functional, we introduce a squared error norm of a deformed shape on its prescribed surface. It is assumed that the shell is varied in the normal direction to the surface and that the thickness is constant. A distributed-parameter shape optimization problem is formulated, and the shape gradient function for this problem is theoretically derived. The non-parametric free-form optimization method for shells, which was developed by the author, is applied to solve this problem. With this method, an optimal arbitrarily formed shell with smoothness can be obtained while minimizing the objective functional. The calculated results show the effectiveness of the proposed method for the optimal free-form design of thin-walled structures with a desired deformed shape.

Free-form optimization of thin-walled structures for achieving a desired deformed shape