Abstract
In this paper we present an optimization method for the optimal free-form design of shell structures in order to control the deformation mode to the desired one. It is assumed that the shell is varied in the normal direction to the surface and the thickness is constant. As an objective functional, we introduced a squared displacements error norm on the prescribed surface. A non-parametric shape optimization problem with a volume constraint is formulated, and the shape gradient function is theoretically derived. The Robin type traction method is used to determine the optimal smooth shell while minimizing the objective functional. The calculated results show the effectiveness of the proposed method for the optimal free-form design of the shell structure with a desired deformation mode.
