Abstract
This paper presents a numerical optimization method for the optimal free form design of shell structures. Using the compliance as an index of stiffness, the stiffness design problem is formulated as a 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 derived for this problem is applied to the Robin-type traction method to determine the optimal and smooth free form, or the optimal curvature distribution. Several shape design problems are solved in order to verify the practical utility of this method. It is also confirmed that the strain energy of the optimal shape is mainly dominated by the membrane component. The calculated results show the proposed method is effective for the shape design of shell structures with the optimal curvature distribution.
