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.

This paper presents an optimization method for the optimal configuration design of shell structures. It is assumed that the shell is varied in the normal direction to the surface and the thickness is constant. The compliance minimization problem is formulated as a non-parametric shape optimization problem. The shape gradient function is theoretically derived considering the variation of the distributed loads on the shell surface. The Robin type traction method is used to determine the optimal smooth shell surface while minimizing the objective functional. The calculated results show the effectiveness of the proposed method for the optimal configuration design of shell structures.

This paper presents a numerical optimization method for optimal configuration design of shell structures. It is assumed that the shell surface is varied in the out-of-plane direction to optimize its configuration, and the thickness is constant. A solution to compliance minimization problem subject to a volume constraint is proposed to maximize the stiffness of shell structures. With this solution, the optimal configuration is obtained without any parameterization of the design variables. The problem is formulated as a non-parametric shape optimization problem. The shape gradient function is theoretically derived using the material derivative formulas, Lagrange multiplier method and the adjoint variable method. The traction method, which was proposed as a gradient method in Hilbert space, is applied to determine the smooth shell surface while minimizing the objective functional. In the design velocity analysis of the traction method, earth spring elements are added to shell surface to restrain a rigid-motion-like shape variation and to stabilize the convergence. The calculated results show the effectiveness of the proposed method for optimal configuration design of shell structures.