Abstract
In this paper, a two-stage parameter-free, or node-based shape optimization methodology is presented for designing the smooth optimal shape of a shell structure concerning stiffness maximization problem subject to a volume constraint. With this methodology, the optimization design problem of a shell structure is divided into two stages, which are a surface optimization stage and a boundary optimization stage. The shape sensitivity, called shape gradient function, is theoretically derived for both stages using the Lagrange multiplier method and the formula of the material derivative. The optimal shape is determined by applying the derived each shape gradient functions on a design surface or boundaries to the multi-stage free-form optimization method, or a H^1 gradient method. By this method, a weight reduced shell with high performance can be obtained, while maintaining the smooth surface and boundaries. Several calculated examples are presented to verify the validity and practical utility of the proposed methodology.
