Parameter-free Shape Optimisation Method for Designing Optimal Surface and Boundary of Shell Structures

A parameter-free, or node-based, shape optimization method is presented for designing the optimal free-form surface and boundary of shell structures. With this method, a shape is varied in the normal direction to the surface in order to determine the optimal curvature distribution and in the tangential direction to the surface in order to maintain the initial curvature distribution. The design problem dealt with here concerns a stiffness design. The optimal shape is determined by applying the derived shape gradient function to a gradient method in a Hilbert space. With this approach, the jagged problem inherent in node-based methods is solved and a smooth optimal free-form surface and boundary with mesh regularity can be obtained. Several examples are presented to verify the validity and practical utility of this method. It was also verified that obtained free-form shapes became membrane-carrying structures as intended.