Abstract
In this paper, a parameter-free, or a node-based optimization method for finding the smooth optimal free-form of shell structures, including global and local curvature distributions such as beads or embossed ribs is presented. The design problems dealt with in this paper involve a stiffness problem and a natural frequency problem. Both optimum design problems are formulated as a distributed-parameter, or non-parametric, shape optimization problem, and the shape gradient functions are then theoretically derived. The optimum free-form, or optimal curvature distribution, is determined by applying the derived shape gradient function to the shell surface as pseudo external forces under a elastically supported condition, for varying the surface and for the mesh regularization. With this method, the smooth optimal global free-form or the smooth optimal local beads of shell structures is created without any shape design parameterization. The validity and practical utility of this method were verified through several design examples. It was confirmed that the obtained structures were changed from the initial bending-carrying structures to membrane-carrying ones.
