Node-based free-form optimization method for vibration problems of shell structures

We have previously proposed a numerical node-based parameter-free shape optimization method for designing the optimal free-form surface of shell structures. In this paper, this method is extended to deal with two vibration problems including a vibration eigenvalue maximization problem and a frequency response minimization problem. To avoid the repeated eigenvalue problem when a specified vibration eigenvalue is maximized, we provide two optional approaches, i.e., tracking the specified natural mode or increasing all the repeated eigenvalues. Each vibration problem is formulated as a distributed parameter shape optimization problem, and the derived shape gradient function is applied to the H-1 gradient method for the shells proposed by the authors, where the shape gradient function is used as a distributed force function to vary the surface. With this method, the optimal and smooth free-form shape including a natural bead pattern can be obtained. Several calculated examples are presented to demonstrate the effectiveness of the proposed method for the free-form design of shell structures involving vibration problems. (C) 2016 Elsevier Ltd. All rights reserved.