Free-Boundary Shape Optimization Method for Natural Vibration Problem of Thin-Walled Structure

Abstract

In this paper, we present a shape optimization method for the natural vibration problem of thin-walled or shell structures with or without sitiffeners. The boundary shapes of a shell or stiffeners are determined under the condition where the boundary is movable in the in-plane direction to the surface. The design problems deal with eigenvalue maximization problem and volume minimization problem, which are subject to a volume constraint and an eigenvalue constraint respectively. The both optimization problems are formulated as distributed-parameter shape optimization problems, and the shape gradient functions are derived using the material derivative method and the adjoint variable method. The optimal free-boundary shapes are obtained by applying the derived shape gradient functions to the H1 gradient method for shells, which is a parameter-free shape optimization method proposed by one of the authors. Several design examples are presented to validate the proposed method and demonstrate its practical utility.