Abstract
This paper presents a shape optimization method for the natural vibration problem of stiffened thin-walled or shell structures. The boundary shapes of stiffeners are determined under the condition where the boundary is movable in the inplane 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 H^1 gradient method for shells, which is a parameterfree shape optimization method proposed by one of the authors. Several design examples are presented to validate the proposed method and demonstrate its practical utility.
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