Parameter-free optimum design method of stiffeners on thin-walled structures |
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Authors: | Yang Liu Masatoshi Shimoda |
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Affiliation: | 1. Department of Advanced Science and Technology, Toyota Technological Institute, 2-12-1 Hisakata, Tenpaku-ku, Nagoya, 468-8511, Japan
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Abstract: | In this paper, we present a shape optimization method for designing stiffeners on thin-walled or shell structures. Solutions are proposed to deal with a stiffness maximization problem and a volume minimization problem, which are subject to a volume constraint and a compliance constraint, respectively. The boundary shapes of the stiffeners are determined under a condition where the stiffeners are movable in the in-plane direction to the surface. Both problems are formulated as distributed-parameter shape optimization problems, and the shape gradient functions are derived using a material derivative method and an adjoint variable method. The optimal free-boundary shapes of the stiffeners are obtained by applying the derived shape gradient function to the $H^{1}$ gradient method for shells, which is a parameter-free shape optimization method proposed by one of the authors. Several stiffener design examples are presented to validate the proposed method and demonstrate its practical utility. |
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