シェル構造の表面と境界に対する2段階フリーフォルム形状最適化手法

概要

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In this paper, a free-form shape optimization methodology is presented for designing the smooth optimal shape of a shell structure concerning stiffness maximization problem subject to a volume constraint. With this methodology, the optimization design problem of a shell structure is divided into two stages. One is a surface optimization stage and the other is a boundary optimization stage. The shape sensitivity, called shape gradient function, is theoretically derived for both stages using the Lagrange multiplier method and the formula of the material derivative. The optimal shape is determined by applying the derived each shape gradient function on a design surface or boundaries to the two-stage free-form optimization method, a H1 gradient method. By this method, a weight reduced shell with high stiffness can be obtained, while maintaining the smooth surface and boundaries. Several calculated examples are presented to verify the validity and practical utility of the proposed methodology.
一般社団法人日本機械学会の論文