フレーム要素を用いたトポロジー最適化 : 固有振動数最大化を目的とした場合(機械力学,計測,自動制御)

概要

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This paper presents a new topology optimization method that maximizes multiple eigen-frequencies to obtain, at the conceptual design phase, the most stable designs of mechanical structures for dynamic problems. This method is developed based on frame elements that can consider the principal direction of the second moment of inertia in the cross-section to obtain optimal results that illustrate the relationship between the objective function and desired cross-sectional properties. For each frame element, an ellipsoidal cross-section is assumed as the simplest case. The normalized cross-sectional area, the rotational angle denoting the principal direction, and the ratio of the lengths of the major and minor axes, are considered as design variables. A method for obtaining the optimal angle is derived, based on the minimization of complementary energy. Finally, several numerical examples confirm the validity and utility of the proposed method, which should be useful for mechanical design engineers at the conceptual design phase.
一般社団法人日本機械学会の論文
2005-10-25