The growth-strain method based on the inverse variational principle. An approach to maximum-stiffness shape analysis.

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  • 逆変分原理に基礎をおく成長ひずみ法 最大剛性形状解析へのアプローチ
  • ギャク ヘンブン ゲンリ ニ キソ オ オク セイチョウ ヒズミホウ サイダイ

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Abstract

The growth-strain method was previously proposed as a shape optimization method which is the deforming of shapes by generating bulk strain. Hitherto, we have shown that the uniform-strength shapes can be analyzed by the method where the bulk strain is generated according to the magnitude of a strength parameter. The objective of the present paper is to devise the formulation of the method in order to apply it to maximum-stiffness shape analysis. First, by reforming the inverse variational principle of the principle of minimum potential energy, we obtain a uniform condition of the potential energy density as a necessary condition to obtain maximum stiffness. Based on the theory, the proposed formulation is to set the potential energy density on the generation measure of the bulk strain. The effectiveness of this formulation is examined on beam and column problems. The notable advantage is confirmed with the latter problem.

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