位相最適化構造形状探索のための変分原理と有限要素法

概要

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This paper presents a progressive type of variational principle for topological shape optimization. The principle makes it possible to derive a finite element method (FEM) for searching structural shapes with minimal weight and high strength in the optimization operation. The principle is based on that of minimum potential energy. In the formulation of this principle, we first assume both a search domain and an optimum one. The search domain includes the optimum one. Then, the search domain is locally eliminated according to the information of minimum strain energy in the domain. When a maximum equivalent stress in the search domain reaches the yield stress as a constraint condition, it is evaluated that the search domain agrees with the optimum one. Therefore, we obtain the variational principle for the topological optimization. Next, we derive the FEM based on this principle. Finally, we obtain the optimum topological shapes of two-dimensional finite element models using the FEM. Hence, the validity of the variational principle is confirmed from the numerical solutions of the models.
一般社団法人日本機械学会の論文
1997-10-25