境界輪体を用いた平板のトポロジー最適化

概要

論文の詳細を見る
In this paper, we propose a topology optimization method for two-dimensional structures. Virtual nodal forces are employed as design variables that are functions of parameters derived from boundary cycles in the homology theory. The density of material in each element is determined by the design variables so that the density of strain energy is equal to the prescribed value. The objective function is the volume of a plate, and it is minimized. The virtual nodal forces always satisfy the equilibrium at each node in the process of optimization without constraints on parameters, although all elastic equations are not satisfied until the process is completed. In other words, the finite element analysis and topology optimization progress simultaneously. This method does not require repeating finite element analysis. Although the optimum structures obtained by this method as numerical examples varied depending on values of constants in the optimization method or the size of elements, the conditions of the density of strain energy were almost satisfied. It can be said that the validity of the proposed method was proved.
一般社団法人日本機械学会の論文
2004-01-25