平板の応力集中部における最適形状の設計法について  [in Japanese] A Method for Optimizing Contour Shape to Minimize Stress Concentration in Flat Plates  [in Japanese]

荷重を受ける構造物の不連続部に生じる応力集中を緩和するためには不連続部の形状に丸みをつけたり,厚板による補強などの経験的な方法が従来より行われている.しかし不連続部の形状を最適化することによって応力の集中率を大幅に低減することが可能であり,その手法の確立が望まれている.本論文で提案する形状最適化手法は有限要素法による応力解析に形状最適化条件を併用して平板構造物の応力集中部における応力分布を平坦化し,周辺応力の最大値を極小化する周辺形状を自動的に決定する方法である.本方法では,有限要素法による解の精度の低下を避けるために,応力集中部付近にメッシュの変更を許容する領域を指定し,最適化の過程において応力集中部の形状が変化するごとに,要素の大きさができる限り等しくなるように,乱数を利用した自動要素分割法によりその領域内を再分割する.また形状最適化の過程において必要な外部境界上の応力値には節点力を用いた応力平滑化法を用い,高精度の応力分布を得ることができる.本方法が平板構造の応力集中部における形状の自動決定法として有用であることを数値実験により示した.

In this paper, the author presents a shape optimization method to minimize the maximum stress around discontinuous parts of a plate without inserting a thick reinforcement plate. The finite element method (FEM) using constant strain triangular elements is applied for calculating the displacement and stress of the structure. The improved values of the stress at nodes on the external boundary of the domain are required in the process of the shape optimization, but the irregular and dispersed values of FEM results include errors which are influenced sensitively by the mesh pattern. The accuracy of stresses at a node on the external boundary of the domain which are approximated by simple averages of stersses of the adjacent elements having the node in common, is generally known to be lower than those of internal ones. The author proposed a smoothing method furnishing more accurate stresses at a node on the boundary of the domain and applied this smoothing method to the optimization system for improving the accuracy of the stress distribution obtained by FEM. Further, the author proposed a method of automatic mesh generation which can effectively adapt to the deformation of the domain shape through the process of optimization. Consideration is taken to avoid the formation of elements having acute angles and to control the size or distribution density of finite elements in order to avoid loss of numerical accuracy in the analysis. A mesh generation method using random numbers enables generating triangular elements for arbitrarily shaped and multiply connected planar domains. It is shown in this paper that this method is highly effective in reducing the stress concentration by optimizing the shape around the discontinuous part of a ship structure and hatch opening.