内点法による最適解を利用した多様な最適トラス·トポロジーの生成法

摘要

The present paper deals with a generation method of various optimal truss topologies which have the same objective value. In this paper, the truss topology optimization is formulated as a multiobjective optimization problem, which is to find the cross-sectional area of truss members, such that both the structural volume and the compliance are minimized. This problem can be written as an equivalent linear programming problem and the optimal truss topology can be obtained by the interior point method. Using this optimal solution by the interior point method, other various optimal truss topologies with the same objective value can be systematically enumerated. The applications of the proposed method are illustrated in numerical examples with discussion on characteristics of design results and computational efficiency.%部材総体積とコンプライアンスを目的関数としたトラス·トポロジ一多目的最適化問題は，等価な線形計画問題に定式化でき，線形計画法によつて最適解の探索が可能である.線形計画問題の許容領域は凸多面体となり最適解は容易に求められるが，対象とするグランドストラクチャによっては同じ目的関数値で異なる形状（軸力分布）の最適トラス.トポロジーが多数存在する場合がある.本稿では，これら多様な最適解の組識的な生成·列挙法を提案し，得られる最適解の特性や本手法の計算効率にっいて考察した.本稿の内容は以下のようにまとめられる.