三項法と双対推定: 張力構造の形状決定問題及び連続体の大変形問題

摘要

関数の極小値を探索する数値解法のうち、関数の勾配の逆方向へ探索してゆく方法を基本とするものを、関数の直接最小化と呼ぶ。関数の直接最小化は仮想仕事の原理を介して静力学と密接に関連している場合がある。%The aim of this work is to propose making use of three-term method, as one of the standard direct minimization approaches, in searches of solutions in various static problems of structures. In the first part of this work, two simple recursive methods, namely two-term and three-term methods are presented as standard iterative direct minimization approaches. The dual estimate is presented as a powerful means of involving equally constraint conditions into direct minimization approaches. In addition, it is argued that while the two-term method is of no use at times, the three-term method always provides remarkable global convergence efficiency. In the second part, the gradient vectors that are appeared in the first part are generalized in natural ways and then the scope of the three-term method is extended for generalized minimization problems. The simultaneous equations that are solved in non-linear finite element methods are typical examples of such generalized problems. Various numerical examples are illustrated to indicate the wide applicability of the three-term method.