梁の３次元大変形解析のための有限要素法定式化 （第１報） 梁モデルと回転軸

Abstract

Finite element analysis of 3-dimensional large rotation problem of a beam is possible by means of the nonlinear beam model by Simo. His beam model is regarded as geometrically exact, and described by a configuration manifold which involves the special orthogonal group SO (3). Then, the tangent stiffness matrix becomes nonsymmetric away from equilibrium. By the way, Argyris describes that the exchanges of the rotations of both fixed axes and follower axes are impossible, but the exchange of the rotations of semitangential axes is possible and the moment becomes conservative. In this paper, it will be shown that the exchanges of the rotations of both fixed axes and follower axes are impossible, but the exchange of the rotations of semitangential axes is possible from Argyris. And the beam model by Simo will be also shown. In the upcoming paper, it will be shown that the tangent stiffness of fixed rotation ΔδΠr is nonsymmetric, and the tangent stiffness of follower rotation ΔδΠf is in reverse order of ΔδΠr, and the tangent stiffness of semitangential rotation ΔδΠs becomes symmetric. Fundamental problems of 3-dimensional large rotation of a beam are solved with three kinds of tangent stiffnesses, that is, ΔδΠr, ΔδΠf and ΔδΠs And the results are compared with theoretical solution and other finite element solutions, so it will be proved that symmetric tangent stiffness is the most effective.