有限要素法による梁の大歪モデル （第２報） Ｕｐｄａｔｅｄ Ｌａｇｒａｎｇｉａｎによる定式化

Abstract

Finite element analysis of 3-dimensional large rotation problem of a beam has been possible by means of nonlinear beam model by J. C. Simo, L. Vu-Quoc. Their beam model is regarded as geometrically exact, and described by a configulation manifold which involves the rotation group. In result, the tangent stiffness matrix becomes non-symmetric away from equilibrium. But I showed that the tangent stiffness of semitangential rotation ΔδΠs became symmetric, and by the comparison of the analyses of the fundamental problems with Miyazaki, ABAQUS and Nour-Omid, B. and Rankin, C. C., it was proved that the symmetric tangent stiffness was valid. By the way, the beam model is assumed large rotation and small strain. Then in the previous report, I showed the geometric stiffness of large strain by the variation of deformation gradiant tensor before rigid body rotation. But, that formulation was total lagrangian formulation parametrized by the coordinate of the center line of the reference configulation. Now, I will show the large strain beam model of updated lagrangian formulation parametrized by the coordinate of the center line of the current configulation.