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 and 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 the author showed that the tangent stiffness of semitangential rotation ΔδΠ
s became symmetric and by the analysis of fundamental problems it was proved that symmetric tangent stiffness was valid. By the way, the beam model is assumed large rotation and small strain. In this report, I will show the geometric stiffness of large strain by the variation of deformation gradiant tensor before rigid body rotation. This formulation is total lagrangian formulation.
View full abstract