Large-Rotation and Large-Strain Analysis of a Beam by Finite-Element Method (Analysis by Updated Lagrangian Beam Element).

Abstract

Finite-element analysis of a 3-dimensional large-rotation problem of a beam has been made possible by means of the nonlinear beam model developed by Simo and Vu-Quoc. Their beam model is regarded as geometrically exact, and is described by a configuration manifold which involves the rotation group. As a result, the tangent stiffness matrix becomes non-symmetric away from equilibrium. However, it have been shown in Ishihara that the tangent stiffness of semitangential rotation became symmetric, and by analyzing of fundamental problem, it was proven that symmetric tangent stiffness was valid. The beam model was assumed to have large rotation and small strain. Next, it was shown in Ishihara that the geometric stiffness of large strain in terms of the variation of the deformation gradient tensor before rigid-body rotation. However, that formulation was a total lagrangian formulation parametrized by the coordinate of the centerline of the reforence configuration. It was also shown in Ishihara that the large-strain beam model of an updated lagrangian formulation pararetrized by the coordinate of the centerline of the current configuration. Here, it will be shown that numerical examples of large-rotation and largestrain analysis of a beam.