A Large Rotation Matrix for Nonlinear Framed Structures, Part 1: Theoretical Derivation

Abstract

In this paper, a large rotation matrix for geometric nonlinear analysis of frame structures is developed by introducing the Rodrigues formula proposed by Argyris to modify the original rotation scheme of Bathe and Bolourchi. In the deduction, the large rigid body rotation of the beam element is decomposed into the relative translational displacements and the axial rotation respectively. Using Rodrigues formula, the large rotation matrix of rigid body can be calculated and sequentially the nodal transformation matrix of the beam element can be derived. And with this transformation matrix, the equilibrium equations of the beam elements established in the current configuration can be transformed into the original configuration, and then assembled and solved finally. The validity verification of the method would be presented and discussed in the part 2 of this paper.