A corotational finite element formulation for the analysis of planar beams

AbstractAn efficient and accurate lockingfree corotational beam finite element for the analysis of large displacements and smallstrain problems is developed in this paper. Three different finite element models based on three different beam theories, namely, the EulerBernoulli, Timoshenko, and simplified Reddy theories are presented. In order to develop a single corotational finite element that incorporates the kinematics of all three theories, the unified linear finite element model of beams developed by Reddy (Comm. Numer. Meth. Eng. 1997; 13:495510) is included in the formulation. An incremental iterative technique based on the NewtonRaphson method is employed for the solution of the nonlinear equilibrium equations. Numerical examples that demonstrate the efficiency and large rotation capability of the corotational formulation are presented. The element is validated by comparisons with exact and/or approximate solutions available in the literature. Very good agreement is found in all cases. Copyright 2005 John Wiley & Sons, Ltd.

A corotational finite element formulation for the analysis of planar beams Academic Article