A corotational finite element formulation for the analysis of planar beams

An efficient and accurate locking-free corotational beam finite element for the analysis of large displacements and small-strain problems is developed in this paper. Three different finite element models based on three different beam theories, namely, the Euler-Bernoulli, 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; 13:495-510) is included in the formulation. An incremental iterative technique based on the Newton-Raphson method is employed for the solution of the non-linear 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 (c) 2005 John Wiley & Sons, Ltd.