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 © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]