Unification of Mixed Euler-Bernoulli-Von Karman Planar Frame Model and Corotational Approach

Abstract

This article presents an efficient and accurate frame element for small-strain but large-displacement/rotation analyses of elastic planar frames. The element formulation is based on the unification of the corotational concept and the Euler-Bernoulli-von Karman beam theory. The Hellinger-Reissner mixed functional is used to construct the locking-free Euler-Bernoulli-von Karman frame element. The directional derivative operator is used to linearize the Hellinger-Reissner mixed functional, thus resulting in the incremental element equations. The derived element stiffness matrix is symmetric and variationally consistent. The standard displacement interpolation functions for a linear frame element are used. With these assumed displacements, the force interpolation functions are derived such that the equilibrium equations in the deformed configuration are strictly satisfied. In the present study, the distributed loads along the element are assumed to be absent and only initially straight prismatic beams are considered. The validity of the proposed nonlinear frame element is confirmed by analyzing five benchmark examples exhibiting two types of critical points, namely snap-through and snap-back and comparing these results with analytical results available in literatures. The efficiency of the proposed nonlinear frame element is also assessed by comparing the numerical results obtained with the proposed model to those obtained with other nonlinear frame models.