Treatment of Warping Deformation of Curved I-Beams for Out-of-Plane Deformational Analysis by Straight-Element Approach

Abstract

Straight elements are a simple tool for tackling the locking problem for curved beams. When a curved I-beam is approximated by chordwise straight elements, the conventional approach is to treat the rate of twisting as the warping degree of freedom (DOF) for the chordwise elements, which involves some confusion. In this article, a new straight element was derived by a mixed formulation by adopting the generalized warping deformation used in the energy composition as the associated nodal DOF based on the Bernoulli-Euler-Vlasov hypothesis. The convergence characteristics of both approaches were theoretically analyzed. The example demonstrated good convergence properties for both the conventional and mixed straight elements, aside from the fact that they are locking-free, unlike some curved elements. The mixed straight element showed a better performance because its treatment of warping deformation is more consistent in energy terms.