A new 2D beam finite element for nonlinear elastic analysis including warping and shear effects

Abstract

In this paper, a finite-element formulation based on positional description is proposed to predict the large deformation behavior of short beams including shear deformation and cross section warping. A higher-order shear deformation beam theory is originally employed by means of two generalized vectors. A linear strain rate is also included in order to enrich the approximation of strains along the transverse direction. The formulation accounts for finite displacements, finite strains and plane stress conditions in elastic regime. Homogeneous materials, as well as functionally graded composite beams with varying properties along the height, are considered. In all, four beam formulations are described, combining the level of transverse enrichment and the cross section kinematics. A short cantilever beam problem with rectangular cross section is analyzed in detail to illustrate the differences among the four element formulations regarding displacements, strains and stresses. The numerical results confirm that the inclusion of both linear strain rate and cross section warping are needed to correctly predict the mechanical behavior of the cantilever beam, reproducing variable shear deformation across the height.