Incorporation of wall finite relative rotations in a geometrically exact thin-walled beam element

Abstract

In this paper, a large displacement and finite rotation thin-walled beam element previously developed by the authors, which accounts for cross-section deformation, is extended by including finite relative rotations of the beam walls in the in-plane kinematic description of the cross-sections. The inclusion of these relative rotations is motivated by the fact that it enables a simple and meaningful representation of the cross-section in-plane distortion and allows for a co-rotational description of the wall "local-plate" behavior, which leads to a computationally efficient numerical implementation. The present extension preserves all features of the original formulation, namely the geometrically exact description of the beam mid-surface and the allowance for arbitrary cross-section deformation modes complying with Kirchhoff's assumption. The efficiency of the resulting beam finite element is demonstrated by means of numerical examples, which include comparisons with solutions obtained by means of the previous beam finite element and standard shell finite elements.