A large displacement and finite rotation thin-walled beam formulation including cross-section deformation

This paper presents a new formulation for thin-walled beams that includes cross-section deformation. The kinematic description of the beam emanates from the geometrically exact Reissner–Simo beam theory and is enriched with arbitrary cross-section deformation modes complying with Kirchhoff’s assumption. The inclusion of these deformation modes makes it possible to capture the cross-section in-plane distortion, wall (plate) transverse bending and out-of-plane (warping), which leads to a computationally efficient numerical implementation. Several illustrative numerical examples are presented and discussed, showing that the resulting beam finite element leads to solutions that are in very good agreement with those obtained with standard shell finite elements, albeit involving much less degrees-of-freedom.