Higher order analysis of thin-walled beams with axially varying quadrilateral cross sections

A thin-walled beam finite element with a varying quadrilateral cross section is formulated based on a higher order beam theory. For the calculation of distortions, the beam frame approach, which models the cross section by using two-dimensional Euler beams, is used. Distortions induced by the Poisson's effect and warpings are analytically derived. Three-dimensional displacements at an arbitrary point of a present beam element can be described by interpolating three-dimensional displacements at the end sections. Straight and curved thin-walled beams with varying cross sections are solved to show the validity of the proposed approach.