Higher-order thin-walled beam analysis for axially varying generally shaped cross sections with straight cross-section edges

A higher-order beam theory is proposed for the analysis of a thin-walled beam with a generally shaped cross section, which consists of straight cross-section edges and is non-uniform along the axial direction. To derive cross-sectional shape functions for the higher-order deformation modes, a new approach is introduced using a set of beam frame models. The distortions with inextensional cross-sectional walls are determined by solving an eigenvalue problem of a beam frame model under inextensional wall constraints. Subsequently, the distortions with extensional cross-sectional walls are evaluated by considering orthogonality with respect to the inextensional distortions. Moreover, the extensional distortions due to the Poisson effect, which is generated due to the uniform axial strain of the rigid-body cross-sectional deformations, are considered. Warpings induced by the inextensional and extensional distortions are consistently defined based on the orders of the tangential displacements of their corresponding distortions. To deal with the varying cross section, three-dimensional displacements at an arbitrary point are interpolated using those at the cross sections of the nodes, where the beam frame analyses are performed. The proposed method is validated by performing static and vibration analyses of beams with varying single- and multi-cell cross sections.