Geometric and material nonlinear analysis of thin-walled members with arbitrary open cross-section

摘要

This paper describes the formulation of a thin-walled beam finite element for arbitrary open cross-sections, including doubly-, singly- and non-symmetric cross-sections. The formulation is developed within the corotational framework of OpenSees - an open source program available for the simulation of structural and geotechnical systems. The formulation accounts for eccentricity between the shear centre and the centroid of the cross-section, as well as warping. Both elastic and inelastic material behaviour is considered. The stiffness relation for the displacement-based beam element is established based on the Green-Lagrange strain. A local cross-section transformation matrix is derived to relate the end actions with the axial force acting at the centroid to the end actions with the axial force acting at the member axis system. The elastic and inelastic performance of the beam finite element is demonstrated through a series of instability problems comprising doubly-, singly- and non-symmetric sections subjected to compression, bending, and torsion. The buckling and post-buckling behavior predicted by the beam element is shown to be in close agreement with the results of shell finite element models, thereby demonstrating its reliability.