A mixed finite element for three-dimensional nonlinear analysis of steel frames

Abstract

This paper develops and demonstrates a mixed beam finite element that can represent the inelastic three-dimensional stability behavior of frames composed of open-walled cross-section members. The kinematics of deformation of the element include finite rotation and warping of the cross-section due to torsion. The material inelasticity is based on a two-space model that includes the effect of shear stresses due to uniform torsion in addition to normal stresses due to axial force, biaxial bending, and bimoment. Initial geometric imperfections and residual stresses are accommodated. The formulation is based on a two-field (displacement and generalized stress) Hellinger–Reissner (HR) variational principle. The interpolation of the generalized stresses (i.e., cross-section stress resultants) along the element length is based on the geometrically-exact nonlinear governing differential equations of equilibrium. This leads to significant improvements in the accuracy over conventional displacement-based elements in problems involving highly nonlinear variations in the curvature along the member lengths due to geometric nonlinearity and/or distributed plasticity effects. Several numerical examples involving two- and three-dimensional elastic and inelastic stability behavior are presented to illustrate the capabilities of the formulation.