Nonlinear finite element analysis of three-dimensional frames

Abstract

This paper presents a numerical model for the nonlinear analysis of three-dimensional frames using the finite element method. The model is based on a general variational formulation for thin-walled beams with open or closed sections; the mathematical development uses an updated Lagrangian description for shallow arches, taking into account geometrical and material nonlinearities, residual stresses, member initial imperfections, warping, and connection flexibility. The model has been used to evaluate second-order effects and the influence of residual stresses and joint flexibility on the behavior of plane frames. A semirigid space frame has been analyzed and the gain in rigidity offered by a horizontal rigid diaphragm has been evaluated. Key words: analysis, connection, finite element, nonlinearity, residual stress, thin-walled beams, warping.