External Stiffness Approach for Thin-Walled Frames with Elastic-Plasticity

Abstract

This work presents a one-dimensional finite element formulation for non-linear analysis of framed structures with thin-walled cross-section. Using the updated Lagrangian (UL) incremental formulation, the assumption of isotropic and linear-elastic material behaviour and the non-linear displacement field of thin-walled cross-section based on inclusion of second-order terms of large rotations, a tangent stiffness matrix of a two-node space beam element is firstly developed. Due to the non-linear displacement field, all internal moments occurring in the geometric stiffness are obtained as those of semitangential behaviour. In this way the joint equilibrium of non-collinear elements is provided. External stiffness approach (ESA) is applied in the force recovery phase. Material non-linearity is introduced for an elastic-perfectly plastic material through the plastic hinge formation at finite element ends and for this a plastic reduction matrix of the element is determined. The interaction of element forces at a hinge and the possibility of elastic unloading are taken into account. The effectiveness of the numerical algorithm discussed is validated through the test problem.