A kinematically exact finite element formulation of elastic–plastic curved beams

Abstract

A finite element, large displacement formulation of static elastic–plastic analysis of slender arbitrarily curved planar beams is presented. Non-conservative and dynamic loads are at present not included. The Bernoulli hypothesis of plane cross-sections is assumed and the effect of shear strains is neglected. Exact non-linear kinematic equations of curved beams, derived by Reissner are incorporated into a generalized principle of virtual work through Lagrangian multipliers. The only function that has to be interpolated in the finite element implementation is the rotation of the centroid axis of a beam. This is an important advantage over other classical displacement approaches since the field consistency problem and related locking phenomena do not arise. Numerical examples, comprising elastic and elastic–plastic, curved and straight beams, at large displacements and rotations, show very nice computational and accuracy characteristics of the present family of finite elements. The comparisons with other published results very clearly show the superior performance of the present elements.