Field-consistent strain interpolations for the quadratic shear flexible beam element

Abstract

A shear flexible (i.e. Timoshenko) quadratic isoparametric beam element with two degrees of freedom per node is critically examined from the point of view of the consistency of the constrained strain fields that arise in the thin-beam limits. The errors, in terms of convergence of displacement fields and violent oscillations of stress fields, that emerge when exactly integrated elements are used are predicted a priori and confirmed with numerical experiments. The rationale behind the use of optimal stress sampling at Gaussian points is also derived directly from these arguments.