Stress oscillations and spurious load mechanisms in variationally inconsistent assumed strain formulations

Abstract

Assumed field-consistent strain formulations of the displacement finite element procedure can lead to poor convergence and spurious stress oscillations if the assumed strain fields are not variationally correct, i.e. they do not satisfy an important orthogonality condition emerging from the equivalence sought between assumed strain displacement procedures and mixed procedures based on the Hellinger-Reissner theorem. Failure to ensure variational correctness introduces errors which can be equated to the presence of spurious loading mechanisms that cause stress oscillations. In this paper, we use the Timoshenko beam element to demonstrate that field-consistency and variational' consistency are two complementary but mutually exclusive principles-one does not imply the other and that both are necessary to successfully implement a displacement type finite element for constrained media.