Field‐consistency and violent stress oscillations in the finite element method

Abstract

Abstract The fact that finite element models can give rise to violent stress oscillations and that there are optimal locations where stresses can be correctly sampled in spite of the presence of these violent stress fluctuations has been known for some time. However, it is less well known that these oscillations arise in a specific class of problems—where there are multiple strainfields arising from one or more field‐variables and where one or more of these strain‐fields must be constrained in particular physical limits. In this paper, we show that unless the interpolations for these constrained strain‐fields are ‘field‐consistent’, violent oscillations would set in. These oscillations represent spurious self‐equilibrating stress‐fields generating spurious energy terms that lead to ‘locking’. The field‐consistency interpretation offers a conceptual scheme to delineate these problems and an operational procedure called the functional reconstitution technique allows the errors resulting from field‐inconsistency to be anticipated a priori . We demonstrate the power of this approach through an interesting example of a multi‐strain‐field problem—the inextensional/nearly inextensional deformation of a shear flexible curved beam.