An isoparametric quadratic thick curved beam element

Abstract

Abstract A three‐noded curved beam element with transverse shear deformation, based on independent isoparametric quadratic interpolations, is designed from field‐consistency principles. It is shown that a quadratic element that is field‐inconsistent in membrane strain suffers from ‘membrane locking’—i.e. an error of the second kind propagates indefinitely as the element length to thickness ratio and/or the element length to radius of curvature ratio increase, in nearly inextensional bending. However, field‐inconsistency in shear strain does not lead to ‘shear locking’ but degrades its performance to exactly that of a field‐consistent linear element. It is also seen that field‐inconsistency leads to severe axial force and shear force oscillations. Error estimates for locking are derived, wherever possible, and confirmed by numerical experiments. The field‐consistent element offered here is the most efficient quadratic curved beam element possible.