A benchmark study of reduced-strain shell finite elements: quadratic schemes

We study experimentally the accuracy and reliability of some low-order shell nite element schemes based on modifying the standard displacement formulation by reduced-strain expressions. We focus on quadrilateral elements with a quadratic displacement approximation. Three benchmark problems with di erent asymptotic behaviour in the limit of zero shell thickness is used in the experiments. Following the error analysis of a reduced-strain scheme, we study two components of the total error, the approximation error and the consistency error. We demonstrate that the performance of the methods is both case and mesh dependent. When a bending dominated problem is solved, none of the methods studied can avoid the usual worst-case locking e ect of the approximation error on general meshes. For a membrane dominated problem the total error is typically dominated by the consistency error which often convergences slowly