Static and dynamic convergence studies of a four-noded membrane finite element with rotational degrees of freedom based on displacement superposition

Static and dynamic performance tests of a four-noded quadrilateral isoparametric membrane finite element enriched with rotational degrees of freedom (DOF) are presented. The formulation is based on displacement superposition whereby the in-plane displacements are decomposed additively into a regular, low-order contribution (governed by the nodal in-plane displacements) and a higher-order contribution (governed by the nodal in-plane rotations). The sensitivity of the element to element distortion and element aspect ratio is investigated. Comparisons with standard bilinear finite elements are made for static and dynamic loading case. It is demonstrated that the studied element exhibits an accuracy per DOF that is superior to the standard bilinear finite element.