A practical quadrilateral membrane element with drilling degrees of freedom

A simple, robust quadrilateral membrane element with drilling degrees of freedom is presented in this paper. This membrane element is based on Allman's approach, and derived from the constrained variational principle which enforces the equality of rotations obtained from the displacement field and independent rotation field by a penalty function. Examples show that the presented membrane element is fully compatible with typical beam element and plate element. And also, the non-conforming shape functions used in this element exhibits excellent performance over both regular and distorted meshes. Based on the presented membrane element, it is very convenient to construct the shear wall element of six degrees of freedom, which is often used in The analysis of general three-dimensional building structures.