A new enhanced assumed strain quadrilateral membrane element with drilling degree of freedom and modified shape functions

A new four‐node quadrilateral membrane finite element with drilling rotational degree of freedom based on the enhanced assumed strain formulation is presented. A simple formulation is achieved by five incompatible modes that are added to the Allman‐type interpolation. Furthermore, modified shape functions are used to improve the behaviour of distorted elements. Numerical results show that the proposed new element exhibits good numerical accuracy and improved performance, and in many cases, superior to existing elements. In particular, Poisson's locking in nearly incompressible elasticity fades and the element performs well when it becomes considerably distorted even when it takes almost triangular shape. Copyright © 2016 John Wiley & Sons, Ltd.