A Review on Membrane Finite Elements with Drilling Degree of Freedom

Membrane finite elements have gained increasing importance since the early years of the finite elements method due to their convenience to a wide range of plane and 3D shell problems. Many research works have been focussing on membrane elements with drilling rotation. These elements are plane stress finite elements with a rotational in-plane degree of freedom. The main motivation for introducing the drilling rotation into membrane/shell elements is to improve the accuracy of the model and to avoid the problem of singularity of the stiffness matrix of shell elements in a natural way. In this article, a comprehensive review has been written for both new and expert researchers in the field. By summarizing the basic theories that have been used, new researchers can get clarification on the relevant computational methods and, gradually get familiarized with the advantages and drawbacks of each formulation. Expert researchers in the field can track-back the history of membrane elements with drilling rotation through a comprehensive review of relevant references.