On Performance of Nine-Node Quadrilateral Shell Elements 9-EAS11 and MITC9i.

The chapter concerns nine-node quadrilateral shell elements derived for the Reissner-Mindlin kinematics and Green strain. They are based on the potential energy functional extended to include drilling rotations. A standard element of this class suffers from locking and over-stiffening; several special techniques are needed to improve its performance. We developed three nine-node shell elements with the membrane strains enhanced by the EAS11 representation of Bischoff and Ramm (Int. J. Num. Meth. Eng. 40:4427-4449, 1997 [2]). The transverse shear strains are treated either by the ANS method of Jang and Pinsky (Int. J. Num. Meth. Eng. 24:2389-2411, 1987 [6]), or are enhanced by the EAS6 representation of Sansour and Kollmann (Comput. Mech. 24:435-447, 2000 [17]), or remain unmodified. We also modify the EAS transformation rule, extending the idea put forward in Park and Lee (Comput. Mech. 15:473-484, 1995 [15]) for curved shells. Several numerical examples provide comparison of three 9-EAS11 elements to our MITC9i shell element of Wisniewski and Turska (Comput. Mech. 62, 499-523, 2018 [20]).