A four-node facet shell element for laminated shells based on the third order zigzag theory

In this work, we develop a facet shell element for deep laminated shells, by extending a successful four-node quadrilateral element for laminated plates based on the efficient third order zigzag theory. The obstacle course test comprising of three standard problems is undertaken to examine its performance for various modes of shell behavior. The absence of shear and membrane locking problems is established through the analysis of ultra thin shells. The accuracy of the element is assessed for the static and free vibration responses of composite and sandwich shells in comparison with the three dimensional elasticity solutions. In terms of accuracy, computational efficiency and robustness, the present element is shown to give better performance than various classical and recent finite elements considered in this study. In the case of sandwich shells, for which the equivalent single layer theories showed a high level of error, the present element is shown to yield more accurate results than even the higher-order sandwich shell theories that have been developed specifically for the three-layer sandwich shells.