An efficient layerwise finite element for shallow composite and sandwich shells

In this work, we extend a previously developed four-node quadrilateral element for laminated plates based on an efficient layerwise theory, called the zigzag theory (ZIGT), to laminated shallow shells. The accuracy of the new element is assessed for static and free vibration responses, by comparing with the available 3D elasticity solutions as well as the 2D analytical and FE solutions for various singly- and doubly-curved composite and sandwich shallow shells. The comparison with other available finite elements shows that the present element with seven degrees of freedom per node, gives by far the best performance in terms of accuracy, computational efficiency and simplicity. The results are more accurate than even the three-layer higher order layerwise theories, which have been developed specifically for sandwich shells. The equivalent single layer theories with the same or even higher number of primary variables yield extremely poor predictions, particularly for sandwich shells.