On the use of the Murakamiʹs zig-zag function in the modeling of layered plates and shells

This paper discusses the use of the Murakami zig-zag function (MZZF) in the two-dimensional modeling of multilayered plates and shells. A literature overview of the available works is first presented. A `simple useʹ of the MZZF is discussed: the MZZF is used to introduce the zig-zag effect in classical and higher order theories which are formulated with only displacement unknowns. An `advanced useʹ of the MZZF is then considered to introduce the zig-zag effect in those theories which are formulated on the basis of both displacement and transverse stress assumptions. A number of new plate/shell theories has been considered. Numerical results encompassing, static, dynamic and thermally loaded orthotropic, simply supported plates and shells are presented to show both the effectiveness and limitations of the MZZF in the modeling of layered structures. Linear up to forth-order expansions for the in-plane and the out-of-plane displacements, in the thickness plate/shell direction, have been compared. It has been concluded that the MZZF is a valuable tool to enhance the performances of both classical and advanced theories. The conducted numerical evaluations have shown in particular that multilayered plate and shell theories can be greatly improved by the use of MZZF.