Refined multilayered plate elements based on Murakami zig–zag functions

Abstract

This paper discusses the FEM use of Murakami zig–zag function (MZZF) in the two-dimensional modeling of multilayered plates. A literature overview is first conducted on the available works in which MZZF has been applied. MZZF is used to introduce the zig–zag effect in classical and higher order theories, which are formulated using only displacements as unknowns. MZZF is also considered to introduce the zig–zag effect in those theories, which are formulated on the basis of both displacement and transverse stress assumptions (mixed formulations). The present FEM formulation is validated by comparing the results with some available papers from the literature. A very thick plate ( a/ h = 4) is studied and the results are compared with the commercial code NASTRAN. Numerical results are presented to show both the effectiveness and limitations of MZZF in the modeling of layered plates. Linear up to forth order expansion for in-plane and out-of-plane displacements, in the thickness plate direction, has been compared. It has been concluded that MZZF consists of a valuable tool to enhance the performances of both classical and advanced theories. In particular, the conducted numerical evaluations have shown that it can be more convenient to enhance a plate theory by introducing the MZZF than refining it by adding two or three higher order terms. However, in order to well approximate local effects or study thick plates, advanced models (layer-wise or three-dimensional) are required.