An assessment of mixed and classical theories on global and local response of multilayered orthotropic plates

Abstract This article assesses two-dimensional theories to evaluate global and local response of orthotropic, multilayered plates. The introductory discussion outlines five, relevant key-points that should be to be addressed in the modeling of multilayered structures. Classical theories formulated on the basis of Principle of Virtual Displacements (PVD) and mixed theories based on the Reissner Mixed Variational Theorem (RMVT) are presented. Theories which preserve the independence of the number of the independent variables from the numbers of the Nl-layers (ESLM, Equivalent Single Layer Models) and theories in which the number of the unknown variables remains Nl-dependent (LWM, Layer-Wise Models) are both considered. Modelings related to linear up-to-fourth order variations of the unknown variables in the thickness direction are treated. Sub-cases have been implemented which permits one to evaluate explicitly the effect of the so-called zig-zag (ZZ) effect, interlaminar continuity (IC) and transverse normal stresses σzz. As a result more than 40 theories have been implemented and compared for both local (displacement and stress distribution in the thickness plate direction) and global (mainly free vibration) response. A number of conclusions have been outlined in the numerical part.