An Improved Shear-Deformation Theory for Moderately Thick Multilayered Anisotropic Shells and Plates

Abstract

The general linear equations governing the motion of moderately thick multilayered anisotropic shells are derived by making use of the principle of virtual work in conjunction with an a priori assumed displacement field. The assumed displacement field is piecewise linear in the u and v components and fulfills the static and geometric continuity conditions between the contiguous layers; furthermore, it takes into account the distortion of the deformed normal. Shear and rotatory inertia terms have also been considered in the formulation. Particularization of the resulting equations to the flat multilayered anisotropic plates is straightforward; thus, only the final expressions are given. The proposed approach gives, as particular cases, the linear equations of motion of the classical shells theory based on the Kirchhoff-Love kinematic hypothesis and those of the shear deformation theory for which it is assumed that the deformed normal do not distort.

Buckling analysis of laminated composite plates using an efficient C0 FE model

“…A major development in this direction is due to Di Sciuva [34], Murakami [23], Liu et al [20], and few others. They proposed zigzag plate theory where layer-wise theory is initially used to represent the in-plane displacements having piecewise linear variation across the thickness.…”

An efficient C0 FE model for the analysis of composites and sandwich laminates with general layup

“…These plate theories perform well but they require significant computational involvement in analyzing a multi-layered plate since the number of unknowns increases with the number of layers. A major development in this direction is due to Di Sciuva [14], Murakami [22], Liu et al [9], and few others. They proposed zigzag plate theory where layer-wise theory is initially used to represent the in-plane displacements having piecewise linear variation across the thickness.…”

“…The mathematical involvement in these plate theories is quite heavy and the solution becomes quite expensive in a multilayered plate, as the unknowns are dependent on number of layers. There is another class of layer wise plate theories [1,6,7,9,14,15,22] where the unknowns of different planes are expressed in terms of those of a particular plane using the condition of shear stress continuity at the layer interfaces. The number of unknowns is reduced in these plate theories considerably [1,6,7,9,14,15,22] .…”

Two-noded zigzag beam element accounting for shear effects based on an extended Euler Bernoulli theory

“…These theories assume that the axial displacement is the superposition of a linear piecewise zigzag distribution and a linear [6,7], quadratic [8,9] or cubic [10][11][12][13] in-plane displacement field. In the most of early zigzag theories the zigzag function is obtained by enforcing the continuity of the transverse shear stresses across the laminate thickness.…”