First-order zig-zag sublaminate plate theory and finite element model for laminated composite and sandwich panels

Abstract

A refined laminated plate theory and three-dimensional finite element based on first-order zig-zag sublaminate approximations has been developed. The in-plane displacement fields in each sublaminate are assumed to be piecewise linear functions and vary in a zig-zag fashion through-the-thickness of the sublaminate. The zig-zag functions are evaluated by enforcing the continuity of transverse shear stresses at layer interfaces. This in-plane displacement field assumption accounts for discrete layer effects without increasing the number of degrees of freedom as the number of layers is increased. The transverse displacement field is assumed to vary linearly through-the-thickness. The transverse normal strain predictions are improved by assuming a constant variation of transverse normal stress in each sublaminate. In the computational model, each finite element represents one sublaminate. The finite element is developed with the topology of an eight-noded brick, allowing the thickness of the plate to be discretized into several elements, or sublaminates, where each sublaminate can contain more than one physical layer. Each node has five engineering degrees of freedom, three translations and two rotations. Thus, this element can be conveniently implemented into general purpose finite element codes. The element stiffness coefficients are integrated exactly, yet the element exhibits no shear locking due to the use of an interdependent interpolation scheme and consistent shear strain fields. Numerical performance of the current element is investigated for a composite armored vehicle panel and a sandwich panel. These tests demonstrate that the element is very accurate and robust.