An efficient zigzag theory based finite element modeling of composite and sandwich plates with multiple delaminations using a hybrid continuity method

Abstract

We present a finite element (FE) formulation based on an efficient layerwise (zigzag) theory for stress and vibration analysis of highly inhomogeneous composite and sandwich plates with multiple delaminations using the region method. The delaminations are assumed to be present at multiple interfacial and/or planar locations, and are not allowed to change in size during the deformations. Following the free mode model, the delaminated faces are assumed to have no mutual interaction during deformations. Using a hybrid method, the continuity of inplane displacements at the delamination front is satisfied exactly at the midplanes of the sublaminates separated by delaminations, while the deviations of their through-thickness variations in the intact and delaminated segments are minimized with respect to the rotation variables, using the least squares method. The formulation is shown to yield accurate results with reference to the full-field three dimensional FE solutions, for the deflection, stresses, natural frequencies and mode shapes for delaminated composite as well as highly inhomogeneous single- and double-core sandwich plates. The conventional point and least squares continuity methods, however, show large error for moderately thick plates and for higher than fundamental vibration modes. The smeared third order theory, which has the same number of degrees of freedom as the zigzag theory, is shown to yield grossly inaccurate results for delaminated sandwich plates. The present formulation is more computationally efficient than the layerwise theories that are usually used for such analysis, but is at the same time accurate, simple and robust.