An efficient standard plate theory

A review of the recent developments in the analysis of laminated beams and plates with an emphasis on shear effects and buckling is presented. A discussion of various shear-deformation theories for plates and beams is given. The available theories are derived assuming a variation of either the in-plane displacement components or the stress components or both in the thickness coordinate. A review of the recently developed finite elements to analyze thin and thick laminated beams and plates is given next. These elements have been derived using the displacement methods, or the mixed methods or the hybrid methods. Recent studies on the buckling and postbuckling behavior of perfect and geometrically imperfect plates are described next. These behaviors have been studied using analytical, numerical, and experimental techniques. Finally, a review of the various studies on the delamination buckling and growth in beams and plates is given. Once again, the studies have been conducted using analytical, numerical, and experimental techniques. The energy release rates have been determined using closed-form solutions or using numerical differentiation. Mention also is made of studies on multiple delaminations and on dynamic response of composite laminates under impact loads.

Recent advances in analysis of laminated beams and plates. Part I - Sheareffects and buckling.

The layerwise laminate theory of Reddy (1987) is used to develop a layerwise, two-dimensional, displacement-based, finite element model of laminated composite plates that assumes a piecewise continuous distribution of the tranverse strains through the laminate thickness. The resulting layerwise finite element model is capable of computing interlaminar stresses and other localized effects with the same level of accuracy as a conventional 3D finite element model. Although the total number of degrees of freedom are comparable in both models, the layerwise model maintains a 2D-type data structure that provides several advantages over a conventional 3D finite element model, e.g. simplified input data, ease of mesh alteration, and faster element stiffness matrix formulation. Two sample problems are provided to illustrate the accuracy of the present model in computing interlaminar stresses for laminates in bending and extension.

Modelling of thick composites using a layerwise laminate theory

An efficient higher order plate theory for laminated composites is developed. A composite plate theory for general lamination configurations is obtained by superimposing a cubic varying displacement field on a zig-zag linearly varying displacement. The theory has the same number of dependent unknowns as first-order shear deformation theory, and the number of unknowns is independent of the number of layers. The displacement satisfies transverse shear stress continuity conditions at the interface between layers as well as shear free surface conditions. Thus, an artificial shear correction factor is not needed. To demonstrate and compare with other theories, the analytical solution for cylindrical bending is obtained. The present theory gives deflections and stresses that compare well with other known theories.

M. di Sciuva

Papers

Bending, vibration and buckling of simply supported thick multilayered orthotropic plates: an evaluation of a new displacement model