Keywords: plate theory, virtual work, laminated composites, sandwich plates, finite element method, transverse shear deformation, zigzag kinematics.

Thick laminated-composite and sandwich structures exhibit pronounced shear deformation and, under certain conditions, transverse normal deformation, and require precise resolution of the stress field particularly in regions of stress concentration. The structural modeling demands computationally intensive three-dimensional finite element analyses that become prohibitively expensive, especially for nonlinear and/or progressive failure predictions. To achieve superior predictive capabilities using plate and shell approximations, the class of so-called zigzag theories has emerged as practical for engineering applications, for example see [1,2]. Studies have shown that these theories provide global response predictions and local bending stresses that are sufficiently accurate for multi-layered composite structures and that are comparable to those of computationally demanding and relatively complex layer-wise and higher-order theories.

Recently, Tessler et al. [3] elucidated several serious shortcomings of the most notable zigzag theories, and proposed a refined zigzag beam theory that overcomes these difficulties in an original and theoretically consistent manner. In this paper, following [3], first-order shear-deformation theory is augmented using an improved zigzag kinematic field to formulate a refined zigzag theory for laminated-composite and sandwich plates that exhibit a high degree of transverse shear flexibility, anisotropy, and heterogeneity. The kinematic assumptions involve a novel C⁰-continuous (across lamina interfaces) representation of the displacement field that is independent of the number of material layers and does not require enforcement of transverse-shear-stress continuity to yield accurate results. Unlike other similar theories, for example [1,2], the zigzag contribution to the axial displacement field is physically realistic, is zero-valued at the top and bottom plate surfaces, and contributes consistently to the shear deformation of every lamina. The equations of equilibrium and associated boundary conditions are derived from the virtual work principle. Finally, several example problems that represent a significant challenge for any approximate theory are examined, and the key results are demonstrated.

1

M. Di Sciuva, "An improved shear-deformation theory for moderately thick multilayered anisotropic shells and plates", ASME Journal of Applied Mechanics, 54, 589-596, 1987.

2

R.C. Averill, "Static and dynamic response of moderately thick laminated beams with damage", Composites Engineering, 4(4), 381-395, 1994. doi:10.1016/S0961-9526(09)80013-0

3

A. Tessler, M. Di Sciuva and M. Gherlone, "Refinement of Timoshenko beam theory for composite and sandwich beams using zigzag kinematics", NASA-TP-2007-215086, National Aeronautics and Space Administration, Washington, D.C., 2007.

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