Efficient Global Zigzag Theory for Elastic Laminated Plates P. KUMARI, J. K. NATH, S. KAPURIA AND P. C. DUMIR* Department of Applied Mechanics, IIT Delhi, New Delhi 110016, India ABSTRACT: An efficient global zigzag theory (GZIGT) is developed for elastic laminated plates, by approximating the in-plane displacements by a cubic expansion in thickness coordinate along with a global zigzag function, which takes values 1 at successive interfaces. The deflection is approximated to account explicitly for transverse thermal strain. The displacement variables are reduced to five, the same as used in first-order shear deformation theory, by imposing the conditions on transverse shear at three a priori selected interfaces/faces. A third order theory (TOT1) is also developed with similar expression of deflection. GZIGT and TOT1 are assessed by comparison with exact three-dimensional solutions for simply-supported square plates for sinusoidal pressure and thermal loads, natural frequencies and buckling. In general, GZIGT yields good results for two-ply, three-ply and four-ply composite plates, but it is inaccurate for a highly inhomogeneous test plate. KEY WORDS: plates, elasticity, analytical modeling, laminate mechanics, 2D theory. INTRODUCTION I N THICK AND moderately thick laminated composite and sandwich plates, transverse shear strain is significant since transverse shear modulus is much smaller than the in-plane Young’s modulus. The thermal normal strain in the thickness direction is significant for thermal loading. The three-dimensional (3D) exact solutions show that there is slope discontinuity in the in-plane displacements at the layer interfaces. These three effects need to be included in two-dimensional (2D) theories of laminated composite and sandwich plates. Reviews of 2D theories have appeared in references [1–4]. The displacements in equivalent single layer (ESL) theories are approximated globally across the thickness, with the same functional dependence on the thickness coordinate. Examples of such theories for laminated plates are: the first-order shear deformation theory (FSDT) [5–7], third-order theory (TOT) [8,9], global zigzag theory [10–13] with a global zigzag piecewise linear function which takes values 1 at successive interfaces, and higher order theories (HOT) [14–16]. FSDT is formulated in terms of five displacement variables, but unlike other theories, it requires arbitrary shear correction factors. If shear traction-free conditions are satisfied at the top and bottom surfaces of the plate, then TOT is also formulated in terms of five displacement variables. In ESL theories, the slope discontinuity in the in-plane displacements and *Author to whom correspondence should be addressed. E-mail: pcdiit@gmail.com Journal of REINFORCED PLASTICS AND COMPOSITES, Vol. 28, No. 9/2009 1025 0731-6844/09/09 1025–23 $10.00/0 DOI: 10.1177/0731684407079770 ß SAGE Publications 2009 Los Angeles, London, New Delhi and Singapore