Higher-order layerwise laminate theory for the prediction of interlaminar shear stresses in thick composite and sandwich composite plates Theofanis S. Plagianakos a, * , Dimitris A. Saravanos b a Empa, Swiss Federal Laboratories of Materials Testing and Research, Center for Synergetic Structures, Duebendorf CH-8600, Switzerland b Department of Mechanical Engineering and Aeronautics, University of Patras, Patras GR-26500, Greece Available online 31 January 2008 Abstract A higher-order layerwise theoretical framework is presented, which enables prediction of the static response of thick composite and sandwich composite plates. The displacement field in each discrete layer through the thickness of the laminate includes quadratic and cubic polynomial distributions of the in-plane displacements, in addition to the linear approximations assumed by linear layerwise the- ories. In-plane and interlaminar shear stiffness matrices of each discrete layer are formulated and interlaminar shear stress compatibility conditions are subsequently imposed to ensure continuity of interlaminar shear stresses through the thickness. A Ritz-type exact solution is further implemented to yield the structural response of thick composite and sandwich composite plates. The advantage of the present formulation in comparison to linear layerwise theories lies in the small number of discrete layers used to model the thick composite lam- inate through-thickness and in the prediction of interlaminar shear stresses at the interface. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Plate; Composite; Sandwich; Layerwise laminate theory; Interlaminar shear stress; Ritz-type solution 1. Introduction The expanding use of composite structures in lightweight applications indicates the significance of developing appro- priate models in order to predict their static and damped dynamic response, as well as, to quantify the effect of param- eters, such as thickness and lamination, on this response. Sandwich structures with composite faces and foam core are widely used as lightweight components in civil engineer- ing, automotive and aerospace applications due to their excellent mechanical properties, such as, high flexural stiff- ness to mass ratio and impressive damping performance. Moreover, in both thick composite and sandwich composite structures the static and damped dynamic response is strongly affected by increased interlaminar shear caused by high thickness and inhomogeneity in properties through the thickness. However, these effects cannot be adequately cap- tured by single-layer theories, thus, formulation of specialty layerwise theories is essential in order to accurately predict the through-thickness displacement, strain and stress fields. The early works in the field of layerwise modeling of structures date from the mid 30s and have been extensively reviewed by Carrera [1]. In the field of composite structures, the layerwise laminate theories developed aim to the efficient prediction of the through-thickness composite laminate response, which was firstly described by the exact three- dimensional solutions of Pagano [2,3]. On the basis of the linear layerwise laminate theory of Reddy [4], various exact solutions and finite element methodologies have been pub- lished, which predict the static or damped dynamic response of thick composite and sandwich composite beams, plates and shells and have been thoroughly reviewed by Reddy and Robbins [5] and Noor et al. [6]. Most of those laminate theories assume linear distributions of the in-plane displace- ments and constant deflection through the thickness of the laminate, while other theories include a linear layerwise through-thickness approximation of the transverse 0263-8223/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.compstruct.2007.12.002 * Corresponding author. Tel.: +41 44 8234047; fax: +41 44 8234211. E-mail address: theofanis.plagianakos@empa.ch (T.S. Plagianakos). www.elsevier.com/locate/compstruct Available online at www.sciencedirect.com Composite Structures 87 (2009) 23–35