Free edge stress analysis of general cross-ply composite laminates under extension and thermal loading Masoud Tahani * , Asghar Nosier Department of Mechanical Engineering, Sharif University of Technology, P.O. Box 11365-9567, Azadi Ave., Tehran, Iran Abstract An elasticity formulation for finite general cross-ply (symmetric and unsymmetric) laminates subjected to extension and/or a layerwise temperature distribution is developed. It is shown that the edge-effect problem of such laminates is actually a quasi-three- dimensional problem and its stress analysis can be restricted to a generic two-dimensional cross-section of the laminates. A layerwise theory is used to investigate analytically the interlaminar stresses near the free edges of general cross-ply composite laminates. The results obtained from this theory are compared with those available in the literature. It is found that the theory can predict very accurately the stresses in the interior region and near the free edges of composite laminates. Ó 2002 Elsevier Science Ltd. All rights reserved. Keywords: Composite laminates; Free edge stresses; Elasticity formulation; Layerwise theory; Extension; Thermal loading 1. Introduction Edge effect in laminated composites may result in delamination and transverse cracking when the applied loading is much lower than the failure strength predicted by the classical lamination theory (CLT). Approximate solutions show that complex stress states, which result from the presence and interactions of the discontinuities of the geometry and materials across the thickness, oc- curred at free edges with a rapid change of gradients and the CLT is inadequate [1,2]. The interlaminar stress distribution at free edges in composite laminates has been investigated for some years [1–29]. However, be- cause of inherent complexities involved in the problem no exact solution is known for elasticity equations. Therefore, various approximate methods for deter- mining the interlaminar stresses are documented in the literature. These methods may, for convenience, be classified as either analytical or numerical. Because of the exceptionally large number of papers on the subject matter only the pertinent pioneering works are referred here. The interested reader will find sufficient references to cover the literature in more depth in the review article by Kant and Swaminathan [3]. 1.1. Analytical methods The first approximate solution of interlaminar shear stresses was proposed by Puppo and Evenson [4] based on a laminated model containing anisotropic layers separated by isotropic adhesive layers with interlaminar normal stress being neglected through the laminate. Other approximate analytical methods used to examine the problem are the employment of the higher-order plate theory by Pagano [2], the perturbation technique by Hsu and Herakovich [5], the boundary layer theory by Tang and Levy [6], and the approximate elasticity solutions by Pipes and Pagano [7]. An approximate theory is also used by Pagano [8,9] based on assumed in- plane stresses and the use of ReissnerÕs variational principle. Wang and Choi [10,11] studied the free edge singularities by means of LekhnistskiiÕs stress potential and the theory of anisotropic elasticity. Kassapoglou and Lagace [12], using the principle of minimum com- plementary energy and the force balance method, ana- lyzed the symmetric laminates under uniaxial loading. Later Kassapoglou [13] generalized this approach for general unsymmetric laminates under combined in-plane and out-of-plane loads. Yin [14,15] used a variational method involving LekhnitskiiÕs stress function to deter- mine the interlaminar stresses in a multilayer strip of a laminate subjected to combinations of mechanical loads. In addition, Yin [16] based on polynomial expansions of * Corresponding author. Tel.: +98-21-600-5716; fax: +98-21-600- 0021. E-mail address: mtahani@mehr.sharif.edu (M. Tahani). 0263-8223/03/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII:S0263-8223(02)00290-8 Composite Structures 60 (2003) 91–103 www.elsevier.com/locate/compstruct