On thermal instability of delaminated composite plates S.F. Nikrad a , H. Asadi a , A.H. Akbarzadeh b,c,⇑ , Z.T. Chen d a Department of Mechanical Engineering, Amirkabir University of Technology, Tehran 15875, Iran b Department of Bioresource Engineering, McGill University, Ste-Anne-de-Bellevue, Island of Montreal, QC H9X 3V9, Canada c Department of Mechanical Engineering, McGill University, Montreal, QC H3A 0C3, Canada d Department of Mechanical Engineering, University of Alberta, Edmonton, AB T6G 2G8, Canada article info Article history: Available online 13 July 2015 Keywords: Thermal instability Delamination Asymmetric composite plate Third-order shear deformation theory abstract This paper examines the thermal instability of rectangular delaminated composite plates. A solution pro- cedure is presented based on the third-order shear deformation theory by taking into consideration the von Karman geometrical nonlinearity. The proposed model is capable of analyzing both local buckling of the delaminated base laminate and sublaminate as well as the global buckling of the plate. The thermo- mechanical properties are temperature-dependent. The nonlinear equilibrium equations, derived by the minimum total potential energy principle, are solved by using the Ritz method along with the Newton– Raphson iterative procedure. Numerical results shed a light on the effects of embedded delamination, stacking sequences, and boundary conditions on the equilibrium path, thermal bifurcation points, buck- ling mode, in-plane displacement, normal/shear strain, and bending moment of the composite plates. It is found that the delamination leads to a substantial reduction in the thermal load-carrying capacity. Furthermore, depending on the boundary conditions and stacking sequence, the response of the perfect composite plates could be either of the bifurcation type or of the unique stable path. Ó 2015 Elsevier Ltd. All rights reserved. 1. Introduction Composite structures have drawn the attention of various industries, including aeronautics, aerospace, and marine, where a high ratio of strength/stiffness-to-weight, high energy absorption, and corrosion resistance are required. Composite materials are conventionally designed and manufactured by stacking layers of dissimilar fiber orientation. The manufacturing of composites, however, is far from being perfect and frequently leads to a geo- metrical or material imperfection, reducing the stiffness and strength of the designed composite structure [1]. In particular, delamination is one of the major failure modes of composites. Delamination has been of great importance for engineering appli- cations of composite materials as it triggers the structural instabil- ity, stiffness degradation, and reduction of the load carrying capacity. A brief literature review on the stability responses of delaminated composites is provided hereinafter [2–24]. A model for the buckling analysis of delaminated composite beams and plates was introduced by Chai et al. [2], where the local delamination growth and the instability were governed by an energy release rate criterion. They observed that the growth of the delamination could be stable, unstable, or an unstable growth followed by a stable growth. An analytical method was presented by Kyoung and Kim [4] to determine the buckling load and the growth of delamination. The buckling load was found to be depen- dent on the geometrical configuration of the delamination. Sallam and Simitses [6] introduced a one-dimensional model based on the classical plate theory to predict the buckling load of a delaminated composite. The buckling load serves as a measure for the load-carrying capacity of the damaged plate with a relatively small delamination length. Davidson [8] conducted theoretical and experimental studies to determine the strain and force at the instance of delamination buckling for a laminated composite with an elliptical delamination. The buckling characteristics of the com- posite beams with through-the-width delaminations were investi- gated by Shu [13]. It was shown that the delaminated segments could buckle either together in a constrained mode, independently in a free mode, or in a mixed partially constrained mode, depend- ing on the thickness of the delaminated layers. Wang and his col- leagues [14,15] determined the local buckling and the strain energy release rate of delaminated composite beams and plates via discontinuous elastic foundation modeling. They found that symmetrically loaded delaminated plates result in a mode I fracture. http://dx.doi.org/10.1016/j.compstruct.2015.07.019 0263-8223/Ó 2015 Elsevier Ltd. All rights reserved. ⇑ Corresponding author at: Department of Bioresource Engineering, McGill University, Ste-Anne-de-Bellevue, Island of Montreal, QC H9X 3V9, Canada. Tel.: +1 (514) 398 7680; fax: +1 (514) 398 7990. E-mail addresses: f.nikrad@aut.ac.ir (S.F. Nikrad), hamed_asadi@aut.ac.ir (H. Asadi), hamid.akbarzadeh@mcgill.ca (A.H. Akbarzadeh), zengtao.chen@ualberta. ca (Z.T. Chen). Composite Structures 132 (2015) 1149–1159 Contents lists available at ScienceDirect Composite Structures journal homepage: www.elsevier.com/locate/compstruct