Solutions of some stability problems in functionally graded rectangular plates

ABSTRACT Laminated composite materials are commonly used in engineering structures. In the laminated structures that are subjected to thermal and/or mechanical loads, a sudden change in material properties at the interfaces can result in locally large deformations, which may trigger the initiation and the propagation of a micro crack in a lamina. Overcoming this problem may be possible by the use of Functionally Graded Materials (FGM) that are composite materials microscopically non-homogeneous in which the mechanical properties vary smoothly and continuously from one surface to the other. As they can be tailored to different applications and working environments, these materials typically made of isotropic components such as ceramics and metals are progressively pulling the attention of the researchers. As having a relatively short manufacturing history back to the 1980s, the research on methods of the theory and analysis of FGMs are still in progress. In this study, a rectangular FGM plate is considered. Through-the-thickness variation of the modulus of elasticity with respect to the mid-plane is analysed for three macro models, Symmetric Reddy, Anti-Symmetric Reddy, Symmetric Exponential and a micro model (Mori-Tanaka). Essentially, three different combinations of clamped and simply supported edge boundary conditions (SSSS, SSCS, CSCS) and three loading types, uniaxial compression, biaxial compression, biaxial compression-tension (R=0, R=l, R= -1) are studied. Initially, the governing equations and applicable boundary conditions are given for the plate. The buckling behaviour of a plate subjected to uniform in-plane loading is analysed for the case of being simply supported at all edges (SSSS) by employing Classical Plate Theory (CPT) and Third order Shear Deformation Plate Theory (TSDPT) regarding the Navier Method whereas, the cases of two opposite edges being simply supported while the other two edges taking any combination of simply supported and clamped conditions (SSSS, SSCS, CSCS) are analysed by employing Classical Plate Theory, Levy Method and State-space technique. For all the cases forementioned, dimensionless critical buckling parameters are investigated with respect to different side-to-thickness ratios, aspect ratios for various types of FGM plates. Keywords: Functionally graded material, rectangular plate, buckling, state space approach, Mori-Tanaka micromechanical method. xm