Thermal buckling of FGM thin plates with variable thickness

Abstract

The main focus of this study is the thermal buckling analysis of plates. In particular, the studies on the problem of the stability of various shapes of plates are extensive but quite little has been reported for the thermal buckling problem of plates. In this thesis, thermal buckling of rectangular and elliptical plates is examined. Plate theories are investigated and Kirchhoff plate theory is applied to derive and formulate thermal buckling problem. Boundary conditions are assumed to be simply supported and clamped in the whole study. Rayleigh-Ritz method is used to solve the energy equations and to obtain the critical buckling loads. The study consists of three main parts. The first part focuses on the thermal buckling of rectangular and elliptical Kirchhoff plates with constant thickness. Critical buckling temperatures for the homogenous, isotropic plates are obtained; the results are presented in graphical and tabular forms and compared with previously obtained results of the available literature. The second part of the study covers the thermal buckling analyses of functionally graded material (FGM) Kirchhoff plates with constant thickness. FGM plates are advanced composites with properties that vary continuously through the thickness of the plate. Metal-ceramic FGM plates are proposed for the use in thermal analyses where a metal-rich interior surface of the plate gradually transitions to a ceramic-rich exterior surface of the plate. The effect of the FGM on the thermal buckling of rectangular and elliptical plates is discussed. In the last part of the study, elliptical and rectangular FGM Kirchhoff plates with variable thicknesses are studied. The effect of parabolic thickness variation on the critical buckling load parameter is investigated. Then, parametric studies are carried out to examine the effects of material properties and thickness variation on the critical buckling temperatures. As a consequence, since the exact solution of thermally induced general buckling problems of plates is very difficult and in many cases even impossible, thermal buckling problem of plates is simplified and the critical buckling temperatures for homogenous and FGM plates with constant thicknesses and FGM plates with variable thicknesses are presented.