Thermal buckling of annular microstructure-dependent functionally graded material plates resting on an elastic medium

Abstract

First, modified couple stress theory is extended in the presence of thermo-mechanical loading. To this end, the generalized form of Hamilton's principle as well as constitutive relations are derived in general curvilinear coordinates. Then using the developed formalism, the bifurcation-type buckling of heated annular plates composed of functionally graded materials (FGMs) and resting on an elastic foundation is analytically studied. The non-classical FGM plate model contains a material length scale parameter and can interpret size effect. The adjacent equilibrium criterion is employed to derive stability equations. Thermo-mechanical properties of FGM plates are assumed to be graded across the thickness direction according to a power law form. Various types of thermal loading including uniform temperature rise, linear temperature distribution and heat conduction across the thickness are considered. A parametric study is conducted to investigate the influences of the material length scale parameter, power law index, inner and outer radii and also elastic foundation coefficients on thermal stability characteristics of FGM plates. The results reveal the existence of bifurcation-type buckling for a certain type of boundary conditions in which case the buckling patterns are asymmetric. Furthermore, the material length scale parameter and the geometry of annular FGM plates are shown to be more influential.