Thermo-mechanical buckling analysis of embedded nanosize FG plates in thermal environments via an inverse cotangential theory

Abstract In this article, thermal buckling behavior of size-dependent functionally graded nanoplates resting on two-parameter elastic foundation under various types of thermal environments is studied based on a new refined trigonometric shear deformation theory for the first time. It is assumed that the FG nanoplate is exposed to uniform, linear and sinusoidal temperature rises. Mori–Tanaka model is adopted to describe gradually variation of material properties along the plate thickness. Size-dependency of nanosize FG plate is captured by using nonlocal elasticity theory of Eringen. Through Hamilton’s principle the governing equations are derived for a refined four-variable shear deformation plate theory and then solved analytically. A variety of examples is presented to indicate the importance of elastic foundation parameters, various temperature fields, nonlocality, material composition, aspect and side-to-thickness ratios on critical buckling temperatures of FG nanoplate. Hence, the present study provides beneficial results for the accurate design of FG nanostructures subjected to various thermo-mechanical loadings.