Thermal buckling of clamped thin rectangular FGM plates resting on Pasternak elastic foundation (Three approximate analytical solutions)

Buckling of rectangular plates made of functionally graded material (FGM) under various types of thermal loading is considered. It is assumed that the plate is in contact with an elastic foundation during deformation. The derivation of equations is based on the classical plate theory. It is assumed that the mechanical and thermal non‐homogeneous properties of FGM plate vary smoothly by distribution of power law across the plate thickness. Using the non‐linear strain‐displacement relations, the equilibrium and stability equations of plates made of FGMs are derived. The boundary conditions for the plate are assumed to be clamped for all edges. The elastic foundation is modelled by two parameters Pasternak model, which is obtained by adding a shear layer to the Winkler model. Three distinct analytical solutions are presented to study the thermal buckling problem of thin FGM plates. These methods may be useful to study the eigenvalue problems for other loading types of FGM plates. Closed‐form solutions are presented and effects of various parameters, such as geometric characteristics and Pasternak elastic coefficients, are presented comprehensively. Buckling of rectangular plates made of functionally graded material (FGM) under various types of thermal loading is considered. It is assumed that the plate is in contact with an elastic foundation during deformation. The derivation of equations is based on the classical plate theory. It is assumed that the mechanical and thermal non‐homogeneous properties of FGM plate vary smoothly by distribution of power law across the plate thickness. Using the non‐linear strain‐displacement relations, the equilibrium and stability equations of plates made of FGMs are derived. The boundary conditions for the plate are assumed to be clamped for all edges. The elastic foundation is modelled by two parameters Pasternak model, which is obtained by adding a shear layer to the Winkler model.