Thermal buckling of functionally graded plates according to a 2D higher-order deformation theory

A two-dimensional (2D) global higher-order deformation theory is presented for thermal buckling of plates made of functionally graded materials (FGMs). The modulus of elasticity of functionally graded (FG) plates is assumed to vary according to a power law distribution in terms of the volume fractions of the constituents. By using the method of power series expansion of displacement components, a set of fundamental equations of a 2D higher-order theory for rectangular functionally graded (FG) plates is derived through the principle of virtual work. Several sets of truncated approximate theories are applied to solve the eigenvalue problems of FG plates with simply supported edges. In order to assure the accuracy of the present theory, convergence properties of the critical temperature are examined in detail. A comparison of the present critical temperatures of isotropic and FG plates is also made with previously published results. Critical temperatures of simply supported FG plates are obtained for uniformly and linearly distributed temperatures through the thickness of plates. Modal transverse shear and normal stresses are calculated by integrating the three-dimensional (3D) equations of equilibrium in the thickness direction satisfying the stress boundary conditions at the top and bottom surfaces. The internal and external works are calculated and compared to prove the numerical accuracy of solutions. It is noticed that the present higher-order approximate theories can predict accurately the critical temperatures of simply supported FG plates.