Buckling analysis of functionally graded rectangular microplate in thermal environment based on exponential shear deformation theory using the modified couple stress theory

The aim of this paper is to study the buckling analysis of power law functionally graded rectangular microplates. The modified couple stress theory based on the exponential shear deformation theory has been used to obtain the dimensionless critical buckling load of the functionally graded microplate. In exponential shear deformation theory, exponential functions are used in term of thickness coordinate to include the effect of transverse shear deformation and rotary inertia. To obtain the critical buckling loads for all boundary conditions, the equations of motion are obtained using Rayleigh–Ritz method based on the modified couple stress theory that the this theory contains only one material length scale parameter. The temperature is assumed to be constant in the plane of the plate and to vary in the thickness direction. Material properties are assumed to be temperature dependent and vary continuously through the thickness according to a power law distribution in term of the volume fraction of the constituents. Finally, the effect of various parameters such as n Power Law indexes, aspect ratio (a/b), length to thickness ratio and the length scale parameter on the non-dimensional critical buckling load of rectangular FG micro nano-plates are presented.