An efficient size-dependent plate theory for bending, buckling and free vibration analyses of functionally graded microplates resting on elastic foundation

Based on the strain gradient elasticity theory and a refined shear deformation theory, an efficient size-dependent plate model is developed to analysis the bending, buckling and free vibration problems of functionally graded microplates resting on elastic foundation. The present model contains four displacement variables only and introduces three material length scale parameters. Besides, it satisfies the stress-free boundary conditions on the top and bottom surfaces of the microplate without using a shear correction factor. The elastic foundation is modeled as two-parameter Winkler–Pasternak foundation. The material properties of the microplate are assumed to vary in the thickness direction and estimated through the classical rule of mixture. By using Hamilton’s principle, the equations of motion and boundary conditions are obtained. Closed form solutions are presented for the simply supported microplate. Comparison studies are performed to establish the validity of the derived formulation. The effects of material length scale parameter, material gradient index, elastic foundation, aspect ratio and transverse shear deformation on the bending, buckling and vibration characteristics of the microplate are investigated in detail.