Bending, buckling and free vibration analysis of size-dependent functionally graded circular/annular microplates based on the modified strain gradient elasticity theory

Abstract

Abstract A Mindlin microplate model based on the modified strain gradient elasticity theory is developed to predict axisymmetric bending, buckling, and free vibration characteristics of circular/annular microplates made of functionally graded materials (FGMs). The material properties of functionally graded (FG) microplates are assumed to vary in the thickness direction. In the present non-classical plate model, the size effects are captured through using three higher-order material constants. By using Hamilton's principle, the higher-order equations of motion and related boundary conditions are derived. Afterward, the generalized differential quadrature (GDQ) method is employed to discretize the governing differential equations along with various types of edge supports. Selected numerical results are given to indicate the influences of dimensionless length scale parameter, material index and radius-to-thickness ratio on the deflection, critical buckling load and natural frequency of FG circular/annular microplates.