FGM micro/nano-plates within modified couple stress elasticity

Abstract

A unified formulation for plate bending problems is developed within the modified couple stress theory of elasticity with incorporating the deformation assumptions of three plate bending theories, such as the Kirchhoff-Love theory, 1st and 3rd order shear deformation plate theories. The microscopic structure of material is reflected in this higher-grade continuum theory via one material coefficient called the micro-length scale parameter. Furthermore the material can be composed of two micro-constituents what is included in the employed continuum model by functional gradation of the Young modulus through the plate thickness with assuming power-law dependence of volume fractions of micro-constituents on the transversal coordinate. The boundary restrictions on the bottom and top surfaces of the plate are discussed in details together with derivation of governing equations and physical boundary conditions on the plate edges. For numerical solution a novel method is developed with using the Moving Finite Element approximation for field variables. Several numerical simulations are devoted to study the influence of micro-length scale parameter as well as the level of gradation of Young’s modulus on coupled bending and in-plane deformation response modes.