A size-dependent model for bi-layered Kirchhoff micro-plate based on strain gradient elasticity theory

Abstract

A size-dependent model for bi-layered Kirchhoff micro-plate is developed based on the strain gradient elasticity theory. The governing equations and boundary conditions are derived by using the variational principle. To illustrate the new model, the bending problem of a simply supported bi-layered square micro-plate subjected to constant distributed load is solved. Numerical results reveal that the deflection and axial stress decrease remarkably compared with the classical plate results, and the zero-strain surface deviates significantly from the conventional position, when the thickness of plate is comparable to the material length scale parameters. The size effects, however, are almost diminishing as the thickness of plate is far greater than the material length scale parameters. In addition, the bi-layered plate can be simplified to the monolayer plate as the thickness of one layer is becoming much greater than that of the other layer.