A size-dependent four variable refined plate model for functionally graded microplates based on modified couple stress theory

A new size-dependent model for functionally graded microplates is developed by using the modified couple stress theory. In the model, a four variable refined plate theory rather than the first order or any higher order shear deformation theory is adopted to characterize the transverse shear deformation. Firstly, the equations of motion for functionally graded microplates are derived from Hamilton’s principle. Then based on these equations, closed-form solutions for bending, buckling and free vibration responses are obtained for simply supported rectangular functionally graded microplates. Furthermore, numerical results based on the analytical solutions are also presented and compared with those predicted by size-dependent first order and third order shear deformation plate models. The results demonstrate that the new size-dependent model has comparable accuracy with the size-dependent third order shear deformation plate model. Thus this new size-dependent model can be easily applied to analyze mechanical responses of functionally graded microplates for its simplicity and high accuracy.