A novel size-dependent functionally graded curved mircobeam model based on the strain gradient elasticity theory

A novel size-dependent curved microbeam model made of functionally graded materials (FGMs) is developed based on the strain gradient elasticity theory and n shear deformation theory. The material properties of the FGM curved microbeam are assumed to vary in the thickness direction and are estimated through the Mori-Tanaka homogenization technique. The higher-order governing equations and related boundary conditions are derived by using Hamilton's principle. The Navier solution technique is adopted to derive analytical solutions to simply supported FGM curved microbeams. A parametric study is conducted to investigate the influences of material length scale parameters, gradient index, shear deformation index, central angle and length-to-thickness ratio on the static bending and free vibration characteristics. Some of the present results are compared with the previously published results to establish the validity of the present formulation. The results indicate that the inclusion of size effect results in an increase in microbeam stiffness, and leads to a reduction of deflection and an increase in natural frequency. Such small size effects are significant when the dimensionless thickness is small, but become negligible with increasing dimensionless thickness.