Size-dependent behavior of functionally graded sandwich microbeams based on the modified couple stress theory

Static bending, buckling and free vibration behaviors of size-dependent functionally graded (FG) sandwich microbeams are examined in this paper based on the modified couple stress theory and Timoshenko beam theory. To avoid the use of a shear correction factor, equilibrium equations were used to compute the transverse shear force and shear stress. Two types of sandwich beams were considered: (1) homogeneous core and FG skins and (2) FG core and homogeneous skins. Numerical results were presented to illustrate the small scale effects on the behaviors of FG sandwich beams. The results reveals that the inclusion of the size effects results in an increase in the beam stiffness, and consequently, leads to a reduction of deflections and stresses and an increase in natural frequencies and critical buckling loads. Such effects are more pronounced when the beam depth was small, but they become negligible with the increase of the beam depth.