Shear deformation beam models for functionally graded microbeams with new shear correction factors

A shear deformation beam model and new shear correction factors are presented for nonhomogeneous microbeams. The governing equations and corresponding boundary conditions in bending and buckling are obtained by implementing minimum total potential energy principle. Bending and buckling problems of a simply supported functionally graded microbeam are analytically solved by Navier solution procedure. Several comparative results are given for different material property gradient index, thickness-to-material length scale parameter ratio (or vice versa), slenderness ratio and shear correction factors. It is observed that size effect and shear deformation are more significant for lower values of thickness-to-material length scale parameter and slenderness ratios, respectively.