Generalized Shear Deformation Theory for Bending of Inhomogeneous Beams

Abstract

A simple generalized shear deformation theory was developed to accurately analyze the bending behavior of shear deformable beams composed of inhomogeneous materials such as functionally graded materials. The generalized theory expresses the axial displacement in terms of the transverse shear strain derived from the equilibrium equations of stress in the axial direction. To confirm the validity of the generalized shear deformation theory, we analyzed simply supported beams subjected to a transverse load. The transverse shear strain and stress given by the generalized theory matched the ones by the solutions based on the two-dimensional elasticity. The generalized theory is thus accurate enough for any inhomogeneous beam.