Bending, buckling and free vibration responses of hyperbolic shear deformable FGM beams

This study investigated bending, buckling, and free vibration responses of hyperbolic shear deformable functionally graded (FG) higher order beams. The material properties of FG beams are varied through thickness according to power law distribution; here, the FG beam was made of aluminium/alumina, and the hyperbolic shear deformation theory was used to evaluate the effect of shear deformation in the beam. The theory explains the hyperbolic cosine distribution of transverse shear stress through the thickness of a beam and satisfies zero traction boundary conditions on the top and bottom surfaces without requiring a shear correction factor. Hamilton’s principle was employed to derive the equations of motion, and analytical solutions for simply supported boundary conditions were obtained using Navier’s solution technique. The non-dimensional displacements, stress, natural frequencies, and critical buckling loads of FG beams were obtained for various values of the power law exponent. The numerical results were compared to previously published results and found to be in excellent agreement with these.