A HYPERBOLIC SHEAR DEFORMATION THEORY FOR FLEXURE AND VIBRATION OF THICK ISOTROPIC BEAMS

A Hyperbolic Shear Deformation Theory taking into account transverse shear deformation effects, is presented for the static flexure and free flexural vibration analysis of thick isotropic beams. The displacement field of the theory contains two variables and does not require shear correction factor. The hyperbolic sine function is used in the displacement field in terms of thickness coordinate to represent shear deformation. The most important feature of the theory is that the transverse shear stress can be obtained directly from the use of constitutive relation, satisfying the stress free boundary conditions at top and bottom of the beam. Hence, the theory obviates the need of shear correction factor. Governing differential equations and boundary conditions of the theory are obtained using the principle of virtual work. Results obtained for flexure and free vibration of simply supported uniform, isotropic beams are compared with those of elementary, refined, and exact beam theories to validate the accuracy of the theory.