Higher Order Computational Method for Static Flexural Analysis of Thick Beam

Abstract

This paper proposes a hyperbolic shear deformation theory for thick isotropic cantilever beam. A higher order beam theory which takes into account shear curvature, transverse stresses and rotatory inertia is presented. The displacement field of the present theory was based on a two variable, in which the transverse displacement is partitioned into the bending and shear parts. The proposed theories exactly satisfy the transverse stress boundary conditions on the bottom and top surfaces of the beam which were true in earlier shear deformation theories also. Beam governing equations and boundary conditions are derived by employing the principle of virtual work. The displacement and stresses of cantilever beam under varying load are calculated to verify the accuracy and efficiency of the present theory. Numerical results indicate that the obtained predictions are comparable with those of elementary, Timoshenko and other higher order refined theories.