A single variable parabolic shear deformation theory for flexure and flexural vibration of thick isotropic beams

摘要

A single variable parabolic shear deformation theory (PSDT) 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 theory contains only one unknown variable as compared to the first- and third-order shear deformation theories and does not require shear correction factor. The displacement field of the theory is built upon the classical Bernoulli-Euler theory including the third order polynomial 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 relations, satisfying the stress-free boundary conditions at top and bottom surfaces 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 the static flexure and free vibration of simply suuported uniform, isotropic beams are compared with those of elementary, refined and exact beam theories to validate the accuracy of the theory.