Deflection prediction of a cantilever beam subjected to static co-planar loading by analytical methods

Abstract

In this paper, deflection prediction of a cantilever beam subjected to static co-planar loading is investigated using the Differential Transformation Method (DTM) and the Homotopy Perturbation Method (HPM). An axial compressive force, FA, and a transverse force, QA, are applied to the beam. It is considered that these forces are follower forces, i.e., they will rotate with the end section of the beam during the deformation, and they will remain tangential and perpendicular at all times, respectively. Comparison between DTM and HPM through numerical results demonstrates that DTM can be an exact and highly efficient procedure for solving these kind of problems. Also the influence of the effect of some parameters appeared in mathematical formulations such as area moment of inertia (I), Young’s modulus (E), transverse force (QA) and compressive force (FA) on slope variation are investigated in the present study. The results show that slope parameter as well as compressive force increases. By increasing the QA, slope parameter is increased significantly. By increasing the E, due to stiffness of the material, slope variation is decreased. It is evident that when the size of the beam section increases, the area moment of inertia (I) will be increased and so the slope variation will be decreased.