Large Deflection of Beam with Free Horizontally Sliding Support using Shooting Method

Abstract

This research presents a large deflection analysis of beams with free horizontally sliding support which is subjected to a uniformly distributed load and horizontal compression at the beam tip. The governing equations of the beam are derived by considering the differential geometry relations of the beam segment in a plane curve and the equilibrium of force and moment. The set of governing equations yields the nonlinear first-order differential equations which are categorized as two-point boundary value problem. The numerical solution can be solved by using the shooting method, which is verified by the results obtained from the finite element method. This numerical investigation attempts to study the effects of the uniformly distributed load and the horizontal compression force at the support on the large deflection and buckling behaviors of the beam. The numerical results showed that the uniformly distributed load and compression cause the support movement and induce an instability of the beam.