Bending and Large Deflection Behaviors of Free Horizontally Moving Supported Beam Subjected to Self-weight and Compression at the End

Abstract

This research presents bending and large deflection behaviors of the beams with horizontally moveable support subjected to self-weight and compressive force at a beam tip. A variational formulation of a beam system has been developed based on principle of virtual work, which is written in term of intrinsic coordinate. The geometric relation of deformed infinitesimal length of the beam is derived by considering the elastica theory. The non-linear finite element method incorporated with the Newton-Raphson iterative procedure is used to solve the numerical solution. In addition, the set of nonlinear first-order differential equations obtained from the force and moment equilibrium, moment-curvature relationship, and nonlinear geometric relations of the beam segment, which is categorized as two-point boundary value problem is numerically solved by using the shooting method. Then the numerical results from the finite element method are independently verified by those results from the shooting method. The results also show that the beam self-weight and the compressive force at the beam tip cause the support movement, which induce large deflection.