Large Deflection of Beams under Moment Gradient

Abstract

Two different approaches are presented for the large‐deflection analysis of an inextensible elastic beam under moment gradient. One end of the beam is hinged and at a fixed distance away from this end is a frictionless support where the beam can slide freely. In the first approach, the differential equation based on elastica theory is formulated and solved by using elliptic integrals; which yield a closed‐form solution. In the second approach, the governing differential equations are solved numerically by the shooting‐optimization technique in which the fourth‐order Runge‐Kutta algorithm and an optimization algorithm are employed. Comparison studies of the results obtained from the two methods are made and the results are found to be in very good agreement.