Finite-Element Solution of Variable-Arc-Length Beams under a Point Load

Abstract

In this technical note, a finite-element solution of a simply supported beam with variable arc length under a point load is presented. The beam is hinged at one end and simply supported over the other end. The distance between the two supports is the span length. A point load is applied at various locations along the span of the beam. The finite-element method based on the variational formulation, which involves the bending strain energy, work done by the point load, and the strain energy due to axial forces in beam, is used to solve the problem. Because of the unknown total arc length, the finite-element discretization is made along the span length rather than the total arc length. For a given value of the point load, two possible equilibrium configurations exist, of which one is stable and the other is unstable. For the stable configuration, the finite-element solution gives results that are in good agreement with the results obtained using the elliptic-integral method and the shooting-optimization technique.