Post-Buckling Analysis of a Uniform Self-Weight Beam with Application to Catenary Riser

This paper focused on a simply supported beam under uniform self-weight, subjected to an axial force at the roller end. The principle of virtual work-energy was used to formulate the equation for the nonlinear deformation of the beam, which involves the bending strain energy, the virtual work due to self-weight, and the virtual work of the axial force applied at the free-sliding roller end. The work–energy functional was expressed in terms of the arc-length coordinate. The functional vanished, yielding the static equilibrium configuration of the beam — a highly nonlinear problem. Finite element and Newton–Raphson iterative methods were used to solve the problem. The beam theory was extended to large sag analysis of a catenary riser. With this, some interesting features of the various configurations of the catenary riser under various end forces were evaluated.