Global Elastic Stability of Marine Risers.

Abstract

Marine risers are slender tubular columns connecting the well at the seabed to the drill structure at the ocean surface. They are prone to global static instability under the combined action of their weight, tension applied at their top and fluid static pressure forces from the water and the fluid inside them. A nonlinear mathematical model consisting of a second order equation with integral boundary terms and end rotation conditions is developed and discretized by the finite element method. It can be reduced to the equations of the classical stability theory by linearization. The stability boundaries in the space of the riser's dimensionless effective weight and dimensionless lower end effective tension are studied for the purpose of determining the effect of internal and external pressure, bending rigidity and boundary conditions. It is shown that risers may buckle globally even when they are in tension over their entire length due to internal pressure. The phenomenon of buckling in tension may occur even for relatively short risers and moderate values of the density of the fluid inside the riser. Stability boundaries derived by classical eigensolution methods cannot be extended to the region corresponding to very long risers due to numerical instabilities. The extension of the stability boundaries is achieved by asymptotic and quasiasymptotic analysis of the Airy function form of the buckling mode shape. The analysis shows that the earlier holding theory is in error. The postbuckling behavior is analysed both in the neighborhood and away from the bifurcation point. It is shown that the riser may exhibit unstable postbuckling behavior due to internal pressure. The conditions for initially unstable postbuckling behavior are derived by an analysis of the nonlinear differential equation of equilibrium in the neighborhood of the bifurcation point. The complete secondary equilibrium path of risers is determined by incremental and iterative solution of the discretized nonlinear equations of equilibrium. Lateral load and structural imperfections may cause the actual buckling tension to be higher than that predicted theoretically in the case of unstable postbuckling behavior. The actual buckling tension is determined by locating the limit point on the equilibrium path of the riser.