A variational formulation of an extensible marine riser is formulated based on the work-energy principle. The total unstretched arc-length of marine riser is specified while the top tension is not yet exactly known at the equilibrium position. A Lagrange multiplier is introduced in order to impose the constraint condition, which is the specified total arc-length of the riser. The system unknowns are composed of the nodal degrees of freedom and the Lagrange multiplier. The system of nonlinear finite element equations is derived based on the finite element procedure. The results show that the Lagrange multiplier is identified as the value of top tension adjusting the specified top tension in order to maintain the marine riser in equilibrium condition.
The marine risers have been employed in offshore resource exploration form the 1950s. They are used to contain fluids for well control and to transport hydrocarbons from the wellhead to the platform. In deep water operation, the riser behaves as a flexible structure which experiences large displacement. The mathematical model for marine risers with large deflection analysis had been developed over the past several years. In literature, there are many research works which deal with the large displacement of the risers, for example, Felippa and Chung (1981), McNamara et al. (1986), Bernitsas and Kokarakis (1988), Chung et al. (1994, 1996), Moe and Arntsen (2001), and Chai and Varyani (2006). Most of them used the arc-length of the riser as the independent variable to define the centroidal line of the riser. However, in most cases, the top end of the riser can slip through the slip joint. Consequently, the total stretched arc-length of the riser measured from the seabed to the slip joint may not be known until the equilibrium configuration is evaluated.