Static equilibrium configurations and appropriate applied top tension of extensible marine riser with specified total arc-length using finite element method

This paper presents a finite element method for calculating the static equilibrium configurations and applied top tension of extensible marine riser with specified total arc-length. A variational formulation of an extensible marine riser is formulated based on the work-energy principle. The variational model formulation involves strain energy due to bending and axial stretching, and virtual work done by hydrostatic pressures and other external forces. 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 numerical solutions of the nonlinear system are obtained by the iterative method. The results show that the Lagrange multiplier is identified as the parameter for adjusting the top tension to a proper value that satisfies the constraint condition.

► We develop a model for static analysis of marine riser with given total arc-length.
► The Lagrange multiplier is introduced for imposing the constraint condition.
► The Lagrange multiplier is identified as the adjusting riser’s top tension.
► We present the relations between top tension and unstretched arc-length of riser.