A Finite Element Method for Calculating the Applied Top Tension and Static Configurations of Extensible Marine Riser with Specified Total Arc-Length

摘要

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 numerical solutions of the nonlinear system are obtained by the iterative method. 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.