A formulation to analyze the large displacement problem of a marine riser with two unequal principal moments of inertia of cross sections in three dimensional space is presented. The method involves the utilization of the equilibrium equations in the axial direction and the stationary condition of an energy functional. The coordinates X and Y, twisting angle F, and tension Tare the four dependent variables, while the arc length s in the equilibrium state is the independent variable which is changed to depth Z in the numerical implementation. A finite element method was developed to solve the problem of a riser with equal principal cross sectional moments of inertia.
In literature, procedures to analyze a rise system experiencing large displacements in three dimensions were given by Bernitsas (1982), Chucheepsakul (1983), Felippa and Chung (1981), Garrett (1982), McNamara, O"Brien, and Gilroy (1986), O"Brien, McNamara and Dunne(1988). A system with a layered flexible pipeline section was studied by McNamara and Harte (1989). This paper presents a method of analysis for a riser system having a specified top tension and an unknown total arc length between seabed and the support at the slip joint as shown in Fig. 1. The magnitude of the top tension is governed by either the operation requirement, the lifting capacity or the strength of the riser material. In the formulation a riser having unequal cross sectional moments of inertia is considered, although they are equal in the given numerical example. The hybrid method used previously for two dimensional cases (Huang and Chucheepsakul, 1985), is extended to the present problem. Four dependent variables are used: the two horizontal coordinates of the centroidal curve, the rotation of a section, and the tension in the riser. To obtain these four unknowns, two equilibrium equations and two variational equations are used.