A NONLINEAR FINITE ELEMENT METHOD FOR THE ANALYSIS OF THE OFFSHORE PIPELAYING PROBLEM (BEAM ELEMENT, GEOMETRIC)
MALAHY, ROBERT C., JR.
Doctor of Philosophy
A finite element method is presented for the three (3) dimensional, dynamic analysis of the offshore pipelaying problem. A geometrically nonlinear beam element and elastic bi-linear support elements are utilized to simultaneously model the pipeline, stinger, pipe supports and seabed. Numerical integration is used to obtain a time domain solution for the dynamic response of the pipeline. An iterative Newton's method procedure is used to solve the nonlinear system of algebraic equations, produced by the method, at each timestep. Both the end force equations and stiffness, mass and damping matrices for the beam element are given. The method presented offers several advantages over existing techniques. There are no theoretical limitations on the magnitude of the pipe displacements. It is not assumed that the dynamic response of the pipeline is linear or that it represents a small perturbation about the static solution. The beam element developed is completely general and can be used to model redundant structures. It provides for both the torsional deformation and elongation of the pipeline, and permits the use of different physical properties in each principal direction. Although the element is linearly elastic, it can be extended to nonlinear elasticity by the inclusion of a suitable moment curvature relationship. The results of numerical calculations are presented for a typical offshore pipelaying problem.