Solution of two-point boundary value problems associated with submarine pipelines

Konuk, Ibrahím (1981) Solution of two-point boundary value problems associated with submarine pipelines. University of Southampton, Doctoral Thesis, 130pp.

Record type: Thesis (Doctoral)

Abstract

This thesis is devoted to developing methods for qualitative and numerical treatment of some two-point boundary value problems arising in submarine pipelines and risers. A general problem is formulated in this thesis based on rod theories. The boundary value problems treated in this thesis are all associated with the following ordinary differential system, which is defined along a spacecurve in R3:du/ds + e(u, s)u + & (u,s) = 0 (1) and defined on the interval [L1, L2] and with various types of boundary conditions:Ai(Li) + Bj(Li) = c (2) (linear boundary condition)fi[u(Li), u(Li)] = o (3) (nonlinear boundary condition)fi[L1, L2; u(Li), u(Li)] = o (4)(free boundary condition) where ie, Ai, Bi are matrices in R6 x R6 and u, p, fi, c are vectors in R6 and i = 1 or 2.This thesis gives formulations of several practical pipeline problems and proves the existence and uniqueness of solutions. An asymptotic solution is obtained by using singular perturbation method. This thesis also describes methods for obtaining discrete solutions for general forms of pipeline and riser problems.

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