Page 82 - Pipelines and Risers

BucWing/Collapse of Deepwater Metallic Pipes 55

k, =I-&, k, =I-k,
The equation is valid for the following range of hoop stress and axial force:

(3.56)

3.5 Finite Element Model

3.5.1 General
This section describes how a pipe section is modeled using the finite element method and is
taken from Hauch and Bai (1999). The finite element method is a method where a physical
system, such as an engineering component or structure, is divided into small sub
regiondelements. Each element is an essential simple unit in space for which the behavior can
be calculated by a shape function interpolated from the nodal values of the element. This in
such a way that inter-element continuity tends to be maintained in the assemblage.
Connecting the shape functions for each element now forms an approximating function for the
entire physical system. In the finite element formulation, the principle of virtual work,
together with the established shape functions are used to transform the differential equations
of equilibrium into algebraic equations. In a few words, the finite element method can be
defined as a Rayleigh-Ritz method in which the approximating field is interpolated in piece
wise fashion from the degree of freedom that are nodal values of the field. The modeled pipe
section is subject to pressure, longitudinal force and bending with the purpose to provoke
structural failure of the pipe. The deformation pattern at failure will introduce both
geometrical and material non-linearity. The non-linearity of the bucklinglcollapse
phenomenon makes finite element analyses superior to analytical expressions for estimating
the strength capacity.

In order to get a reliable finite element prediction of the bucklinglcollapse deformation
behavior the following factors must be taken into account:

0 A proper representation of the constitutive law of the pipe material
A proper representation of the boundary conditions
A proper application of the load sequence
The ability to address large deformations, large rotations, and finite strains
The ability to modelldescribe all relevant failure modes

The material definition included in the finite element model is of high importance, since the
model is subjected to deformations long into the elasto-plastic range. In the post buckling