Page 131 - Pipelines and Risers
P. 131
104 Chapter 7
The smoothing is done by ABAQUS creating B6zier surfaces based on the faceted surface of
the seabed formed by the rigid elements (Figure 7.7). The resulting Bbzier surfaces, unlike the
faceted element surface will be smooth and have a continuous outward surface normal. The
B8zier surfaces will not match the faceted geometry of the rigid surface exactly, but the nodes
of the rigid elements defining the seabed will always lie on the Bbzier surface. In addition,
the user can specify the degree of smoothing in order to control the geometry of the smoothed
surface.
In the established model the set of R3D4 elements defining the seabed is used as a so-called
master surface for contact applications with the pipe elements. This means that a contact pair
(pipelseabed) is defined, and an interaction model is specified. This interaction model will
typically consist of a seabed stiffness and friction definition.
7.5 Non-linearity and Seabed Model
The non-linear stress analysis used in the model contains up to three sources of non-linearity
depending on strain level, change in geometry, and load situation:
Material non-linearity.
Geometric non-linearity.
Boundary non-linearity (friction, sliding etc).
7.5.1 Material Model
The material model used is capable of representing the complete stresslstrain relationship for
the pipeline material, including non-linear plastic behavior (Figure 7.8).
In the elastic area the stress/strain relationship is governed by supplying the Young’s modulus
of the material. For the steel types commonly used as structural pipe steel, the Young’s
modulus will be temperature dependent. This can easily be accounted for in the model by
numerically specifying the Young’s modulus as a function of temperature.
The plastic behavior of the material is defined by specifying numerically the complete plastic
stresslstrain curve for the steel (e.g. from test data) in the material definition part of the input
file. The temperature expansion coefficient of the material can also be defined as a function of
temperature if necessary.
