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Clashing between lines
A global method has been developed to deal with clashes between lines. This approach may be divided into two steps i.e. the detection of the contact and the contact forces evaluation.
In 3D, it is very difficult to determine the contact between two slender structures.
To do so, it is necessary to define a series of plane separating both structures and to prevent each of them to pass through. Of course, these planes need to be up-dated by the time the structures are moving.
Thus, the calculations follow three iterative phases :
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1. Contact detection 2. Contact elements definition 3. Global resolution of the Virtual Work Principle, accounting for contact reactions. |
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Contact detection
Area of neighbourhood : An area of neighbourhood consists in two parts of the seabed connections which are close to each other. The area is defined by the abscissa \((a_1,b_1)\) and \((a_2,b_2)\) giving the beginning and the end of each part. In a first step, control points are equally displayed along the first mean line. Their orthogonal projection on the second line are determined. This gives a first assessment of the distance between the structures. Every first time the distance is lower than the criterion, an area of neighbourhood is entered. The abscissa \(a_1\) and \(a_2\) are stored. By the time, the criterion is no longer respected, the area of neighbourhood is exited.
Control mean lines
In each area, a control mean line is created. This lines is defined by a series of points and tangential vectors. The positions and vectors are the mean of the positions and the tangent vectors on both lines.
Contact detector planes
These planes are composed of a point on the control mean line and a normal vector tangent to the mean line.
Contact elements definition
A contact element is a couple of points, each point belonging to one of the neighbour structures. These points are the intersections of each structure with a control detector plane. These directions are necessary to calculate the gap between the particles of a contact element. They finally define different planes through which both risers can not pass.
Virtual Work Principle
Depending on the relative positions of these two particles, each contact element generates reaction and friction forces. The contribution from each contact element is included in the global system of equations thanks to the interpolation functions.
