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6D buoy theory: Contact forces |
Interactions with shapes and the seabed are calculated as if the buoy consists of a series of lumps, one at each vertex.
| Notes: | For a lumped buoy you can specify the number and location of the vertices. If you specify no vertices then the 6D buoy will not react to contact with the seabed or with any solids. |
| If wire frame symmetry is specified then the additional vertices implied by the symmetry are used for contact interactions. | |
| For a spar buoy or towed fish, the vertices used are the vertices which are automatically created for the draw square cylinders drawing option. These vertices are used even if the draw circular cylinders option is selected. |
If any buoy vertex penetrates the seabed or an elastic solid then it is subject to a reaction force $\vec{f}_\mathrm{R}$ of the form \begin{equation} \vec{f}_\mathrm{R} = r(d)\ a\ \vec{n} \end{equation} where \begin{align*} d&=\text{depth of penetration of the vertex}\\ r(d)&=\text{reaction force per unit contact area at penetration $d$}\\ a&=\text{contact area, as defined below}\\ \vec{n}&=\text{unit vector in the reaction force direction for $\href{SeabedTheory.htm#SeabedTheoryStiffness}{\text{seabed}}$ or $\href{ShapeTheory.htm#PenetrationModel}{\text{shapes}}$} \end{align*}
If explicit integration is used in the dynamic analysis, the vertex may also experience a damping force. For details of both the reaction force and the damping force, see seabed theory and shape theory.
Frictional forces are also modelled when contact occurs, using the seabed friction coefficient and friction coefficient data, and following the model described in friction theory.
Because the vertices are (in general) offset from the buoy origin, these seabed or shape reaction forces give rise to reaction moments about the buoy origin.
The reaction force at a vertex depends on the contact area of the vertex, $a$. This vertex contact area is taken to equal the specified total contact area of the buoy, $a_\mathrm{t}$, divided equally amongst all the buoy vertices \begin{equation} a = a_\mathrm{t} / \textrm{number of vertices} \end{equation} If total contact area is set to zero, then the buoy experiences no contact forces.
If total contact area is set to ~ then OrcaFlex calculates and uses a default value of $a_\mathrm{t}$ that is based on the buoy geometry as follows.
For a lumped buoy, the default total contact area is given by \begin{equation} a_\mathrm{t} = \textrm{volume} / \textrm{height} \end{equation} where volume and height are as given on the buoy data form.
For spar buoys and towed fish the default total contact area is given by \begin{equation} a_\mathrm{t} = \max\{ a_\textrm{axial}, a_\textrm{lateral} \} \end{equation} where \begin{align*} a_\textrm{axial}&=\text{maximum cylinder cross sectional area}\\ a_\textrm{lateral}&=\text{sum over all cylinders of the projected lateral area}\\ &= \displaystyle \sum(\textrm{cylinder diameter}\times\textrm{cylinder length}) \end{align*}