(GL 2005) are reduced to a static worst case consideration. This was done to give a
first approximation of the additional loading on OWEC support structures. In the
OWEC dimensioning process extreme load cases like the 50 year wave or emergency stops were taken into account. Thus, the extreme load case of the 50 year
wave was simulated as a quasi-static simulation. No dynamics and thus no inertia
forces were taken into account. The very time consuming process of dynamic
modelling would be necessary for fatigue analysis. In that case, the varying loads
caused by the longline were of interest. Modal analysis of these loads was also
important on the support structure to avoid excitation in or near the eigenmodes of
the plant. In any case, the dynamics were highly depending on the sea state. This
was modelled by wave theories and current assumptions. These were highly statistic
inputs and could only be a rough approximation of reality.
For these reasons, a static analysis of the problem was a reasonable first
approach to the complex problem. The forces of the longline were depending on the
single collector forces. These were considered to be concentrated loads, which were
all applied in the same angle of attack relative to the longline and with similar force
value. In this case, the reactions were maximal because there was no neutralization
of the forces taking place. The longline was oriented in one plane. In consequence
the LL could be approximated by a 2D model as shown in Fig. 11.26a.
The schematic 2D LL picture in Fig. 11.26a shows the pre-deformed model as a
starting point of simulation. This deformation was the approximate form of a
catenary curve. A curve like that would be obtained for a cable under self-weight or
in a uniform loading caused by even very low currents perpendicular to the LL. The
pre-deformation was needed to define the maximum sag without loading. It was
also needed for better convergence of the numerical calculation.
The following parametric studies for this model were conducted: First, a single
load was applied vertically in the middle of the LL. The maximum sag was variable.
For this case an analytical calculation was carried out to validate the model itself
and to understand the main parameters of interest in the problem.
The second parametric study was made for forces on each FE node that represents a single or V-mussel collector under varying angles of attack. The loads in
both parametric studies were applied as ramped loads to ensure convergence. The
reaction forces in both supports were calculated. All simulations were
quasi-statically calculations for the worst case loading investigated.
According to theoretical analysis, a single load in the middle of the longline led
to a V-like deformation (Fig. 11.26b). The relative force in a single loaded cable in
equilibrium without consideration of strain and mass is defined as
F s
F
¼
1
2 sinðbÞ
ð5Þ
where F s is the force in the cable and F is the external load. ß is the angle between
cable and horizontal axis. F s equals the absolute value of the reactions. This formula
shows the fundamental difference between cables and beams. Beams could carry
bending moments and cables could not. This was due to the fact that at angle ß of 0°
11 The German Case Study: Pioneer Projects of Aquaculture …
299
first approximation of the additional loading on OWEC support structures. In the
OWEC dimensioning process extreme load cases like the 50 year wave or emergency stops were taken into account. Thus, the extreme load case of the 50 year
wave was simulated as a quasi-static simulation. No dynamics and thus no inertia
forces were taken into account. The very time consuming process of dynamic
modelling would be necessary for fatigue analysis. In that case, the varying loads
caused by the longline were of interest. Modal analysis of these loads was also
important on the support structure to avoid excitation in or near the eigenmodes of
the plant. In any case, the dynamics were highly depending on the sea state. This
was modelled by wave theories and current assumptions. These were highly statistic
inputs and could only be a rough approximation of reality.
For these reasons, a static analysis of the problem was a reasonable first
approach to the complex problem. The forces of the longline were depending on the
single collector forces. These were considered to be concentrated loads, which were
all applied in the same angle of attack relative to the longline and with similar force
value. In this case, the reactions were maximal because there was no neutralization
of the forces taking place. The longline was oriented in one plane. In consequence
the LL could be approximated by a 2D model as shown in Fig. 11.26a.
The schematic 2D LL picture in Fig. 11.26a shows the pre-deformed model as a
starting point of simulation. This deformation was the approximate form of a
catenary curve. A curve like that would be obtained for a cable under self-weight or
in a uniform loading caused by even very low currents perpendicular to the LL. The
pre-deformation was needed to define the maximum sag without loading. It was
also needed for better convergence of the numerical calculation.
The following parametric studies for this model were conducted: First, a single
load was applied vertically in the middle of the LL. The maximum sag was variable.
For this case an analytical calculation was carried out to validate the model itself
and to understand the main parameters of interest in the problem.
The second parametric study was made for forces on each FE node that represents a single or V-mussel collector under varying angles of attack. The loads in
both parametric studies were applied as ramped loads to ensure convergence. The
reaction forces in both supports were calculated. All simulations were
quasi-statically calculations for the worst case loading investigated.
According to theoretical analysis, a single load in the middle of the longline led
to a V-like deformation (Fig. 11.26b). The relative force in a single loaded cable in
equilibrium without consideration of strain and mass is defined as
F s
F
¼
1
2 sinðbÞ
ð5Þ
where F s is the force in the cable and F is the external load. ß is the angle between
cable and horizontal axis. F s equals the absolute value of the reactions. This formula
shows the fundamental difference between cables and beams. Beams could carry
bending moments and cables could not. This was due to the fact that at angle ß of 0°
11 The German Case Study: Pioneer Projects of Aquaculture …
299