Environmental Engineering Reference
In-Depth Information
element, the Young modulus and the cable straight section [
13
]. This section is a
normal section of the floating barrier which is composed of three kinds of materials:
the curtain fabric, the upper aerial leach and the subsea chain.
The approximation of the continuous equilibrium equation permits to define a
discrete problem. The curvilinear derivative operator on the internal force
d
)
is transformed into a vectorial difference at each node between neighbouring element
tensions. A weighted summation of the external force
F
ext
(
ds
F
int
(
s
is made at each node
over its two adjacent elements. The nodal displacement vector is denoted
U
.We
use the same notations
F
int
and
F
ext
after the transformations from the continuous
to the discrete formulations. They depend on the discrete problem unknown
U
, i.e.,
the equivalent internal force vector
F
int
(
s
)
U
)
and external force vector
F
ext
(
U
)
.The
non-linear discrete equation is written in term of the residual vector
R
(
U
)
R
(
U
)
=
F
int
(
U
)
−
F
ext
(
U
)
=
0
.
(7.8)
The equation is solved using the Newton-Raphson method. The method uses the
derivative
d
. The derivative of the internal force vector is defined on each
element by a stiffness matrix. The external force vector derivative is not taken into
account here.
dU
R
(
U
)
Remark 7.3
The current pressure
p
(
s
)
is defined by a classical hydrodynamic rule
1
2
ˁ
w
Cv
2
p
(
s
)
=
(
s
)
,
(7.9)
where
ˁ
w
is the water density,
C
the drag coefficient and
v
(
s
)
the current velocity.
The atmospheric wind action on the aerial part of the barrier can be defined by
using a similar rule than those for the current pressure by considering the air density
ˁ
air
and the wind velocity taken at the altitude of the float.
The waves generated by the wind act on the subsea part of the barrier. A wave
pressure can be added to the current pressure by using an incident velocity
v
w
sup-
plementary to the current velocity
v
. The velocity
v
w
can be defined by using the
square root of the significant wave height.
(
s
)
7.2.4 Operational Point of View of the Numerical Results
From the operational point of view the 2D model gives the boom tensions
t
(
A
)
and
(
)
t
at both end-points
A
and
B
of a boom section. The direction of the mooring
tensions
T
B
(
)
(
)
are also given by the numerical model. The hydrodynamic
current can vary in time depending on the tide stages. As a consequence boom tension
and boom tangent direction can be time-dependent.
A
and
T
B
Search WWH ::
Custom Search