Environmental Engineering Reference
In-Depth Information
7.3 Floating Booms as a 3D Elastic Membrane
7.3.1 Context
This section presents a 3D model representing an oil-spill boom by using an elastic
surface. For a numerical convergence reason, this approach is described after the
2D curvilinear model described in Sect.
7.2
. The convergence of the 3D non-linear
problem solution is a tricky question. The convergence can be accelerated or obtained
at least if the 3D domain equilibrium geometry possesses a valuable initial position.
This one can be given by the extrapolation of the curvilinear domain result.
7.3.2 Non-Linear Elastic Membrane
A floating boom is supposed to be a domain
composed of several parts. For curtains
(Fig.
7.1
) we define four parts having different geometries and roles. The float inflated
by air is a cylinder; the skirt is a rectangle made of fabric material composed by one
or two layers; the chain at the bottom of the skirt permits to weight the curtain and to
concentrate the longitudinal tension is a rectangle made of steel material, the leach
at the top the float permits to handle by hand the boom and to concentrate equally
longitudinal tension is a rectangle made of fabric material. An eventual fifth part is
another leach in the vicinity of the waterline.
For barriers which have a simplified design, the float and the skirt are gathered
(Fig.
7.2
). We define three parts. The float and the skirt are composed of rigid vertical
bodies assembled between two fabric sheets are a rectangle made of a fabric material.
Bottom chain and upper leach parts are defined in a same way than curtains.
During the displacement
u
of
ˉ
ˉ
the domain can be deformed and the strainmeasure
is given by the Green tensor
x
defined in term of the displacement differential
du
.
The mechanical stress inside the membrane is defined by the Piola-Kirchhoff tensor
of second kind
(
u
)
. Taking into account the high stiffness of the constitutive coated
fabric we use an approximation by considering a linear behaviour law between strain
and stress tensors. The material is supposed elastic having a high Young modulus.
The internal elastic energy
e
˃(
u
)
(
u
)
inside the elastic membrane is defined by
1
2
e
(
u
)
=
tr
(˃ (
u
)
x
(
u
))
d
ˉ,
(7.11)
ˉ
where tr denotes the trace operator.
Moored in sea water to contain floating oil, the external loads on booms are the
normal pressure of the float pneumatic inflation, the normal hydrodynamic pressure
of the flow on its submarine part (skirt and subsea float part), the normal hydrostatic
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