Biomedical Engineering Reference
In-Depth Information
The reservoir is assumed to be filled with an incompressible fluid. Close
to the origin of the
xyz
-coordinate system the (stationary) two dimensional
velocity field is given by
v
=
c
(
−
xe
x
+
ye
y
) with
c
a constant,
where
e
y
are unit vectors along the
x
- and
y
-axis.
Determine the associated acceleration field:
e
x
and
=
˙
a
(
x
)
v
(
x
).
9.6
In the reference configuration (at time
t
)
of a cubic material specimen are parallel to the axes of a Cartesian
xyz
-
coordinate system. See the figure left. The specimen is loaded in shear,
cyclically in the time
t
.
=
0) the edges (with length
y
y
t
t
=
0
x
x
z
z
The time-dependent deformation is, in the Lagrangian approach, described
by
2
sin
2
π
,
y
0
t
T
x
=
x
0
+
with
T
the (constant) time of one cycle.
y
=
y
0
z
=
z
0
,
with
x
0
,
y
0
,
z
0
the coordinates of the material points at time
t
0 and
with
x
,
y
,
z
the associated coordinates at time
t
. Attention is focussed on
the material point P that at time
t
=
=
T
/
4 is located at the position
x
=
2
/
0.
Determine the position vector
∼
P
of the point P as a function of the time
t
.
3,
y
=
/
3,
z
=
