Biomedical Engineering Reference
In-Depth Information
(a) Determine the stress tensor.
(b) Determine the
s
tress ve
ct
or
s
acting on a plane with unit normal
2
√
2
e
y
.
(c) Determine the components of
2
√
2
e
x
+
1
1
vector
n
=
s
perpendicular and parallel to the
plane defined in item (b).
8.3
On an infinitesimal area segment two sets of stress components are working
as shown in the figures (a) and (b).
(a) Determine the stress tensor for both situations.
(b) Determine the stress vector on the plane with normal
n
=
e
x
cos(
α
)
+
e
y
sin(
α
). The angle
α
represents the angle of the normal
vector with the
x
-axis.
(c) Determine for both situations the length of the stress vector as a
function of
α
.
20
5
5
10
10
5
y
y
5
20
x
x
(a)
(b)
n
y
α
x
8.4
In a material a stress state is observed that is characterized by the principal
stresses (in [MPa]) and the principal stress directions (unit vectors, defined
with respect to a fixed Cartesian coordinate system):
σ
1
=
0
with
n
1
=
e
z
4
3
σ
2
=
0
with
n
2
=−
5
e
x
+
5
e
y
3
4
σ
3
=
25 with
n
3
=
5
e
x
+
5
e
y
.
σ
e
x
,
Calculate the associated stress tensor
with respect to the basis vectors
e
y
and
e
z
.
8.5
Consider a cube of material, with the edges oriented in the direction of
the axes of a
xyz
-coordinate system, see the figure. In this figure also the
