Biomedical Engineering Reference
In-Depth Information
statically loaded with pure shear (plane stress state). The accompanying
boundary conditions are shown in the figure below.
For an arbitrary point of the midplane, with the coordinates (
x
0
,
y
0
)in
the unloaded reference configuration, the displacements in the
x
- and
y
-
direction, as a result of the stress
τ
, are indicated with
u
x
(
x
0
,
y
0
),
u
y
(
x
0
,
y
0
),
respectively.
Why does no unique solution exist for the fields
u
x
(
x
0
,
y
0
),
u
y
(
x
0
,
y
0
), based
on the information that is given above?
y
σ
yy
=
0
σ
xy
=
τ
σ
xx
=
0
σ
yx
=
τ
σ
xx
=
0
σ
yx
=
τ
x
σ
yy
=
0
σ
xy
=
τ
13.3 A thin trapezium shaped plate is clamped on the left side and statically
loaded on the right side with an extensional load (local extensional stress
p
), as given in the figure below.
y
p
x
2d
d
z
In the plate plane stress conditions occur (
0).
With respect to the stress components still relevant for the plane stress
conditions, the following assumptions are made:
σ
xx
=
p
x
+
2
σ
xz
=
σ
yz
=
σ
zz
=
,
σ
yy
=
0,
σ
xy
=
0.
Give two reasons why this assumed stress field cannot be correct.
13.4 Consider a rectangular plate of some material (
×
b
). The thickness
h
is
small with respect to
and
b
, see figure.
