Biomedical Engineering Reference
In-Depth Information
Fig. 5.44 a Normal stress
r
XX
obtained along x = 0
and y = [0, D]. b Shear
stress r
XY
obtained along
x = L/2 and y = [0, D]
(a)
(b)
5.4.1 Free Vibration of a Cantilever Beam
The NNRPIM is applied to analyse the free vibration of a cantilever beam,
Fig.
5.55
a.
The
geometrical
parameters
of
the
beam
are,
L = 100 mm,
D = 10 mm
and
thickness
h = 1 mm.
The
material
properties
are
Young's
E = 2.1 9 10
5
N/mm
2
,
modulus
Poisson
ratio
t = 0.3
and
mass
density
q ΒΌ 8
:
0
10
10
kg s
2
/mm
4
.
Firstly some optimization studies are conducted considering the 2D plane stress
deformation theory. In order to obtain the optimal integration scheme the problem
is discretized in two distinct nodal discretizations, a regular nodal distribution and
an irregular nodal distribution, both with 306 nodes, Fig.
5.55
b, c.
