Biomedical Engineering Reference
In-Depth Information
Fig. 7.20 a Maxillary central incisive for the two dimensional analysis. b Nodal discretization
and considered essential and natural boundary conditions
Table 7.1 Mechanical
properties of the anatomical
structures
Anatomical structure
Young modulus (GPa)
Poisson's ratio
Pulp
0.02
0.45
Dentin
18.60
0.31
Enamel
41.00
0.30
Trabecular bone
1.37
0.30
Cortical bone
13.70
0.30
Periodontal ligament
0.0689
0.45
7.2.1.1 NNRPIM/FEM Comparison
This first presented analysis regards a comparison study between the NNRPIM and
the FEM. The previously described 2D model is analysed considering the material
properties suggested in the literature [
7
], which are presented in Table
7.1
for the
biologic structures indicated in Fig.
7.20
a.
In this comparison study the same load suggested in the FEM study [
7
]is
applied: a localized load F
1
¼ F
0
f
cos h
;
sin h
g
, being F
0
¼ 100 N and the
angle h ¼ 22
:
5
þ
a
1
, as indicated in Fig.
7.20
b. In this example, in order to
eliminate local stress concentrations, the localized load F
1
was distributed along 5
boundary nodes.
In the end of the elastostatic analysis the meshless results were compared with
the FEM results [
7
]. The von Mises effective stress distribution map obtained with
the NNRPIM is presented in Fig.
7.21
. Comparing the obtained NNRPIM stress
distribution, Fig.
7.21
, with the FEM results available in the literature [
7
]itis
visible that the NNRPIM results are considerably smoother.
In Table
7.2
are presented the maximum principal stresses obtained in regions 1
to 8 with the NNRPIM. The meshless results are compared with the results
obtained with a 2D linear triangular finite element (CTRIA3) and a quadratic
quadrilateral finite element (CQUAD8), [
7
].
The results presented in Table
7.2
show that the NNRPIM solution is very close to
both FEM solutions. Additionally it is important to refer that the NNRPIM solution
was obtained using a discretization with 4,245 nodes and the CTRIA3 FEM and
