Biomedical Engineering Reference
In-Depth Information
Fig. 5.10 Shape parameter
p effect on the V1P3
NNRPIM solution accuracy.
a Regular nodal distribution.
b Irregular nodal distribution.
Logarithmic scales
1.0E+03
(a)
E
f
med
tot
1.0E+00
1.0E-03
1.0E-06
1.0E-09
1.0E-12
p
1.0E-15
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+00
1.0E+01
1.0E+03
(b)
E
f
med
tot
1.0E+00
1.0E-03
1.0E-06
1.0E-09
1.0E-12
p
1.0E-15
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+00
1.0E+01
In Table
5.5
the obtained E
med
and f
tot
using the optimal MQ-RBF shape
parameters for the distinct NNRPIM formulations are summarized.
As Table
5.5
shows, for irregular nodal distributions, the lowest medium dis-
placement error E
med
is obtained with the V2P1 NNRPIM formulation, is very
close with the error obtained with the RPIM. Notice as well that generally the error
obtained for regular meshes with NNRPIM is lower than the error obtained with
RPIM.
In this section the patch test study will continue considering only the V1P0,
V1P1, V2P0 and V2P1 NNRPIM formulations, since the lowest medium dis-
placement errors are obtained with these four NNRPIM formulations. It is important
to refer that the RPIM analysis is an optimized analysis because adequate MQ-RBF
shape parameters and proper integration schemes were applied [
9
,
10
]. However in
the case of the NNRPIM it was applied only the basic nodal based integration
