Biomedical Engineering Reference
In-Depth Information
Fig. 5.9 Shape parameter p
effect on the V1P1 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
chosen optimal value is p
opt
ΒΌ 1
:
0001. Regarding the V2P3 NNRPIM formulation,
Fig.
5.17
, the optimization curves only stabilize for p [ 0.1, however it is possible
to identify an optimal value for the shape parameter p near the value 1.0. Although
for p % 1 the f
tot
value as not reached the minimum, it is already sufficiently low:
f
tot
% 10
-11
.
For the V2P6 NNRPIM formulation it is perceptible in Fig.
5.18
that the
optimization curves become flat for p C 0.1. It is not possible to identify a clear
optimal value, therefore for the V2P6 NNRPIM formulation p
opt
= 0.1.
It was observed that the stress field obtained with the NNRPIM, using the
second degree influence-cells, is constant, as it should be, unlike the stress field
obtained with the NNRPIM considering first degree influence-cells. This is an
important feature, which influences the accuracy and smoothness of the stress
field.
