Biomedical Engineering Reference
In-Depth Information
Fig. 5.6 Shape parameter c
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
γ
1.0E-12
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
γ
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+00
1.0E+01
As Fig.
5.8
shows, for the V1P0 NNRPIM formulation the optimization curves
only stabilize for p [ 0.01. Therefore, the optimal value suggested for the V1P0
NNRPIM formulation is p
opt
= 0.0001. For the V1P1 NNRPIM formulation,
Fig.
5.9
, it is perceptible that the optimization curves only stabilize for p [ 0.1,
however an optimal value for the shape parameter p is achieved near the value 1.0.
Thus, for the V1P1 NNRPIM formulation it is assumed p
opt
= 1.0001. Regarding
the V1P3 NNRPIM formulation, Fig.
5.10
, the optimization curves become flat for
p [ 0.1 and it is possible to identify an optimal shape parameter near the value 3.0.
Therefore, the optimal value suggested for the V1P3 NNRPIM formulation is
p
opt
= 3.0001.
It is important to refer that the V1P0 NNRPIM formulation it is not capable to
produce an acceptable smooth stress field, for this reason the study of this for-
mulation is abandoned.
