Biomedical Engineering Reference
In-Depth Information
Fig. 5.3 Shape parameter c
effect on the RPIM solution
accuracy. a Regular nodal
distribution. b Irregular nodal
distribution. Logarithmic
scales
1.0E+12
(a)
E
f
ϕ
1.0E+09
med
tot
med
1.0E+06
1.0E+03
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+12
(b)
E
f
ϕ
1.0E+09
med
tot
med
1.0E+06
1.0E+03
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
where n
t
is the number of nodes that do not belong to the essential boundary and
f
eq
is the equivalent force obtained with,
f
eq
¼
Z
B
T
r dX
ð
5
:
4
Þ
X
In Fig.
5.3
the medium displacement error E
med
is presented, together with f
tot
,
as a function of the shape parameter c. It is visible that E
med
stabilizes for values
c
1. The stabilization and the minimization of f
tot
is achieved for lower values of
c : c
0
:
1.
The shape parameters values suggested in the RPIM early works [
9
,
10
] are
c
¼
1
:
43 and p
¼
1
:
03. Notice that the shape parameter c is obtained with: c
¼
ch,
