Biomedical Engineering Reference
In-Depth Information
Fig. 5.12 Shape parameter c
effect on the V2P1 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
γ
1.0E-12
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+00
1.0E+01
It is possible to confirm that, for the RPIM formulation, 3 9 3 Gauss-Legendre
integration points per integration cell is sufficient to integrate accurately the in-
tegro-differential equations ruling the present solid mechanics problem. Using
more integration points per cell does not increase the precision of the solution.
Regarding the patch test analysis using the NNRPIM formulation, several
numerical integration schemes were used. The medium displacement errors, E
med
,
for each analysis are presented in Fig.
5.20
. The first integration scheme consid-
ered was the simple nodal based integration scheme described in Section ''
Basic
Integration Scheme
'
'. In Fig.
5.20
this simple integration scheme is called ''basic''.
The other k 9 k integrations schemes presented in Fig.
5.20
are obtained fol-
lowing
the
procedure
indicated
in
Section
''
Gauss-Legendre
Quadrature
Integration Scheme
'
' .
