Biomedical Engineering Reference
In-Depth Information
Fig. 5.17 Shape parameter
p effect on the V2P3
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
5.3 Elastostatic Numerical Examples
In this section three benchmark elastostatic numerical problems are analysed. All
the solid mechanics examples studied in the present section are solved using the
RPIM formulation suggested in [
9
,
10
] and the NNRPIM formulation suggested in
[
13
].
Therefore, for the RPIM formulation the RPI shape functions are constructed
using the MQ-RBF and a linear polynomial basis. The MQ-RBF shape parameters
are: c = 1.43 and p = 1.03. The nodal connectivity is imposed using square
support-domains: d
s
ΒΌ 2
:
5 h, as Fig.
5.2
shows. The background integration mesh
respects the layout presented in Fig.
5.1
and for each integration cell are used
3 9 3 Gauss-Legendre quadrature integration points.
Regarding the NNRPIM formulation, the RPI shape functions are constructed
using the MQ-RBF and a constant unit basis. The MQ-RBF shape parameters are:
