Biomedical Engineering Reference
In-Depth Information
Fig. 5.4 Shape parameter
p effect on the RPIM 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
p
1.0E-12
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+00
1.0E+01
Nevertheless, the obtained results also permitted to conclude that p cannot be
equal to 1, or any other integer value, because when p assumes an integer value the
moment matrix is singular. Others authors [
9
,
10
] suggested a similar value for p,
p = 1.03.
5.2.2 NNRPIM Patch Test
The process to obtain the optimal shape parameters c and p using the NNRPIM is
similar with the previously presented RPIM procedure. All previous example
assumptions regarding: the problem discretization; the material properties; the
patch geometry; and boundary conditions, remain unchanged.
