Biomedical Engineering Reference
In-Depth Information
Fig. 4.24
RPI shape functions compatibility representation
Fig. 4.25
a Nodal discretization X
1
. b Nodal discretization X
2
4.4.5.7 RPI Shape Functions Examples
The RPI approach is capable to produce smooth shape functions with interpolating
properties. In the present subsection are shown two distinct RPI shape functions,
both constructed in the two-dimensional space. One of the RPI shape functions is
obtained using a reduced size support-domain and the other RPI shape function is
constructed considering a large support-domain.
Thus, consider a two-dimensional domain X
2
R
discretized by two distinct
2
,
nodal
sets:
X
1
¼ x
1
;
x
2
;
...
;
x
8
f
g 2
R
Fig.
4.25
a,
and
X
2
¼ x
1
;
x
2
;
...
;
x
13
f
g
2
, Fig.
4.25
b. The nodes of the studied nodal sets are irregularly distributed in
the two-dimensional space.
Both RPI shape functions were constructed for the central node, x
1
, following
the procedure indicated in
Sect. 4.4.3
. In the RPI formulation it was considered the
linear polynomial basis and the MQ-RBF with c = 0.1 and p = 0.9. The size
parameter d
a
of Eq. (
4.108
) was obtained with: d
a
¼ max x
i
x
1
2
R
k
k; 8
x
i
2
X
J
.
