Biomedical Engineering Reference
In-Depth Information
Fig. 3.13 Triangular shape and quadrilateral shape and the respective integration points x
I
using
the Gauss-Legendre integration scheme
Nodal Integration Scheme
The nodal integration scheme is as simple as considering the integration point, x
I
,
coincident with barycentre of each Voronoï cell, V
I
. Thus, the weight of each
integration point,
_
I
, is the sum of each of the areas of the respective sub-cells, i.e.,
it is the area of the respective Voronoï cell V
I
, obtained with Eq. (
3.10
). The
spatial location of each integration point can be determined by,
x
I
¼
P
i¼1
x
S
i
A
S
Ii
P
i¼1
A
S
Ii
ð
3
:
14
Þ
Being x
S
i
the barycentre of the sub-cell S
Ii
and A
S
Ii
is the area of sub-cell S
Ii
.
Notice that the nodal integration is not sufficient to integrate accurately the
meshless shape functions, it is necessary to apply stabilization techniques [
4
,
36
,
