Biomedical Engineering Reference
In-Depth Information
Fig. 3.15
Solid domain and applied volume and external forces and displacement constrains
Fig. 3.16
a Example of a nodal distribution. b Example of a background integration mesh
domain X, the solid boundary C does not contains any integration point. Being
_
I
the integration weight of the Ith integration point, q
I
2
Q, then
Vol
X
¼
Z
X
_
ð
q
Þ
dX ¼
X
Q
_
I
ð
3
:
15
Þ
I¼1
where Vol
X
is the volume of the solid domain. The integration weight
_
I
is the
infinitesimal volume of the integration point q
I
. The mass of the solid domain
Mass
X
is obtained by,
Mass
X
¼
Z
X
_
ð
q
Þ
q
ð
q
Þ
dX ¼
X
Q
_
I
q
ð
q
I
Þ
ð
3
:
16
Þ
I¼1
In
Sect. 2.3
it was shown that the Galerkin weak formulation permits to obtain
the following system of equations,
