Civil Engineering Reference
In-Depth Information
As piecewise functions are used for the pressure interpolation, this equation has to be integrated on each
element:
1
V
1
1
------
V
t
1
0
1,
div
v
()
d
w
h
(
)
0
(5.33)
t
t
1
V
t
1
V
1
where:
is the volume of the l element at time
t,
and
is the volume of this element at time
t
t
0
.
This equation is substituted to Eq. (5.25) and introduced in the new penalty formulation:
m
1
˙
h
˙
h
:
B
K
k
,2
K
(
3
)
(
d
w
h
)
1
V
t
1
0
V
1
V
t
1
tr
B
k
pen
()
div
v
()
d
w
h
()
d
w
h
-------------------------
t
1
1
1
c
q
1
v
ht
.
N
k
K
v
ht
d
h
0
(5.34)
This method makes it possible to reduce the volume losses to less than 0.01% [Fou95b].
Remeshing and Transfer of State Variables
The large deformations of the material drive large deformations of the finite element mesh which get
distorted and badly adapted to the problem. So, as soon as one of the following remeshing criteria has
been reached, a new mesh has to be automatically generated:
• distortion of a finite element, or distortion of a segment of the boundary,
• penetration of a part of the mesh inside the tool: as the contact condition is enforced only for the
nodes of the mesh, some parts of boundary segments may penetrate the tools while the nodes cannot
• large curvature of the segments of the free boundary.
FIGURE 5.20
Folding defect noticed by the remeshing procedure when two boundary segments cross each other—
Elimination of the folded area by the remeshing procedure.
