4.12 TORUS NO.12 WITH 12 NODES
This is a curvilinear Serendipity
torus element with cubic shape functions. The transformation is
isoparametric.
The integration is carried out numerically in both axises according to
Gauss-
Legendre. Thus, the integration order can be selected in Z88I1.TXT in the material information lines. The
order 3 is mostly sufficient. This element calculates both
displacements and
stresses with outstanding precision. The integration order can be
chosen again
for the stress calculation. The stresses are calculated in the corner
nodes
(good for an overview) or calculated in the Gauss points (substantially
more
exactly). Because of its 24*24 element stiffness matrices the element
No.11
needs a lot of memory and computing power. Pay attention to edge loads
when
using forces, cf. chapter 3.4. It is easier to
enter
edge loads via the surface and pressure loads file Z88I5.TXT.
Torus
elements No.8 can
be generated by the mesh generator Z88N
from super elements torus elements No.12. Thus,
the torus element No.12 is well suited as super element. But torus
elements
No.12 cannot be generated by the net generator Z88N from super elements
torus
elements No.12.
Input:
CAD (see chapter 2.7.2): 1-5-6-2-7-8-3-9-10-4-11-12-1
Z88I1.TXT
> In principle cylindrical coordinates are expected: KFLAG must
be 0 !
R
coordinate (= X), always
positive
Z coordinate (= Y), always positive
> IQFLAG=1 if edge loads for this
element are filed in Z88I5.TXT
> 2 degrees of freedom for each
node, DOF R and Z (= X and Y).
> Element type is 12
> 12 nodes per element
> Cross-section parameter QPARA is 0 or any value, no influence
> Integration order per each mat info line. 3 is usually good.
Z88I3.TXT
> Integration order INTORD: Basically, it is a good idea to
use the
same value as chosen in Z88I1.TXT , but different values are permitted
0 = Calculation of the stresses in the corner nodes
1,2,3,4 = Calculation of the stresses in the Gauss points
> KFLAG , any, has no influence
> Reduced stress flag
ISFLAG:
0 = no calculation of reduced
stresses
1 = von Mises stresses in the Gauss points ( INTORD not 0 !)
2 = principal stresses in the Gauss points (INTORD not 0!)
3 = Tresca stresses in the Gauss
points (INTORD not 0!)
This file is
optional and only used if in
addition to nodal forces edge loads applied onto element no.12:
>
Element number with surface and pressure
load
>
Pressure, positive if poiting towards the
edge
>
Tangential shear, positive in local r
direction
> 2
corner nodes and 2 mid nodes of the
loaded surface
The local r
direction is defined by the nodes
1-2. The local nodes 1, 2, 3, 4 may differ from the local nodes 1, 2,
3, 4 used
for the coincidence.
Results:
Displacements in R and Z (= X and Y).
Stresses: The stresses are calculated in the corner nodes or
Gauss
points and printed along with their locations. It is: SIGRR = stress in
R
direction = radial stress (= X direction), SIGZZ = stress in Z
direction (= Y
direction), TAURZ = shear stress in RZ plane (= XY plane), SIGTE =
stress in
peripherical direction = tangential stress. Optional von Mises stresses.
Nodal forces in R (= X) and Z (= Y) for each element and each
node.