4.8 TORUS NO.8 WITH 8 NODES
This is a curvilinear Serendipity
torus element with square 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 very exactly. 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). 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. You may combine this element
with elements no.15.
Torus elements No.8 can be
generated by the mesh
generator Z88N from the super
elements torus elements No.8 or No.12.
Thus, Torus No.8 is well suited as
super element.
Torus element No.8 is
recommended for all sort of axialsymmetric computation. This element is well-balanced in
respect to the precision of displacement and stress calculation as well
as to
its needs for memory and computing power.
Input:
CAD (see chapter 2.7.2): 1-5-2-6-3-7-4-8-1
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 8
> 8 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.8:
>
Element number with surface and pressure
load [Long]
>
Pressure, positive if poiting towards the
edge [Double]
>
Tangential shear, positive in local r
direction [Double]
> 2
corner nodes and one mid node of the
loaded surface [3 x Long]
The local r
direction is defined by the nodes
1-2. The local nodes 1, 2, 3 may differ from the local nodes 1, 2, 3
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.