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!)

Z88I5.TXT

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.