4.15 TORUS NO.15 WITH 6 NODES

This is a curvilinear Serendipity torus element with square shape functions. The transformation is isoparametric. The integration is carried out numerically according to Gauss- Legendre. Thus, the integration order can be selected in Z88I1.TXT in the material information lines. The order 7 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.

This element type is implemented for use with automeshers e.g. Pro/MECHANICA for the 3D CAD system Pro/ENGINEER by Parametric Technology. Thus, a mesh generation with Z88N is not possible. Use torus elements No.8 for Z88N.

Use torus element No.8 whenever possible. It is substantially more precise than this isoparametric triangle.

Input:

CAD (see chapter 2.7.2): 1-4-2-5-3-6-1

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 15
> 6 nodes per element
> Cross-section parameter QPARA is 0 or any value, no influence
> Integration order INTORD per each mat info line. 7 is usually good. Possible is: 3 for 3 Gauss points, 7 for 7 Gauss points and 13 for 13 Gausspoints. For easy use with torus element No.8 (e.g. with Pro/ENGINEER), function ISOD88 of Z88 uses internally these values:
integration order 1 or 2 in Z88I1.TXT: 3 Gauss points
integration order 4 in Z88I1.TXT: 7 Gauss points
Example: Z88I1.TXT uses an entry of 2 for INTORD: Thus, torus elements No.8 use 2*2 = 4 Gauss points and torus elements No.14 use 3 Gauss points for integration.

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, 7, 13 = Calculation of the stresses in the Gauss points (e.g. 7 Gauss points) See note for Z88I1.TXT.

> 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.15:

> 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 one mid node of the loaded surface

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.