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, cf. chapter 3.4.

This element type is implemented for use with automeshers e.g. Pro/MESH for the 3D CAD system Pro/ENGINEER by Parametric Technology. Thus, a net 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.

Attention: This element is not directly integrated into Z88G, because e.g. Pro/MESH for Pro/ENGINEER does not deal at all with these torus elements. But it is easy to overcome this problem: Generate shell in Pro/ENGINEER, lauch Z88G and "find & replace" with an editor the element types No.7 and/or No.14 against element types No.8 and/or No.15. Every better editor has this feature.

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

> 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 computed for the Gauss points (INTORD not 0 !)

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.