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, cf. chapter 3.4.

Torus elements No.8 can be generated by the net 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

> 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 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.