4

4.16 TETRAHEDRON NO.16 WITH 10 NODES

This is a curvilinear Serendipity volume 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 4 is good. The quality of the displacement and stress calculations are far better than the results of the tetrahedron element No.17 but less precise than hexahedron No.10. Pay attention to edge load, 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 and a DXF data exchange with Z88X is not possible, because this will make no sense.

Tetrahedron No.16 also applies well for thick plate elements, if the plate's thickness is not too small compared to the other dimensions.

The element causes a big computing load and needs a large amount of memory because the element stiffness matrix has the order 30*30.

The nodal numbering of the element No.16 must be done carefully and must exactly match the sketch below. Pay attention to the location of the axis system ! The possible error message " Jacobi determinant zero or negative " is a hint for incorrect node numbering.

Tetrahedron No.16 cannot be generated by the net generator Z88N. A DXF data exchange with Z88X is not implemented because tetrahedrons due to their strange geometry are very difficult to arrange in space. This element's main purpose is the use with automeshers from third-party suppliers. Caution: Sometimes the automeshers of CAD systems produce very bad element and nodal numbering resulting in an useless large amount of memory needs of Z88F. In this case, renumber especially the nodes.

Input:

Z88I1.TXT

> KFLAG for cartesian (0) or cylindrical coordinates (1)

> 3 degrees of freedom for each node

> Element type is 16

> 10 nodes per element

> Cross-section parameter QPARA is 0 or any value, has no influence

> Integration order INTORD for each mat info line. 4 is usually good. Allowed are 1 for 1 Gauss point, 4 for 4 Gauss points and 5 for 5 Gauss points.

Z88I3.TXT

> Integration order INTORD for stress calculation:

Can be different from INTORD in Z88I1.TXT.

0 = Calculation of stresses in the corner nodes

1, 4, 5 = Calculation of stresses in the Gauss points (e.g. 4 = 4 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!)

Results:

Displacements in X, Y and Z

Stresses: SIGXX, SIGYY, SIGZZ, TAUXY, TAUYZ, TAUZX, respectively for corner nodes or Gauss points. Optional von Mises stresses.

Nodal forces in X, Y and Z for each element and each node.