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 when using forces, cf. Chapter 3.4. It is easier to enter pressure
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
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)
> IQFLAG=1 if pressure loads for this element are filed in Z88I5.TXT
> 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 !)
2 = principal stresses in the Gauss points (INTORD not 0!)
3 = Tresca stresses in the Gauss
points (INTORD not 0!)
This file is
optional and only used if in
addition to nodal forces pressure loads applied onto element no.16:
>
Element number with pressure load
>
Pressure, positive if poiting towards the
edge
> 3
corner nodes and 3 mid nodes of the
loaded surface
The local
nodes 1 to 6 may differ from the
local nodes 1 to 6 used for the coincidence.
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.