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1. Purpose
TET10 returns the values of shape functions and their
derivatives at a specified point for a tennoded
tetrahedral element;
the approximated function will be
continuous across element boundaries.
2. Specification
SUBROUTINE TET10(FUN,IFUN,DER,IDER,JDER,XI,ETA,ZETA,ITEST)
INTEGER IFUN,IDER,JDER,ITEST
XI,ETA,ZETA
FUN(IFUN),DER(IDER,JDER)
3. Description
This routine returns the values of the ten shape functions
and their derivatives associated with a tennoded tetrahedral
element. The shape functions are specified in terms of
local coordinates, the origin being at the centroid
of the element. The element, node numbering and local
coordinates are shown in Figure 1.
Figure 1:
TET10 element description

The shape functions in terms of the local coordinates are:
Typical corner node:
Typical midside node:
where and are the volume coordinates of the
standard tetrahedral. These in terms of the local cartesian coordinates are:
When these shape functions are use to approximate a
threedimensional problem, the resulting elements will
give continuity in the approximated function across
element boundaries.
Any variable defined on the element
may be approximated by
where are the nodal values of the variable .
4. References
 [1]
 ZIENKIEWICZ, O.C.
The Finite Element Method, pp 172174.
McGrawHill, London, 1977.
5. Parameters
 FUN 
array of DIMENSION (IFUN) where IFUN 10.

On successful exit, FUN() contains the value the shape
function
at the the specified point (XI,ETA,ZETA),
for =1,2,...,10.
 IFUN  INTEGER.

On entry, IFUN specifies the dimension of array FUN as
declared in the calling (sub)program.

Unchanged on exit.
 DER 
array of DIMENSION (IDER,JDER) where IDER 3
and JDER 10.

On successful exit, DER() contains the value of the
derivative of the shape function
with respect to
the the coordinate at the specified point (XI,ETA,ZETA),
for =1,2,3 and =1,2,...,10.
 IDER  INTEGER.

On entry, IDER specifies the first dimension of array
DER as declared in the calling (sub)program.

Unchanged on exit.
 JDER  INTEGER.

On entry, JDER specifies the second dimension of array
DER as declared in the calling (sub)program.

Unchanged on exit.
 XI 
.

On entry, XI specifies the value of the local coordinate
at which the function and derivative values are required.

Unchanged on exit.
 ETA 
.

On entry, ETA specifies the value of the local coordinate
at which the function and derivative values are required.

Unchanged on exit.
 ZETA 
.

On entry, ZETA spcifies the value of the local coordinate
at which the function and derivative values are required.

Unchanged on exit.
 ITEST  INTEGER.

Before entry, ITEST must be set to 0, 1 or 1.

Users not familiar with this parameter (described in routine
ERRMES) are advised to assign ITEST to 0.

Unless the routine detects an error (see next section), ITEST is
set to 0 on exit.
6. Error Indicators and Warnings
 ITEST=1 On entry IFUN 10.
 ITEST=2 On entry IDER 3 or JDER 10.
 ITEST=3 On entry (XI,ETA,ZETA) outside range of definition.
7. Auxiliary Rouines
This routine uses the Level 0 Library routine ERRMES.
8. Timing
Not available.
9. Storage
There are no internally declared arrays.
10. Accuracy
arithmetic is used.
11. Further Comments
None.
Next: TET20
Up: Contents
Previous: SURBRK
Files: PostScript PDF
Chris Greenough (c.greenough@rl.ac.uk): October 2000