This example compares linear shape functions
tetrahedrons with 4 nodes and square shape functions tetrahedrons with
10
nodes. However, the pressure load is applied by the surface and
pressure loads
file Z88I5.TXT. Both the NASTRAN files were
compiled
with Pro/ENGINEER Wildfire 2:

Diesel engine piston
of an AUDI engine (simplyfied), modelled by Dipl.-Ing. Jens-Uwe
Goering.

Diesel engine piston
with pressure load of 50 bar, max. mesh size 2mm.
The piston was modelled similar to the pistons
of modern AUDI diesel engines. The pressure load of 50 bar = 5 N/mm2
and the
light alloy material with  E = 73,000
N/mm2 und nue = 0.33 were chosen with arbitrariness. Of
course, in
reality higher pressures and other kinds of light alloy are used – but
this is
not important for our test runs here. We compiled a fine-meshed
structure by
allowing a max. mesh size of only 2 mm in Pro/ENGINEER. 

The compiled mesh
resulting in ~ 280,000 tetrahedrons.
Here we go with linear shape functions
tetrahedrons. For your convenience a NASTRAN input file B21_LIN_G.NAS
 is prepared
and Z88.DYN should look as follows:
  COMMON
START
   
MAXGS   
3600000
   
MAXKOI  
1120000
   
MAXK      
58000
    MAXE     
280000
   
MAXNFG   
172000 
   
MAXNEG        32
   
MAXPR     
50000
   
MAXRBD      4000
   
MAXIEZ  
3600000
   
MAXGP    1200000
  COMMON
END
The surface and pressure loads file Z88I5.TXT
looks as follows (please check with the chapters
3.7 and 4.17):
4430   Z88I5.TXT,via Z88G V12 NASTRAN
  265
+5.00000E+000   731  
728  
732
  292
+5.00000E+000   344  
345   847
  525
+5.00000E+000 16105 16106 15009
  640
+5.00000E+000 15582 15584 15583
  658
+5.00000E+000 15582 15548 15547
  701
+5.00000E+000   812  
817   815
  .........
Part 1 of the sparse matrix solver Z88I1 needs 31 MB
memory, part 2 of the sparse matrix solver Z88I2 needs 89 MB if you’ll
choose the Cholesky preconditioning with an alpha
= 0.0001. Then, the solver does 202 iterations and will finish the job
on a
modern PC running Windows XP within one minute.
Z88 computes: 
SigmavonMises = 35.1 N/mm2              
ymax = -0.0121 mm
Now we’ll run the job with square shape
functions tetrahedrons resulting in this Z88.DYN:
  COMMON
START
   
MAXGS  
51000000
   
MAXKOI  
2800000
   
MAXK     
416000
   
MAXE     
280000
   
MAXNFG  
1250000
   
MAXNEG        32
    MAXPR     
50000
    MAXRBD    
12000
    MAXIEZ 
51000000
   
MAXGP    1500000
  COMMON
END
Use the NASTRAN input file B21_PARA_G.NAS.
The surface and pressure loads file Z88I5.TXT
looks as follows (please check with the chapters
3.7 and 4.16):
4430  
Z88I5.TXT,via Z88G V12 NASTRAN
   
5
+5.00000E+000   394  
734  
610 59815 61330 59813
  128
+5.00000E+000 16135 16138 16136 167350
167355 167348
  292
+5.00000E+000 15401 15400 15399 162081
162074 162075
  369
+5.00000E+000 15319 15302 15317 161397
161396 161503
  379
+5.00000E+000   828  
833   831 63009 63029 63008
  682
+5.00000E+000 15582 15548 15547 163056
163041 163044
  .........
Part 1 of the sparse matrix solver Z88I1 needs 250 MB
memory, part 2 of the sparse matrix solver Z88I2 needs 1,072 MB if
you’ll choose the Cholesky preconditioning with an alpha = 0.0001
(you may reduce this amount by ~1/3 if you’ll choose the SOR
preconditioning
with an omega = 1.2). Then the solver
does 668
iterations and finishes the run on a PC with an AMD Athlon 64 X2 3800+
and 4 GByte
memory running Windows XP in 45 min. 
Z88 computes: 
SigmavonMises = 36.5 N/mm2              
ymax = -0.0128 mm

Stresses plotted by
Z88O for tetrahedrons No.16.
As you see the results differ only minimally
and the big time and memory expense for the square shape functions
tetrahedrons
No.16 was completely useless. But just this is the art of finite
elements
computing – to choose the best suitable element types!