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 MPa and the
light alloy material with E = 73,000
N/mm2 und nue = 0.33 were choosen 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 2mm 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
MAXSOR
12000000
MAXPUF
3000000
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 iteration solver -Z88I1- needs
157 MB memory, part 2 of the iteration 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
MAXSOR 120000000
MAXPUF
10000000
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 iteration solver -Z88I1- needs
1,441 MB memory, part 2 of the iteration 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 3500+ and 4 GByte
memory running Windows XP in half an hour. Even faster runs the 64 bit version
of Z88 with a 64 bit LINUX kernel (but needs about twice the memory because of
the large 64 bit integers!).
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!