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!