## 5.10 DIESEL ENGINE PISTON, TETRAHEDRONS NO.16 & 17

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!