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!