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<title>@UEBER = 5.8 BEISPIEL 7: ROHR UNTER INNENDRUCK, TORI NR.7</title>
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<div class="Section1">
<p><b><span style="font-size: 18pt;" lang="EN-GB">5.8
MOTORCYCLE CRANKSHAFT, TETRAHEDRON NO. 16 </span></b><span style=""
lang="EN-GB"><o:p></o:p></span></p>
<p><span style="" lang="EN-GB">Copy the sample file
B11_G.COS to the Z88 input file Z88G.COS. <o:p></o:p></span></p>
<p><span style="" lang="EN-GB">We want to compute a
crankshaft for a monocylinder motorcycle engine and put a force of
-5,000 N
onto the piston. The meshing will do Pro/ENGINEER. <o:p></o:p></span></p>
<p><span style="" lang="EN-GB">The boundary conditions are
a bit tricky for this example: Put a reference (or datum) point to the
center
of the face of the crankshaft. We'll need this point to fix the
crankshaft in Z
direction, i.e. lengthwise.<o:p></o:p></span></p>
<p><span style="" lang="EN-GB">The ball bearings, which
allow always some angular movement, and, thus, should be regarded as
moment-
free supports, are fastened to the larger shaft axises. The flange
facings of
the shaft axises are to be fixed in X and Y direction. Because whole
surfaces
are fixed, don't allow one ore more of these surfaces to be fixed in Z
direction, too. This would result in blocking the angular movement -
try it, if
you won't believe it.<o:p></o:p></span></p>
<p><span style="" lang="EN-GB">A total force of -5,000 N
will be put onto the peripheral surface of the crankshaft journal. <o:p></o:p></span></p>
<p><span style="" lang="EN-GB">The mesh is automatically
generated by Pro/MECHANICA featuring parabolic tetrahedrons. After
storing the
COSMOS file, a Z88 session may start:<o:p></o:p></span></p>
<p><b><span style="" lang="EN-GB">Copy B11_G.COS to
Z88G.COS, the COSMOS file for the converter </span><a href="e88g.htm"><span
style="" lang="EN-GB">Z88G</span></a></b><span style="" lang="EN-GB"><o:p></o:p></span></p>
<p><span style="" lang="EN-GB">Start converting Z88G.COS
with <b>Z88G</b> <br>
<br>
</span><img src="e88s801.jpg" alt=""><span style="" lang="EN-GB"><o:p></o:p></span></p>
<p><i><span style="" lang="EN-GB">Windows: COSMOS
converter Z88G. Looks quite similar on UNIX machines.</span></i><span
style="" lang="EN-GB"><o:p></o:p></span></p>
<p><span style="" lang="EN-GB">and proceed with the
Cuthill- McKee algorithm </span><a href="e88h.htm"><b><span style=""
lang="EN-GB">Z88H</span></b></a><span style="" lang="EN-GB">,
because
we'll expect a very bad node-numbering for the parabolic tetrahedrons. <br>
<br>
</span><img src="e88s802.jpg" alt=""><span style="" lang="EN-GB"><o:p></o:p></span></p>
<p><i><span style="" lang="EN-GB">Windows: Cuthill-McKee
program Z88H. Looks quite similar on UNIX machines.</span></i><span
style="" lang="EN-GB"><o:p></o:p></span></p>
<p><span style="" lang="EN-GB">The first line of </span><a
href="e88i1.htm"><span style="" lang="EN-GB">Z88I1.TXT</span></a><span
style="" lang="EN-GB"> tells you the following values: <o:p></o:p></span></p>
<ul type="disc">
<li style="" class="MsoNormal">6,826 nodes </li>
<li style="" class="MsoNormal">3,941 elemente </li>
<li style="" class="MsoNormal">20,478 dof </li>
</ul>
<p><span style="" lang="EN-GB">MAXKOI must have as a
minimum 3,941 elements * 10 nodes per element = 39,410.<o:p></o:p></span></p>
<p><span style="" lang="EN-GB">Thus, </span><a href="e88dy.htm"><b><span
style="" lang="EN-GB">Z88.DYN</span></b></a><span style="" lang="EN-GB">
should look as follows: <o:p></o:p></span></p>
<p><span style="font-size: 14pt; font-family: Courier;" lang="EN-GB">MAXGS
<span style=""> </span>when
starting, any value<br>
MAXKOI <span style=""> </span>minimum
39410<br>
MAXK <span style=""> </span>minimum
6826<br>
MAXE <span style=""> </span>minimum
3941<br>
MAXNFG <span style=""> </span>minimum
20478<br>
MAXNEG <span style=""> </span>minimum
1<o:p></o:p></span></p>
<p><span style="" lang="EN-GB">Proceed with a look at the
structure with </span><a href="e88o.htm"><b><span style="" lang="EN-GB">Z88O</span></b></a><span
style="" lang="EN-GB"> </span><span style="" lang="EN-GB">.<o:p></o:p></span></p>
<p><span style="" lang="EN-GB">The computing time with </span><a
href="e88f.htm"><b><span style="" lang="EN-GB">Z88F</span></b></a><span
style="" lang="EN-GB"> is about 16 sec. on a PC (AMD Athlon 64 X2
3800+ processor, 4 GByte memory, Windows XP). Enter a value of about
11,400,000 for
MAXGS..<o:p></o:p></span></p>
<p><span style="" lang="EN-GB">See the deflected structure
with </span><a href="e88o.htm"><b><span style="" lang="EN-GB">Z88O</span></b></a><span
style="" lang="EN-GB">. The
angular deflection of the axises is quite amazing. Now you would read
off the
deflections of distinguished nodes, multiply with the appropriate lever
arms
and check with the bearing catalogue if your ball bearings will allow
this
angular movement without problems.<br>
<br>
</span><span style="font-style: italic;"><img src="e88s803.jpg" alt=""
style="width: 520px; height: 360px;"></span><span style="" lang="EN-GB"><o:p></o:p></span></p>
<p><i><span style="" lang="EN-GB">Windows: Computing
deflections with Z88F. Looks quite similar on UNIX machines.<o:p></o:p></span></i></p>
<span ="">
<p><i><span style="" lang="EN-GB"><img src="e88s804.jpg" alt=""><br>
Windows: Plot programm
Z88O, undeflected structure.<br>
<br>
</span></i><span style="" lang="EN-GB"><o:p></o:p></span></p>
<p><i><span style="" lang="EN-GB"><img src="e88s805.jpg" alt=""
style="width: 1024px; height: 740px;"><br>
Windows: Plot programm
Z88O, deflected structure.</span></i><span style="" lang="EN-GB"><o:p></o:p></span></p>
<p><span style="" lang="EN-GB">Now we'll launch the
sparse matrix iteration solver </span><a href="e88ite.htm"><span
style="" lang="EN-GB">Z88I1 and Z88I2</span></a><span style=""
lang="EN-GB">. To begin with, we'll try 1,000,000 for MAXIEZ in </span><a
href="e88dy.htm"><span style="" lang="EN-GB">Z88.DYN</span></a><span
style="" lang="EN-GB"> :<br>
</span></p>
<p><span style=""></span></p>
</span>
<p class="MsoNormal" style="line-height: 12pt;"><span lang="EN-US"
style="font-size: 12pt; font-family: "Courier New";">COMMON
START<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: 12pt;"><span lang="EN-US"
style="font-size: 12pt; font-family: "Courier New";"><span style="">
</span>MAXGS<span style="">
</span>11500000<span style="">
</span></span><span style="font-size: 12pt; font-family: Wingdings;"><span
style="">></span></span><span lang="EN-US"
style="font-size: 12pt; font-family: "Courier New";"> has
for Z88I1
no meaning !<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: 12pt;"><span lang="EN-US"
style="font-size: 12pt; font-family: "Courier New";"><span style="">
</span>MAXKOI<span style="">
</span>40000<span style="">
</span></span><span style="font-size: 12pt; font-family: Wingdings;"><span
style="">></span></span><span lang="EN-US"
style="font-size: 12pt; font-family: "Courier New";">
must always be
large enough !<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: 12pt;"><span lang="EN-US"
style="font-size: 12pt; font-family: "Courier New";"><span style="">
</span>MAXK<span style="">
</span>7000<span style="">
</span></span><span style="font-size: 12pt; font-family: Wingdings;"><span
style="">></span></span><span lang="EN-US"
style="font-size: 12pt; font-family: "Courier New";">
read off from
Z88I1.TXT<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: 12pt;"><span lang="EN-US"
style="font-size: 12pt; font-family: "Courier New";"><span style="">
</span>MAXE<span style="">
</span>4000<span style="">
></span></span><span lang="EN-US"
style="font-size: 12pt; font-family: "Courier New";">
read off from
Z88I1.TXT<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: 12pt;"><span lang="EN-US"
style="font-size: 12pt; font-family: "Courier New";"><span style="">
</span>MAXNFG<span style="">
</span>21000 <span style=""> ></span></span><span
lang="EN-US" style="font-size: 12pt; font-family: "Courier New";">
read off from
Z88I1.TXT<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: 12pt;"><span lang="EN-US"
style="font-size: 12pt; font-family: "Courier New";"><span style="">
</span>MAXNEG<span style="">
</span>1<span style="">
</span></span><span style="font-size: 12pt; font-family: Wingdings;"><span
style="">></span></span><span lang="EN-US"
style="font-size: 12pt; font-family: "Courier New";">
read off from
Z88I1.TXT<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: 12pt;"><span lang="EN-US"
style="font-size: 12pt; font-family: "Courier New";"><span style="">
</span>MAXPR<span style="">
</span>1<span style="">
</span></span><span style="font-size: 12pt; font-family: Wingdings;"><span
style="">></span></span><span
style="font-size: 12pt; font-family: "Courier New";"> <span
lang="EN-US">has no meaning for this example<span style="">
</span><o:p></o:p></span></span></p>
<p class="MsoNormal" style="line-height: 12pt;"><span lang="EN-US"
style="font-size: 12pt; font-family: "Courier New";"><span style="">
</span>MAXRB<span style="">
</span>903<span style="">
</span></span><span style="font-size: 12pt; font-family: Wingdings;"><span
style="">></span></span><span lang="EN-US"
style="font-size: 12pt; font-family: "Courier New";">
read off from
Z88I2.TXT<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: 12pt;"><span lang="EN-US"
style="font-size: 12pt; font-family: "Courier New";"><span style="">
</span>MAXIEZ <span style=""> </span>1000000<span style="">
></span></span><span lang="EN-US"
style="font-size: 12pt; font-family: "Courier New";">
important for Z88I1<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: 12pt;"><span lang="EN-US"
style="font-size: 12pt; font-family: "Courier New";"><span style="">
</span>MAXGP<span style="">
</span><span style=""> </span>500000<span style="">
</span></span><span style="font-size: 12pt; font-family: Wingdings;"><span
style="">></span></span><span lang="EN-US"
style="font-size: 12pt; font-family: "Courier New";">
used by Z88O
for the Gauss points<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: 12pt;"><span
style="font-size: 12pt; font-family: "Courier New";">COMMON
END<o:p></o:p></span></p>
<span ="">
<p><span style="" lang="EN-GB"><o:p></o:p></span><tt><span
style="font-size: 14pt;" lang="EN-GB"></span></tt><span
style="font-size: 14pt; font-family: "Courier New";" lang="EN-GB"><a
name="OLE_LINK1"><br>
</a></span><span style=""><span
style="font-size: 10pt; font-family: "Courier New";" lang="EN-GB"><br>
<img src="e88s806.jpg" alt="" style="width: 520px; height: 320px;"></span></span></p>
<p><span style="font-style: italic;">Windows: Part 1 of the Sparse
Matrix Solver</span><br>
<span style=""><span
style="font-size: 10pt; font-family: "Courier New";" lang="EN-GB"></span></span><span
style=""><span style="font-size: 10pt; font-family: "Courier New";"></span></span><span
style=""></span><span style="" lang="EN-GB"><o:p></o:p></span></p>
<p><span style="" lang="EN-GB">Our entries did work
properly (otherwise, you would have to increase MAXIEZ) and
the
sorting times was just a breeze.<o:p></o:p></span></p>
<p><span style="" lang="EN-GB">Read off for MAXGS:
768,687, rounded up 770,000. This looks fairly better than the direct
Cholesky
solver Z88F with its need of 11,381,064 8-Byte elements = 87 Mbyte.
The second
part of the iteration solver, i.e. Z88I2, will only need 768,687
8-Bytes
elements = 6 MByte.<o:p></o:p></span></p>
<p><span style="" lang="EN-GB">Thus, we would adjust the
memory in </span><a href="e88dy.htm"><span style="" lang="EN-GB">Z88.DYN</span></a><span
style="" lang="EN-GB"> as
follows (feel free to enter even bigger values):<o:p></o:p></span></p>
<p><span style="font-size: 14pt;">
</span></p>
</span>
<p class="MsoNormal" style="line-height: 12pt;"><span lang="EN-US"
style="font-size: 12pt; font-family: "Courier New";">COMMON
START<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: 12pt;"><span lang="EN-US"
style="font-size: 12pt; font-family: "Courier New";"><span style="">
</span>MAXGS<span style="">
</span>770000<span style="">
></span></span><span lang="EN-US"
style="font-size: 12pt; font-family: "Courier New";">
important !<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: 12pt;"><span lang="EN-US"
style="font-size: 12pt; font-family: "Courier New";"><span style="">
</span>MAXKOI<span style="">
</span>40000<span style="">
</span></span><span style="font-size: 12pt; font-family: Wingdings;"><span
style="">></span></span><span lang="EN-US"
style="font-size: 12pt; font-family: "Courier New";">
must always be
large enough !<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: 12pt;"><span lang="EN-US"
style="font-size: 12pt; font-family: "Courier New";"><span style="">
</span>MAXK<span style="">
</span>7000<span style="">
></span></span><span style="font-size: 12pt; font-family: Wingdings;"><span
style=""></span></span><span lang="EN-US"
style="font-size: 12pt; font-family: "Courier New";">
read off from
Z88I1.TXT<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: 12pt;"><span lang="EN-US"
style="font-size: 12pt; font-family: "Courier New";"><span style="">
</span>MAXE<span style="">
</span>4000<span style="">
</span></span><span style="font-size: 12pt; font-family: Wingdings;"><span
style="">></span></span><span lang="EN-US"
style="font-size: 12pt; font-family: "Courier New";">
read off from
Z88I1.TXT<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: 12pt;"><span lang="EN-US"
style="font-size: 12pt; font-family: "Courier New";"><span style="">
</span>MAXNFG<span style="">
</span>21000 ><span style=""></span></span><span
style="font-size: 12pt; font-family: Wingdings;"><span style=""></span></span><span
lang="EN-US" style="font-size: 12pt; font-family: "Courier New";">
read off from
Z88I1.TXT<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: 12pt;"><span lang="EN-US"
style="font-size: 12pt; font-family: "Courier New";"><span style="">
</span>MAXNEG<span style="">
</span>1<span style="">
</span></span><span style="font-size: 12pt; font-family: Wingdings;"><span
style="">></span></span><span lang="EN-US"
style="font-size: 12pt; font-family: "Courier New";">
read off from
Z88I1.TXT<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: 12pt;"><span lang="EN-US"
style="font-size: 12pt; font-family: "Courier New";"><span style="">
</span>MAXPR<span style="">
</span>1<span style="">
</span></span><span style="font-size: 12pt; font-family: Wingdings;"><span
style="">></span></span><span
style="font-size: 12pt; font-family: "Courier New";"> <span
lang="EN-US">has no meaning for this example<span style="">
</span><o:p></o:p></span></span></p>
<p class="MsoNormal" style="line-height: 12pt;"><span lang="EN-US"
style="font-size: 12pt; font-family: "Courier New";"><span style="">
</span>MAXRB<span style="">
</span>903<span style="">
</span></span><span style="font-size: 12pt; font-family: Wingdings;"><span
style="">></span></span><span lang="EN-US"
style="font-size: 12pt; font-family: "Courier New";">
read off from
Z88I2.TXT<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: 12pt;"><span lang="EN-US"
style="font-size: 12pt; font-family: "Courier New";"><span style="">
</span>MAXIEZ<span style="">
</span>1000000<span style="">
</span></span><span style="font-size: 12pt; font-family: Wingdings;"><span
style="">></span></span><span lang="EN-US"
style="font-size: 12pt; font-family: "Courier New";"> not
used by
Z88I2<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: 12pt;"><span lang="EN-US"
style="font-size: 12pt; font-family: "Courier New";"><span style="">
</span>MAXGP<span style="">
</span><span style=""> </span>500000<span style="">
</span></span><span style="font-size: 12pt; font-family: Wingdings;"><span
style="">></span></span><span lang="EN-US"
style="font-size: 12pt; font-family: "Courier New";">
used by Z88O
for the Gauss points<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: 12pt;"><span lang="EN-US"
style="font-size: 12pt; font-family: "Courier New";">COMMON
END<o:p></o:p></span></p>
<span ="">
<p><span style="font-size: 14pt; font-family: "Courier New";"
lang="EN-GB"><tt><span style=""></span></tt></span><span
style="font-size: 14pt;" lang="EN-GB"><o:p></o:p></span></p>
<p><span style="" lang="EN-GB">If you adjust the iteration
parameters in </span><a href="e88i4.htm"><span style="" lang="EN-GB">Z88I4.TXT</span></a><span
style="" lang="EN-GB">
(chapter 3.6) as follows:<o:p></o:p></span></p>
<p><tt><span style="" lang="EN-GB">10000 1e-7 0.0001
1. 1</span></tt><span style="" lang="EN-GB"><o:p></o:p></span></p>
<p><span style="" lang="EN-GB">i.e. a maximum of 10,000
iterations, <i>EPS</i> with 1E-7 and <i>ALPHA </i>with 0.0001, then
this results in a computing time </span><span style=""><span
lang="EN-US" style="font-size: 12pt; font-family: "Times New Roman";">of
about 12 sec. on a PC (</span><span lang="EN-GB"
style="font-size: 12pt; font-family: "Times New Roman";">AMD
Athlon 64 X2 3800+ processor, 4 GByte memory, Windows XP)</span><span
lang="EN-US" style="font-size: 12pt; font-family: "Times New Roman";">.
</span></span><span style="" lang="EN-GB"> <o:p></o:p></span></p>
<p><span style="" lang="EN-GB">In this case, both the
iteration solver and the direct Cholesky solver need about the same
time, but
the iteration solver needs fewer than one tenth of memory. For large
structures, things get even worse for the Cholesky solver! But pay
attention to
the fact, that you can't really compare the computing times. Try other
entries
for <i>EPS</i>, for example 1E-5 (resulting in 296 iterations and 11
seconds)
or 1E-10 (resulting in 329 iterations and 13 sec.), and see the
different
computing times. <br>
<br>
</span><img src="e88s807.jpg" alt=""
style="width: 550px; height: 360px;"><span style="" lang="EN-GB"><o:p></o:p></span></p>
<p><i><span style="" lang="EN-GB">Windows: The sparse matrix iteration
solver Part 2, i.e. Z88I2.</span></i><span style="" lang="EN-GB"><o:p></o:p></span></p>
<p><u><span style="" lang="EN-GB">However, a very nice
experiment is this:</span></u><span style="" lang="EN-GB">
<o:p></o:p></span></p>
<p><span style="" lang="EN-GB">Start from the very
beginning, run Z88G, but <u>not</u> the Cuthill- McKee algorithm Z88H.
Launch
directly after Z88G a test run with </span><a href="e88f.htm"><span
style="" lang="EN-GB">Z88F</span></a><span style="" lang="EN-GB"> :<br>
<br>
</span><img src="e88s808.jpg" alt=""
style="width: 520px; height: 360px;"><span style="" lang="EN-GB"><o:p></o:p></span></p>
<p><i><span style="" lang="EN-GB">Windows: The direct
Cholesky solver in test mode.</span></i><span style="" lang="EN-GB"><o:p></o:p></span></p>
<p><span style="" lang="EN-GB">Gee, see the faces falling:
now we would need 184,122,663 8- Byte elements = 1,4 GByte. Absolutely
no need
for this!<o:p></o:p></span></p>
<p><span style="" lang="EN-GB">However, run again the
iteration solver part 1, i.e. Z88I1. This will again result in only
768,687
elements for the total stiffness matrix. Calculate, please:<o:p></o:p></span></p>
<p><span style="" lang="EN-GB">184,122,663 : 768,687 = 240
: 1<o:p></o:p></span></p>
<p><span style="" lang="EN-GB">The second part of the
iteration solver, i.e. Z88I2, needs now some more iterations (350 in
contrary
to 415 with an equal <i>EPS</i> of 1E-7), because the matrix features
the same
number of non-zero elements, though, but the condition is worse
because of the
very bad node-numbering of Pro/MECHANICA. That means: When using the
iteration
solver you don't need to run the Cuthill-McKee algorithm Z88H for
reducing the
storage needs of the iteration solver (in contrary to the direct
Cholesky
solver Z88F, which may depend heavily on Z88H for larger structures!). </span>However,
Z88H may improve the matrix condition anyway.<br>
</p>
<p></p>
</span>
<p class="TNChar" style="page-break-after: auto;"><i style=""><span
lang="EN-GB" style="font-size: 12pt;">Try now the direct Sparse Matrix
Solver with Fill-In: <o:p></o:p></span></i></p>
<p class="TNChar" style="page-break-after: auto;"><span lang="EN-GB"
style="font-size: 12pt;">Much faster runs
the solver pair Z88I1 and Z88PAR. Adjust the 5<sup>th</sup> entry in <b
style="">Z88I4.TXT</b> to the number of CPUs. Keep
in mind that Z88PAR deals heavily with dynamic memory when running.
This may
cause serious trouble when computing very large structures. For this
example
the elapsed time was ~ 4 sec. with two CPUs.<br>
</span></p>
<p class="TNChar" style="page-break-after: auto;"><span lang="EN-GB"
style="font-size: 12pt;"><img alt="" src="e88s809.jpg"></span></p>
<p class="TNChar" style="page-break-after: auto;"><span lang="EN-GB"
style="font-size: 12pt;"><span style="font-style: italic;">Windows:
The direct Sparse
Matrix Solver Z88PAR.</span><br>
<o:p></o:p></span></p>
<span ="">
<p> </p>
</span></div>
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