File: e88h.htm

package info (click to toggle)
z88 13.0.0+dfsg2-6
  • links: PTS, VCS
  • area: main
  • in suites: buster, sid
  • size: 107,792 kB
  • sloc: ansic: 45,530; sh: 71; makefile: 14
file content (258 lines) | stat: -rw-r--r-- 11,688 bytes parent folder | download | duplicates (3)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
<html xmlns="http://www.w3.org/TR/REC-html40"
 xmlns:w="urn:schemas-microsoft-com:office:word"
 xmlns:o="urn:schemas-microsoft-com:office:office">
<head>
  <meta content="text/html; charset=us-ascii" http-equiv="Content-Type">
  <meta content="Word.Document" name="ProgId">
  <meta content="Microsoft Word 10" name="Generator">
  <meta content="Microsoft Word 10" name="Originator">
  <link href="e88h-Dateien/filelist.xml" rel="File-List">
  <title>2</title>
<!--[if gte mso 9]><xml>
 <o:DocumentProperties>
  <o:Author>Prof. Frank Rieg</o:Author>
  <o:Template>Normal</o:Template>
  <o:LastAuthor>Prof. Frank Rieg</o:LastAuthor>
  <o:Revision>6</o:Revision>
  <o:Created>2006-02-09T17:30:00Z</o:Created>
  <o:LastSaved>2006-02-10T15:34:00Z</o:LastSaved>
  <o:Pages>1</o:Pages>
  <o:Words>734</o:Words>
  <o:Characters>4626</o:Characters>
  <o:Company>Uni Bayreuth</o:Company>
  <o:Lines>38</o:Lines>
  <o:Paragraphs>10</o:Paragraphs>
  <o:CharactersWithSpaces>5350</o:CharactersWithSpaces>
  <o:Version>10.2625</o:Version>
 </o:DocumentProperties>
</xml><![endif]--><!--[if gte mso 9]><xml>
 <w:WordDocument>
  <w:HyphenationZone>21</w:HyphenationZone>
  <w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel>
 </w:WordDocument>
</xml><![endif]-->
  <style>
<!--
 /* Style Definitions */
 p.MsoNormal, li.MsoNormal, div.MsoNormal
	{mso-style-parent:"";
	margin:0cm;
	margin-bottom:.0001pt;
	mso-pagination:widow-orphan;
	font-size:12.0pt;
	font-family:"Times New Roman";
	mso-fareast-font-family:"Times New Roman";}
a:link, span.MsoHyperlink
	{color:blue;
	text-decoration:underline;
	text-underline:single;}
a:visited, span.MsoHyperlinkFollowed
	{color:blue;
	text-decoration:underline;
	text-underline:single;}
p
	{mso-margin-top-alt:auto;
	margin-right:0cm;
	mso-margin-bottom-alt:auto;
	margin-left:0cm;
	mso-pagination:widow-orphan;
	font-size:12.0pt;
	font-family:"Times New Roman";
	mso-fareast-font-family:"Times New Roman";}
@page Section1
	{size:595.3pt 841.9pt;
	margin:70.85pt 70.85pt 2.0cm 70.85pt;
	mso-header-margin:35.4pt;
	mso-footer-margin:35.4pt;
	mso-paper-source:0;}
div.Section1
	{page:Section1;}
-->
  </style><!--[if gte mso 10]>
<style>
 /* Style Definitions */
 table.MsoNormalTable
	{mso-style-name:"Normale Tabelle";
	mso-tstyle-rowband-size:0;
	mso-tstyle-colband-size:0;
	mso-style-noshow:yes;
	mso-style-parent:"";
	mso-padding-alt:0cm 5.4pt 0cm 5.4pt;
	mso-para-margin:0cm;
	mso-para-margin-bottom:.0001pt;
	mso-pagination:widow-orphan;
	font-size:10.0pt;
	font-family:"Times New Roman";}
</style>
<![endif]-->
</head>
<body style="" vlink="blue" link="blue" lang="DE">
<div class="Section1">
<p><b><span style="font-size: 18pt;" lang="EN-GB">2.9 THE
CUTHILL-McKEE PROGRAM Z88H</span></b><span style="" lang="EN-GB"><o:p></o:p></span></p>
<p><b><span style="" lang="EN-GB">The choice of the nodal
numbers is extremely important for the compilation of the stiffness
matrix and
bad nodal numbering may result in huge memory needs which are not
really
necessary. </span></b><span style="" lang="EN-GB"><o:p></o:p></span></p>
<p><b><span style="" lang="EN-GB">However, Z88H may reduce
the memory needs for the direct Cholesky Solver </span><a
 href="e88f.htm"><span style="" lang="EN-GB">Z88F</span></a></b><b><span
 style="" lang="EN-GB"> greatly. The sparse matrix solver </span><a
 href="e88ite.htm"><span style="" lang="EN-GB">Z88I1/Z88I2</span></a></b><b><span
 style="" lang="EN-GB"> may also gain some advantages from
a Z88H run, but the iteration solver is a-priori very stable regarding
node
numbering because of storing the non- zero elements only.</span></b><span
 style="" lang="EN-GB"><o:p></o:p></span></p>
<p><span style="" lang="EN-GB">Basically, it it always
good to achieve a small difference of nodal numbers for each finite
element.
This results in nodal numbers of similar size for an element. However,
this is
not always possible: consider a circular structur starting with nodal
numbering
at 0&#176; with increasing numbers clockwise. When reaching 360&#176;, elements
with large differences of nodal numbers will occur. <o:p></o:p></span></p>
<p><span style="" lang="EN-GB">Sometimes 3D CAD programs
include so-called automeshers which devide a CAD model into finite
elements.
This generated mesh can be stored in some output format to fit the
needs of the
various FEA programs. But many of these automeshers generate meshes
with very
large nodal differences. This is true for Pro/ENGINEER's Pro/MECHANICA:
If you
choose </span><a href="e88g.htm"><i><span style="" lang="EN-GB">Tet
Mesh parabolic</span></i></a><span style="" lang="EN-GB">,
Pro/MECHANICA in a first operation generates linear tetrahedrons, i.e.
with 4 rather than 10 nodes per element, with straight element edges.
Then
midnodes are put on the element edges resulting in parabolic elements
with 10
nodes. These midnodes have relatively large nodal numbers because the
corner
nodes were numbered in the first step. Thus, every finite element
features
relatively small corner node numbers and relatively large mid node
numbers
resulting in large differences of nodal numbering. When choosing </span><a
 href="e88g.htm"><i><span style="" lang="EN-GB">Shell,
triangle, parabolic</span></i></a><i><span style="" lang="EN-GB">,</span></i><span
 style="" lang="EN-GB"> the same
situation occurs. This means that meshes built with Pro/MECHANICA will
always have
bad nodal numbering.<o:p></o:p></span></p>
<p><span style="" lang="EN-GB">For large meshes one needs
to re-number the nodes to get finite elements with small differences of
nodal
numbers. Several proper procedures do exist in literature for this
task.
However, the so-called <i>Cuthill- McKee</i> procedure is a good
compromise.
One modification of it is the <i>reverse Cuthill- McKee algorithm</i>.
</span>For
more information, consult <i>Schwarz, H.R.: Die Methode der finiten
Elemente.</i>
<span style="" lang="EN-GB">The C program Z88H is based on
a FORTRAN77 program of Prof. Schwarz and is specially adapted to Z88.
The core
algorithm of H.R. Schwarz decides internally wether to use the normal <i>Cuthill-
McKee procedure</i> or the <i>reverse Cuthill- McKee algorithm.</i><o:p></o:p></span></p>
<p><span style="" lang="EN-GB">The Cuthill-McKee program
Z88H was originally designed for finite element meshes generated by 3D
converter
</span><a href="e88g.htm"><span style="" lang="EN-GB">Z88G</span></a><span
 style="" lang="EN-GB">. However, Z88H can deal with all
Z88 meshes. Z88H reads the Z88 input files </span><a href="e88i1.htm"><span
 style="" lang="EN-GB">Z88I1.TXT</span></a><span style="" lang="EN-GB">
(general structure information)
and </span><a href="e88i2.htm"><span style="" lang="EN-GB">Z88I2.TXT</span></a><span
 style="" lang="EN-GB"> (boundary conditions) and &#8211;if
needed- <a href="e88i5.htm">Z88I5.TXT</a> (surface and pressure
loads), files
backups Z88I1.OLD, Z88I2.OLD and Z88I5.OLD (if needed) and computes the
modified input files Z88I1.TXT, Z88I2.TXT and Z88I5.TXT.<o:p></o:p></span></p>
<p><span style="" lang="EN-GB">Own research studies showed
that sometimes a second run of Z88H may improve again the numbering of
a first
run of Z88H. A third run seems to make things worse. In contrast, Z88H
may
sometimes compute a worse nodal numbering then the original mesh. You
should
have some experiments because the <i>Cuthill-McKee algorithm</i> may
not
always improve a given mesh.<o:p></o:p></span></p>
<p><span style="" lang="EN-GB">And here's how you proceed:<o:p></o:p></span></p>
<p><b><span style="" lang="EN-GB">1) Generate a finite
elements mesh</span></b><span style="" lang="EN-GB">, i.e.
the Z88 input files </span><a href="e88i1.htm"><span style=""
 lang="EN-GB">Z88I1.TXT</span></a><span style="" lang="EN-GB"> and </span><a
 href="e88i2.htm"><span style="" lang="EN-GB">Z88I2.TXT</span></a><span
 style="" lang="EN-GB"> and &#8211;if needed- <a href="e88i5.htm">Z88I5.TXT</a>.
This can be done by:<o:p></o:p></span></p>
<p><span style="" lang="EN-GB">- </span><a href="e88ia.htm"><span
 style="" lang="EN-GB">hand</span></a><span style="" lang="EN-GB"> <br>
- Z88 mesh generator </span><a href="e88n.htm"><span style=""
 lang="EN-GB">Z88N</span></a><span style="" lang="EN-GB"> (Z88I1.TXT
only, then edit Z88I2.TXT and
Z88I5.TXT by hand) <br>
- a DXF file and </span><a href="e88x.htm"><span style="" lang="EN-GB">Z88X</span></a><span
 style="" lang="EN-GB"> <br>
- a COSMOS file and </span><a href="e88g.htm"><span style=""
 lang="EN-GB">Z88G</span></a><span style="" lang="EN-GB"><o:p></o:p></span></p>
<p><b><span style="" lang="EN-GB">2) Adjust </span><a href="e88dy.htm"><span
 style="" lang="EN-GB">Z88.DYN</span></a></b><b><span style=""
 lang="EN-GB"> if necessary: MAXKOI is very
important (Number of nodes per element * total number of elements) and
MAXK,
MAXE and MAXNFG.</span></b><span style="" lang="EN-GB"><o:p></o:p></span></p>
<p><b><span style="" lang="EN-GB">3) Launch </span><a href="e88f.htm"><span
 style="" lang="EN-GB">Z88F</span></a></b><b><span style="" lang="EN-GB">
with test option</span></b><span style="" lang="EN-GB">, i.e.<o:p></o:p></span></p>
<p><i><span style="" lang="EN-GB">Windows: Z88F &gt; Mode
&gt; Test Mode, Compute &gt; Go</span></i><span style="" lang="EN-GB"> <br>
<i>UNIX: z88f -t (console) or Z88F -T (Z88COM)</i><o:p></o:p></span></p>
<p><span style="" lang="EN-GB">Fix the value for GS, i.e.
the number of storage entries in the stiffness matrix (multiplying this
values
by 8 gives the memory need in bytes).<o:p></o:p></span></p>
<p><b><span style="" lang="EN-GB">4) Launch Z88H.</span></b><span
 style="" lang="EN-GB"><o:p></o:p></span></p>
<p><b><span style="" lang="EN-GB">5) Repeat step 3</span></b><span
 style="" lang="EN-GB">, i.e. run </span><a href="e88f.htm"><span
 style="" lang="EN-GB">Z88F</span></a><span style="" lang="EN-GB"> with
the test option and check wether GS got
smaller. This will be mostly the case if your mesh was generated by
Z88G using
a COSMOS file. Otherwise, restore Z88I1.TXT, Z88I2.TXT and Z88I5.TXT
from the backup
files Z88I1.OLD, Z88I2.OLD and Z88I5.OLD. <o:p></o:p></span></p>
<p><b><span style="" lang="EN-GB">6) Enter the value of GS
into </span><a href="e88dy.htm"><span style="" lang="EN-GB">Z88.DYN</span></a></b><b><span
 style="" lang="EN-GB"> in the line MAXGS and lauch Z88F
with a compute mode, e.g.</span></b><span style="" lang="EN-GB"><o:p></o:p></span></p>
<p><i><span style="" lang="EN-GB">Windows: Z88F &gt; Mode
&gt; Compute Mode, Compute &gt; Go</span></i><span style="" lang="EN-GB">
<br>
<i>UNIX: z88f -c (console) or Z88F -C (Z88COM) </i><o:p></o:p></span></p>
<p><b><span style="font-size: 13.5pt;" lang="EN-GB">Remark:</span></b><span
 style="" lang="EN-GB"> <o:p></o:p></span></p>
<p><span style="" lang="EN-GB">Z88H features a section in
the memory header file </span><a href="e88dy.htm"><span style=""
 lang="EN-GB">Z88.DYN</span></a><span style="" lang="EN-GB">: <o:p></o:p></span></p>
<p><b><span style="" lang="EN-GB">CUTKEE START<br>
&nbsp;&nbsp;&nbsp;&nbsp; MAXGRA 200 (</span></b><span style=""
 lang="EN-GB">maximum
degree of nodes)<br>
&nbsp;&nbsp;&nbsp;&nbsp;
<b>MAXNDL 1000 (</b>steps of the algorithm)<br>
<b>CUTKEE END</b> <o:p></o:p></span></p>
<p style="margin-bottom: 12pt;"><span style="" lang="EN-GB">Increase
these entries for very large structures.<br>
<o:p></o:p></span></p>
</div>
</body>
</html>