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Contents of /trunk/doc/user/finleyelements.tex

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Revision 1316 - (show annotations)
Tue Sep 25 03:18:30 2007 UTC (12 years, 9 months ago) by ksteube
File MIME type: application/x-tex
File size: 10930 byte(s)
Quickly edited chapters 1 and 2 of the User Guide, but it needs more work.
Ran entire document through spell checker.

1 %
2 % $Id$
3 %
4 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
5 %
6 % Copyright 2003-2007 by ACceSS MNRF
7 % Copyright 2007 by University of Queensland
8 %
9 % http://esscc.uq.edu.au
10 % Primary Business: Queensland, Australia
11 % Licensed under the Open Software License version 3.0
12 % http://www.opensource.org/licenses/osl-3.0.php
13 %
14 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
15 %
16
17 \setlength{\unitlength}{1mm}
18
19 \newsavebox{\HLa}
20 \savebox{\HLa}(0,0)
21 {\put(0,0){\circle*{2}}
22 \thicklines \put(1,0){\line(1,0){28}}
23 \put(30,0){\circle*{2}} }
24
25 \newsavebox{\HLathin}
26 \savebox{\HLathin}(0,0)
27 {\put(0,0){\circle{2}}
28 \thinlines \put(1,0){\line(1,0){28}}
29 \put(30,0){\circle{2}} }
30
31 \newsavebox{\VLa}
32 \savebox{\VLa}(0,30)
33 {\put(0,0){\circle*{2}}
34 \thicklines \put(0,1){\line(0,1){28}}
35 \put(0,30){\circle*{2}} }
36
37 \newsavebox{\VLathin}
38 \savebox{\VLathin}(0,30)
39 {\put(0,0){\circle{2}}
40 \thinlines \put(0,1){\line(0,1){28}}
41 \put(0,30){\circle{2}} }
42
43 \newsavebox{\SLax}
44 \savebox{\SLax}(0,30)
45 {\thicklines \put(0,0){\line(-1,1){30}}
46 \put(0,0){\circle*{2}}
47 \put(-30,30){\circle*{2}} }
48
49 \newsavebox{\SLaa}
50 \savebox{\SLaa}(0,15)
51 {\thicklines \put(0,0){\line(-4,3){20}}
52 \put(0,0){\circle*{2}}
53 \put(-20,15){\circle*{2}} }
54
55 \newsavebox{\SLab}
56 \savebox{\SLab}(0,-15)
57 {\thicklines \put(0,0){\line(-4,-3){20}}
58 \put(0,0){\circle*{2}}
59 \put(-20,-15){\circle*{2}} }
60
61 \newsavebox{\SLabthin}
62 \savebox{\SLabthin}(0,-15)
63 {\thinlines \put(-0.7,-0.7){\line(-4,-3){18.7}}
64 \put(0,0){\circle{2}}
65 \put(-20,-15){\circle{2}} }
66
67 \newsavebox{\SLac}
68 \savebox{\SLac}(0,15)
69 {\thicklines \put(0,0){\line(-2,3){10}}
70 \put(0,0){\circle*{2}}
71 \put(-10,15){\circle*{2}} }
72
73 \newsavebox{\SLacthin}
74 \savebox{\SLacthin}(0,15)
75 {\thinlines \put(0,0){\line(-2,3){9.4}}
76 \put(0,0){\circle{2}}
77 \put(-10,15){\circle{2}} }
78
79
80 \newsavebox{\HLd}
81 \savebox{\HLd}(0,0)
82 {\put(0,0){\circle*{2}}
83 \put(10,0){\circle*{2}}
84 \thicklines \put(1,0){\line(1,0){28}}
85 \put(20,0){\circle*{2}}
86 \put(30,0){\circle*{2}} }
87
88 \newsavebox{\HLdthin}
89 \savebox{\HLdthin}(0,0)
90 {\put(0,0){\circle{2}}
91 \put(10,0){\circle{2}}
92 \thinlines \multiput(1,0)(10,0){3}{\line(1,0){8}}
93 \put(20,0){\circle{2}}
94 \put(30,0){\circle{2}} }
95
96 \newsavebox{\VLd}
97 \savebox{\VLd}(0,30)
98 {\put(0,0){\circle*{2}}
99 \put(0,10){\circle*{2}}
100 \thicklines \put(0,1){\line(0,1){28}}
101 \put(0,20){\circle*{2}}
102 \put(0,30){\circle*{2}} }
103
104 \newsavebox{\VLdthin}
105 \savebox{\VLdthin}(0,30)
106 {\put(0,0){\circle{2}}
107 \put(0,10){\circle{2}}
108 \thinlines \multiput(0,1)(0,10){3}{\line(0,1){8}}
109 \put(0,20){\circle{2}}
110 \put(0,30){\circle{2}} }
111
112 \newsavebox{\SLf}
113 \savebox{\SLf}(0,30)
114 {\thicklines \put(0,0){\line(-1,1){30}}
115 \put(0,0){\circle*{2}}
116 \put(-10,10){\circle*{2}}
117 \put(-20,20){\circle*{2}}
118 \put(-30,30){\circle*{2}} }
119
120 \newsavebox{\SLad}
121 \savebox{\SLad}(0,15)
122 {\thicklines \put(0,0){\line(-4,3){20}}
123 \put(0,0){\circle*{2}}
124 \put(-6.66,5){\circle*{2}}
125 \put(-13.33,10){\circle*{2}}
126 \put(-20,15){\circle*{2}} }
127
128 \newsavebox{\SLbd}
129 \savebox{\SLbd}(0,-15)
130 {\thicklines \put(0,0){\line(-4,-3){20}}
131 \put(0,0){\circle*{2}}
132 \put(-6.66,-5){\circle*{2}}
133 \put(-13.33,-10){\circle*{2}}
134 \put(-20,-15){\circle*{2}} }
135
136 \newsavebox{\SLbdthin}
137 \savebox{\SLbdthin}(0,-15)
138 {\thinlines \multiput(-0.7,-0.7)(-6.66,-5){3}{\line(-4,-3){5.1}}
139 \put(0,0){\circle{2}}
140 \put(-6.66,-5){\circle{2}}
141 \put(-13.33,-10){\circle{2}}
142 \put(-20,-15){\circle{2}} }
143
144 \newsavebox{\SLcd}
145 \savebox{\SLcd}(0,15)
146 {\thicklines \put(0,0){\line(-2,3){10}}
147 \put(0,0){\circle*{2}}
148 \put(-3.33,5){\circle*{2}}
149 \put(-6.66,10){\circle*{2}}
150 \put(-10,15){\circle*{2}} }
151
152 \newsavebox{\SLcdthin}
153 \savebox{\SLcdthin}(0,15)
154 {\thinlines \multiput(-0.6,0.8)(-3.33,5){3}{\line(-2,3){2.35}}
155 \put(0,0){\circle{2}}
156 \put(-3.33,5){\circle{2}}
157 \put(-6.66,10){\circle{2}}
158 \put(-10,15){\circle{2}} }
159
160 \newsavebox{\HLe}
161 \savebox{\HLe}(0,0)
162 {\put(0,0){\circle*{2}}
163 \put(15,0){\circle*{2}}
164 \thicklines \put(1,0){\line(1,0){28}}
165 \put(30,0){\circle*{2}} }
166
167 \newsavebox{\HLethin}
168 \savebox{\HLethin}(0,0)
169 {\put(0,0){\circle{2}}
170 \put(15,0){\circle{2}}
171 \thinlines \multiput(1,0)(15,0){2}{\line(1,0){13}}
172 \put(30,0){\circle{2}} }
173
174 \newsavebox{\VLe}
175 \savebox{\VLe}(0,30)
176 {\put(0,0){\circle*{2}}
177 \put(0,15){\circle*{2}}
178 \thicklines \put(0,1){\line(0,1){28}}
179 \put(0,30){\circle*{2}} }
180
181 \newsavebox{\VLethin}
182 \savebox{\VLethin}(0,30)
183 {\put(0,0){\circle{2}}
184 \put(0,15){\circle{2}}
185 \thinlines \multiput(0,1)(0,15){2}{\line(0,1){13}}
186 \put(0,30){\circle{2}} }
187
188 \newsavebox{\SLe}
189 \savebox{\SLe}(0,30)
190 {\thicklines \put(0,0){\line(-1,1){30}}
191 \put(0,0){\circle*{2}}
192 \put(-15,15){\circle*{2}}
193 \put(-30,30){\circle*{2}} }
194
195 \newsavebox{\SLae}
196 \savebox{\SLae}(0,15)
197 {\thicklines \put(0,0){\line(-4,3){20}}
198 \put(0,0){\circle*{2}}
199 \put(-10,7.5){\circle*{2}}
200 \put(-20,15){\circle*{2}} }
201
202 \newsavebox{\SLbe}
203 \savebox{\SLbe}(0,-15)
204 {\thicklines \put(0,0){\line(-4,-3){20}}
205 \put(0,0){\circle*{2}}
206 \put(-10,-7.5){\circle*{2}}
207 \put(-20,-15){\circle*{2}} }
208
209 \newsavebox{\SLbethin}
210 \savebox{\SLbethin}(0,-15)
211 {\thinlines \multiput(-0.7,-0.7)(-10,-7.5){2}{\line(-4,-3){8.4}}
212 \put(0,0){\circle{2}}
213 \put(-10,-7.5){\circle{2}}
214 \put(-20,-15){\circle{2}} }
215
216 \newsavebox{\SLce}
217 \savebox{\SLce}(0,15)
218 {\thicklines \put(0,0){\line(-2,3){10}}
219 \put(0,0){\circle*{2}}
220 \put(-5,7.5){\circle*{2}}
221 \put(-10,15){\circle*{2}} }
222
223 \newsavebox{\SLcethin}
224 \savebox{\SLcethin}(0,15)
225 {\thinlines \multiput(-0.6,0.8)(-5,7.5){2}{\line(-2,3){3.9}}
226 \put(0,0){\circle{2}}
227 \put(-5,7.5){\circle{2}}
228 \put(-10,15){\circle{2}} }
229
230 %=====================================================================
231 %
232 % order 1
233 % -------
234 %
235
236 \begin{figure}
237
238
239 \begin{picture}(170,210) \thicklines
240
241
242
243 \put(20,205){\circle*{2}}
244 \put(10,195){\parbox[t]{45mm}
245 \finleyelement{Point1}}
246
247 \put(90,205){\usebox{\HLa}}
248 \put(90,195){\parbox[t]{45mm}
249 \finleyelement{LINE2} }
250
251 \put(10,145){\usebox{\HLa}}
252 \put(40,145){\usebox{\SLax}}
253 \put(10,145){\usebox{\VLa}}
254 \put(10,135){\parbox[t]{45mm}
255 \finleyelement{Tri3} }
256
257 \put(90,145){\usebox{\HLa}}
258 \put(90,175){\usebox{\HLa}}
259 \put(90,145){\usebox{\VLa}}
260 \put(120,145){\usebox{\VLa}}
261 \put(90,135){\parbox[t]{45mm}
262 \finleyelement{Rec4} }
263
264 \put(50,90){\usebox{\HLa}}
265 \put(80,90){\usebox{\SLax}}
266 \put(50,90){\usebox{\VLa}}
267 \put(80,90){\usebox{\SLac}}
268 \put(70,105){\usebox{\SLabthin}}
269 \put(70,105){\usebox{\SLaa}}
270 \put(50,80 ){\parbox[t]{45mm}
271 \finleyelement{Tet4} }
272
273 \put(90,20){\usebox{\HLa}}
274 \put(90,50){\usebox{\HLa}}
275 \put(90,20){\usebox{\VLa}}
276 \put(120,20){\usebox{\VLa}}
277 \put(110,35){\usebox{\SLabthin}}
278 \put(140,35){\usebox{\SLab}}
279 \put(110,65){\usebox{\SLab}}
280 \put(140,65){\usebox{\SLab}}
281 \put(110,35){\usebox{\HLathin}}
282 \put(110,65){\usebox{\HLa}}
283 \put(110,35){\usebox{\VLathin}}
284 \put(140,35){\usebox{\VLa}}
285 \put(90,10 ){\parbox[t]{45mm}
286 \finleyelement{Hex8} }
287
288 % nummerierung der punkte:
289 \put(19,208){{\it 1}} % Point
290 \put(89,208){{\it 1}} % line
291 \put(119,208){{\it 2}}
292 \put(6,174){{\it 3}} % Triangle
293 \put(6,144){{\it 1}}
294 \put(43,144){{\it 2}}
295 \put(86,174){{\it 4}} % quadrilateral
296 \put(86,144){{\it 1}}
297 \put(123,174){{\it 3}}
298 \put(123,144){{\it 2}}
299 \put(46,119){{\it 4}} % Tetrahedron
300 \put(46,89){{\it 1}}
301 \put(83,89){{\it 2}}
302 \put(73,104){{\it 3}}
303 \put(86,49){{\it 5}} % Hexahedron
304 \put(86,19){{\it 1}}
305 \put(123,49){{\it 6}}
306 \put(123,19){{\it 2}}
307 \put(106,64){{\it 8}}
308 \put(106,34){{\it 4}}
309 \put(143,64){{\it 7}}
310 \put(143,34){{\it 3}}
311
312 \end{picture}
313 \caption{\label{FINLEY.FIG:1} Elements of order 1}
314 \end{figure}
315 %=====================================================================
316 %
317 %
318 % order 2
319 % -------
320 % (boxes in 'fesubelm')
321
322
323 \begin{figure}
324 \setlength{\unitlength}{1mm}
325
326
327
328 \begin{picture}(170,210) \thicklines
329
330 \put(20,205){\circle*{2}}
331 \put(10,195){\parbox[t]{45mm}
332 \finleyelement{Point1} }
333
334 \put(90,205){\usebox{\HLe}}
335 \put(90,195){\parbox[t]{45mm}
336 \finleyelement{LINE3} }
337
338 \put(10,145){\usebox{\HLe}}
339 \put(40,145){\usebox{\SLe}}
340 \put(10,145){\usebox{\VLe}}
341 \put(10,135){\parbox[t]{45mm}
342 \finleyelement{Tri6} }
343
344 \put(90,145){\usebox{\HLe}}
345 \put(90,175){\usebox{\HLe}}
346 \put(90,145){\usebox{\VLe}}
347 \put(120,145){\usebox{\VLe}}
348 \put(90,135){\parbox[t]{45mm}
349 \finleyelement{Rec8} }
350
351 \put(50,90){\usebox{\HLe}}
352 \put(80,90){\usebox{\SLe}}
353 \put(50,90){\usebox{\VLe}}
354 \put(80,90){\usebox{\SLce}}
355 \put(70,105){\usebox{\SLbethin}}
356 \put(70,105){\usebox{\SLae}}
357 \put(50,80 ){\parbox[t]{45mm}
358 \finleyelement{Tet10} }
359
360 \put(90,20){\usebox{\HLe}}
361 \put(90,50){\usebox{\HLe}}
362 \put(90,20){\usebox{\VLe}}
363 \put(120,20){\usebox{\VLe}}
364 \put(110,35){\usebox{\SLbethin}}
365 \put(140,35){\usebox{\SLbe}}
366 \put(110,65){\usebox{\SLbe}}
367 \put(140,65){\usebox{\SLbe}}
368 \put(110,35){\usebox{\HLethin}}
369 \put(110,65){\usebox{\HLe}}
370 \put(110,35){\usebox{\VLethin}}
371 \put(140,35){\usebox{\VLe}}
372 \put(90,10 ){\parbox[t]{45mm}
373 \finleyelement{Hex20} }
374
375
376 % nummerierung der punkte:
377 \put(19,208){{\it 1}} % Point
378 \put(89,208){{\it 1}} % line
379 \put(104,208){{\it 3}}
380 \put(119,208){{\it 2}}
381 \put(6,174){{\it 3}} % Triangle
382 \put(6,159){{\it 6}}
383 \put(6,144){{\it 1}}
384 \put(28,159){{\it 5}}
385 \put(43,144){{\it 2}}
386 \put(24,140){{\it 4}}
387 \put(104,140){{\it 5}} % quaTrilateral
388 \put(86,174){{\it 4}}
389 \put(86,159){{\it 8}}
390 \put(86,144){{\it 1}}
391 \put(104,178){{\it 7}}
392 \put(123,174){{\it 3}}
393 \put(123,159){{\it 6}}
394 \put(123,144){{\it 2}}
395 \put(64,85){{\it 5}} % Tetrahedron
396 \put(46,119){{\it 4}}
397 \put(46,104){{\it 8}}
398 \put(46,89){{\it 1}}
399 \put(61,104){{\it 9}}
400 \put(83,89){{\it 2}}
401 \put(56,96.5){{\it 7}}
402 \put(78,96.5){{\it 6}}
403 \put(73,104){{\it 3}}
404 \put(62.5,111.5){{\it 10}}
405 \put(104,15){{\it 9}} % Hexahedron
406 \put(86,49){{\it 5}}
407 \put(85,34){{\it 13}}
408 \put(86,19){{\it 1}}
409 \put(104,52){{\it 17}}
410 \put(123,49){{\it 6}}
411 \put(115,37){{\it 14}}
412 \put(123,19){{\it 2}}
413 \put(125,37){{\it 11}}
414 \put(106,64){{\it 8}}
415 \put(112,46){{\it 16}}
416 \put(106,34){{\it 4}}
417 \put(124,68){{\it 19}}
418 \put(143,64){{\it 7}}
419 \put(142,49){{\it 15}}
420 \put(143,34){{\it 3}}
421 \put(94.5,26.5){{\it 12}}
422 \put(132.5,26.5){{\it 10}}
423 \put(94.5,56.5){{\it 20}}
424 \put(132.5,56.5){{\it 18}}
425
426 \end{picture}
427 \caption{\label{FINLEY.FIG:2} Elements of order 2}
428 \end{figure}
429
430 %
431 % additional elements
432 %
433 \begin{figure}
434 \begin{picture}(170,210) \thicklines
435
436 \put(50,095){\usebox{\HLe}}
437 \put(50,125){\usebox{\HLe}}
438 \put(50,095){\usebox{\VLe}}
439 \put(80,095){\usebox{\VLe}}
440 \put(65,110){\circle*{2}}
441 \put(50,085){\parbox[t]{45mm}
442 \finleyelement{Rec9} }
443
444
445 \put(64,090){{\it 5}}
446 \put(46,124){{\it 4}}
447 \put(46,109){{\it 8}}
448 \put(46,094){{\it 1}}
449 \put(64,128){{\it 7}}
450 \put(83,124){{\it 3}}
451 \put(83,109){{\it 6}}
452 \put(83,094){{\it 2}}
453 \put(64,105){{\it 9}}
454
455
456 \end{picture}
457 \caption{\label{FINLEY.FIG:4} Additional shape functions}
458 \end{figure}

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