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1 %
2 % Copyright © 2006 by ACcESS MNRF
3 % \url{http://www.access.edu.au
4 % Primary Business: Queensland, Australia.
5 % Licensed under the Open Software License version 3.0
6 % http://www.opensource.org/licenses/osl-3.0.php
7 %
8 \setlength{\unitlength}{1mm}
9
10 \newsavebox{\HLa}
11 \savebox{\HLa}(0,0)
12 {\put(0,0){\circle*{2}}
13 \thicklines \put(1,0){\line(1,0){28}}
14 \put(30,0){\circle*{2}} }
15
16 \newsavebox{\HLathin}
17 \savebox{\HLathin}(0,0)
18 {\put(0,0){\circle{2}}
19 \thinlines \put(1,0){\line(1,0){28}}
20 \put(30,0){\circle{2}} }
21
22 \newsavebox{\VLa}
23 \savebox{\VLa}(0,30)
24 {\put(0,0){\circle*{2}}
25 \thicklines \put(0,1){\line(0,1){28}}
26 \put(0,30){\circle*{2}} }
27
28 \newsavebox{\VLathin}
29 \savebox{\VLathin}(0,30)
30 {\put(0,0){\circle{2}}
31 \thinlines \put(0,1){\line(0,1){28}}
32 \put(0,30){\circle{2}} }
33
34 \newsavebox{\SLax}
35 \savebox{\SLax}(0,30)
36 {\thicklines \put(0,0){\line(-1,1){30}}
37 \put(0,0){\circle*{2}}
38 \put(-30,30){\circle*{2}} }
39
40 \newsavebox{\SLaa}
41 \savebox{\SLaa}(0,15)
42 {\thicklines \put(0,0){\line(-4,3){20}}
43 \put(0,0){\circle*{2}}
44 \put(-20,15){\circle*{2}} }
45
46 \newsavebox{\SLab}
47 \savebox{\SLab}(0,-15)
48 {\thicklines \put(0,0){\line(-4,-3){20}}
49 \put(0,0){\circle*{2}}
50 \put(-20,-15){\circle*{2}} }
51
52 \newsavebox{\SLabthin}
53 \savebox{\SLabthin}(0,-15)
54 {\thinlines \put(-0.7,-0.7){\line(-4,-3){18.7}}
55 \put(0,0){\circle{2}}
56 \put(-20,-15){\circle{2}} }
57
58 \newsavebox{\SLac}
59 \savebox{\SLac}(0,15)
60 {\thicklines \put(0,0){\line(-2,3){10}}
61 \put(0,0){\circle*{2}}
62 \put(-10,15){\circle*{2}} }
63
64 \newsavebox{\SLacthin}
65 \savebox{\SLacthin}(0,15)
66 {\thinlines \put(0,0){\line(-2,3){9.4}}
67 \put(0,0){\circle{2}}
68 \put(-10,15){\circle{2}} }
69
70
71 \newsavebox{\HLd}
72 \savebox{\HLd}(0,0)
73 {\put(0,0){\circle*{2}}
74 \put(10,0){\circle*{2}}
75 \thicklines \put(1,0){\line(1,0){28}}
76 \put(20,0){\circle*{2}}
77 \put(30,0){\circle*{2}} }
78
79 \newsavebox{\HLdthin}
80 \savebox{\HLdthin}(0,0)
81 {\put(0,0){\circle{2}}
82 \put(10,0){\circle{2}}
83 \thinlines \multiput(1,0)(10,0){3}{\line(1,0){8}}
84 \put(20,0){\circle{2}}
85 \put(30,0){\circle{2}} }
86
87 \newsavebox{\VLd}
88 \savebox{\VLd}(0,30)
89 {\put(0,0){\circle*{2}}
90 \put(0,10){\circle*{2}}
91 \thicklines \put(0,1){\line(0,1){28}}
92 \put(0,20){\circle*{2}}
93 \put(0,30){\circle*{2}} }
94
95 \newsavebox{\VLdthin}
96 \savebox{\VLdthin}(0,30)
97 {\put(0,0){\circle{2}}
98 \put(0,10){\circle{2}}
99 \thinlines \multiput(0,1)(0,10){3}{\line(0,1){8}}
100 \put(0,20){\circle{2}}
101 \put(0,30){\circle{2}} }
102
103 \newsavebox{\SLf}
104 \savebox{\SLf}(0,30)
105 {\thicklines \put(0,0){\line(-1,1){30}}
106 \put(0,0){\circle*{2}}
107 \put(-10,10){\circle*{2}}
108 \put(-20,20){\circle*{2}}
109 \put(-30,30){\circle*{2}} }
110
111 \newsavebox{\SLad}
112 \savebox{\SLad}(0,15)
113 {\thicklines \put(0,0){\line(-4,3){20}}
114 \put(0,0){\circle*{2}}
115 \put(-6.66,5){\circle*{2}}
116 \put(-13.33,10){\circle*{2}}
117 \put(-20,15){\circle*{2}} }
118
119 \newsavebox{\SLbd}
120 \savebox{\SLbd}(0,-15)
121 {\thicklines \put(0,0){\line(-4,-3){20}}
122 \put(0,0){\circle*{2}}
123 \put(-6.66,-5){\circle*{2}}
124 \put(-13.33,-10){\circle*{2}}
125 \put(-20,-15){\circle*{2}} }
126
127 \newsavebox{\SLbdthin}
128 \savebox{\SLbdthin}(0,-15)
129 {\thinlines \multiput(-0.7,-0.7)(-6.66,-5){3}{\line(-4,-3){5.1}}
130 \put(0,0){\circle{2}}
131 \put(-6.66,-5){\circle{2}}
132 \put(-13.33,-10){\circle{2}}
133 \put(-20,-15){\circle{2}} }
134
135 \newsavebox{\SLcd}
136 \savebox{\SLcd}(0,15)
137 {\thicklines \put(0,0){\line(-2,3){10}}
138 \put(0,0){\circle*{2}}
139 \put(-3.33,5){\circle*{2}}
140 \put(-6.66,10){\circle*{2}}
141 \put(-10,15){\circle*{2}} }
142
143 \newsavebox{\SLcdthin}
144 \savebox{\SLcdthin}(0,15)
145 {\thinlines \multiput(-0.6,0.8)(-3.33,5){3}{\line(-2,3){2.35}}
146 \put(0,0){\circle{2}}
147 \put(-3.33,5){\circle{2}}
148 \put(-6.66,10){\circle{2}}
149 \put(-10,15){\circle{2}} }
150
151 \newsavebox{\HLe}
152 \savebox{\HLe}(0,0)
153 {\put(0,0){\circle*{2}}
154 \put(15,0){\circle*{2}}
155 \thicklines \put(1,0){\line(1,0){28}}
156 \put(30,0){\circle*{2}} }
157
158 \newsavebox{\HLethin}
159 \savebox{\HLethin}(0,0)
160 {\put(0,0){\circle{2}}
161 \put(15,0){\circle{2}}
162 \thinlines \multiput(1,0)(15,0){2}{\line(1,0){13}}
163 \put(30,0){\circle{2}} }
164
165 \newsavebox{\VLe}
166 \savebox{\VLe}(0,30)
167 {\put(0,0){\circle*{2}}
168 \put(0,15){\circle*{2}}
169 \thicklines \put(0,1){\line(0,1){28}}
170 \put(0,30){\circle*{2}} }
171
172 \newsavebox{\VLethin}
173 \savebox{\VLethin}(0,30)
174 {\put(0,0){\circle{2}}
175 \put(0,15){\circle{2}}
176 \thinlines \multiput(0,1)(0,15){2}{\line(0,1){13}}
177 \put(0,30){\circle{2}} }
178
179 \newsavebox{\SLe}
180 \savebox{\SLe}(0,30)
181 {\thicklines \put(0,0){\line(-1,1){30}}
182 \put(0,0){\circle*{2}}
183 \put(-15,15){\circle*{2}}
184 \put(-30,30){\circle*{2}} }
185
186 \newsavebox{\SLae}
187 \savebox{\SLae}(0,15)
188 {\thicklines \put(0,0){\line(-4,3){20}}
189 \put(0,0){\circle*{2}}
190 \put(-10,7.5){\circle*{2}}
191 \put(-20,15){\circle*{2}} }
192
193 \newsavebox{\SLbe}
194 \savebox{\SLbe}(0,-15)
195 {\thicklines \put(0,0){\line(-4,-3){20}}
196 \put(0,0){\circle*{2}}
197 \put(-10,-7.5){\circle*{2}}
198 \put(-20,-15){\circle*{2}} }
199
200 \newsavebox{\SLbethin}
201 \savebox{\SLbethin}(0,-15)
202 {\thinlines \multiput(-0.7,-0.7)(-10,-7.5){2}{\line(-4,-3){8.4}}
203 \put(0,0){\circle{2}}
204 \put(-10,-7.5){\circle{2}}
205 \put(-20,-15){\circle{2}} }
206
207 \newsavebox{\SLce}
208 \savebox{\SLce}(0,15)
209 {\thicklines \put(0,0){\line(-2,3){10}}
210 \put(0,0){\circle*{2}}
211 \put(-5,7.5){\circle*{2}}
212 \put(-10,15){\circle*{2}} }
213
214 \newsavebox{\SLcethin}
215 \savebox{\SLcethin}(0,15)
216 {\thinlines \multiput(-0.6,0.8)(-5,7.5){2}{\line(-2,3){3.9}}
217 \put(0,0){\circle{2}}
218 \put(-5,7.5){\circle{2}}
219 \put(-10,15){\circle{2}} }
220
221 %=====================================================================
222 %
223 % order 1
224 % -------
225 %
226
227 \begin{figure}
228
229
230 \begin{picture}(170,210) \thicklines
231
232
233
234 \put(20,205){\circle*{2}}
235 \put(10,195){\parbox[t]{45mm}
236 \finleyelement{Point1}}
237
238 \put(90,205){\usebox{\HLa}}
239 \put(90,195){\parbox[t]{45mm}
240 \finleyelement{LINE2} }
241
242 \put(10,145){\usebox{\HLa}}
243 \put(40,145){\usebox{\SLax}}
244 \put(10,145){\usebox{\VLa}}
245 \put(10,135){\parbox[t]{45mm}
246 \finleyelement{Tri3} }
247
248 \put(90,145){\usebox{\HLa}}
249 \put(90,175){\usebox{\HLa}}
250 \put(90,145){\usebox{\VLa}}
251 \put(120,145){\usebox{\VLa}}
252 \put(90,135){\parbox[t]{45mm}
253 \finleyelement{Rec4} }
254
255 \put(50,90){\usebox{\HLa}}
256 \put(80,90){\usebox{\SLax}}
257 \put(50,90){\usebox{\VLa}}
258 \put(80,90){\usebox{\SLac}}
259 \put(70,105){\usebox{\SLabthin}}
260 \put(70,105){\usebox{\SLaa}}
261 \put(50,80 ){\parbox[t]{45mm}
262 \finleyelement{Tet4} }
263
264 \put(90,20){\usebox{\HLa}}
265 \put(90,50){\usebox{\HLa}}
266 \put(90,20){\usebox{\VLa}}
267 \put(120,20){\usebox{\VLa}}
268 \put(110,35){\usebox{\SLabthin}}
269 \put(140,35){\usebox{\SLab}}
270 \put(110,65){\usebox{\SLab}}
271 \put(140,65){\usebox{\SLab}}
272 \put(110,35){\usebox{\HLathin}}
273 \put(110,65){\usebox{\HLa}}
274 \put(110,35){\usebox{\VLathin}}
275 \put(140,35){\usebox{\VLa}}
276 \put(90,10 ){\parbox[t]{45mm}
277 \finleyelement{Hex8} }
278
279 % nummerierung der punkte:
280 \put(19,208){{\it 1}} % Point
281 \put(89,208){{\it 1}} % line
282 \put(119,208){{\it 2}}
283 \put(6,174){{\it 3}} % Triangle
284 \put(6,144){{\it 1}}
285 \put(43,144){{\it 2}}
286 \put(86,174){{\it 4}} % quadrilateral
287 \put(86,144){{\it 1}}
288 \put(123,174){{\it 3}}
289 \put(123,144){{\it 2}}
290 \put(46,119){{\it 4}} % Tetrahedron
291 \put(46,89){{\it 1}}
292 \put(83,89){{\it 2}}
293 \put(73,104){{\it 3}}
294 \put(86,49){{\it 5}} % Hexahedron
295 \put(86,19){{\it 1}}
296 \put(123,49){{\it 6}}
297 \put(123,19){{\it 2}}
298 \put(106,64){{\it 8}}
299 \put(106,34){{\it 4}}
300 \put(143,64){{\it 7}}
301 \put(143,34){{\it 3}}
302
303 \end{picture}
304 \caption{\label{FINLEY.FIG:1} Elements of order 1}
305 \end{figure}
306 %=====================================================================
307 %
308 %
309 % order 2
310 % -------
311 % (boxes in 'fesubelm')
312
313
314 \begin{figure}
315 \setlength{\unitlength}{1mm}
316
317
318
319 \begin{picture}(170,210) \thicklines
320
321 \put(20,205){\circle*{2}}
322 \put(10,195){\parbox[t]{45mm}
323 \finleyelement{Point1} }
324
325 \put(90,205){\usebox{\HLe}}
326 \put(90,195){\parbox[t]{45mm}
327 \finleyelement{LINE3} }
328
329 \put(10,145){\usebox{\HLe}}
330 \put(40,145){\usebox{\SLe}}
331 \put(10,145){\usebox{\VLe}}
332 \put(10,135){\parbox[t]{45mm}
333 \finleyelement{Tri6} }
334
335 \put(90,145){\usebox{\HLe}}
336 \put(90,175){\usebox{\HLe}}
337 \put(90,145){\usebox{\VLe}}
338 \put(120,145){\usebox{\VLe}}
339 \put(90,135){\parbox[t]{45mm}
340 \finleyelement{Rec8} }
341
342 \put(50,90){\usebox{\HLe}}
343 \put(80,90){\usebox{\SLe}}
344 \put(50,90){\usebox{\VLe}}
345 \put(80,90){\usebox{\SLce}}
346 \put(70,105){\usebox{\SLbethin}}
347 \put(70,105){\usebox{\SLae}}
348 \put(50,80 ){\parbox[t]{45mm}
349 \finleyelement{Tet10} }
350
351 \put(90,20){\usebox{\HLe}}
352 \put(90,50){\usebox{\HLe}}
353 \put(90,20){\usebox{\VLe}}
354 \put(120,20){\usebox{\VLe}}
355 \put(110,35){\usebox{\SLbethin}}
356 \put(140,35){\usebox{\SLbe}}
357 \put(110,65){\usebox{\SLbe}}
358 \put(140,65){\usebox{\SLbe}}
359 \put(110,35){\usebox{\HLethin}}
360 \put(110,65){\usebox{\HLe}}
361 \put(110,35){\usebox{\VLethin}}
362 \put(140,35){\usebox{\VLe}}
363 \put(90,10 ){\parbox[t]{45mm}
364 \finleyelement{Hex20} }
365
366
367 % nummerierung der punkte:
368 \put(19,208){{\it 1}} % Point
369 \put(89,208){{\it 1}} % line
370 \put(104,208){{\it 3}}
371 \put(119,208){{\it 2}}
372 \put(6,174){{\it 3}} % Triangle
373 \put(6,159){{\it 6}}
374 \put(6,144){{\it 1}}
375 \put(28,159){{\it 5}}
376 \put(43,144){{\it 2}}
377 \put(24,140){{\it 4}}
378 \put(104,140){{\it 5}} % quaTrilateral
379 \put(86,174){{\it 4}}
380 \put(86,159){{\it 8}}
381 \put(86,144){{\it 1}}
382 \put(104,178){{\it 7}}
383 \put(123,174){{\it 3}}
384 \put(123,159){{\it 6}}
385 \put(123,144){{\it 2}}
386 \put(64,85){{\it 5}} % Tetrahedron
387 \put(46,119){{\it 4}}
388 \put(46,104){{\it 8}}
389 \put(46,89){{\it 1}}
390 \put(61,104){{\it 9}}
391 \put(83,89){{\it 2}}
392 \put(56,96.5){{\it 7}}
393 \put(78,96.5){{\it 6}}
394 \put(73,104){{\it 3}}
395 \put(62.5,111.5){{\it 10}}
396 \put(104,15){{\it 9}} % Hexahedron
397 \put(86,49){{\it 5}}
398 \put(85,34){{\it 13}}
399 \put(86,19){{\it 1}}
400 \put(104,52){{\it 17}}
401 \put(123,49){{\it 6}}
402 \put(115,37){{\it 14}}
403 \put(123,19){{\it 2}}
404 \put(125,37){{\it 11}}
405 \put(106,64){{\it 8}}
406 \put(112,46){{\it 16}}
407 \put(106,34){{\it 4}}
408 \put(124,68){{\it 19}}
409 \put(143,64){{\it 7}}
410 \put(142,49){{\it 15}}
411 \put(143,34){{\it 3}}
412 \put(94.5,26.5){{\it 12}}
413 \put(132.5,26.5){{\it 10}}
414 \put(94.5,56.5){{\it 20}}
415 \put(132.5,56.5){{\it 18}}
416
417 \end{picture}
418 \caption{\label{FINLEY.FIG:2} Elements of order 2}
419 \end{figure}
420
421 %
422 % additional elements
423 %
424 \begin{figure}
425 \begin{picture}(170,210) \thicklines
426
427 \put(50,095){\usebox{\HLe}}
428 \put(50,125){\usebox{\HLe}}
429 \put(50,095){\usebox{\VLe}}
430 \put(80,095){\usebox{\VLe}}
431 \put(65,110){\circle*{2}}
432 \put(50,085){\parbox[t]{45mm}
433 \finleyelement{Rec9} }
434
435
436 \put(64,090){{\it 5}}
437 \put(46,124){{\it 4}}
438 \put(46,109){{\it 8}}
439 \put(46,094){{\it 1}}
440 \put(64,128){{\it 7}}
441 \put(83,124){{\it 3}}
442 \put(83,109){{\it 6}}
443 \put(83,094){{\it 2}}
444 \put(64,105){{\it 9}}
445
446
447 \end{picture}
448 \caption{\label{FINLEY.FIG:4} Additional shape functions}
449 \end{figure}

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