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GS_program_FDM_(v1.2)

1279 days ago by fresl


Metoda gustoća sila

(Force Density Method)


[Ćelije u kojima je prvi redak %auto ne trebate izvoditi ( evaluate ); one se izvode „same” pri otvaranju radnoga lista.  Međutim, ako radni list ponovno pokrenete—ne izlazeći iz njega—s  Restart worksheet  (u izborniku  Action... ), i njih ćete morati izvesti.]
       


Primjer 1.:


– čvorovi:
        
400
400

– kabeli, štapovi i ležajevi:
       
       

– gustoće sila:
       

– prvi korak:
       
       

– zadavanje vrijednosti sila u kabelima:
       

– iteracija:

       
       
        
steps: 571
maximal force error:  9.985972574955149e-06
steps: 571
maximal force error:  9.985972574955149e-06
       

 

Primjer 2.:

 
        
[0,
 1,
 2,
 3,
 4,
 5,
 6,
 7,
 8,
 9,
 10,
 63,
 157,
 210,
 211,
 212,
 213,
 214,
 215,
 216,
 217,
 218,
 219,
 220]
[0,
 1,
 2,
 3,
 4,
 5,
 6,
 7,
 8,
 9,
 10,
 63,
 157,
 210,
 211,
 212,
 213,
 214,
 215,
 216,
 217,
 218,
 219,
 220]
        
0 :  [1, 11, 21]
1 :  [2, 12, 22, 32, 42]
2 :  [3, 13, 23, 33, 43, 53, 63]
3 :  [4, 14, 24, 34, 44, 54, 64, 74, 84]
4 :  [5, 15, 25, 35, 45, 55, 65, 75, 85, 95, 105]
5 :  [6, 16, 26, 36, 46, 56, 66, 76, 86, 96, 106, 116, 126]
6 :  [7, 17, 27, 37, 47, 57, 67, 77, 87, 97, 107, 117, 127, 137, 147]
7 :  [8, 18, 28, 38, 48, 58, 68, 78, 88, 98, 108, 118, 128, 138, 148, 158, 168]
8 :  [9, 19, 29, 39, 49, 59, 69, 79, 89, 99, 109, 119, 129, 139, 149, 159, 169,
179, 189]
9 :  [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160,
170, 180, 190, 200, 210]
10 :  [31, 41, 51, 61, 71, 81, 91, 101, 111, 121, 131, 141, 151, 161, 171, 181,
191, 201, 211]
11 :  [52, 62, 72, 82, 92, 102, 112, 122, 132, 142, 152, 162, 172, 182, 192,
202, 212]
12 :  [73, 83, 93, 103, 113, 123, 133, 143, 153, 163, 173, 183, 193, 203, 213]
13 :  [94, 104, 114, 124, 134, 144, 154, 164, 174, 184, 194, 204, 214]
14 :  [115, 125, 135, 145, 155, 165, 175, 185, 195, 205, 215]
15 :  [136, 146, 156, 166, 176, 186, 196, 206, 216]
16 :  [157, 167, 177, 187, 197, 207, 217]
17 :  [178, 188, 198, 208, 218]
18 :  [199, 209, 219]
19 :  [189, 200, 211]
20 :  [168, 179, 190, 201, 212]
21 :  [147, 158, 169, 180, 191, 202, 213]
22 :  [126, 137, 148, 159, 170, 181, 192, 203, 214]
23 :  [105, 116, 127, 138, 149, 160, 171, 182, 193, 204, 215]
24 :  [84, 95, 106, 117, 128, 139, 150, 161, 172, 183, 194, 205, 216]
25 :  [63, 74, 85, 96, 107, 118, 129, 140, 151, 162, 173, 184, 195, 206, 217]
26 :  [42, 53, 64, 75, 86, 97, 108, 119, 130, 141, 152, 163, 174, 185, 196, 207,
218]
27 :  [21, 32, 43, 54, 65, 76, 87, 98, 109, 120, 131, 142, 153, 164, 175, 186,
197, 208, 219]
28 :  [0, 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143, 154, 165, 176,
187, 198, 209, 220]
29 :  [1, 12, 23, 34, 45, 56, 67, 78, 89, 100, 111, 122, 133, 144, 155, 166,
177, 188, 199]
30 :  [2, 13, 24, 35, 46, 57, 68, 79, 90, 101, 112, 123, 134, 145, 156, 167,
178]
31 :  [3, 14, 25, 36, 47, 58, 69, 80, 91, 102, 113, 124, 135, 146, 157]
32 :  [4, 15, 26, 37, 48, 59, 70, 81, 92, 103, 114, 125, 136]
33 :  [5, 16, 27, 38, 49, 60, 71, 82, 93, 104, 115]
34 :  [6, 17, 28, 39, 50, 61, 72, 83, 94]
35 :  [7, 18, 29, 40, 51, 62, 73]
36 :  [8, 19, 30, 41, 52]
37 :  [9, 20, 31]
38 :  [0, 21, 42, 63, 84, 105, 126, 147, 168, 189, 210]
39 :  [10, 31, 52, 73, 94, 115, 136, 157, 178, 199, 220]

0 :  [0, 1]
1 :  [2, 3, 4, 5]
2 :  [6, 7, 8, 9, 10, 11]
3 :  [12, 13, 14, 15, 16, 17, 18, 19]
4 :  [20, 21, 22, 23, 24, 25, 26, 27, 28, 29]
5 :  [30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41]
6 :  [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55]
7 :  [56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71]
8 :  [72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89]
9 :  [90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106,
107, 108, 109]
10 :  [110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123,
124, 125, 126, 127]
11 :  [128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141,
142, 143]
12 :  [144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157]
13 :  [158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169]
14 :  [170, 171, 172, 173, 174, 175, 176, 177, 178, 179]
15 :  [180, 181, 182, 183, 184, 185, 186, 187]
16 :  [188, 189, 190, 191, 192, 193]
17 :  [194, 195, 196, 197]
18 :  [198, 199]
19 :  [200, 201]
20 :  [202, 203, 204, 205]
21 :  [206, 207, 208, 209, 210, 211]
22 :  [212, 213, 214, 215, 216, 217, 218, 219]
23 :  [220, 221, 222, 223, 224, 225, 226, 227, 228, 229]
24 :  [230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241]
25 :  [242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255]
26 :  [256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269,
270, 271]
27 :  [272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285,
286, 287, 288, 289]
28 :  [290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303,
304, 305, 306, 307, 308, 309]
29 :  [310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323,
324, 325, 326, 327]
30 :  [328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341,
342, 343]
31 :  [344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357]
32 :  [358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369]
33 :  [370, 371, 372, 373, 374, 375, 376, 377, 378, 379]
34 :  [380, 381, 382, 383, 384, 385, 386, 387]
35 :  [388, 389, 390, 391, 392, 393]
36 :  [394, 395, 396, 397]
37 :  [398, 399]
38 :  [400, 401, 402, 403, 404, 405, 406, 407, 408, 409]
39 :  [410, 411, 412, 413, 414, 415, 416, 417, 418, 419]
0 :  [1, 11, 21]
1 :  [2, 12, 22, 32, 42]
2 :  [3, 13, 23, 33, 43, 53, 63]
3 :  [4, 14, 24, 34, 44, 54, 64, 74, 84]
4 :  [5, 15, 25, 35, 45, 55, 65, 75, 85, 95, 105]
5 :  [6, 16, 26, 36, 46, 56, 66, 76, 86, 96, 106, 116, 126]
6 :  [7, 17, 27, 37, 47, 57, 67, 77, 87, 97, 107, 117, 127, 137, 147]
7 :  [8, 18, 28, 38, 48, 58, 68, 78, 88, 98, 108, 118, 128, 138, 148, 158, 168]
8 :  [9, 19, 29, 39, 49, 59, 69, 79, 89, 99, 109, 119, 129, 139, 149, 159, 169, 179, 189]
9 :  [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 210]
10 :  [31, 41, 51, 61, 71, 81, 91, 101, 111, 121, 131, 141, 151, 161, 171, 181, 191, 201, 211]
11 :  [52, 62, 72, 82, 92, 102, 112, 122, 132, 142, 152, 162, 172, 182, 192, 202, 212]
12 :  [73, 83, 93, 103, 113, 123, 133, 143, 153, 163, 173, 183, 193, 203, 213]
13 :  [94, 104, 114, 124, 134, 144, 154, 164, 174, 184, 194, 204, 214]
14 :  [115, 125, 135, 145, 155, 165, 175, 185, 195, 205, 215]
15 :  [136, 146, 156, 166, 176, 186, 196, 206, 216]
16 :  [157, 167, 177, 187, 197, 207, 217]
17 :  [178, 188, 198, 208, 218]
18 :  [199, 209, 219]
19 :  [189, 200, 211]
20 :  [168, 179, 190, 201, 212]
21 :  [147, 158, 169, 180, 191, 202, 213]
22 :  [126, 137, 148, 159, 170, 181, 192, 203, 214]
23 :  [105, 116, 127, 138, 149, 160, 171, 182, 193, 204, 215]
24 :  [84, 95, 106, 117, 128, 139, 150, 161, 172, 183, 194, 205, 216]
25 :  [63, 74, 85, 96, 107, 118, 129, 140, 151, 162, 173, 184, 195, 206, 217]
26 :  [42, 53, 64, 75, 86, 97, 108, 119, 130, 141, 152, 163, 174, 185, 196, 207, 218]
27 :  [21, 32, 43, 54, 65, 76, 87, 98, 109, 120, 131, 142, 153, 164, 175, 186, 197, 208, 219]
28 :  [0, 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143, 154, 165, 176, 187, 198, 209, 220]
29 :  [1, 12, 23, 34, 45, 56, 67, 78, 89, 100, 111, 122, 133, 144, 155, 166, 177, 188, 199]
30 :  [2, 13, 24, 35, 46, 57, 68, 79, 90, 101, 112, 123, 134, 145, 156, 167, 178]
31 :  [3, 14, 25, 36, 47, 58, 69, 80, 91, 102, 113, 124, 135, 146, 157]
32 :  [4, 15, 26, 37, 48, 59, 70, 81, 92, 103, 114, 125, 136]
33 :  [5, 16, 27, 38, 49, 60, 71, 82, 93, 104, 115]
34 :  [6, 17, 28, 39, 50, 61, 72, 83, 94]
35 :  [7, 18, 29, 40, 51, 62, 73]
36 :  [8, 19, 30, 41, 52]
37 :  [9, 20, 31]
38 :  [0, 21, 42, 63, 84, 105, 126, 147, 168, 189, 210]
39 :  [10, 31, 52, 73, 94, 115, 136, 157, 178, 199, 220]

0 :  [0, 1]
1 :  [2, 3, 4, 5]
2 :  [6, 7, 8, 9, 10, 11]
3 :  [12, 13, 14, 15, 16, 17, 18, 19]
4 :  [20, 21, 22, 23, 24, 25, 26, 27, 28, 29]
5 :  [30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41]
6 :  [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55]
7 :  [56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71]
8 :  [72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89]
9 :  [90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109]
10 :  [110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127]
11 :  [128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143]
12 :  [144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157]
13 :  [158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169]
14 :  [170, 171, 172, 173, 174, 175, 176, 177, 178, 179]
15 :  [180, 181, 182, 183, 184, 185, 186, 187]
16 :  [188, 189, 190, 191, 192, 193]
17 :  [194, 195, 196, 197]
18 :  [198, 199]
19 :  [200, 201]
20 :  [202, 203, 204, 205]
21 :  [206, 207, 208, 209, 210, 211]
22 :  [212, 213, 214, 215, 216, 217, 218, 219]
23 :  [220, 221, 222, 223, 224, 225, 226, 227, 228, 229]
24 :  [230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241]
25 :  [242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255]
26 :  [256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271]
27 :  [272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289]
28 :  [290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309]
29 :  [310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327]
30 :  [328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343]
31 :  [344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357]
32 :  [358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369]
33 :  [370, 371, 372, 373, 374, 375, 376, 377, 378, 379]
34 :  [380, 381, 382, 383, 384, 385, 386, 387]
35 :  [388, 389, 390, 391, 392, 393]
36 :  [394, 395, 396, 397]
37 :  [398, 399]
38 :  [400, 401, 402, 403, 404, 405, 406, 407, 408, 409]
39 :  [410, 411, 412, 413, 414, 415, 416, 417, 418, 419]
       
       
       
       
       
       
       
       
       
       
        
[(400, 0.18174023278726328),
 (401, 0.19124211210790643),
 (402, 0.20465782335658972),
 (403, 0.13396804473616256),
 (404, 0.12470954771875425),
 (405, 0.11868300472368883),
 (406, 0.114155484964674),
 (407, 0.11048659125488906),
 (408, 0.10744679463722318),
 (409, 0.10509918180696431),
 (410, 0.1368528752591429),
 (411, 0.13554148015659226),
 (412, 0.13635243668885008),
 (413, 0.13886421293484177),
 (414, 0.14313366996333296),
 (415, 0.14966220161629),
 (416, 0.15991006158234483),
 (417, 0.17414179718353073),
 (418, 0.16421209028176276),
 (419, 0.1585758669472648)]
[(400, 0.18174023278726328),
 (401, 0.19124211210790643),
 (402, 0.20465782335658972),
 (403, 0.13396804473616256),
 (404, 0.12470954771875425),
 (405, 0.11868300472368883),
 (406, 0.114155484964674),
 (407, 0.11048659125488906),
 (408, 0.10744679463722318),
 (409, 0.10509918180696431),
 (410, 0.1368528752591429),
 (411, 0.13554148015659226),
 (412, 0.13635243668885008),
 (413, 0.13886421293484177),
 (414, 0.14313366996333296),
 (415, 0.14966220161629),
 (416, 0.15991006158234483),
 (417, 0.17414179718353073),
 (418, 0.16421209028176276),
 (419, 0.1585758669472648)]
       
        
steps: 876
maximal force error:  9.98469516735323e-05
maximal length error:  5.405160680849175e-05
steps: 876
maximal force error:  9.98469516735323e-05
maximal length error:  5.405160680849175e-05