Processing math: 100%

NS_Truss_3_(v0.6)

914 days ago by fresl

 

Složeniji sistemi

 

       

 

Primjer 1.

 

       
joints:
   0:   (-1.73205080756888, -1.00000000000000)
   1:   (0.000000000000000, -2.00000000000000)
   2:   (1.73205080756888, -1.00000000000000)
   3:   (1.73205080756888, 1.00000000000000)
   4:   (0.000000000000000, 2.00000000000000)
   5:   (-1.73205080756888, 1.00000000000000)
   6:   (-1.93205080756888, -1.00000000000000)
   7:   (-1.73205080756888, -1.20000000000000)
   8:   (1.73205080756888, -1.20000000000000)

bars:
   0:   (0, 1)
   1:   (1, 2)
   2:   (2, 3)
   3:   (3, 4)
   4:   (4, 5)
   5:   (5, 0)
   6:   (0, 3)
   7:   (1, 4)
   8:   (2, 5)
   9:   (0, 6)
   10:  (0, 7)
   11:  (2, 8)

supports: [6, 7, 8]
joints:
   0:   (-1.73205080756888, -1.00000000000000)
   1:   (0.000000000000000, -2.00000000000000)
   2:   (1.73205080756888, -1.00000000000000)
   3:   (1.73205080756888, 1.00000000000000)
   4:   (0.000000000000000, 2.00000000000000)
   5:   (-1.73205080756888, 1.00000000000000)
   6:   (-1.93205080756888, -1.00000000000000)
   7:   (-1.73205080756888, -1.20000000000000)
   8:   (1.73205080756888, -1.20000000000000)

bars:
   0:   (0, 1)
   1:   (1, 2)
   2:   (2, 3)
   3:   (3, 4)
   4:   (4, 5)
   5:   (5, 0)
   6:   (0, 3)
   7:   (1, 4)
   8:   (2, 5)
   9:   (0, 6)
   10:  (0, 7)
   11:  (2, 8)

supports: [6, 7, 8]
       
       
[0, 1, 2, 3, 4, 5]
[0, 1, 2, 3, 4, 5]
       
2 * 6 - 12  ==  0
2 * 6 - 12  ==  0
       
(0.8660250.0000000.0000000.0000000.0000000.0000000.8660250.0000000.0000001.000000.0000000.0000000.5000000.0000000.0000000.0000000.0000001.000000.5000000.0000000.0000000.0000001.000000.0000000.8660250.8660250.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.5000000.5000000.0000000.0000000.0000000.0000000.0000001.000000.0000000.0000000.0000000.0000000.0000000.8660250.0000000.0000000.0000000.0000000.0000000.0000000.8660250.0000000.0000000.0000000.0000000.5000001.000000.0000000.0000000.0000000.0000000.0000000.5000000.0000000.0000001.000000.0000000.0000000.0000000.8660250.0000000.0000000.8660250.0000000.0000000.0000000.0000000.0000000.0000000.0000001.000000.5000000.0000000.0000000.5000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.8660250.8660250.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.5000000.5000000.0000000.0000001.000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.8660250.0000000.0000000.0000000.8660250.0000000.0000000.0000000.0000000.0000000.0000000.0000000.5000001.000000.0000000.0000000.5000000.0000000.0000000.000000)
                                
                            

                                
       
       
Column space:
   Vector space of degree 12 and dimension 11
Column space:
   Vector space of degree 12 and dimension 11
       
Row space:
   Vector space of degree 12 and dimension 11
Row space:
   Vector space of degree 12 and dimension 11
       
Kernel:
   Vector space of degree 12 and dimension 1
   Basis:
     (-1.0, -1.0, -1.0000000000000002, -1.0, -1.0, -1.0000000000000002, 1.0,
1.0000000000000002, 1.0, -0.0, -0.0, -0.0)
Kernel:
   Vector space of degree 12 and dimension 1
   Basis:
     (-1.0, -1.0, -1.0000000000000002, -1.0, -1.0, -1.0000000000000002, 1.0, 1.0000000000000002, 1.0, -0.0, -0.0, -0.0)
       
0:   -1.0
1:   -1.0
2:   -1.0000000000000002
3:   -1.0
4:   -1.0
5:   -1.0000000000000002
6:   1.0
7:   1.0000000000000002
8:   1.0
9:   -0.0
10:  -0.0
11:  -0.0
0:   -1.0
1:   -1.0
2:   -1.0000000000000002
3:   -1.0
4:   -1.0
5:   -1.0000000000000002
6:   1.0
7:   1.0000000000000002
8:   1.0
9:   -0.0
10:  -0.0
11:  -0.0
       
       
Left kernel:
   Vector space of degree 12 and dimension 1
   Basis:
     (0.0, 0.0, 0.5, 0.8660254037844385, 1.0, 0.0, 0.0, 0.0, 0.5,
0.8660254037844385, 1.0, 0.0)
Left kernel:
   Vector space of degree 12 and dimension 1
   Basis:
     (0.0, 0.0, 0.5, 0.8660254037844385, 1.0, 0.0, 0.0, 0.0, 0.5, 0.8660254037844385, 1.0, 0.0)
       

 

Primjer 2.

 

       
joints:
   0:   (-1.73205080756888, -1.00000000000000)
   1:   (0.000000000000000, -0.666666666666667)
   2:   (1.73205080756888, -1.00000000000000)
   3:   (1.73205080756888, 1.00000000000000)
   4:   (0.000000000000000, 1.33333333333333)
   5:   (-1.73205080756888, 1.00000000000000)
   6:   (-1.93205080756888, -1.00000000000000)
   7:   (-1.73205080756888, -1.20000000000000)
   8:   (1.73205080756888, -1.20000000000000)

bars:
   0:   (0, 1)
   1:   (1, 2)
   2:   (2, 3)
   3:   (3, 4)
   4:   (4, 5)
   5:   (5, 0)
   6:   (0, 3)
   7:   (1, 4)
   8:   (2, 5)
   9:   (0, 6)
   10:  (0, 7)
   11:  (2, 8)

supports: [6, 7, 8]
joints:
   0:   (-1.73205080756888, -1.00000000000000)
   1:   (0.000000000000000, -0.666666666666667)
   2:   (1.73205080756888, -1.00000000000000)
   3:   (1.73205080756888, 1.00000000000000)
   4:   (0.000000000000000, 1.33333333333333)
   5:   (-1.73205080756888, 1.00000000000000)
   6:   (-1.93205080756888, -1.00000000000000)
   7:   (-1.73205080756888, -1.20000000000000)
   8:   (1.73205080756888, -1.20000000000000)

bars:
   0:   (0, 1)
   1:   (1, 2)
   2:   (2, 3)
   3:   (3, 4)
   4:   (4, 5)
   5:   (5, 0)
   6:   (0, 3)
   7:   (1, 4)
   8:   (2, 5)
   9:   (0, 6)
   10:  (0, 7)
   11:  (2, 8)

supports: [6, 7, 8]
       
       
[0, 1, 2, 3, 4, 5]
[0, 1, 2, 3, 4, 5]
       
2 * 6 - 12  ==  0
2 * 6 - 12  ==  0
       
(0.9819810.0000000.0000000.0000000.0000000.0000000.8660250.0000000.0000001.000000.0000000.0000000.1889820.0000000.0000000.0000000.0000001.000000.5000000.0000000.0000000.0000001.000000.0000000.9819810.9819810.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.1889820.1889820.0000000.0000000.0000000.0000000.0000001.000000.0000000.0000000.0000000.0000000.0000000.9819810.0000000.0000000.0000000.0000000.0000000.0000000.8660250.0000000.0000000.0000000.0000000.1889821.000000.0000000.0000000.0000000.0000000.0000000.5000000.0000000.0000001.000000.0000000.0000000.0000000.9819810.0000000.0000000.8660250.0000000.0000000.0000000.0000000.0000000.0000000.0000001.000000.1889820.0000000.0000000.5000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.9819810.9819810.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.1889820.1889820.0000000.0000001.000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.9819810.0000000.0000000.0000000.8660250.0000000.0000000.0000000.0000000.0000000.0000000.0000000.1889821.000000.0000000.0000000.5000000.0000000.0000000.000000)
                                
                            

                                
       
       
Column space:
   Vector space of degree 12 and dimension 12
Column space:
   Vector space of degree 12 and dimension 12
       
Row space:
   Vector space of degree 12 and dimension 12
Row space:
   Vector space of degree 12 and dimension 12
       
Kernel:
   Vector space of degree 12 and dimension 0
Kernel:
   Vector space of degree 12 and dimension 0
       
Left kernel:
   Vector space of degree 12 and dimension 0
Left kernel:
   Vector space of degree 12 and dimension 0

 

Primjer 3. — „Ely”


       
joints:
   0:   (0.000000000000000, 0.000000000000000, 0.000000000000000)
   1:   (2.00000000000000, 0.000000000000000, 0.000000000000000)
   2:   (2.00000000000000, 2.00000000000000, 0.000000000000000)
   3:   (0.000000000000000, 2.00000000000000, 0.000000000000000)
   4:   (1.00000000000000, 0.000000000000000, 1.00000000000000)
   5:   (2.00000000000000, 1.00000000000000, 1.00000000000000)
   6:   (1.00000000000000, 2.00000000000000, 1.00000000000000)
   7:   (0.000000000000000, 1.00000000000000, 1.00000000000000)

bars:
   0:   (0, 4)
   1:   (1, 4)
   2:   (1, 5)
   3:   (2, 5)
   4:   (2, 6)
   5:   (3, 6)
   6:   (3, 7)
   7:   (0, 7)
   8:   (7, 4)
   9:   (4, 5)
   10:  (5, 6)
   11:  (6, 7)

supports: [0, 1, 2, 3]
joints:
   0:   (0.000000000000000, 0.000000000000000, 0.000000000000000)
   1:   (2.00000000000000, 0.000000000000000, 0.000000000000000)
   2:   (2.00000000000000, 2.00000000000000, 0.000000000000000)
   3:   (0.000000000000000, 2.00000000000000, 0.000000000000000)
   4:   (1.00000000000000, 0.000000000000000, 1.00000000000000)
   5:   (2.00000000000000, 1.00000000000000, 1.00000000000000)
   6:   (1.00000000000000, 2.00000000000000, 1.00000000000000)
   7:   (0.000000000000000, 1.00000000000000, 1.00000000000000)

bars:
   0:   (0, 4)
   1:   (1, 4)
   2:   (1, 5)
   3:   (2, 5)
   4:   (2, 6)
   5:   (3, 6)
   6:   (3, 7)
   7:   (0, 7)
   8:   (7, 4)
   9:   (4, 5)
   10:  (5, 6)
   11:  (6, 7)

supports: [0, 1, 2, 3]
       
       
3 * 4 - 12  ==  0
3 * 4 - 12  ==  0
       
[4, 5, 6, 7]
[4, 5, 6, 7]
       
(0.70710.70710.00000.00000.00000.00000.00000.00000.70710.70710.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.70710.70710.00000.00000.70710.70710.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.70710.70710.00000.00000.00000.70710.70710.00000.00000.00000.00000.00000.70710.70710.00000.00000.00000.70710.70710.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.70710.70710.00000.00000.00000.00000.70710.70710.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.70710.70710.00000.00000.00000.00000.70710.70710.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.70710.00000.00000.70710.00000.00000.00000.00000.00000.00000.70710.70710.70710.00000.00000.70710.00000.00000.00000.00000.00000.00000.70710.70710.00000.00000.00000.0000)
                                
                            

                                
       
       
Row space:
   Vector space of degree 12 and dimension 11
   Basis:
     (1.0, -1.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.0, 1.0, -1.0, -0.0, -0.0)
     (0.0, 1.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.5, 0.5, -0.0, -0.0)
     (0.0, 0.0, 1.0, -1.0, -0.0, -0.0, -0.0, -0.0, -0.0, 1.0, -1.0, -0.0)
     (0.0, 0.0, 0.0, 1.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.5, 0.5, -0.0)
     (0.0, 0.0, 0.0, 0.0, 1.0, -1.0, 0.0, 0.0, 0.0, 0.0, 1.0, -1.0)
     (0.0, 0.0, 0.0, 0.0, 0.0, 1.0, -0.0, -0.0, -0.0, -0.0, -0.5, 0.5)
     (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, -1.0, -1.0, 0.0, 0.0, 1.0)
     (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.5, -0.0, -0.0, -0.5)
     (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0)
     (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, -0.0)
     (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0)
Row space:
   Vector space of degree 12 and dimension 11
   Basis:
     (1.0, -1.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.0, 1.0, -1.0, -0.0, -0.0)
     (0.0, 1.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.5, 0.5, -0.0, -0.0)
     (0.0, 0.0, 1.0, -1.0, -0.0, -0.0, -0.0, -0.0, -0.0, 1.0, -1.0, -0.0)
     (0.0, 0.0, 0.0, 1.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.5, 0.5, -0.0)
     (0.0, 0.0, 0.0, 0.0, 1.0, -1.0, 0.0, 0.0, 0.0, 0.0, 1.0, -1.0)
     (0.0, 0.0, 0.0, 0.0, 0.0, 1.0, -0.0, -0.0, -0.0, -0.0, -0.5, 0.5)
     (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, -1.0, -1.0, 0.0, 0.0, 1.0)
     (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.5, -0.0, -0.0, -0.5)
     (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0)
     (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, -0.0)
     (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0)
       
Column space:
   Vector space of degree 12 and dimension 11
   Basis:
     (-0.7071067811865475, 0.0, -0.7071067811865475, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0)
     (0.7071067811865475, 0.0, -0.7071067811865475, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0)
     (0.0, 0.0, 0.0, 0.0, -0.7071067811865475, -0.7071067811865475, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0)
     (0.0, 0.0, 0.0, 0.0, 0.7071067811865475, -0.7071067811865475, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0)
     (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.7071067811865475, 0.0,
-0.7071067811865475, 0.0, 0.0, 0.0)
     (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -0.7071067811865475, 0.0,
-0.7071067811865475, 0.0, 0.0, 0.0)
     (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.7071067811865475,
-0.7071067811865475)
     (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -0.7071067811865475,
-0.7071067811865475)
     (-0.7071067811865475, 0.7071067811865475, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.7071067811865475, -0.7071067811865475, 0.0)
     (0.7071067811865475, 0.7071067811865475, 0.0, -0.7071067811865475,
-0.7071067811865475, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0)
     (0.0, 0.0, 0.0, -0.7071067811865475, 0.7071067811865475, 0.0,
0.7071067811865475, -0.7071067811865475, 0.0, 0.0, 0.0, 0.0)
Column space:
   Vector space of degree 12 and dimension 11
   Basis:
     (-0.7071067811865475, 0.0, -0.7071067811865475, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0)
     (0.7071067811865475, 0.0, -0.7071067811865475, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0)
     (0.0, 0.0, 0.0, 0.0, -0.7071067811865475, -0.7071067811865475, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0)
     (0.0, 0.0, 0.0, 0.0, 0.7071067811865475, -0.7071067811865475, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0)
     (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.7071067811865475, 0.0, -0.7071067811865475, 0.0, 0.0, 0.0)
     (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -0.7071067811865475, 0.0, -0.7071067811865475, 0.0, 0.0, 0.0)
     (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.7071067811865475, -0.7071067811865475)
     (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -0.7071067811865475, -0.7071067811865475)
     (-0.7071067811865475, 0.7071067811865475, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.7071067811865475, -0.7071067811865475, 0.0)
     (0.7071067811865475, 0.7071067811865475, 0.0, -0.7071067811865475, -0.7071067811865475, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0)
     (0.0, 0.0, 0.0, -0.7071067811865475, 0.7071067811865475, 0.0, 0.7071067811865475, -0.7071067811865475, 0.0, 0.0, 0.0, 0.0)
       
Kernel:
   Vector space of degree 12 and dimension 1
   Basis:
     (1.0, -1.0, -1.0, 1.0, 1.0, -1.0, -1.0, 1.0, -1.0, 1.0, -1.0, 1.0)
Kernel:
   Vector space of degree 12 and dimension 1
   Basis:
     (1.0, -1.0, -1.0, 1.0, 1.0, -1.0, -1.0, 1.0, -1.0, 1.0, -1.0, 1.0)
       
0:   1.0
1:   -1.0
2:   -1.0
3:   1.0
4:   1.0
5:   -1.0
6:   -1.0
7:   1.0
8:   -1.0
9:   1.0
10:  -1.0
11:  1.0
0:   1.0
1:   -1.0
2:   -1.0
3:   1.0
4:   1.0
5:   -1.0
6:   -1.0
7:   1.0
8:   -1.0
9:   1.0
10:  -1.0
11:  1.0
       
       
Left kernel:
   Vector space of degree 12 and dimension 1
   Basis:
     (0.0, -1.0, 0.0, -1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 1.0, 0.0, 0.0)
Left kernel:
   Vector space of degree 12 and dimension 1
   Basis:
     (0.0, -1.0, 0.0, -1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 1.0, 0.0, 0.0)
       

 

Primjer 4. — Nesimetrični „Ely”

 

       
joints:
   0:   (0.000000000000000, -0.250000000000000, 0.000000000000000)
   1:   (2.00000000000000, 0.000000000000000, 0.000000000000000)
   2:   (2.00000000000000, 2.00000000000000, 0.000000000000000)
   3:   (0.000000000000000, 2.00000000000000, 0.000000000000000)
   4:   (1.00000000000000, 0.000000000000000, 1.00000000000000)
   5:   (2.00000000000000, 1.00000000000000, 1.00000000000000)
   6:   (1.00000000000000, 2.00000000000000, 1.00000000000000)
   7:   (0.000000000000000, 1.00000000000000, 1.00000000000000)

bars:
   0:   (0, 4)
   1:   (1, 4)
   2:   (1, 5)
   3:   (2, 5)
   4:   (2, 6)
   5:   (3, 6)
   6:   (3, 7)
   7:   (0, 7)
   8:   (7, 4)
   9:   (4, 5)
   10:  (5, 6)
   11:  (6, 7)

supports: [0, 1, 2, 3]
joints:
   0:   (0.000000000000000, -0.250000000000000, 0.000000000000000)
   1:   (2.00000000000000, 0.000000000000000, 0.000000000000000)
   2:   (2.00000000000000, 2.00000000000000, 0.000000000000000)
   3:   (0.000000000000000, 2.00000000000000, 0.000000000000000)
   4:   (1.00000000000000, 0.000000000000000, 1.00000000000000)
   5:   (2.00000000000000, 1.00000000000000, 1.00000000000000)
   6:   (1.00000000000000, 2.00000000000000, 1.00000000000000)
   7:   (0.000000000000000, 1.00000000000000, 1.00000000000000)

bars:
   0:   (0, 4)
   1:   (1, 4)
   2:   (1, 5)
   3:   (2, 5)
   4:   (2, 6)
   5:   (3, 6)
   6:   (3, 7)
   7:   (0, 7)
   8:   (7, 4)
   9:   (4, 5)
   10:  (5, 6)
   11:  (6, 7)

supports: [0, 1, 2, 3]
       
       
[4, 5, 6, 7]
[4, 5, 6, 7]
       
(0.69630.70710.00000.00000.00000.00000.00000.00000.70710.70710.00000.00000.17410.00000.00000.00000.00000.00000.00000.00000.70710.70710.00000.00000.69630.70710.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.70710.70710.00000.00000.00000.70710.70710.00000.00000.00000.00000.00000.70710.70710.00000.00000.00000.70710.70710.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.70710.70710.00000.00000.00000.00000.70710.70710.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.70710.70710.00000.00000.00000.00000.70710.70710.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.70710.00000.00000.70710.00000.00000.00000.00000.00000.00000.70710.78090.70710.00000.00000.70710.00000.00000.00000.00000.00000.00000.70710.62470.00000.00000.00000.0000)
                                
                            

                                
       
       
Kernel:
   Vector space of degree 12 and dimension 0
   Basis:
     []
Kernel:
   Vector space of degree 12 and dimension 0
   Basis:
     []
       
Left kernel:
   Vector space of degree 12 and dimension 0
   Basis:
     []
Left kernel:
   Vector space of degree 12 and dimension 0
   Basis:
     []

 

Primjer 5. — „Ely” s jednom osi simetrije

 

       
joints:
   0:   (-0.250000000000000, -0.250000000000000, 0.000000000000000)
   1:   (2.00000000000000, 0.000000000000000, 0.000000000000000)
   2:   (2.00000000000000, 2.00000000000000, 0.000000000000000)
   3:   (0.000000000000000, 2.00000000000000, 0.000000000000000)
   4:   (1.00000000000000, 0.000000000000000, 1.00000000000000)
   5:   (2.00000000000000, 1.00000000000000, 1.00000000000000)
   6:   (1.00000000000000, 2.00000000000000, 1.00000000000000)
   7:   (0.000000000000000, 1.00000000000000, 1.00000000000000)

bars:
   0:   (0, 4)
   1:   (1, 4)
   2:   (1, 5)
   3:   (2, 5)
   4:   (2, 6)
   5:   (3, 6)
   6:   (3, 7)
   7:   (0, 7)
   8:   (7, 4)
   9:   (4, 5)
   10:  (5, 6)
   11:  (6, 7)

supports: [0, 1, 2, 3]
joints:
   0:   (-0.250000000000000, -0.250000000000000, 0.000000000000000)
   1:   (2.00000000000000, 0.000000000000000, 0.000000000000000)
   2:   (2.00000000000000, 2.00000000000000, 0.000000000000000)
   3:   (0.000000000000000, 2.00000000000000, 0.000000000000000)
   4:   (1.00000000000000, 0.000000000000000, 1.00000000000000)
   5:   (2.00000000000000, 1.00000000000000, 1.00000000000000)
   6:   (1.00000000000000, 2.00000000000000, 1.00000000000000)
   7:   (0.000000000000000, 1.00000000000000, 1.00000000000000)

bars:
   0:   (0, 4)
   1:   (1, 4)
   2:   (1, 5)
   3:   (2, 5)
   4:   (2, 6)
   5:   (3, 6)
   6:   (3, 7)
   7:   (0, 7)
   8:   (7, 4)
   9:   (4, 5)
   10:  (5, 6)
   11:  (6, 7)

supports: [0, 1, 2, 3]
       
       
[4, 5, 6, 7]
[4, 5, 6, 7]
       
(0.77150.70710.00000.00000.00000.00000.00000.00000.70710.70710.00000.00000.15430.00000.00000.00000.00000.00000.00000.00000.70710.70710.00000.00000.61720.70710.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.70710.70710.00000.00000.00000.70710.70710.00000.00000.00000.00000.00000.70710.70710.00000.00000.00000.70710.70710.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.70710.70710.00000.00000.00000.00000.70710.70710.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.70710.70710.00000.00000.00000.00000.70710.70710.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.15430.70710.00000.00000.70710.00000.00000.00000.00000.00000.00000.70710.77150.70710.00000.00000.70710.00000.00000.00000.00000.00000.00000.70710.61720.00000.00000.00000.0000)
                                
                            

                                
       
       
Kernel:
   Vector space of degree 12 and dimension 1
   Basis:
     (0.9165151389911679, -0.8, -1.0, 1.0, 1.0, -1.0, -0.8, 0.9165151389911681,
-0.8, 1.0, -1.0, 1.0)
Kernel:
   Vector space of degree 12 and dimension 1
   Basis:
     (0.9165151389911679, -0.8, -1.0, 1.0, 1.0, -1.0, -0.8, 0.9165151389911681, -0.8, 1.0, -1.0, 1.0)
       
0:   0.9165151389911679
1:   -0.8
2:   -1.0
3:   1.0
4:   1.0
5:   -1.0
6:   -0.8
7:   0.9165151389911681
8:   -0.8
9:   1.0
10:  -1.0
11:  1.0
0:   0.9165151389911679
1:   -0.8
2:   -1.0
3:   1.0
4:   1.0
5:   -1.0
6:   -0.8
7:   0.9165151389911681
8:   -0.8
9:   1.0
10:  -1.0
11:  1.0
       
       
Left kernel:
   Vector space of degree 12 and dimension 1
   Basis:
     (-0.11111111111111112, 1.0, -0.11111111111111112, 0.8888888888888888, 0.0,
0.0, 0.0, -0.8888888888888888, 0.0, -1.0, 0.11111111111111115,
0.11111111111111115)
Left kernel:
   Vector space of degree 12 and dimension 1
   Basis:
     (-0.11111111111111112, 1.0, -0.11111111111111112, 0.8888888888888888, 0.0, 0.0, 0.0, -0.8888888888888888, 0.0, -1.0, 0.11111111111111115, 0.11111111111111115)
       

 

Primjer 18. — Ely

 

       
joints:
   0:   (0.000000000000000, -2.00000000000000, 0.000000000000000)
   1:   (1.41421356237310, -1.41421356237310, 0.000000000000000)
   2:   (2.00000000000000, 0.000000000000000, 0.000000000000000)
   3:   (1.41421356237310, 1.41421356237310, 0.000000000000000)
   4:   (0.000000000000000, 2.00000000000000, 0.000000000000000)
   5:   (-1.41421356237310, 1.41421356237310, 0.000000000000000)
   6:   (-2.00000000000000, 0.000000000000000, 0.000000000000000)
   7:   (-1.41421356237310, -1.41421356237310, 0.000000000000000)
   8:   (sin(0.125000000000000*pi), -cos(0.125000000000000*pi),
1.41421356237310)
   9:   (sin(0.375000000000000*pi), -cos(0.375000000000000*pi),
1.41421356237310)
   10:  (sin(0.625000000000000*pi), -cos(0.625000000000000*pi),
1.41421356237310)
   11:  (sin(0.875000000000000*pi), -cos(0.875000000000000*pi),
1.41421356237310)
   12:  (sin(1.12500000000000*pi), -cos(1.12500000000000*pi), 1.41421356237310)
   13:  (sin(1.37500000000000*pi), -cos(1.37500000000000*pi), 1.41421356237310)
   14:  (sin(1.62500000000000*pi), -cos(1.62500000000000*pi), 1.41421356237310)
   15:  (sin(1.87500000000000*pi), -cos(1.87500000000000*pi), 1.41421356237310)

bars:
   0:   (0, 8)
   1:   (1, 8)
   2:   (1, 9)
   3:   (2, 9)
   4:   (2, 10)
   5:   (3, 10)
   6:   (3, 11)
   7:   (4, 11)
   8:   (4, 12)
   9:   (5, 12)
   10:  (5, 13)
   11:  (6, 13)
   12:  (6, 14)
   13:  (7, 14)
   15:  (7, 15)
   16:  (0, 15)
   17:  (15, 8)
   18:  (8, 9)
   19:  (9, 10)
   20:  (10, 11)
   21:  (11, 12)
   22:  (12, 13)
   23:  (13, 14)
   24:  (14, 15)

supports: [0, 1, 2, 3, 4, 5, 6, 7]
joints:
   0:   (0.000000000000000, -2.00000000000000, 0.000000000000000)
   1:   (1.41421356237310, -1.41421356237310, 0.000000000000000)
   2:   (2.00000000000000, 0.000000000000000, 0.000000000000000)
   3:   (1.41421356237310, 1.41421356237310, 0.000000000000000)
   4:   (0.000000000000000, 2.00000000000000, 0.000000000000000)
   5:   (-1.41421356237310, 1.41421356237310, 0.000000000000000)
   6:   (-2.00000000000000, 0.000000000000000, 0.000000000000000)
   7:   (-1.41421356237310, -1.41421356237310, 0.000000000000000)
   8:   (sin(0.125000000000000*pi), -cos(0.125000000000000*pi), 1.41421356237310)
   9:   (sin(0.375000000000000*pi), -cos(0.375000000000000*pi), 1.41421356237310)
   10:  (sin(0.625000000000000*pi), -cos(0.625000000000000*pi), 1.41421356237310)
   11:  (sin(0.875000000000000*pi), -cos(0.875000000000000*pi), 1.41421356237310)
   12:  (sin(1.12500000000000*pi), -cos(1.12500000000000*pi), 1.41421356237310)
   13:  (sin(1.37500000000000*pi), -cos(1.37500000000000*pi), 1.41421356237310)
   14:  (sin(1.62500000000000*pi), -cos(1.62500000000000*pi), 1.41421356237310)
   15:  (sin(1.87500000000000*pi), -cos(1.87500000000000*pi), 1.41421356237310)

bars:
   0:   (0, 8)
   1:   (1, 8)
   2:   (1, 9)
   3:   (2, 9)
   4:   (2, 10)
   5:   (3, 10)
   6:   (3, 11)
   7:   (4, 11)
   8:   (4, 12)
   9:   (5, 12)
   10:  (5, 13)
   11:  (6, 13)
   12:  (6, 14)
   13:  (7, 14)
   15:  (7, 15)
   16:  (0, 15)
   17:  (15, 8)
   18:  (8, 9)
   19:  (9, 10)
   20:  (10, 11)
   21:  (11, 12)
   22:  (12, 13)
   23:  (13, 14)
   24:  (14, 15)

supports: [0, 1, 2, 3, 4, 5, 6, 7]
       

 

       
3 * 8 - 24  ==  0
3 * 8 - 24  ==  0
       
[8, 9, 10, 11, 12, 13, 14, 15]
[8, 9, 10, 11, 12, 13, 14, 15]
       
24 x 24 dense matrix over Real Double Field (use the '.str()' method to see the
entries)
24 x 24 dense matrix over Real Double Field (use the '.str()' method to see the entries)
       
       
Row space:
   Vector space of degree 24 and dimension 23
Row space:
   Vector space of degree 24 and dimension 23
       
Column space:
   Vector space of degree 24 and dimension 23
Column space:
   Vector space of degree 24 and dimension 23
       
Kernel:
   Vector space of degree 24 and dimension 1
Kernel:
   Vector space of degree 24 and dimension 1
       
0:   2.1943069386526513
1:   -2.1943069386526513
2:   -2.1943069386526517
3:   2.1943069386526517
4:   2.1943069386526526
5:   -2.1943069386526526
6:   -2.194306938652653
7:   2.194306938652653
8:   2.1943069386526557
9:   -2.1943069386526557
10:  -2.194306938652659
11:  2.1943069386526592
12:  2.1943069386526624
13:  -2.194306938652662
15:  -2.1943069386526552
16:  2.1943069386526557
17:  -0.9999999999999946
18:  0.999999999999995
19:  -0.9999999999999953
20:  0.9999999999999953
21:  -0.9999999999999962
22:  0.9999999999999972
23:  -0.9999999999999994
24:  1.0
0:   2.1943069386526513
1:   -2.1943069386526513
2:   -2.1943069386526517
3:   2.1943069386526517
4:   2.1943069386526526
5:   -2.1943069386526526
6:   -2.194306938652653
7:   2.194306938652653
8:   2.1943069386526557
9:   -2.1943069386526557
10:  -2.194306938652659
11:  2.1943069386526592
12:  2.1943069386526624
13:  -2.194306938652662
15:  -2.1943069386526552
16:  2.1943069386526557
17:  -0.9999999999999946
18:  0.999999999999995
19:  -0.9999999999999953
20:  0.9999999999999953
21:  -0.9999999999999962
22:  0.9999999999999972
23:  -0.9999999999999994
24:  1.0
       
       
Left kernel:
   Vector space of degree 24 and dimension 1
Left kernel:
   Vector space of degree 24 and dimension 1