Civil Engineering Reference
In-Depth Information
Table 2.3.
Example 2.6 Method of adjoints
1
1
1
1
10
A
=
8
4
2
1
C
=
26
1
1
2
−1
−1
0
0
0
1
4
4
2
1
8
2
1
8
4
1
8
4
2
A
=
1
1
1
1
1
+
1
1
1
1
1
−1
−
−1
−1
−1
−
−1
−1
0
0
1
0
0
1
0
0
1
0
0
0
A
=
+
6
+
12
+
0
A
=
12
−6
4
2
1
8
2
1
8
4
1
8
4
2
(−1)
1+1
(−1)
1+2
(−1)
1+3
(−1)
1+4
c
11
=
1
1
c
21
=
1
c
31
=
1
1
c
41
=
1
−1
−1
−1
−1
−1
−1
0
0
1
0
0
1
0
0
1
0
0
0
c
21
= 6
c
31
= 12
c
41
= 0
c
11
= −6
1
1
1
1
1
1
1
1
1
1
1
1
(−1)
2+1
(−1)
2+2
(−1)
2+3
(−1)
2+3
c
12
=
1
1
c
22
=
1
c
32
=
1
1
c
42
=
1
−1
−1
−1
−1
−1
−1
0
0
1
0
0
1
0
0
1
0
0
0
c
12
= 2
c
22
= 0
c
42
= 0
c
32
= −2
1
1
1
1
1
1
1
1
1
1
1
1
(−1)
3+1
(−1)
3+2
(−1)
3+3
(−1)
3+4
c
13
=
4
2
1
c
23
=
8
2
1
c
33
=
8
4
1
c
43
=
8
4
2
0
0
1
0
0
1
0
0
1
0
0
0
c
23
= 6
c
43
= 0
c
13
= −2
c
33
= −4
1
1
1
1
1
1
1
1
1
1
1
1
(−1)
4+1
(−1)
4+2
(−1)
4+3
(−1)
4+4
c
14
=
4
2
1
c
24
=
8
2
1
c
34
=
8
4
1
c
44
=
8
4
2
1
1
1
1
1
1
−1
−1
−1
−1
−1
−1
c
14
= 6
c
44
= 12
c
24
= −12
c
34
= −6
2
6
−6
−2
c
=
6
0
6
−12
12
−2
−4
−6
0
0
0
12
0.1667
0.5000
1
−0.5000
−0.1667
=
0.5000
0.0000
0.5000
-1.0000
x
=
2
A−
1
1.0000
−0.1667
−0.3333
−0.5000
3
0.0000
0.0000
0.0000
1.0000
4
