Graphics Programs Reference
In-Depth Information
7.
Invert the matrix with any method;
⎡
⎣
⎤
⎦
13
−
964
2
1671
32
−
A
=
−
3155
8
−
114 2
11
1
−
2187
and commenton the reliability of the result.
8.
The joint displacements
u
of the planetruss in Prob. 14, ProblemSet 2.2 are
related to the appliedjointforces
p
by
Ku
=
p
(a)
where
⎡
⎣
⎤
⎦
27
.
580
7
.
004
−
7
.
004
0
.
000
0
.
000
7
.
004
29
.
570
−
5
.
253
0
.
000
−
24
.
320
K
=
−
.
−
.
.
.
.
MN/m
7
004
5
253
29
5700
000
0
000
0
.
000
0
.
000
0
.
000
27
.
580
−
7
.
004
0
.
000
−
24
.
3200
.
000
−
7
.
004
29
.
570
iscalled the
stiffness matrix
of the truss. If Eq. (a) is invertedbymultiplying each
side by
K
−
1
where
K
−
1
isknown as the
flexibilitymatrix
. The
physicalmeaning of the elements of the flexibilitymatrix is:
K
−
1
i j
K
−
1
p
,
weobtain
u
=
,
=
displacements
u
i
(
i
Compute (a) the flexibility
matrix of the truss; (b) the displacements of the joints due to the load
p
5
=−
=
1
,
2
,...
5) producedbythe unitload
p
j
=
1
.
45 kN
(the load shown in Problem14, ProblemSet 2.2).
9.
Invert the matrices
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
3
−
7
451
1111
1222
2344
4 567
12
11
10
17
A
=
B
=
6 5
−
80
−
24
17
55
−
9
7
10.
Write aprogram for inverting a
n
n
lower triangular matrix. The inversion
procedure should contain only forward substitution. Test the program by invert-
ing the matrix
×
⎡
⎣
⎤
⎦
36 000
18 36 00
91236 0
5
A
=
4 936
Let the program also check the result by computing and printing
AA
−
1
.
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