Graphics Programs Reference
In-Depth Information
0.4515
0.2685
-0.1725
0.3961
0.4711
0.0677
0.3052
0.5361
0.4089
0.1986
0.4471
0.5704
0.0988
0.2602
0.4334
0.0270
0.0778
0.1486
The first three modeshapes, which represent the relative displacements of the
buckledbeam, are plottedbelow (we appended the zeroend displacements to the
eigenvectors before plotting the points).
0.6
1
0.4
0.2
0.0
3
-0.2
2
-0.4
1
)
2
The buckling loads are givenby
P
i
=
(
n
+
λ
i
E I
/
L
2
. Thus
(11)
2
(0
.
1641)
E I
L
2
86
E I
L
2
P
1
=
=
19
.
(11)
2
(0
.
4720)
E I
L
2
11
E I
L
2
P
2
=
=
57
.
(11)
2
(0
.
9022)
E I
L
2
2
E I
L
2
P
3
=
=
.
109
L
2
. It
can be seen that the errorintroducedbythe finite element approximationincreases
with the mode number (the errorin
P
i
+
1
islarger than in
P
i
). Of course, the accuracy
of the finite difference model can be improvedbyusing larger
n
, but beyond
n
L
2
,
P
2
=
L
2
and
P
3
=
The analytical values are
P
1
=
20
.
19
E I
/
59
.
68
E I
/
118
.
9
E I
/
=
20
the cost of computationwith the Jacobi methodbecomes rather high.
9.3
Inverse Power and Power Methods
Inverse Power Method
The inverse powermethodis a simple iterative procedurefor finding the smallest
eigenvalue
λ
1
and the corresponding eigenvector
x
1
of
Ax
=
λ
x
(9.27)
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