Graphics Programs Reference
InDepth Information
Use the finite difference method to determine the maximumdisplacementofthe
beam using
n
=
21 and
γ
=
1
.
5 and compare it with the exact solution
w
0
L
4
E I
0
61
9216
v
max
=
12.
M
0
d
0
d
d
1
x
L
v
The simply supported,taperedbeam has a circular cross section. A couple of
magnitude
M
0
is applied to the left end of the beam. The differentialequation for
the displacement
v
is
d
2
v
dx
2
M
E I
=−
M
0
(1
−
x
/
L
)
=−
/
d
0
)
4
E I
0
(
d
where
d
0
1
d
1
d
0
−
1
x
L
d
0
64
π
=
+
I
0
=
d
Substituting
x
L
E I
0
M
0
L
2
v
d
1
d
0
ξ
=
y
=
δ
=
changes the differentialequation to
d
2
y
d
1
−
ξ
=−
2
]
4
ξ
[1
+
(
δ
−
1)
ξ
with the boundary conditions
y

ξ
=
0
=
y

ξ
=
1
=
0
Solve the problemwith the finite differencemethodusing
δ
=
1
.
5 and
n
=
21; plot
y
vs.
ξ
. The exact solutionis
2
(3
+
2
δξ
−
3
ξ
)
ξ
3
y
=−
+
δ
13.
Solve Example 8.4 by the finite difference methodwith
n
6(1
+
δξ
−
ξ
)
2
21.
Hint
:Compute
the end slopes from the second noncentral differences in Tables 5.3.
=
14.
SolveProb. 20 in ProblemSet 8.1 with the finite difference method. Use
n
=
21.
15.
w
0
x
v
L
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