Graphics Programs Reference
In-Depth 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
Search WWH ::

Custom Search