EN0175
09 / 12 / 06
Intro to FEM (continued)
Examples of using FEM to solve a problem and comparison with exact solution:
We consider a problem already discussed in the previous class:
g
ρ
x
Solution by exact method:
(
)
x
L
x
E
g
u
−
=
2
ρ
(
)
x
L
g
2
2
−
=
ρ
σ
0
L
x
u
2
L
2
gL
ρ
2
gL
ρ
−
L
2
L
0
σ
x
Now we will solve the same problem by FEM:
In FEM, the displacement is discretized as
and the governing equation is
reduced to algebraic equation:
∑
=
=
n
k
k
k
x
w
u
x
u
1
)
(
)
(
F
KU
=
or
j
n
k
k
jk
F
u
K
=
∑
=
1
where
,
(see notes of
( )
( )
∫
=
L
k
j
jk
x
x
w
x
w
E
K
0
'
'
d
( )
( )
x
x
w
g
x
x
w
f
F
L
j
L
j
j
d
d
0
0
∫
∫
=
=
ρ
1

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