EN0175
09 / 07 / 06
1.2 Introduction to FEM
Finite element method is a very powerful tool for numerical analysis in solid and structural
mechanics as well as in many other engineering disciplines. Here we present an introduction to the
basic concepts of FEM in the simplest context of a one dimensional elasticity of a bar.
In lecture 1, we have derived the governing equation for 1D elasticity of a bar as,
x
L
P
2
2
t
u
f
x
∂
∂
=
+
∂
∂
ρ
σ
ε
σ
E
=
x
u
∂
∂
=
ε
We can consider two simple problems, one with traction BC and one with displacement BC.
P1:
P2:
g
ρ
( )
0
0
=
u
( )
P
L
=
σ
P
g
ρ
( )
0
0
=
u
( )
0
=
L
u
( )
( )
⎩
⎨
⎧
=
=
=
+
P
L
u
E
u
g
u
E
'
'
'
,
0
0
0
ρ
( )
( )
⎩
⎨
⎧
=
=
=
+
0
0
0
'
'
L
u
u
g
u
E
ρ
1

This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*