ModelEqn 1D -
1
JN Reddy
FINITE ELEMENT ANALYSIS OF
A 1D MODEL PROBLEM
WITH A SINGLE VARIABLE
Finite element model development of a linear
1D model differential equation involving a single
dependent unknown (governing equations,
FE model development weak form).

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ModelEqn 1D -
2
JN Reddy
GOVERNING EQUATION
GOVERNING EQUATION
point
boundary
a
at
)
(
)
(
in
)
(
)
(
)
(
P
u
u
b
dx
du
a
L
,
x
f
u
x
c
dx
du
x
a
dx
d
=
−
+
=
Ω
=
+
⎟
⎠
⎞
⎜
⎝
⎛
−
0
0
E, A
b=k
L
u
(
L
)
u
0
P
x, u
a
=
EA
k, A
L
u
(
L
)
u
0
P
x, u
a
=
kA
Elastic deformation of a bar
Heat transfer in a bar
uninsulated bar

0
=
−
+
−
f
cu
dx
du
a
dx
d

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