Civil Engineering Reference
In-Depth Information
1
1
1
12
5
12
5
6
11
6
11
4
2
4
2
10
7
10
7
8
9
9
8
3
3
(a) Displacement function
N
1
(b) Displacement function
N
2
1
1
1
1
12
12
11
11
6
4
4
2
2
7
10
7
10
9
8
8
9
3
3
(c) Displacement function
N
6
Figure 3.5
(a-d) 3D views of displacement functions of a 12-node rectangle element
(cubic function).
(d) Displacement function
N
7
where ε is the strain at any equilibrium point. When elastic is assumed, the
curve in Figure 3.6 will become a straight line, and Equation 3.22 can be
simplified as
=
1
T
U
2
σ ε
(3.23)
Substituting σ
with Equation 3.11, the strain energy density can be obtained
in Equation 3.24.
=
1
T
U
2
ε
D
ε
(3.24)
The total strain energy is the integration of strain energy density over the
entire elastic body as shown in Equation 3.25.
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