The Finite Element Method for the Analysis of Non-Linear and ...
The Finite Element Method for the Analysis of Non-Linear and ...
The Finite Element Method for the Analysis of Non-Linear and ...
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2D Axisymmetric, Plane Strain <strong>and</strong> Plane Stress <strong>Element</strong>s<br />
Example<br />
<strong>The</strong> nodal coordinates at time<br />
t are:<br />
t<br />
u 1 2=0.5<br />
t<br />
u 1 1= 1<br />
t u 1 1 = 1<br />
t u 2 1 = 0<br />
t u 3 1 = 0<br />
t u 4 1 = 1<br />
t u 1 2 = 0.5<br />
t u 2 2 = 0.5<br />
t u 3 2 = 0<br />
t u 4 2 = 0<br />
<strong>The</strong> Jacobian <strong>for</strong> a 2D system is defined as:<br />
009 Example 6.18<br />
7<br />
⎡<br />
⎤ ⎡ ⎤<br />
0 J =<br />
⎢<br />
⎣<br />
∂ t x 1<br />
∂r<br />
∂ t x 1<br />
∂s<br />
∂ t x 2<br />
∂r<br />
∂ t x 2<br />
∂s<br />
⎥<br />
⎦ =<br />
⎢<br />
⎣<br />
3<br />
2<br />
0<br />
0<br />
3<br />
2<br />
⎥<br />
⎦<br />
Institute <strong>of</strong> Structural Engineering <strong>Method</strong> <strong>of</strong> <strong>Finite</strong> <strong>Element</strong>s II 8