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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Truss <strong>and</strong> Cable <strong>Element</strong>s - Example<br />
Finally, t 0 K NL =<br />
t P<br />
0 L + ∆L<br />
⎡<br />
⎢<br />
⎣<br />
1 0 −1 0<br />
0 1 0 −1<br />
−1 0 1 0<br />
0 −1 0 1<br />
⎤<br />
⎥<br />
⎦<br />
<strong>and</strong>, t 0 K N = t 0 K L + t 0 K NL<br />
<strong>and</strong> <strong>the</strong> <strong>for</strong>ce vector is obtained as (see relevant table <strong>for</strong> (TL) <strong>for</strong>mulation):<br />
⎡<br />
∫<br />
t<br />
0 F = t Tt<br />
0 B L 0 S 11 d 0 V = (0 L + ∆L)<br />
0 V ( 0 L) 2 ⎢<br />
⎣<br />
⎡ ⎤<br />
−cosθ<br />
t<br />
0 F = t −sinθ<br />
P<br />
⎢<br />
⎣ cosθ<br />
⎥<br />
⎦<br />
sinθ<br />
−cosθ<br />
−sinθ<br />
cosθ<br />
sinθ<br />
⎤<br />
0 L t P<br />
⎥<br />
0 ⎦<br />
0 L + ∆L 0 V ⇒<br />
A<br />
Institute <strong>of</strong> Structural Engineering <strong>Method</strong> <strong>of</strong> <strong>Finite</strong> <strong>Element</strong>s II 25