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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Timoshenko Beam<br />
Chapter 9: THE TL TIMOSHENKO PLANE BEAM ELEMENT 9–8<br />
2-node C 1 (cubic) element<br />
<strong>for</strong> Euler-Bernoulli beam model:<br />
plane sections remain plane <strong>and</strong><br />
normal to de<strong>for</strong>med longitudinal axis<br />
2-node C 0 linear-displacement-<strong>and</strong>-rotations<br />
element <strong>for</strong> Timoshenko beam model:<br />
plane sections remain plane but not<br />
normal to de<strong>for</strong>med longitudinal axis<br />
(a)<br />
(b)<br />
C 1 element<br />
with same DOFs<br />
Figure 9.6. Sketch <strong>of</strong> <strong>the</strong> kinematics <strong>of</strong> two-node beam finite element models based on<br />
(a) Euler-Bernoulli beam <strong>the</strong>ory, <strong>and</strong> (b) Timoshenko beam <strong>the</strong>ory. <strong>The</strong>se<br />
models are called C 1 <strong>and</strong> C 0 beams, respectively, in <strong>the</strong> FEM literature.<br />
Institute <strong>of</strong> Structural Engineering <strong>Method</strong> <strong>of</strong> <strong>Finite</strong> <strong>Element</strong>s II 33
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