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## Large deflections of flexible beams

Although not mentioned in the documentation, the flexible beam component of MapleSim allows for simulation of large deflections.

In the animation, a flexible beam is loaded with a moment (red arrow) at its free end. Assuming an Euler-Bernoulli beam and slow loading (i.e., no dynamic forces), the beam should deform to an arc of constant radiusNot only the deformation of the beam can be described analytically, also the path (red trace) of the free end follows an analytical curve.

I used this test case to get a better understanding of nonlinearities observed in an oscillating system using flexible beams. The system required tuning of the structure to develop mode coupling. This could not be explained by linear theory. It was unclear whether the large deflections (nonlinear kinematics of the beam) themselves or the implementation of the flexible beam component were responsible for that.

What I have learned so far with the test case using only default settings:

• For moderate deflections there is no difference to textbook formulas.
• Up to 15 degrees rotation of the end frame, the difference between observed displacement and the Bernoulli beam stays bellow 5%.
• Up to 30 degrees rotation of the end frame (as in the mode coupling example) the trace of the end frame conforms well with the analytical path.
• To simulate very large deflections beyond 45 degrees rotation, the beam needs to be segmented to closely follow the analytical path.

For those that are unsure about the fidelity of their models, I can suggest increasing the numbers of flexible beam components and to compare. I did this in the case of the mode coupling example and noticed no difference. So, the component was not responsible for the nonlinearities. It were the kinematics.

It's unclear whether this good performance in large deflections was intended or is a byproduct of the sophisticated multibody dynamics under the hood.  Maybe an expert can tell more.

Overall, to what I have seen the (static) performance was very satisfying. Judging dynamic performance is much more difficult. Has anyone experience to share with that?

Flexible_beams_const_moment_curve_MP.mw

Flexible_beams_const_Moment_single_beam_MP.msim

Flexible_beams_const_Moment_7_beams_MP.msim

is what I have used.

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