Possibly every changing, dynamic system in the world depends on a host of other factors. These relationships can get pretty complex. They are united by equations. Thats called mathematics. :) And most equations are differential type. Some can be solved. But what happens if you find youself with too big of an equation that there is no way on earth you can do it yourself. Unless you were a scientist in the early days working on solving the subsonic and supersonic issues of an airplane wing or nose tip. I hear these guys would sit down with papers and pencils and spent hours trying to solve equations with matrices and what not, which they did. But its their work that helped revolutionize the FEM field. Nowadays, computer processing technology has changed everything. One depends on computers to solve these equations and run simulations. Some of these simulations can run well into hours, or days!

Knowing the factors also might not tell you how it would affect the design unless you test it out. These days, many companies resort to an FEM analysis of their design. That helps study complex relationships, and helps for a sturdier design. It helps in studying complex models and thermodynamic properties of materials as well. The idea behind it is to discretely solve complex equations bottom up, using boundary conditions.

Good bicycle companies that have the IT resources for such endeavors also resort to such testing. TREK, for example, uses Solidworks.

Aah, the beauty of partial differential equations. Like sunflowers on a breezy day...

I haven't come as close to simulating anything on an FEM application yet. Sadly, I opted not to take the FEM or Pro Mechanica course in the Pro/E series at school, I chose Virtual Reality instead. I think I'll just learn it myself on Solidworks or something. The closest I have come to FEM was in a computational fluid dynamics course that taught us about finite difference and Runge Kutta methods. In the end, all we used was MATLAB.

But here are a few FEM clips that sort of show you the forces at work and the effects on a bicycle. You'll now appreciate the deflections in the various regions of a frame, although I think the ones in these clips are slightly exaggerated. Which is good, because we can learn! Thank you, mmagnasco. These clips show what happens on minute scales in your bike as you ride. Now you will apreciate the meanings behind a downtube, which I think is the most important in a frame, and the seat stays. Check it out!

Ciao amici!

## Friday, November 30, 2007

### 0 A few bicycle FEM samples

Labels:
Designs and Materials
Pollinated by
Ron George

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