Quick update on optimal beams

2010 January 13
by Daniel Lakeland

I've got a maxima script that calculates an approximate deflection curve as a closed form expression involving multiquadric radial basis functions. it has three parameters, an initial deflection (as a fraction of the length), a single localized force applied at the center (as a fraction of the uniform total force) and a width for the localized force (as a fraction of the length). By some simple plotting I can solve for approximate optimal force applied to the center of the beam to minimize some measure of deflection...

I'm going to clean it up and post it coming up in the next few days, but classes are ramping up again and it will probably be another week before I get to it. For those who want the quick answer, it looks like around 0.82 times the total applied load should be put upward at the center to de-sag a simply supported beam with initial deflection 1/100 of the length.

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