I thought my model was pretty close to right so I thought that it should predict a critical spoke stress for buckling or the condition when you turn a nipple and the wheel spontaneously assumes a warped taco shape.
The method I used was the classic stored energy method. I calculated the stored energy and tried to take the second derivatives with respect to all the displacements and solve for a maximum. The result was no maximum, no unstable mode, no critical stress. It was always stable. I know this is wrong so the model must be wrong. This got me to thinking and reading the buckling chapter in Bauchau and Craig and reading a classic book, Timoshenko's Theory of Elastic Stability (that I was able to get off Amazon for something like $50!) I realized that in my transverse bending models I did not consider the term for longitudinal stress that leads to buckling so I am spending a bit of time putting the azimuthal compression term in the differential equation. This is going to make a huge difference in the solution. Timoshenko solves the radial buckling mode but not with an elastic restoring force like the spokes. I don't know if the revised equation with the axial term will be solvable or not. The original equations work for low levels of azimuthal stress so it may not affect the truing control problem.
This is still fun.
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