I'm an optical/electronic engineer/physicist trying to do a structural calculation for experimental equipment design.
Which is probably not a good idea, tho' no one gets hurt if I get it wrong!
I need to calculate the buckling instability limit of thin columns.
I'm using Euler's formula as a start & comparing to COMSOL/FEMLAB calculations. I want to add some complications later when I understand this case!
The formula involves the second moment of area of the shape, initially a circle.
*Several* references on the web give it as (pi*D^4)/64 whilst one gives /32 When I do it from the definition of second moment of area I get /32And /32 gives a result which agrees well with FEMLAB/COMSOL, whereas /64 is a factor of two wrong - but that might be luck, I dont think I should
*expect* very good agreement should I?So.... Is it /32 or /64? And if /64 what schoolboy mistake am I making? Integral 0-2Pi, 0-R of (r^2) r dr dtheta seems easy enough! Too much Christmas CH3CH2OH perhaps lingering.........
And how good a guide is Eulers formula, how good an agreement might I expect with COMSOL/FEMLAB? (1cm diameter 20 cm long, bottom constrained x,y,z & top constrained x,y loaded z. Default 316 properties. Side load in x of 10^4N/m^2 to break the symmetry. Nonlinear solver, large deformations enabled. Fails to converge above about 6.5e8N/m^2 in z, which I take as the buckling limit. Just below that slowly converges to deflections of several mm near the centre.)
Harvey