large rotation of hinged rigid beam

[EcoMan]

Hello,
My new workplace just has linear FEA software (for now), so can anyone help me out by running VM40 (

http://www.kxcad.net/ansys/ANSYS/ansyshelp/Hlp_V_VM40.html)

with and without NLGEOM,ON to determine the minimum rotation for which the nonlinear and linear solutions significantly differ? Thanks for any assistance with this urgent matter!

 

[cbrn]

Hi,
just a small premise: "small displacements" hypothesis is the hypothesis under which the sinus of a dimension can be approximated by the dimension itsels: sin(alfa) = alfa.
So, for example: is your rigid beam rotating of more than some tenths of degrees (some thousandths of radians)? If NO, then small displacements is OK; if YES, large displacements is necessary OR you know you will use small-displacements hypothesis with larger and larger error... It's up to you.

Regards

 

[EcoMan]

Thanks, cbrn.

The large deflection solution for cantilever beams (

http://users.cybercity.dk/~bcc25154/Webpage/largedeflection.htm)

differs from elementary theory when delta/L > ~0.3. For small delta, delta/L = sin(phi_0). sin(phi_0) = phi_0 for phi_0 < ~0.3 rad (~17.5 deg). Yes, this solution then differs when sin(phi_0) <> phi_0.

I would think, though, the condition for a difference between nonlinear and linear solutions is problem specific. That is, the sine approximation indicates no large deflection of a cantilever beam but maybe isn't an indicator of no large rotation of a hinged rigid beam. This would be easy to check if someone can run VM40 with and without NLGEOM,ON for 17.5 deg rotation...

 

[EcoMan]

The approximation sin(phi_0) = phi_0 reaches just 1% error at ~14 deg (

http://hyperphysics.phy-astr.gsu.edu/HBASE/trgser.html)...