Q: cantilevered cylindrical shell

[Andy Resnick]

I'm trying to find a decent reference that discusses the (static) deformation of a cantilevered cylindrical shell under a transverse load- for example, how a horizontal cantilevered pipe will deform due to gravitational loading. Everything I can find either discusses axial loading or considers non-cylindrical beams (I-beams, etc.).

Thanks in advance!

 

[Nidum]

Depends on the wall thickness of the tube .

Tubes with walls which are relatively thick compared to tube diameter can be treated as simple beams .

Tubes with walls that are relatively thin compared to tube diameter have to be treated as shell structures and analysed in detail . Some simple configurations of tube geometry and loads can be analysed mathematically but most real world problems require use of either direct numerical methods or FEA .

Can you tell me if you have a specific problem to deal with ?

 

[Andy Resnick]

Depends on the wall thickness of the tube .

Tubes with walls which are relatively thick compared to tube diameter can be treated as simple beams .

Tubes with walls that are relatively thin compared to tube diameter have to be treated as shell structures and analysed in detail . Some simple configurations of tube geometry and loads can be analysed mathematically but most real world problems require use of either direct numerical methods or FEA .

Can you tell me if you have a specific problem to deal with ?

Thanks!

Specifically, we want to better model a primary cilium:
http://www.physiology.org/doi/abs/10.1152/ajprenal.00172.2017

We are 'inspired' by some work on modeling microtubules as either orthotropic beams or as isotropic shells (honestly, not sure which is more appropriate). At this point, I'm mostly just surprised that this 'simple' problem doesn't seem to be so simple...

 

[Nidum]

Just for interest this is an example of a very simple FEA of a thin wall tubular cantilever beam with tip load .

(From one of my past engineering projects) .

 

[Andy Resnick]

View attachment 217467
Just for interest this is an example of a very simple FEA of a thin wall tubular cantilever beam with tip load .

(From one of my past engineering projects) .

Thanks! Sorry for the late reply... had to deal with a bit of nasty business. That simulation is *exactly* the phenomenon we are interested in; is there no analytic solution, even for a small (linear) strain?