Radial displacement in hollow cylinders

[farrukh.hafeez]

For an axisymmetric long tube, it is said that radial displacement is independent of axial coordinate. What is the justification for this simplification?.
If u, v and w are axial , tangential and radial displacements then
u=u(x,θ,r)
v=v(x,θ,r)
w=w(x,θ,r)
Where x,θ,r are polar coordinates.
Due to axisymmetry all displacements are independent of θ. For a long tube ,also only radial displacement is independent of axial coordinate i.e. x axis. Why?

u=u(x,r)
v=v(x,r)
w=w(r)?
For example
See section 10.2.1 and equation 10.3 of "Mechanics of Fibrous composites" by Carl T Herakovich 1999 ISBN: 978-0-471-10636-4

 

[Simon Bridge]

Welcome to PF;

For an axisymmetric long tube, it is said that radial displacement is independent of axial coordinate. What is the justification for this simplification?.

Symmetry.
http://homepages.engineering.auckla...lasticityPolar/ElasticityPolars_01_Polars.pdf

Due to axisymmetry all displacements are independent of θ.

Hmmm... I don't think so... did you leave something out?

For a long tube ,also only radial displacement is independent of axial coordinate i.e. x axis. Why?

Try a few problems without assuming the independence and see what happens (do still use cylindrical-polar coordinates though).

 

[farrukh.hafeez]

Welcome to PF;

Symmetry.
http://homepages.engineering.auckla...lasticityPolar/ElasticityPolars_01_Polars.pdf

Hmmm... I don't think so... did you leave something out?

Yes, you are right. I think I didnot mention axisymmetric and uniform loading along the length

Try a few problems without assuming the independence and see what happens (do still use cylindrical-polar coordinates though).

Underprogress...will ask for help if required.

Do you know any reference which provides full expression for compatibility equations in polar coordinates by any chance?[/QUOTE]

Thanks

 

[Simon Bridge]

full expression for compatibility equations in polar coordinates
http://en.wikipedia.org/wiki/Compatibility_(mechanics )
http://en.wikipedia.org/wiki/Del_in_cylindrical_and_spherical_coordinates