Stress Tensor Transformation within Cylindrical Coordinates

[kost]

Hi. I am having diffuculty in figuring out stress transformation from cylindrical coordinates to cylindrical coordinates. It is pretty easy in cartesian c. system with direction cosines to move the tensor x y z to x’ y’ z’ by [σ’]=[D][σ][D]^-1. Transferring cylindrical to cartesian is also available. However, I cannot find anything about r θ z to r’ θ‘ z’(neither for spherical c.) Any suggestion like referring a textbook is welcomed.

 

[rb1957]

how about cylindrical to cartesian to cylindrical ? Then seeing that transformation, you may be able to see the direct transformation ?

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[hacksaw]

Any text book dealing with stress analysis covers that transformation.

 

[kost]

Thanks @rb but it’s a bit cumbersome.

@Hacksaw, I am pretty sure either you’re being provocative or wasn’t able to catch. Refer me any book with its chapter. I’ll present my apologies.

 

[rb1957]

I think it's only cumbersome in the way it's presented.

There's a "simple" transformation matrix from cylindrical to cartesian, call it [T1]
and a "simple" transformation from cartesian to cylindrical, call it [T2]
I've used different symbols as you want different parameters, [T2} is not the inverse of [T1] (that would return you to the original cylindrical co-ords ... yes?

so to transform from cylindrical to cylindrical its "just" [T2]*[T1]

and in the land of the blind (ie no other solution) then the one-eyed man (the cumbersome solution) is king.

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.