Discussion Forum

Hi,

In Structural Mechanics, I would like to compute the polar moment of inertia Izz of a cylinder on which appy a centrifugal force for example.
For this purpose, I am doing a integration over all domains using the integrator coupling variable, i.e. intop1.
I have defined Izz as intop1(solid.rho((x-xcm)^2 + (y-ycm)^2) where xcm and ycm are the coordinate of the center of mass in the x resp. y direction.
Depending on the frame selection for the integration (Spatial or Material) and depending on using captial or lower-case letters for x and y I get 4 different results.

I assume that the moment of Inertia before deformation should be computed in the material frame, using capital letter, so Izz = intop1(solid.rho((X-xcm)^2 + (Y-ycm)^2) where intop1 is integrating in the material frame. But how should I compute the polar moment of inertia of the deformed geometry? I would assume that I still have to integrated in the material frame but that x and y should be lower-case letters. Otherwise the mass won't be consider correctly. But I am not sure at all. Can someone confirm this? I am also not sure to unterdstand what is difference between an integration of X in the spatial frame and an Integration of x in the material frame. I went trought the very interesting Ivar's Paper (Structural Analysis: Going beyond standard Load Cases) but I am still stuck here.

Regards
Vincent