stiffness matrix output in form of polar coordinate system in Abaqus

Hi everyone, 

My project is about the trolological properities of piston ring and cylinder linder. I have a question to ask you. I have build a 2-D half ring in Abaqus/CAE and  I hope to obtain the stiffness matrix of the half ring. The Yong's Modules of the half ring is 105GPa and the poisson's ratio is 0.3. The boundary conditions are as follows: the leftest node is totally fixed and the other nodes on the edge are limited in the U2 direction (seen in .cae file). I have write some commands in the end of the .inp file and the stiffness matrix can be output in .mix file(seen in attachment). 

As we know, the ring suffers radial contact pressure on the outside surface and the nodes' displacements along the outside surface are also radial. So I hope all the ring's analysis can be done under cylindrical coordinate system. I have looked up the manual, it seems that Abaqus just has one global Cartesian coordinate system and not be changed. Although we can build new cylindrical system or spherical system, they are all local system and the basic coordinate system would still be Cartesian. 

My problem is: how can I obtain the stiffness matrix in form of cylindrical coordinate system，not rectangular coordinate system？If it can not be obtained from Abaqus, do you know how to transform it in form of cylindrical coordinate system?I have asked a lot people, but none of them know how to do that. Could you give me a favor?

 Thank you very much in advance.

Best wishes,

Yuwei