Kim model for stress distribution in a hollow cylindrical superconductor

In the present work, the distributions of the stress induced by flux pinning in a cylindrical superconductor with a concentric elliptic hole are studied. The Kim model is considered for the critical state, and the analytical expression of the stress in the cylinder is derived when the concentric hole is circular. Based on the finite element method, at first, the validity of the calculation process and the accuracy of the numerical results are proved by comparing with the analytical results. Subsequently, the distributions of the stress are obtained for different ratio of the major axis and the minor axis of the elliptic hole. It is found that due to the effect of stress concentration, as the value of ratio the major axis and the minor axis becomes large, the radial and hoop stress in superconductor just increase significantly in the vicinity of the hole, and the variation of the hoop stress is more sensitive. These results have significant effects on the safety in applications of superconductor.