FEM analysis of stress distribution in force-balanced coils

Distributions of stress in force-balanced coils (FBCs) for the superconducting magnetic energy storage (SMES) are analyzed numerically by a finite element method (FEM). Recently, we had developed the FBC concept using the virial theorem, and derived the winding pitch of helical coils as a function of the coil aspect ratio, where the distribution of stress is nearly uniform and working stress is minimized. Coils with the winding pitch were named as FBCs with the virial-limit condition or simply virial-limit coils (VLC), and their excellent characters of stress were confirmed by experiments of a two-layered helical coil which can simulate arbitrary winding pitch numbers. Measurements of distributions of stress on the winding form of the coil proved that a minimum working stress and uniform stress were achieved under the VLC condition. In this paper, stress distributions in FBCs with a monolithic winding form were investigated by FEM, and the results by FEM were compared with the experiments and the analytic solutions of a two-dimensional ideal shell model. Although the shell model could not explain the experimental results, qualitative agreements between FEM and the experiment were obtained.