STRESS-ANALYSIS OF STRUCTURALLY GRADED LONG SOLENOID COILS

A long solenoid coil can be considered from the structural viewpoint as a thick cylinder with a distributed radial body force due to the magnetic loads. The coil structure consists of conducting material and reinforcing structure bonded together by insulation. Since the conductor dimensions are small compared to that of the solenoid, smeared elastic properties can be used to represent the overall mechanical behaviour of the winding. Varying the proportion of structural material across the radius can produce a graded solenoid. Although finite element analysis can be applied to such situations, a better understanding of the stress behaviour can be achieved by solving the governing equilibrium and compatibility equations directly. It is shown that even radially uniform solenoid coils must contain radially non-uniform axial stresses to maintain plane strain conditions. Without vertical compression, vertical tensile stresses can exist between the insulation layers. Uniform solenoids are under conditions of radial compression which are beneficial to the insulation system. Structural grading easily creates conditions of radial tension.