Stress analysis of structurally graded long solenoid coils

The equilibrium and compatibility equations are derived for a cylinder with `smeared´ elastic and current density properties. These can then be solved self-consistently. It is shown that even radially uniform solenoid coils must contain radially nonuniform 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 creates conditions of radial tension