A stress analysis of superconducting solenoids is presented which includes a generalized plane strain (GPS) condition for the axial strain. The GPS condition is introduced on the assumption that the deformation of a solenoid from a right circular cylinder is small. The GPS assumption results in an analytic solution for all three components of stress and strain in a solenoid. The work is presented in the context of the historical development of stress analysis for solenoids. The general stress equations for a magnetic solenoid are formulated. The relationship between a right cylinder deformation and the generalized plane strain condition is examined for the physical conditions in the central region of a solenoid magnet. The general analytic solutions of the stress equations are given for the cases of magnetic and thermal loading. The constant coefficients are determined for cases of common interest in solenoid magnet design. The analytic results are compared with numerical analysis results for an example solenoid consisting of a single coil with external reinforcement. In particular, the degree to which the axial strain is a constant and satisfies the GPS assumption is examined for the example solenoid. The analysis reveals features of the axial stress in solenoids, including the Poisson’s ratio induced axial stress and the axial stress distribution between coil and reinforcement during cooldown and operation. The strong agreement between the GPS and numerical analysis results shows that the assumptions contained in the GPS analysis accurately represent the conditions in the central region of a solenoid magnet.
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Markiewicz et al. (1999) studied this question.