Magnetoelastic bending and buckling of three-coil superconducting partial torus

A new theoretical model for characterizing the magnetoelastic bending and buckling/snapping of superconducting coils is proposed on the basis of bending theory of curved beams and the Biot-Savart law. Both in-plane and out-of-plane bending coupled with axial extension and torsion about the centerline of the coil are considered in this theoretical study. After the closed form of general solutions to the homogeneous differential equations of the curved beam for a circular coil is analytically found, a numerical iterative technique from the difference method which is independent of the boundary conditions is chosen to obtain a set of particular solutions to the inhomogeneous equations of the problem. The initial parameter method is employed to determine integral constants and an iteration is chosen to solve the nonlinear interaction between the magnetic field and deformation of the coil. The magnetoelastic buckling/snapping current is predicted from the Southwell plot of the maximum transverse deflection of the deformed coil. The theoretical predictions are in excellent agreement with the existing experimental data, and show that there is a noticeable influence of the in-plane deformation on the critical value of magnetoelastic buckling/snapping current.