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Y. Vetyukov:
"Stability and Supercritical Deformation of a Circular Ring with Intrinsic Curvature";
in: "Dynamics and Control of Advanced Structures and Machines", H Irschik, A. Belyaev, M. Krommer (ed.); Springer International Publishing, 2017, ISBN: 978-3-319-43079-9, 23 - 32.

Stability of a circular ring, pre-stressed by a temperature-like intrinsic deformation, is studied using the equations of the nonlinear theory of rods. The temperature gradient in the radial direction results in a bending moment. The critical state depends on the ratio of the bending stiffness coefficients. In the supercritical range, the ring begins to turn inside out as its cross-sections rotate about the axis. The analytical solutions are successfully compared against results of finite element simulations for a shell model of the ring.

http://dx.doi.org/10.1007/978-3-319-43080-5