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The parametric equations of the plane curves determining the equilibriumshapes that a uniform inextensible elastic ring or tube could take subject to auniform hydrostatic pressure are presented in an explicit analytic form. Thedetermination of the equilibrium shape of such a structure corresponding to agiven pressure is reduced to the solution of two transcendental equations. Theshapes with points of contact and the corresponding (contact) pressures aredetermined by the solutions of three transcendental equations. The analyticresults presented here confirm many of the previous numerical results on thissubject but the results concerning the shapes with lines of contact reported upto now are revised.

Analytic description and explicit parametrization of the equilibrium shapes of elastic rings and tubes under uniform hydrostatic pressure