On the stability of the rings backed by threads of unilateral action

The problem of the stability of the rings with one-sided restrictions on the movement is analytically solved. Two cases of external pressure: normal pressure and the external pressure of the central forces are considered. A comparative analysis of the obtained results is made. The influence of two types of strengthening on the critical load is studied: central bracing wires and bracing wires located on the sides of a regular polygon. This problem is in determination of parameters at which a bifurcation of the solution of some problem of nonlinear programming takes place.