On the question of nonrigidity in the nonlinear theory of gently sloping shells

It is shown here that sufficiently thin elastic shells of arbitrary convexity and with a mobile hinged support are nonrigid. That is, for such shells, in the absence of external loading, it is proved by an asymptotic method that the boundary-value problem for the corresponding system of nonlinear partial differential equations in the theory of shells has at least one solution besides the trivial one. The former solution corresponds to an equilibrium shape close to the buckled shape obtained from the original shell surface by reflection in the plane containing the supporting contour.