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One of the consequential problems in the theory of infinitesimal bendings of surfaces is the problem of the rigidity of surfaces in various classes of their deformations. The magnitude of this is dictated not only by the internal development of the very theory of infinitesimal bendings of surfaces and its connection with the analytical rigidity of the surface, but also by its applied side since the strength conditions of structures containing circular shells as elements require, as a rule, the geometric mean rigidity shell surface. This paper investigates infinitesimal bendings of convex surfaces, which along with a certain curve on the surface, are fixed simultaneously with respect to a point and a plane. It is proved that such surfaces in the indicated class of deformations enable rigidity not higher than the second order, and, therefore, are analytically non-bendable.
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