Mechanical interpretation of the Berger's hypothesis for the global stability of statically loaded shells

In the present paper the mechanical interpretation of the Berger's hypothesis is considered. Using the geometrical method of Pogorelov and the asymptotic representation of the solutions of the non-linear partial differential equations, the values of the first and second invariants of the strain tensor are evaluated. This method confirms the hypothesis of Berger for the class of non-linear problems of shells under static loading. The result obtained is valid for isotropic and anisotropic shells.