Mechanical interpretation of Berger's hypothesis for the global stability of statically loaded shells (Q1083899)

In the present paper the mechanical interpretation of Berger's hypothesis is considered. Using the geometrical method of Pogorelov [\textit{A. V. Pogorelov}, Geometrical method in the nonlinear theory of shells (1967; Zbl 0168.452)] and the asymptotic representation of the solutions of the nonlinear 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 nonlinear problems of shells under static loading. The result obtained is valid for isotropic and anisotropic shells.