Composite spherical shells at large deflections. Asymptotic analysis and applications

The asymptotic method for spherical shells at large deflections was developed in the case of composite shell subject to external pressure. Reissner's equations describing axially symmetric deformation of deep shells with arbitrary deflections and rotation angles were considered as initial ones. They were significantly simplified and asymptotic formulae for deformation energy, external pressure and stresses depending on deflection amplitude were obtained. The energy barrier criterion was applied for the composite shell for estimation of the shell metastability. Formula for design buckling pressure was derived for composite shells. It improves the significantly more conservative NASA SP-8032 recommendations. The full inversion of the shell was studied as well. Asymptotic formulae were obtained for evaluation of stresses and load deflection dependencies. They can be useful for design of diaphragms for positive expulsion propellant spherical tanks of launch vehicles and for other applications.