Abstract
The static and dynamic non-linear axisymmetric response of a shallow spherical shell with a circular opening at the apex has been investigated. The shell consists of a number of radially orthotropic layers perfectly bonded together but symmetrically laminated. The governing equations are expressed in terms of the transverse displacement, rotation and stress function. The effects of transverse shear and rotatory inertia are included in the analysis. The shell edge is elastically restrained against rotation and in-plane displacement. The vanishing of the rotation and in-plane displacement at the opening are assumed. A Fourier-Bessel series solution is formulated for the postbuckling and large amplitude free vibration of the shell. The Galerkin procedure furnishes a set of non-linear ordinary differential equations for time functions which are solved by the method of harmonic balance. Numerical results in postbuckling response and non-linear free vibration are presented for various boundary conditions, ratios of base radius to thickness, and shell rise to thickness, and numbers of layers. The results are also compared with available data.
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