Effect of transverse shear on static and dynamic buckling of antisymmetrically laminated polar orthotropic shallow spherical shells

Abstract

This paper deals with the static and dynamic buckling of polar orthotropic antisymmetrically laminated, moderately thick shallow spherical shells under uniformly distributed loading. Considering the effects of transverse shear and rotatory inertia, the governing equations of motion for shells undergoing large deformations are derived and expressed in terms of normal deflection W, slope ϑ and stress function Ψ. the Chebyshev series technique is used for spatial discretization and the Houbolt scheme is used for temporal discretization. Considering step function loading, both clamped and simply supported immovable laminated spherical shells are analyzed. The effects of transverse shear, rotatory inertia, shell rise, base-radius-to-thickness ratio and material properties on the static and dynamic snap-through buckling of antisymmetrically laminated shells have been studied.