In order to better understand the response of spherical portions of composite material pressure vessels, the stresses and deformations in a thin, specially polar orthotropic shallow spherical shell subjected to a localized loading at the apex are analyzed. Although the shell studied is geometrically thin, transverse shear deformation is included because the ratio of in-plane modulus of elasticity to transverse shear modulus is between 20 and 50 for many composite materials of interest. Methods of analysis are presently available for analyzing the effects of localized loads on thin isotropic spherical and cylindrical shells, and isotropic, shallow spherical, sandwich shells. The methods presented herein provide the ability to treat the use of composite materials. The analytic solutions are obtained in terms of modified Bessel functions of noninteger order and complex argument. In digital computation these functions are transformed into a set of nondimensionalized, rapidly convergent infinite series. Over 500 computer runs have been made and reported on herein to provide a better understanding of the effects of parameters such as ratio of circumferential to meridional modulus of elasticity, ratio of circumferential modulus of elasticity to transverse shear modulus, various boundary conditions, degree of shell shallowness, and loaded area.

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