The arbitrarily and the periodically laminated elastic hollow sphere: Exact solutions and homogenization.(English)Zbl 0927.74015

Summary: The aim of this paper is: (1) to develop a rational method for the analysis of an arbitrarily laminated elastic, isotropic or transversely isotropic hollow sphere under internal and/or external pressure; (2) to solve the problem of a periodically layered sphere consisting of many equal groups of $$n$$ different thin layers. The transfer matrix method is used, and exact closed-form solutions are worked out, supplemented by a numerical example. It turns out that by means of the proposed homogenization an originally (periodically) inhomogeneous isotropic sphere is replaced by a homogeneous anisotropic one belonging to the type of spherically symmetric anisotropy.

MSC:

 74E30 Composite and mixture properties 74Q05 Homogenization in equilibrium problems of solid mechanics
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