Axisymmetric Thermal Stresses in a Spherical Shell of Arbitrary Thickness

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Abstract
This paper contains an explicit series solution, exact within the classical theory of elasticity, for the steady-state thermal stresses and displacements induced in a spherical shell by an arbitrary axisymmetric distribution of surface temperatures. The corresponding solutions for a solid sphere and for a spherical cavity in an infinite medium are obtained as limiting cases. The convergence of the series solutions obtained is discussed. Numerical results are presented appropriate to a solid sphere if two hemispherical caps of its boundary are maintained at distinct uniform temperatures.

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