Geodesic
Elastic Equilibrium State of Thick-Walled Heavy Transversally-Isotropic Spheres Fixed on the Interior Surface
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 5 (2010), pp. 85-95.

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Using decomposition of hoop and radial components of displacement vector to the trigonometrical and generalized power series, the new precise analytical solution to problem on equilibrium state of thick-walled heavy transversally-isotropic central-symmetric body, which is fixed on the interior surface and is subject to the action of uniform external lateral pressure, is obtained. This can set a pattern for precise solutions in particular cases of the relations for displacements, stresses and strains at the points inside thick-walled heavy isotropic sphere, the interior surface of which is fixed, while the exterior one being under the uniform pressure. The estimation of an initial strength of solid-cast reinforced concrete sphere is carried out on the basis of a multicriteria approach taking into account real damage mechanisms (i.e. damage from tension or compression in radial, hoop and axial directions, and from transversal and antiplane shear) of anisotropic central-symmetric bodies.
Keywords: thick-walled heavy transversally-isotropic, exact analytical solutions, multi-criteria estimation of an initial strength. 
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A. V. Zaitsev; A. A. Fukalov. Elastic Equilibrium State of Thick-Walled Heavy Transversally-Isotropic Spheres Fixed on the Interior Surface. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 5 (2010), pp. 85-95. http://geodesic.mathdoc.fr/item/VSGTU_2010_5_a9/

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