Elastic equilibrium state of thick-walled heavy transversally-isotropic spheres fixed on the interior surface

Abstract

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