A quasistatic process of layerwise forming of a spherical solid due to a continuous centrally symmetric inflow of separate particles of a self-gravitating substance to a certain point center is considered. The solid being formed is considered to be linearly elastic, isotropic, with uniformly distributed mass but with radially non-uniform elastic properties. On the basis of the general theory of accreted solid mechanics in small strain approximation, a non-classical initial-boundary value problem that describes the development of stress-strain state of the solid under consideration during the process of its forming is formulatesd. Closed analytical solutions of the problem are constructed for two particular cases of material inhomogeneity: for the case of shear modulus constancy and for the case of compression modulus constancy. The constructed solutions are analyzed and compared with the solution of the classical elasticity theory problem formulated for an instantly formed self-gravitating spherical solid similar to the accreted one in size and properties. Fundamental quantitative and qualitative peculiarities of the stress- strain state which are inherent for a spherical body gradually formed in the field of self-gravitation are revealed.
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