Abstract
The application of the method, i.e. component expansion of hoop and radial coordinate displacement vectors into trigonometric and generalized power series, helped obtain a new exact analytical solution for a heavy transversally-isotropic combined sphere in the equilibrium state of gravity forces. Uniformly distributed pressure was set on the internal surface, the external surface was considered to be rigidly fixed; stress and strain expressions are shown. The obtained new analytical solution helped analyze the influence of geometry on the distribution of independent invariants of stress tensor in the cross-sections of concrete monolithic supports for spherical mine workings and sedimentary rock mass surrounding mine; besides, a comprehensive multicriterion approach enabled the description of damage mechanisms.
Published Version
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