Abstract
An axisymmetric problem of deformation of a space weakened by a spherical cut with the external forces or displacements given at the edges of the cut, is solved in quadratures. The state of stress is expressed in terms of the analytic functions of a complex variable. The holomorphic character of these functions is studied and the nonholomorphic terms separated. Explicit formulas for the stresses on a surface complementing the cut to a complete sphere, are given for the case of uniform extension at infinity. The erroneous character of a number of solutions obtained earlier, is indicated.
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