The equilibrium of an elastic space weakened by two spherical cavities and an external circular crack

Using the relationship between the basic solutions of Laplace's equation in toroidal and spherical coordinates, the Fourier method is employed to solve the problem of the equilibrium of an elastic space weakened by two spherical cavities and an external circular crack. The proposed approach leads to an infinite system of linear algebraic equations of the second kind with exponentially decaying matrix coefficients. A small-parameter expansion is used to obtain an asymptotic formula for the normal stress intensity factor.