The Stress State of an Elastic Orthotropic Medium with an Ellipsoidal Cavity

The stress-concentration problem for an elastic orthotropic medium containing an ellipsoidal cavity is solved. The stress state in the elastic space is represented as a superposition of the principal state and the perturbed state due to the cavity. The equivalent-inclusion method, the triple Fourier transform in spatial variables, and the Fourier-transformed Green function for an infinite medium are used. Double integrals over a finite domain are evaluated using the Gaussian quadrature formulas. The results for particular cases are compared with those obtained by other authors. The influence of the geometry of the cavity and the elastic properties of the material on stress concentration is studied