Stochastic model of the stress state of anisotropic body in the theory of complex potential

The structure of the complex stochastic potential of the stress-strain state of an anisotropic medium has been studied. With its help, boundary-value problems are posed for determining unknown stresses and strains. An algorithm for their solution has been developed. The difference between the indicated boundary value problems and the used boundary value problems of the classical theory of elasticity is that the deterministic boundary conditions are replaced by stochastic ones. This allows you to expand the scope of the model to media that are not completely homogeneous. In addition, the proposed form of the stochastic complex potential makes it possible to take into account the internal stresses of the samples under study. To illustrate the operation of the algorithm, the solution of the main problem of the theory of elasticity for an anisotropic medium weakened by a hole close to elliptical is given.