Approximate solution of plane problems about stress concentrations in elastic bodies with voids

The article considers the case of plane deformation for the Cowin–Nunziato linear model, which describes the static equilibrium of elastic bodies with voids. The general solution of the system of two-dimensional equations corresponding to this model is represented by any two harmonic functions and the solution of the Helmholtz equation. Based on the general solution and using the method of fundamental solutions, an algorithm is presented that allows one to approximately solve the corresponding boundary value problems. Approximate solutions of various boundary value problems for square domains with circular holes are constructed using this algorithm.