Аннотация:

In this paper, a new stochastic simulation method is proposed to solve a mixed boundary value problem for the system of Lamé equations, which describes the displacement vector of an elastic body. Both planar and spatial problems with mixed boundary conditions are considered in detail. The basic idea is to use the Slobodyanskii representation of the solution through auxiliary harmonic functions. In our work, we use an approximation of the solution in the form of linear combinations of fundamental solutions for the Laplace equation, as is done in the method of fundamental solutions. As a result, the problem reduces to solving a system of linear algebraic equations for the coefficients in this linear combination. This system is solved by a special stochastic projection method.