The Approximate Solution of Some Plane Boundary Value Problems of the Moment Theory of Elasticity

Abstract EN

We consider a two-dimensional system of differential equations of the moment theory of elasticity.

The general solution of this system is represented by two arbitrary harmonic functions and solution of the Helmholtz equation.

Based on the general solution, an algorithm of constructing approximate solutions of boundary value problems is developed.

Using the proposed method, the approximate solutions of some problems on stress concentration on the contours of holes are constructed.

The values of stress concentration coefficients obtained in the case of moment elasticity and for the classical elastic medium are compared.

In the final part of the paper, we construct the approximate solution of a nonlocal problem whose exact solution is already known and compare our approximate solution with the exact one.

Supposedly, the proposed method makes it possible to construct approximate solutions of quite a wide class of boundary value problems.