"PIES" in problems of 2D elasticity with body forces on polygonal domains

The paper presents a thorough review of the effective approach to solving problems of plane elasticity with body forces of different types. The proposed method bases on generalization of the parametric integral equation system (PIES), which was successfully applied to solving boundary problems without body forces. The main aim of the mentioned generalization was to create such an approach which does not require physical discretization of the domain, or division it into cells, like it is done in the classic boundary element method (BEM). First, only problems defined on polygons were considered. The paper also contains the analysis of the accuracy of obtained solutions in comparison with analytical or other numerical results.