Solution of Contact Problems for Half-Space by Boundary Element Methods Based on Singular Solutions of Flamant and Boussinesq’s Problems

Abstract

The paper considers normal contact problems formulated as follows: an indenter with negligible weight presses the surface half-space with a certain force, i.e., normal stress acts on the contact surface and tangential stress is zero. In particular, we consider two types of distributed load that correspond to the following cases: when half-space is subjected to frictionless flat rigid indenter, and when half-space is subject to frictionless cylindrical rigid indenter. The paper considers plane deformation. Problems are solved by boundary element methods (BEM), which are based on singular solutions of Flamant (BEMF) and Boussinesq (BEMB) problems. The stress–strain state of the half-plane, particularly the constructed contours (isolines) of stresses in half-plane, was studied. The results obtained by BEMF and BEMB are discussed and compared.