The first-kind and the second-kind boundary integral equation systems for solution of frictionless contact problems
An original approach to the numerical solution of displacement boundary integral equation (BIE) and traction hypersingular boundary integral equation (HBIE) by the boundary element method (BEM) for contact problems is given. The main point is to show, how the contact conditions are used to formulate the first-kind and the second-kind BIE systems in the case of frictionless two-body elastic contact. The solution of the first-kind BIE is performed by symmetric Galerkin BEM; the second-kind BIE is solved by an appropriate collocation BEM. The contact problem in itself is solved by the method of subsequent approximations of contact region. Both forms of BIE system are compared in several numerical examples. This comparison is made for different kinds of contact problem. The major emphasis is put on the evaluation of contact pressure. The obtained results are compared with referenced numerical and with the analytical ones.
boundary integral equation contact problem boundary element method symmetric galerkin bem bie of the second kind