The Boundary Element Method applied to Two-Dimensional Contact Problems with Friction

Abstract

Contact problems and the study of load transfer in mechanical assemblages are of great importance in mechanical engineering. For nearly one century, since H Hertz (1881) published his famous work on normal contact between elastic bodies, much research has been performed in this area, both theoretical and experimental work. An interesting survey of the mechanics of contact between solid bodies is given by Kalker (1977). He gives an account for the classical formulation of the contact problem as well as for the variational one. The latter has been used especially for numerical calculations, for instance with the finite element method, (FEM). In most contact problems the contact area is a function of the external forces. When friction has to be taken into account, the whole load history has to be followed. Thus when using numerical methods, contact problems have to be solved by iteration and in the frictional case also with incremental technique. A lot of computer time has to be spent which makes it important for the system matrix to be small. When sliding occurs in the contact zone, the normal and tangential forces have to be coupled with a friction parameter. The possibility of coupling the normal- and tangential tractions in the matrix system is an advantage for the Boundary Element Method (BEM) over the displacement FEM. This makes it fruitful to use BEM for solving contact problems with friction.