Friction Problems in the Theory of Elasticity

Abstract

In this chapter we shall concentrate our attention on two typical inequality problems, one static and one dynamic, formulated within the framework of linear elasticity. They are the friction B.V.P.s, which were first studied by G. Duvaut and J. L. Lions [83] [84]. Because of the boundary conditions expressing the friction phenomenon, variational inequalities arise both in the static and dynamic cases. After deriving these variational inequalities, we shall study the existence and the uniqueness of the solution in an appropriate functional setting. For the static case, the propositions of minimum potential and complementary energy are derived and their duality is proved. Finally, some other types of friction B.V.P.s are also considered, and the corresponding variational inequalities are derived.