Constraint Methods Applied in Contact Problems with Small Displacements

Abstract

Abstract Contact problems are characterized by contact constraints which must be imposed on contacting boundaries. To impose the contact constraints, two basic methods are available. These two basic methods are the Lagrange multiplier method and the penalty method (Kikuchi and Oden 1988). Other constraint methods based on the basic methods have also been proposed and applied. For example, a perturbed Lagrangian method is discussed in Simo et al. (1985). In this chapter, alternative constraint methods are introduced and applied in contact problems with small displacements. Basic features of the alternative constraint methods in different applications will be identified. It must be pointed out, however, that the discussions on constraint methods are not exclusive to this chapter. The performance of alternative constraint methods will also be examined in subsequent chapters, for example in Chapters 7 and 9.