The boundary integral approach to static and dynamic contact problems: equality and inequality methods
The aim of the present book is the formulation and study of boundary integral equation methods for static and dynamic contact problems. In the first chapter, after some historical information concerning the evolution of the boundary integral equation methods, we give some elements of nonsmooth convex and nonconvex analysis and certain propositions concerning minimization problems, variational inequalities and hemivariational inequalities. In the second chapter, direct and indirect boundary integral equation methods are presented for the case of equality constraints. Attention is paid to the method of weighted residuals, the use of reciprocal theorems and the singularity method. In the third chapter the above methods are illustrated with respect to certain problems from the theory of bars and of beams, and from the theory of Kirchhoff and Reissner plates. The fourth chapter deals with the numerical implementation of the boundary integral equations for equality problems. We pay attention to the point collocation method and to the Galerkin boundary element method. Chapter five extends the results of the previous chapters to dynamic equality problems. Chapter six is the last chapter dealing with equality problems. Here, certain dynamic interaction problems as the fluid- structure interaction problem and the unilateral contact problem, treated with trial and error methods, are presented. The aim of chapter seven is to smoothly introduce the reader into the area of unequality problems. In this chapter we deal with the Signorini- Fichera boundary value problem. We derive two-multivalued integral equations holding on the boundary of the body. A numerical application illustrates the theory. In the next chapter the multivalued boundary integral equations derived in the previous chapter are studied concerning the existence and uniqueness of their solutions. Chapter nine deals with the frictional unilateral contact boundary value problem. In chapter ten certain general contact boundary conditions of monotone, possibly multivalued type, are considered. Chapter eleven deals with dynamic inequality problems. Using time discretization, a time difference boundary integral equation is obtained. Numerical applications concerning dynamic inequality problems illustrate the theory. Chapter twelve deals with certain general contact boundary conditions of nonmonotone, possibly multivalued type. Chapter thirteen is the last chapter of the book. Here we have included certain highly innovative topics. In the first section we deal with cracks having unilateral contact and friction interface conditions, in the second section with adhesively bonded cracks, in the third section we consider fractal interfaces subjected to unilateral contact and friction interface conditions and in the last two sections we deal with the treatment of the multivalued boundary integral equations.
scientific article; zbMATH DE number 54070