The boundary integral approach to static and dynamic contact problems: equality and inequality methods
type: Item
instance of: scholarly article
title: The boundary integral approach to static and dynamic contact problems: equality and inequality methods
zbMATH Open document ID: 0764.73002
published in: ISNM. International Series of Numerical Mathematics
publication date: 1993-01-23T00:00:00Z
review text: 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 …
Mathematics Subject Classification ID: 74-02
Mathematics Subject Classification ID: 74S15
Mathematics Subject Classification ID: 74A55
Mathematics Subject Classification ID: 74M15
zbMATH DE Number: 54070
zbMATH Keywords: variational equalities
zbMATH Keywords: nonsmooth convex and nonconvex analysis
zbMATH Keywords: variational inequalities
zbMATH Keywords: hemivariational inequalities
zbMATH Keywords: equality constraints
zbMATH Keywords: method of weighted residuals
zbMATH Keywords: reciprocal theorems
zbMATH Keywords: singularity method
zbMATH Keywords: bars
zbMATH Keywords: beams
zbMATH Keywords: plates
zbMATH Keywords: point collocation method
zbMATH Keywords: Galerkin boundary element method
zbMATH Keywords: fluid-structure interaction
zbMATH Keywords: unilateral contact problem
zbMATH Keywords: multivalued boundary integral equations
zbMATH Keywords: dynamic inequality problems
zbMATH Keywords: cracks
zbMATH Keywords: friction interface conditions
author: H. Antes
author: Panagiotis D. Panagiotopoulos
describes a project that uses: CONTACT
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 54070