Eck / Jarusek / Krbec Unilateral Contact Problems

Variational Methods and Existence Theorems
1. Auflage 2005
ISBN: 978-1-4200-2736-5
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 398 Seiten

Reihe: Chapman & Hall/CRC Pure and Applied Mathematics

The mathematical analysis of contact problems, with or without friction, is an area where progress depends heavily on the integration of pure and applied mathematics. This book presents the state of the art in the mathematical analysis of unilateral contact problems with friction, along with a major part of the analysis of dynamic contact problems without friction.

Much of this monograph emerged from the authors' research activities over the past 10 years and deals with an approach proven fruitful in many situations. Starting from thin estimates of possible solutions, this approach is based on an approximation of the problem and the proof of a moderate partial regularity of the solution to the approximate problem. This in turn makes use of the shift (or translation) technique - an important yet often overlooked tool for contact problems and other nonlinear problems with limited regularity. The authors pay careful attention to quantification and precise results to get optimal bounds in sufficient conditions for existence theorems.

Unilateral Contact Problems: Variational Methods and Existence Theorems a valuable resource for scientists involved in the analysis of contact problems and for engineers working on the numerical approximation of contact problems. Self-contained and thoroughly up to date, it presents a complete collection of the available results and techniques for the analysis of unilateral contact problems and builds the background required for further research on more complex problems in this area.

Zielgruppe

Applied mathematicians, numerical analysts, mechanical and construction engineers, and geophysicists

Autoren/Hrsg.

Eck, Christof

Jarusek, Jiri

Krbec, Miroslav

Fachgebiete

• Naturwissenschaften Physik Mechanik

Inhaltsverzeichnis

PREFACE
INTRODUCTION
Notations
Linear Elasticity
Formulation of Contact Problems
Variational Principles in Mechanics
The Static Contact Problem
Geometry of Domains
The Method of Tangential Translations
BACKGROUND
Fixed Point Theorems
Some General Remarks
Crash Course in Interpolation
Besov and Lizorkin-Triebel Spaces
The Potential Spaces
Vector-Valued Sobolev and Besov Spaces
Extensions and Traces
Spaces on Domains
STATIC AND QUASISTATIC CONTACT PROBLEMS
Coercive Static Case
Semicoercive Contact Problem
Contact Problems for Two Bodies
Quasistatic Contact Problem
DYNAMIC CONTACT PROBLEMS
A Short Survey About Results for Elastic Materials
Results for Materials With Singular Memory
Viscoelastic Membranes
Problems With Given Friction
DYNAMIC CONTACT PROBLEMS WITH COULOMB FRICTION
Solvability of Frictional Contact Problems
Anisotropic Material
Isotropic Material
Thermo-Viscoelastic Problems
BIBLIOGRAPHY
LIST OF NOTATION
SUBJECT INDEX