Analysis and Approximation of Contact Problems with Adhesion or Damage

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CRC Press, Sep 26, 2005 - Mathematics - 220 pages
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Research into contact problems continues to produce a rapidly growing body of knowledge. Recognizing the need for a single, concise source of information on models and analysis of contact problems, accomplished experts Sofonea, Han, and Shillor carefully selected several models and thoroughly study them in Analysis and Approximation of Contact Problems with Adhesion or Damage. The book describes very recent models of contact processes with adhesion or damage along with their mathematical formulations, variational analysis, and numerical analysis.

Following an introduction to modeling and functional and numerical analysis, the book devotes individual chapters to models involving adhesion and material damage, respectively, with each chapter exploring a particular model. For each model, the authors provide a variational formulation and establish the existence and uniqueness of a weak solution. They study a fully discrete approximation scheme that uses the finite element method to discretize the spatial domain and finite differences for the time derivatives. The final chapter summarizes the results, presents bibliographic comments, and considers future directions in the field.

Employing recent results on elliptic and evolutionary variational inequalities, convex analysis, nonlinear equations with monotone operators, and fixed points of operators, Analysis and Approximation of Contact Problems with Adhesion or Damage places these important tools and results at your fingertips in a unified, accessible reference.

 

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Contents

Basic Equations and Boundary Conditions
3
Preliminaries on Functional Analysis
25
Preliminaries on Numerical Analysis
51
Frictionless Contact Problems with Adhesion
79
Quasistatic Viscoelastic Contact with Adhesion
81
Dynamic Viscoelastic Contact with Adhesion
103
Quasistatic Viscoplastic Contact with Adhesion
117
Contact Problems with Damage
147
Quasistatic Viscoelastic Contact with Damage
149
Dynamic Viscoelastic Contact with Damage
163
Quasistatic Viscoplastic Contact with Damage
173
Notes Comments and Conclusions
193
Bibliographical Notes Problems for Future Research and Conclusions
195
References
207
Index
217
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Page i - EDITORIAL BOARD MS Baouendi University of California, San Diego Jane Cronin Rutgers University Jack K. Hale Georgia Institute of Technology S. Kobayashi University of California, Berkeley Marvin Marcus University of California, Santa Barbara WS Massey Yale University Anil Nerode Cornell University Donald Passman University of Wisconsin, Madison Fred S. Roberts Rutgers University David L. Russell Virginia Polytechnic Institute and State University Walter Schempp Universitšt Siegen Mark Teply University...
Page i - ... Lecture Notes EXECUTIVE EDITORS Earl J. Taft Rutgers University New Brunswick, New Jersey Zuhair Nashed University of Delaware Newark, Delaware CHAIRMEN OF THE EDITORIAL BOARD S.
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Page i - California, San Diego Jane Cronin Rutgers University Jack K. Hale Georgia Institute of Technology S. Kobayashi University of California, Berkeley Marvin Marcus University of California, Santa Barbara WS Massey Yale University Anil Nerode Cornell University Donald Passman University of Wisconsin, Madison Fred S. Roberts Rutgers University David L. Russell Virginia Polytechnic Institute and State University Walter Schempp Universitdt Siegen Mark Teply University of Wisconsin, Milwaukee MONOGRAPHS AND...
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