Variational Methods in Theoretical Mechanics

1. Front Matter

   Pages I-X

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2. Introduction

   • J. T. Oden, J. N. Reddy

   Pages 1-6

3. Mathematical Foundations of Classical Variational Theory

   • J. T. Oden, J. N. Reddy

   Pages 7-51

4. Mechanics of Continua-A Brief Review

   • J. T. Oden, J. N. Reddy

   Pages 52-81

5. Complementary and Dual Variational Principles in Mechanics

   • J. T. Oden, J. N. Reddy

   Pages 82-138

6. Variational Principles in Continuum Mechanics

   • J. T. Oden, J. N. Reddy

   Pages 139-214

7. Variational Boundary-Value Problems, Monotone Operators, and Variational Inequalities

   • J. T. Oden, J. N. Reddy

   Pages 215-261

8. Variational Methods of Approximation

   • J. T. Oden, J. N. Reddy

   Pages 262-290

9. Back Matter

   Pages 291-304

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This is a textbook written for use in a graduate-level course for students of mechanics and engineering science. It is designed to cover the essential features of modern variational methods and to demonstrate how a number of basic mathematical concepts can be used to produce a unified theory of variational mechanics. As prerequisite to using this text, we assume that the student is equipped with an introductory course in functional analysis at a level roughly equal to that covered, for example, in Kolmogorov and Fomin (Functional Analysis, Vol. I, Graylock, Rochester, 1957) and possibly a graduate-level course in continuum mechanics. Numerous references to supplementary material are listed throughout the book. We are indebted to Professor Jim Douglas of the University of Chicago, who read an earlier version of the manuscript and whose detailed suggestions were extremely helpful in preparing the final draft. He also gratefully acknowledge that much of our own research work on variational theory was supported by the U.S. Air Force Office of Scientific Research. He are indebted to Mr. Ming-Goei Sheu for help in proofreading. Finally, we wish to express thanks to Mrs. Marilyn Gude for her excellent and pains­ taking job of typing the manuscript. J. T. ODEN J. N. REDDY Table of Contents PREFACE 1. INTRODUCTION 1.1 The Role of Variational Theory in Mechanics. 1 1.2 Some Historical Comments ......... . 2 1.3 Plan of Study ............... . 5 7 2. MATHEMATICAL FOUNDATIONS OF CLASSICAL VARIATIONAL THEORY 7 2.1 Introduction . . . . . . . .

• calculus
• continuum mechanics
• design
• function
• mechanics
• proof
• science

• The University of Texas at Austin, USA

  J. T. Oden

• The University of Oklahoma, USA

  J. N. Reddy

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