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Energy Principles and Variational Methods in Applied Mechanics, 2nd Edition

ISBN: 978-0-471-17985-6
608 pages
August 2002
Energy Principles and Variational Methods in Applied Mechanics, 2nd Edition (047117985X) cover image
A systematic presentation of energy principles and variational methods

The increasing use of numerical and computational methods in engineering and applied sciences has shed new light on the importance of energy principles and variational methods. Energy Principles and Variational Methods in Applied Mechanics provides a systematic and practical introduction to the use of energy principles, traditional variational methods, and the finite element method to the solution of engineering problems involving bars, beams, torsion, plane elasticity, and plates.

Beginning with a review of the basic equations of mechanics and the concepts of work, energy, and topics from variational calculus, this book presents the virtual work and energy principles, energy methods of solid and structural mechanics, Hamilton’s principle for dynamical systems, and classical variational methods of approximation. A unified approach, more general than that found in most solid mechanics books, is used to introduce the finite element method. Also discussed are applications to beams and plates.

Complete with more than 200 illustrations and tables, Energy Principles and Variational Methods in Applied Mechanics, Second Edition is a valuable book for students of aerospace, civil, mechanical, and applied mechanics; and engineers in design and analysis groups in the aircraft, automobile, and civil engineering structures, as well as shipbuilding industries.

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Preface xv

1 Introduction 1

2 Mathematical Preliminaries 8

3 Review Of Equations Of Solid Mechanics 48

4 Work, Energy, And Variational Calculus 79

5 Energy Principles Of Structural 133

6 Dynamical Systems: Hamilton's Principle 177

7 Direct Variational Methods 204

8 Theory And Analysis Of Plates 299

9 The Finite Element Method 433

10 Mixed Variational Formulations 502

Answers / Solutions to Selected Problems 544

Index 583

About the Author 591

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J. N. REDDY, PhD, is University Distinguished Professor and inaugural holder of the Oscar S. Wyatt Endowed Chair in Mechanical Engineering at Texas A&M University in College Station. He has authored and coauthored several books, including Energy and Variational Methods in Applied Mechanics, Advanced Engineering Analysis (with M. L. Rasmussen), and A Mathematical Theory of Finite Elements (with J. T. Oden), all published by Wiley.
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This book has been completely revised and updated. Beginning with a review of mechanics and the concepts of work, energy, and topics from variational calculus, this book presents virtual work and energy principles, energy methods of solid and struc-tural mechanics, Hamilton's principle for dynamic systems, and classical variational methods of approximation. A unified approach, more general than that found in most solid mechanics books, is used to introduce the finite element method. Also discusse are applications to beams and plates.

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  1. Completely revised and updated.
  2. Covers both traditional implementation of energy/variational principles as well as finite element implementation.
  3. Contains expanded problems and examples of applications.
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