Energy Principles and Variational Methods in Applied Mechanics

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John Wiley & Sons, Aug 9, 2002 - Science - 592 pages
A systematic presentation of energy principles and variationalmethods

The increasing use of numerical and computational methods inengineering and applied sciences has shed new light on theimportance of energy principles and variational methods. EnergyPrinciples and Variational Methods in Applied Mechanicsprovides a systematic and practical introduction to the use ofenergy principles, traditional variational methods, and the finiteelement method to the solution of engineering problems involvingbars, beams, torsion, plane elasticity, and plates.

Beginning with a review of the basic equations of mechanics andthe concepts of work, energy, and topics from variational calculus,this book presents the virtual work and energy principles, energymethods of solid and structural mechanics, Hamilton'sprinciple for dynamical systems, and classical variational methodsof approximation. A unified approach, more general than that foundin most solid mechanics books, is used to introduce the finiteelement method. Also discussed are applications to beams andplates.

Complete with more than 200 illustrations and tables, EnergyPrinciples and Variational Methods in Applied Mechanics, SecondEdition is a valuable book for students of aerospace, civil,mechanical, and applied mechanics; and engineers in design andanalysis groups in the aircraft, automobile, and civil engineeringstructures, as well as shipbuilding industries.
 

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One of the very useful and well-organised books with mathematical concepts for those who wish to specialize in the field of mechanics

Contents

MATHEMATICAL PRELIMINARIES
8
ViM CONTENTS
36
REVIEW OF EQUATIONS OF SOLID MECHANICS
48
WORK ENERGY AND VARIATIONAL CALCULUS
79
ENERGY PRINCIPLES OF STRUCTURAL MECHANICS
133
HAMILTONS PRINCIPLE
177
DIRECT VARIATIONAL METHODS
204
References
297
References
430
References
499
Stationary Variational Principles
506
l The EulerBernoulli Beam Theory
517
Closure
539
ANSWERSSOLUTIONS TO SELECTED PROBLEMS
544
INDEX
583
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About the author (2002)

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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