Energy Principles and Variational Methods in Applied Mechanics

J.N. Reddy

608 pages, parution le 29/11/2002 (2^eme édition)

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Résumé

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.

Contents

1 Introduction.

Preliminary Comments.
The Role of Energy Methods and Variational Principles.
Some Historical Comments.
Present Study.

2 Mathematical Preliminaries.

Introduction.
Vectors.
Tensors.

3 Review of Equations of Solid Mechanics.

Introduction.
Conservation of Linear and Angular Momenta.
Kinematics of Deformation.
Constitutive Equations.

4 Work, Energy, and Variational Calculus.

Concepts of Work and Energy.
Strain Energy and Complementary Strain Energy.
VirtualWork.
Calculus of Variations.

5 Energy Principles of Structural Mechanics.

Virtual Work Principles.
Principle of Total Potential Energy and Castigliano's Theorem I.
Principles of Virtual Forces and Complementary Potential Energy.
Principle of Complementary Potential Energy and Castigliano's Theorem II.
Betti's and Maxwell's Reciprocity Theorems.

6 Dynamical Systems: Hamilton's Principle.

Introduction.
Hamilton's Principle for Particles and Rigid Bodies.
Hamilton's Principle for a Continuum.
Hamilton's Principle for Constrained Systems.
Rayleigh's Method.

7 Direct Variational Methods.

Introduction.
Concepts from Functional Analysis.
The Ritz Method.
General Boundary-Value Problems.
Weighted-Residual Methods.
Summary.

8 Theory and Analysis of Plates.

Introduction.
Classical Plate Theory.
Shear Deformation Plate Theory.

9 The Finite Element Method.

Introduction.
Finite Element Analysis of Bars.
Finite Element Analysis of the Euler-Bernoulli Beam Theory.
Finite Element Models of the Timoshenko Beam Theory.
Finite Element Models of the Classical Plate Theory.
Finite Element Models of the First-Order Shear Deformation Plate Theory.

10 Mixed Variational Formulations.

Introduction.
Stationary Variational Principles.
Variational Solutions Based on Mixed Formulations.
Mixed Finite Element Models of Beams.
Mixed Finite Element Models of the Classical Plate Theory.
Closure.

L'auteur - J.N. Reddy

J.N. Reddy est professeur émérite de l'Oscar S. Wyatt Endowed Chair in the Department of Mechanical Engineering à la Texas A&M University.

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Wiley
Auteur(s)	J.N. Reddy
Parution	29/11/2002
Édition	2^eme édition
Nb. de pages	608
Format	16 x 24
Couverture	Relié
Poids	975g
Intérieur	Noir et Blanc
EAN13	9780471179856
ISBN13	978-0-471-17985-6