Energy principles and variational methods in applied mechanics

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.

Author Notes

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.

Preface

1 Introduction

1.1 Preliminary Comments

1.2 The Role of Energy Methods and Variational Principles

1.3 Some Historical Comments

1.4 Present Study

References

2 Mathematical Preliminaries

2.1 Introduction

2.2 Vectors

2.2.1 Definition of a Vector

2.2.2 Scalar and Vector Products

2.2.3 Components of a Vector

2.2.4 Summation Convention

2.2.5 Vector Calculus

2.2.6 Integral Relations

2.3 Tensors

2.3.1 Second-Order Tensors

2.3.2 General Properties of a Dyadic

2.3.3 Nonion Form of a Dyadic

2.3.4 Eigenvectors Associated with Dyadics

Exercises

References

3 Review of Equations of Solid Mechanics

3.1 Introduction

3.1.1 Classification of Equations

3.1.2 Descriptions of Motion

3.2 Conservation of Linear and Angular Momenta

3.2.1 Equations of Motion

3.2.2 Symmetry of Stress Tensor

3.3 Kinematics of Deformation

3.3.1 Strain Tensor

3.3.2 Strain Compatibility Equations

3.4 Constitutive Equations

3.4.1 Introduction

3.4.2 Generalized Hooke's Law

3.4.3 Plane Stress Constitutive Relations

3.4.4 Thermoelastic Constitutive Relations

Exercises

References

4 Work, Energy, and Variational Calculus

4.1 Concepts of Work and Energy

4.2 Strain Energy and Complementary Strain Energy

4.3 VirtualWork

4.4 Calculus of Variations

4.4.1 The Variational Operator

4.4.2 Functionals

4.4.3 The First Variation of a Functional

4.4.4 Fundamental Lemma of Variational Calculus

4.4.5 Extremum of a Functional

4.4.6 Euler Equations

4.4.7 Natural and Essential Boundary Conditions

4.4.8 Minimization of Functionals with Equality Constraints

Exercises

References

5 Energy Principles of Structural Mechanics

5.1 VirtualWork Principles

5.1.1 Introduction

5.1.2 The Principle of Virtual Displacements

5.1.3 Unit-Dummy-Displacement Method

5.2 Principle of Total Potential Energy and Castigliano's Theorem I

5.2.1 Principle of Minimum Total Potential Energy

5.2.2 Castigliano's Theorem I

5.3 Principles of Virtual Forces and Complementary Potential Energy

5.4 Principle of Complementary Potential Energy and Castigliano's Theorem II

5.5 Betti's and Maxwell's Reciprocity Theorems

Exercises

References

6 Dynamical Systems: Hamilton's Principle

6.1 Introduction

6.2 Hamilton's Principle for Particles and Rigid Bodies

6.3 Hamilton's Principle for a Continuum

6.4 Hamilton's Principle for Constrained Systems

6.5 Rayleigh's Method

Exercises

References

7 Direct Variational Methods

7.1 Introduction

7.2 Concepts from Functional Analysis

7.2.1 General Introduction

7.2.2 Linear Vector Spaces

7.2.3 Normed and Inner Product Spaces

7.2.4 Transformations, and Linear and Bilinear Forms

7.2.5 Minimum of a Quadratic Functional

7.3 The Ritz Method

7.3.1 Introduction

7.3.2 Description of the Method

7.3.3 Properties of Approximation Functions

7.3.4 Ritz Equations for the Parameters

7.3.5 General Features of the Method

7.3.6 Examples

7.4 General Boundary-Value Problems

7.4.1 Variational Formulations

7.4.2 Ritz Approximations

7.5 Weighted-Residual Methods

7.5.1 Introduction

7.5.2 Galerkin's Method

7.5.3 Least-Squares Method

7.5.4 Collocation Method

7.5.5 Eigenvalue and Time-Dependent Problems

7.5.6 Equations for Undetermined Parameters

7.5.7 Examples

7.6 Summary

Exercises

References

8 Theory and Analysis of Plates

8.1 Introduction

8.1.1 General Comments

8.1.2 An Overview of Plate/Shell Theories

8.2 Classical Plate Theory

8.2.1 Governing Equations of Circular Plates

8.2.2 Analysis of Circular Plates

8.2.3 Governing Equations in Rectangular Coordinates

8.2.4 Navie

Mevcut:*

Bound With These Titles

On Order

Özet

Özet

Author Notes

Table of Contents