Energy Principles and Variational Methods in Engineering

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.

Table of Contents

PREFACE.

1 INTRODUCTION.

2 MATHEMATICAL PRELIMINARIES.  

3 REVIEW OF EQUATIONS OF SOLID MECHANICS.

4 WORK, ENERGY, AND VARIATIONAL CALCULUS.

5 ENERGY PRINCIPLES OF STRUCTURAL MECHANICS.

6 DYNAMICAL SYSTEMS: HAMILTON'S PRINCIPLE.

7 DIRECT VARIATIONAL METHODS.

8 THEORY AND ANALYSIS OF PLATES.

9 THE FINITE ELEMENT METHOD.

10 MIXED VARIATIONAL FORMULATIONS.

ANSWERS/SOLUTIONS TO SELECTED PROBLEMS.

INDEX.

ABOUT THE AUTHOR.