Energy and Variational Methods in Applied Mechanics

A practical introduction to the use of the finite-element method and variational methods to solve engineering problems about beams, bars, torsion, and plane elasticity. Includes a concise section on composite-material laminated plates and shells. Contains numerous examples, exercises, problems, and references. A REVIEW OF THE EQUATIONS OF MECHANICS.

Introduction.

Kinetics.

Kinematics.

Thermodynamic Principles.

Constitutive Equations.

Boundary-Value Problems of Mechanics.

Equations of Bars, Beams, Torsion, and Plane Elasticity.

ENERGY AND VARIATIONAL PRINCIPLES.

Preliminary Concepts.

Calculus of Variations.

Virtual Work and Energy Principles.

Stationary Variational Principles.

Hamilton's Principle.

Energy Theorems of Structural Mechanics.

VARIATIONAL METHODS OF APPROXIMATION.

Some Preliminaries.

The Ritz Method.

Weighted-Residual Methods.

The Finite-Element Method.

THEORY AND ANALYSIS OF PLATES AND SHELLS.

Classical Theory of Plates.

Shear Deformation Theories of Plates.

Laminated Composite Plates.

Theory of Shells.

Finite-Element Analysis of Plates and Shells.

Bibliography.

Answers to Selected Exercises.

Index.

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, and A Mathematical Theory of Finite Elements, all published by Wiley.