The Linearized Theory of Elasticity / Edition 1

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Overview

The linearized theory of elasticity has long played an important role in engineering analysis. From the cast-iron and steel truss bridges of the eighteenth century to the international Space station, engineers have used the linearized theory of elasticity to help guide them in making design decisions effecting the strength, stiffness, weight, and cost of structures and components.

The Linearized Theory of Elasticity is a modern treatment of the linearized theory of elasticity, presented as a specialization of the general theory of continuum mechanics. It includes a comprehensive introduction to tensor analysis, a rigorous development of the governing field equations with an emphasis on recognizing the assumptions and approximations inherent in the linearized theory, specification of boundary conditions, and a survey of solution methods for important classes of problems. It covers two- and three-dimensional problems, torsion of noncircular cylinders, variational methods, and complex variable methods.

The mathematical framework behind the theory is developed in detail, with the assumptions behind the eventual linearization made clear, so that the reader will be adequately prepared for further studies in continuum mechanics, nonlinear elasticity, inelasticity, fracture mechanics, and/or finite elements. Prior to linearization, configurations and general (finite deformation) measures of strain and stress are discussed. A modern treatment of the theory of tensors and tensor calculus is used. General curvilinear coordinates are described in an appendix.

An extensive treatment of important solutions and solution methods, including the use of potentials, variational methods, and complex variable methods, follows the development of the linearized theory. Special topics include antiplane strain, plane strain/stress, torsion of noncircular cylinders, and energy minimization principles. Solutions for dislocations, inclusions, and crack-tip stress fields are discussed. Development of the skills and physical insight necessary for solving problems is emphasized. In presenting solutions to problems, attention is focused on the line of reasoning behind the solution.

Topics and Features:

* Can be used without prerequisite course in continuum mechanics

* Includes over one hundred problems

* Maintains a clear connection between linearized elasticity and the general theory of continuum mechanics

* Introduces theory in the broader context of continuum mechanics prior to linearization, providing a strong foundation for further studies

* Promotes the development of the skills and physical intuition necessary for deriving analytic solutions

* Provides readers with tools necessary to solve original problems through extensive coverage of solution methods

The book is ideal for a broad audience including graduate students, professionals, and researchers in the field of solid mechanics. This new text/reference is an excellent resource designed to introduce students in mechanical or civil engineering to the linearized theory of elasticity.

"...an advanced introduction to the linearized theory of elasticity using a problem solving approach & offering the reader complete solutions to aid in gaining a solid understanding of the different solution methods."

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Editorial Reviews

From the Publisher

"There is a good balance between theory and practical applications…[the] approach acknowledges the basic concepts of continuum mechanics without burdening the presentation with excessive generalities. The assumptions required to obtain linear results from nonlinear results are clearly described. This enables students to clearly understand the limitations of linear results…the book includes a good range of discussion and examples…to motivate and complement the theory…[it] is written in a clear style…[and] can be recommended as a good example of a modern textbook in this field." —Applied Mechanics Review

"This very accessible book will be of interest in teaching or learning linear elasticity." —Zentralblatt Math

"The book presents classical parts of the linearized theory of elasticity in a selfcontained way that seems to be a fine compromise between the necessity of a deep mathematical insight and the accessibility of exposition. The author points out that the book is intended as a text for a first-year graduate course in mechanical or civil engineering. ...Many figures and solved examples contribute to the clarity of exposition. Moreover, each chapter finishes with a subsection of unresolved problems, hints being often given. The material in the book is well organized, presented in a lucid way, and can reach a fairly broad audience spanning from advanced undergraduate students to graduate students. Professionals and researchers may enjoy this book for its clarity and instructive examples, as well as a refreshing reminder of the classical results of the linearized theory of elasticity." —Applications of Mathematics

"This book is a modern treatment of the linearized theory of elasticity, presented as a specialization of the general theory of continuum mechanics. It is derived from notes used by the author in teaching a first-year graduate-level course in elasticity…. Presented [are] various results connected to functions of a complex variable, strain, plane strain/stress, etc.… Each chapter ends with a useful list of problems.

The book is clearly written, with rigorous presentation, in a pleasant and accessible style. This new text is an excellent resource devoted to introduce the students in mechanical or civil engineering to the linearized theory of elasticity. It is warmly recommended to all researchers in the field." —Revue D’Analyse Numérique et de Théorie de L’Approximation

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Product Details

  • ISBN-13: 9780817641177
  • Publisher: Birkhauser Verlag
  • Publication date: 12/14/2001
  • Edition description: 2002
  • Edition number: 1
  • Pages: 543
  • Product dimensions: 9.21 (w) x 6.14 (h) x 1.25 (d)

Table of Contents

Preface
List of Figures
List of Tables
1 Review of Mechanics of Materials 1
2 Mathematical Preliminaries 23
3 Kinematics 97
4 Forces and Stress 157
5 Constitutive Equations 193
6 Linearized Elasticity Problems 221
7 Two-Dimensional Problems 255
8 Torsion of Noncircular Cylinders 305
9 Three-Dimensional Problems 331
10 Variational Methods 387
11 Complex Variable Methods 431
App General Curvilinear Coordinates 513
References 533
Index 537
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