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Elasticity: Tensor, Dyadic, and Engineering Approaches (Dover Books on Engineering)

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Elasticity: Tensor, Dyadic, and Engineering Approaches (Dover Books on Engineering) Cover

 

Synopses & Reviews

Publisher Comments:

Exceptionally clear text treats elasticity from both engineering and mathematical viewpoints. Comprehensive coverage of stress, strain, equilibrium, compatibility, Hooke's law, plane problems, torsion, energy, stress functions, more. Prerequisites are a working knowledge of statics and strength of materials, plus calculus and vector analysis. Extensive problems. Bibliography. 114 illustrations. 1967 edition.

Synopsis:

Exceptionally clear text treats elasticity from both engineering and mathematical viewpoints. Stress, strain, torsion, energy, many other topics. Problems. Bibliography. 1967 edition.

Synopsis:

Written for advanced undergraduates and beginning graduate students, this exceptionally clear text treats both the engineering and mathematical aspects of elasticity. It is especially useful because it offers the theory of linear elasticity from three standpoints: engineering, Cartesian tensor, and vector-dyadic. In this way the student receives a more complete picture and a more thorough understanding of engineering elasticity. Prerequisites are a working knowledge of statics and strength of materials plus calculus and vector analysis. The first part of the book treats the theory of elasticity by the most elementary approach, emphasizing physical significance and using engineering notations. It gives engineering students a clear, basic understanding of linear elasticity. The latter part of the text, after Cartesian tensor and dyadic notations are introduced, gives a more general treatment of elasticity. Most of the equations of the earlier chapters are repeated in Cartesian tensor notation and again in vector-dyadic notation. By having access to this threefold approach in one book, beginning students will benefit from cross-referencing, which makes the learning process easier. Another helpful feature of this text is the charts and tables showing the logical relationships among the equations--especially useful in elasticity, where the mathematical chain from definition and concept to application is often long. Understanding of the theory is further reinforced by extensive problems at the end of of each chapter.

Synopsis:

Exceptionally clear text treats elasticity from engineering and mathematical viewpoints. Comprehensive coverage of stress, strain, equilibrium, compatibility, Hooke's law, plane problems, torsion, energy, stress functions, more. 114 illustrations. 1967 edition.

Table of Contents

PREFACE

INTRODUCTION

1 ANALYSIS OF STRESS

  1.1 Introduction

  1.2 "Body Forces, Surface Forces, and Stresses"

  1.3 Uniform State of Stress (Two-Dimensional)

  1.4 Principal Stresses

  1.5 Mohr's Circle of Stress

  1.6 State of Stress at a Point

  1.7 Differential Equations of Equilibrium

  1.8 Three-Dimensional State of Stress at a Point

  1.9 Summary

    Problems

2 STRAIN AND DISPLACEMENT

  2.1 Introduction

  2.2 Strain-Displacement Relations

  2.3 Compatibility Equations

  2.4 State of Strain at a Point

  2.5 General Displacements

  2.6 Principle of Superposition

  2.7 Summary

    Problems

3 STRESS STRAIN RELATIONS

  3.1 Introduction

  3.2 Generalized Hooke's Law

  3.3 Bulk Modulus of Elasticity

  3.4 Summary

    Problems

4 FORMULATION OF PROBLEMS IN ELASTICITY

  4.1 Introduction

  4.2 Boundary Conditions

  4.3 Governing Equations in Plane Strain Problems

  4.4 Governing Equations in Three-Dimensional Problems

  4.5 Principal of Superposition

  4.6 Uniqueness of Elasticity Solutions

  4.7 Saint-Venant's Principle

  4.8 Summary

    Problems

5 TWO-DIMENSIONAL PROBLEMS

  5.1 Introduction

  5.2 Plane Stress Problems

  5.3 Approximate Character of Plane Stress Equations

  5.4 Polar Coordinates in Two-Dimensional Problems

  5.5 Axisymmetric Plane Problems

  5.6 The Semi-Inverse Method

    Problems

6 TORSION OF CYLINDRICAL BARS

  6.1 General Solution of the Problem

  6.2 Solutions Derived from Equations of Boundaries

  6.3 Membrane (Soap Film) Analogy

  6.4 Multiply Connected Cross Sections

  6.5 Solution by Means of Separation of Variables

    Problems

7 ENERGY METHODS

  7.1 Introduction

  7.2 Strain Energy

  7.3 Variable Stress Distribution and Body Forces

  7.4 Principle of Virtual Work and the Theorem of Minimum Potential Energy

  7.5 Illustrative Problems

  7.6 Rayleigh-Ritz Method

    Problems

8 CARTESIAN TENSOR NOTATION

  8.1 Introduction

  8.2 Indicial Notation and Vector Transformations

  8.3 Higher-Order Tensors

  8.4 Gradient of a Vector

  8.5 The Kronecker Delta

  8.6 Tensor Contraction

  8.7 The Alternating Tensor

  8.8 The Theorem of Gauss

    Problems

9 THE STRESS TENSOR

  9.1 State of Stress at a Point

  9.2 Principal Axes of the Stress Tensor

  9.3 Equations of Equilibrium

  9.4 The Stress Ellipsoid

  9.5 Body Moment and Couple Stress

    Problems

10 "STRAIN, DISPLACEMENT, AND THE GOVERNING EQUATIONS OF ELASTICITY"

  10.1 Introduction

  10.2 Displacement and Strain

  10.3 Generalized Hooke's Law

  10.4 Equations of Compatibility

  10.5 Governing Equations in Terms of Displacement

  10.6 Strain Energy

  10.7 Governing Equations of Elasticity

    Problems

11 VECTOR AND DYADIC NOTATION IN ELASTICITY

  11.1 Introduction

  11.2 Review of Basic Notations and Relations in Vector Analysis

  11.3 Dyadic Notation

  11.4 Vector Representation of Stress on a Plane

  11.5 Equations of Transformation of Stress

  11.6 Equations of Equilibrium

  11.7 Displacement and Strain

  11.8 Generalized Hooke's Law and Navier's Equation

  11.9 Equations of Compatibility

  11.10 Strain Energy

  11.12 Governing Equations of Elasticity

    Problems

12 ORTHOGONAL CURVILINEAR COORDINATES

  12.1 Introduction

  12.2 Scale Factors

  12.3 Derivatives of the Unit Vectors

  12.4 Vector Operators

  12.5 Dyadic Notation and Dyadic Operators

  12.6 Governing Equations of Elasticity in Dyadic Notation

  12.7 Summary of Vector and Dyadic Operators in Cylindrical and Spherical Coordinates

    Problems

13 DISPLACEMENT FUNCTIONS AND STRESS FUNCTIONS

  13.1 Introduction

  13.2 Displacement Functions

  13.3 The Galerkin Vector

  13.4 The Solution of Papkovich-Neuber

  13.5 Stress Functions

    Problems

    References

INDEX

Product Details

ISBN:
9780486669588
With:
Pagano, Nicholas J.
Author:
Pagano, Nicholas J.
Author:
Engineering
Author:
Chou, Pei Chi
Author:
Chou
Publisher:
Dover Publications
Subject:
Engineering - Civil
Subject:
Engineering - General
Subject:
Material Science
Subject:
Nanostructures
Subject:
Elasticity
Subject:
Civil
Subject:
Science Reference-General
Edition Description:
Trade Paper
Series:
Dover Civil and Mechanical Engineering
Publication Date:
19920131
Binding:
TRADE PAPER
Grade Level:
General/trade
Language:
English
Illustrations:
Y
Pages:
320
Dimensions:
8.5 x 5.38 in 0.76 lb

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Elasticity: Tensor, Dyadic, and Engineering Approaches (Dover Books on Engineering) New Trade Paper
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Product details 320 pages Dover Publications - English 9780486669588 Reviews:
"Synopsis" by , Exceptionally clear text treats elasticity from both engineering and mathematical viewpoints. Stress, strain, torsion, energy, many other topics. Problems. Bibliography. 1967 edition.

"Synopsis" by , Written for advanced undergraduates and beginning graduate students, this exceptionally clear text treats both the engineering and mathematical aspects of elasticity. It is especially useful because it offers the theory of linear elasticity from three standpoints: engineering, Cartesian tensor, and vector-dyadic. In this way the student receives a more complete picture and a more thorough understanding of engineering elasticity. Prerequisites are a working knowledge of statics and strength of materials plus calculus and vector analysis. The first part of the book treats the theory of elasticity by the most elementary approach, emphasizing physical significance and using engineering notations. It gives engineering students a clear, basic understanding of linear elasticity. The latter part of the text, after Cartesian tensor and dyadic notations are introduced, gives a more general treatment of elasticity. Most of the equations of the earlier chapters are repeated in Cartesian tensor notation and again in vector-dyadic notation. By having access to this threefold approach in one book, beginning students will benefit from cross-referencing, which makes the learning process easier. Another helpful feature of this text is the charts and tables showing the logical relationships among the equations--especially useful in elasticity, where the mathematical chain from definition and concept to application is often long. Understanding of the theory is further reinforced by extensive problems at the end of of each chapter.
"Synopsis" by ,
Exceptionally clear text treats elasticity from engineering and mathematical viewpoints. Comprehensive coverage of stress, strain, equilibrium, compatibility, Hooke's law, plane problems, torsion, energy, stress functions, more. 114 illustrations. 1967 edition.
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