Elasticity: Tensor, Dyadic and Engineering Aproaches

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Overview

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.

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Product Details

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
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