Elasticity : tensor, dyadic, and engineering approaches
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| Main Author | |
|---|---|
| Other Authors | |
| Format | Electronic eBook |
| Language | English |
| Published |
New York :
Dover Publications,
1992.
|
| Series | Dover books on engineering.
|
| Subjects | |
| Online Access | Full text |
| ISBN | 9781628708196 1628708190 0486669580 9780486669588 |
| Physical Description | 1 online resource (xiv, 290 pages) : illustrations |
Cover
Table of Contents:
- Machine derived contents note: 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 Vect.