Download Introduction to Solid Mechanics

Introduction to Solid Mechanics
Contents
Chapter 0 Introduction
0.1
Solid mechanics
0.2
Structural mechanics
Chapter 1 Mathematical Preliminaries
1.1
Index notation
1.1.1
Summation convention
1.1.2
Krönecker delta
1.1.3
Alternating symbol (permutation symbol)
1.1.4
Relationship between alternating symbol and Krönecker delta
1.2
Vectors
1.2.1
Rectangular Cartesian coordinate systems
1.2.2
Scalar product (dot product) of two vectors
1.2.3
Vector product (cross product) of two vectors
1.2.4
Change of basis
1.2.5
The tensor product (dyadic product) of two vectors
1.3
Cartesian tensors
1.3.1
Contraction
1.4
Eigenvalues and eigenvectors
1.5
Vector and tensor calculus
1.5.1
Divergence theorem
Chapter 2 Stress and Strain
2.1
Introduction
2.2
Force distribution and stresses
2.3
Traction vector
2.4
Equations of equilibrium
2.5
Stress tensor
2.6
Principal stress components and principal axes of stress
2.7
Stationary shear stresses
2.8
Some commonly used definitions of stresses
2.8.1
Octahedral shear stress
2.8.2
Stress deviator
2.8.3
Von Mises stress
2.9
Strain tensor
2.10 Rigid - body displacement components in rectangular Cartesian coordinates
2.11 Compatibility conditions
2.12 Cylindrical polar coordinates
2.13 Rigid - body displacement components in cylindrical coordinates
2.14 Equilibrium equations in cylindrical coordinates
Chapter 3 Linear Elasticity
3.1
Introduction
3.2
Material symmetry and Hooke's law
3.3
Isotropic elastic materials
3.4
Solution schemes
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Chapter 4 Elastostatic Plane Problems
4.0
Classification of two-dimensional elasticity problems
4.0.1
In-plane problems
4.0.2
Antiplane shear
4.1
Combined Hooke's law for in-plane problems
4.2
Airy stress functions for isotropic elastic plane problems
4.3
Isotropic elastic plane problems in cylindrical coordinates
4.3.1
Michell solution
Table 4.1 Stress functions, stresses and displacements in polar coordinates
4.4
Examples of infinite plane problems
4.4.1
Uniform tension in x1 -direction
4.4.2
Infinite plane under uniform tension disturbed by circular hole (Kirsch, 1898)
4.4.3
Infinite plane subjected to a uniform body force in a circular region
4.4.4
Infinite plane subjected to a concentrated force
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