Table of Content
PREFACE
ACKNOWLEDGEMENTS
CONTENTS AND COVERAGE
CHAPTER 1 INTRODUCTION TO CONTINUUM MECHANICS
1.1 Overview of continuum mechanics
1.2 Background of continuum mechanics
1.3 Overview of theory of elasticity
1.4 Differences between elementary theory and
Theory of elasticity
1.5 Procedure to be followed in theory of elasticity
1.6 Conditions applied in theory of elasticity
1.7 Assumptions made in elementary theory and
Theory of elasticity
1.8 Classification of materials
1.9 Applications of elasticity
1.10 Overview of fluid dynamics
Review questions
CHAPTER 2 THE STRESS FIELD
2.1 Introduction
2.2 Types of forces
2.3 Concept of three-dimensional stress
2.4 General state of stress on an element
2.4.1 Sign conventions
2.4.2 Index notation
2.4.3 Two-dimensional state of stress
2.5 Differential equation of equilibrium in a general
Three-dimensional stress system
2.6 Stress on a general plane
2.6.1 Direction cosines
2.6.2 Axis transformation
2.6.3 Stress on oblique plane through a point
(Cauchy’s Formula)
2.6.4 Stress transformation
2.7 Principal stresses and planes
2.8 Boundary conditions
Summary
Review questions
CHAPTER 3 THE DISPLACEMENT FIELD AND STRAIN FIELD
3.1 Introduction
3.2 Elementary concept of strain
3.3 Strain displacement relation
3.4 Strain at a point
3.5 Strain components at a given point in any direction
3.6 Principle strains and their directions
3.7 Strain rosettes
3.7.1 Rectangular strain rosette
3.7.2 Delta rosette
3.8 Mohr’s circle of strain
Summary
Review questions
CHAPTER 4 CONSTITUTIVE RELATIONS
4.1 Introduction
4.2 Response model
4.3 1-D Hooke’s law
4.4 Generalized Hooke’s law (Anisotropic Form)
4.5 Non-isotropic linear elastic behavior
4.6 Stress-strain relation for isotropic material
4.7 Stress-strain relation for orthotropic material
4.8 Stress-strain relation for transverse isotropic material
Review questions
CHAPTER 5 TWO-DIMENSIONAL PROBLEMS OF ELASTICITY
5.1 Introduction
5.1.1 Two-dimensional state of stress
5.1.2 Two-dimensional state of strain
5.2 Plane stress problems
5.3 Plane strain problems
5.4 Equation of compatibility
5.5 Mathematical conditions of compatibility
Summary
Review questions
CHAPTER 6 TWO-DIMENSIONAL PROBLEMS IN CARTESIAN
COORDINATE SYSTEM
6.1 Introduction
6.2 Airy’s stress functions
6.3 Saint-Venaunts’ principle
6.4 Two-dimensional problems in Cartesian coordinate
6.4.1 Airy’s stress function method
6.4.2 Solution by polynomials
6.5 Solution for bending of a cantilever loaded at the
free end using stress function as a polynomial
6.6 Bending of a beam by uniform load using
the stress function as a polynomial
Summary
Review questions
CHAPTER 7 TWO-DIMENSIONAL PROBLEMS IN POLAR
COORDINATES SYSTEM
7.1 Introduction
7.2 Two-dimensional differential equation of equilibrium
in polar coordinates
7.3 Derivations of Airy’s stress function in
polar coordinates
7.4 Stress-strain relationship in polar coordinates
7.5 Strain displacement relations
7.6 Compatibility equation
7.7 Stresses due to concentrated loads
7.8 Bending of a curved bar by a force at the end
7.9 Semi-infinite medium loaded with a concentrated
force at the boundary
Summary
Review questions
CHAPTER 8 AXI-SYMMETRIC STRESS DISTRIBUTION
8.1 Introduction
8.2 Plane stress and plane strain
8.3 Compatibility equation for axi-symmetric case
8.4 Rotating circular disc 237
8.5 Thick cylinder subjected to internal and external
radial pressure or Lame’s problem
8.6 Pure bending of curved bars
Summary
Review questions
CHAPTER 9 TORSION ON PRISMATIC BARS
9.1 Introduction
9.2 Saint-Venants’ theory
9.3 Torsion of elliptical cross-section
9.4 Torsion of equilateral triangle cross-section bar
Summary
Review questions
CHAPTER 10 THEOREMS OF ELASTICITY
10.1 Introduction
10.2 Uniqueness theorem
10.3 Principle of superposition
10.4 Method of virtual work and minimum potential
energy principle of elasticity
10.5 Complimentary strain energy
10.6 The Crotti-Engesser theorem
10.7 Castigliano’s theorem
10.8 Maxwell reciprocal theorem
10.9 Clapeyron’s theorem in linear elastic theory
Review questions
CHAPTER 11 STRESS CONCENTRATION
11.1 Introduction
11.2 Stresses concentration around circular hole
Review questions
CHAPTER 12 STRESSES DUE TO ROTATION
12.1 Introduction
12.2 Rotational stresses in thin cylinder or rotating ring
12.3 Expression for stresses in a rotating thin disc
12.3.1 Expression for radial and circumferential
stresses in a solid disc
12.3.2 Expression for radial and circumferential
stresses for disc with central hole
12.4 Disc of uniform strength
12.5 Long cylinders
Summary
Review questions
CHAPTER 13 CURVED BEAMS
13.1 Introduction
13.2 Assumptions made in the derivation
of stresses in a curved bar
13.3 Expression for stresses in a curved bar
13.3.1 To fi nd the position of neutral axis
13.4 Determination of factor ‘k’ for various sections
13.4.1 Rectangular section
13.4.2 Triangular section
13.4.3 Trapezoidal section
13.4.4 Circular section
13.4.5 T-section
13.4.6 I-section
13.5 Resultant stress in a curved bar subjected to
direct stresses and bending stresses
13.5.1 Resultant stress in a hook
13.5.2 Stresses in circular ring
13.5.3 Stresses in a chain link
Summary
Review questions
CHAPTER 14 SHEAR CENTRE
14.1 Introduction
14.2 Shear flow
14.3 Principle involved in finding the shear centre
14.3.1 Shear centre for a channel section
14.3.2 Shear centre for unequal I-section
14.3.3 Shear centre for an angle section
14.3.4 T-Section
14.3.5 I-Section
14.3.6 Half thin walled cylindrical section
Summary
Review questions
CHAPTER 15 UNSYMMETRICAL BENDING
15.1 Introduction
15.2 Product of inertia for an area
15.3 Parallel – axis theorem
15.4 Moment of inertia of an area about inclined axes
15.5 Principal moments of inertia
15.6 Shear centre (unsymmetrical sections)
15.7 Unsymmetrical bending
15.8 Determination of bending stress through product
of inertia
Summary
Review questions
CHAPTER 16 FLUID STATICS
16.1 Fluid flow concepts
16.2 Continuum concept
16.3 Fundamental concepts
16.4 Stress relationships at a point in a fluid
16.5 Pressure at a point
16.6 Pressure variation in an incompressible static fluid
16.7 Pressure variation in a compressible fluid
Summary
Review questions
CHAPTER 17 KINEMATICS
17.1 Introduction
17.2 Relation between the local and individual
time rates
17.3 Acceleration
17.4 Scalar, vector and tensor quantities – fields
17.5 Types of fluid flow
17.5.1 Three-, two- and one-dimensional flow
17.5.2 Steady and unsteady flows
17.5.3 Uniform and non-uniform flow
17.5.4 Laminar and turbulent flows
17.5.5 Compressible and incompressible flow
17.5.6 Rotational and irrotational flow
17.5.7 Ideal and real fluid flow
17.6 Description of fluid motion
17.6.1 Components of acceleration in other
coordinate systems
17.7 Fundamentals of flow visualization
Summary
Review questions
CHAPTER 18 FLOW EQUATIONS-CONTINUITY EQUATIONS
18.1 System and control volume
18.1.1 Intensive and extensive properties
18.2 Control volume transformation equation
18.3 Continuity equation for a control volume
18.4 Continuity equation for an infinitesimal control
volume
18.5 Mass conservation (or continuity) equation
along a stream tube
18.6 Three dimensional continuity equation in
Cartesian coordinates
18.7 Equation of continuity in the Lagrangian method
18.8 Equivalence of the two forms of the equation
of continuity
18.9 Equation of continuity in polar coordinates
18.10 Continuity equation in cylindrical polar coordinates
18.11 Continuity equation in spherical coordinates
18.12 Conservation of mass in orthogonal
curvilinear coordinates
Summary
Review questions
CHAPTER 19 FLOW EQUATIONS
19.1 Euler’s equation of motion
19.2 Energy equation
19.3 Boundary surface
19.4 Momentum equation
19.5 Control volume momentum equation
19.6 Law of conservation of angular momentum or
law of conservation of momentum of momentum
19.7 Equation of motion under impulsive forces
19.8 Kinetic energy and momentum correction factors
(Coriolis coefficients)
Summary
Review questions
CHAPTER 20 CIRCULATION AND ROTATION
20.1 Circulation
20.2 Energy dissipation, shear deformation and
rotationality
Summary
Review questions
CHAPTER 21 SCALAR FUNCTIONS
21.1 Potential function
21.2 Stream function
21.3 Cauchy Riemann equation
21.4 Relationship between stream function ψ and
the velocity components Vr and V in cylindrical
polar coordinates
21.5 Orthogonality of stream lines and potential lines
Summary
Review questions
CHAPTER 22 POTENTIAL FLOW
22.1 Introduction
22.2 Uniform flow (u or u0)
22.2.1 Uniform flow parallel to x –axis
22.2.2 Uniform flow parallel to y-axis
22.3 Source flow (q or m)
22.4 Sink flow (-q or -m)
22.5 Free vortex flow
22.6 Super-imposed flow
22.6.1 Source–sink pair
22.6.2 Source kept near a wall (Method of image)
22.6.3 A plane source in a uniform flow/ source
placed in a rectilinear flow/flow past
a half body
22.6.4 Doublet
22.6.5 A source and a sink pair in a uniform
flow/flow past a Rankine oval shape
22.6.6 A doublet in a uniform flow
(Flow past a circular cylinder)
22.6.7 Flow past a circular cylinder
with circulation
22.7 Drag and lift
22.8 To find drag and lift in the case of a circular cylinder
without circulation
22.9 To find drag and lift in the case of circular cylinder
with circulation
Summary
Review questions
CHAPTER 23 REAL FLUID FLOW
23.1 Introduction
23.1.1 Classification of viscous flow
23.1.2 Relation between shear and pressure
gradient in laminar flow
23.2 Navier-Stokes’ equation
23.3 Exact solutions of Navier-Stokes’ equations
23.3.1 Flow through a circular pipe
(Hagen-Poiseuille theory)
23.3.2 Flow of viscous fluid between two parallel
stationary plates
23.3.3 Flow of viscous fluid between two parallel
plates, if one plate is moving with a
constant velocity
Summary
Review questions
CHAPTER 24 APPLICATION OF COMPLEX VARIABLES TO
TWO-DIMENSIONAL FLUID FLOW
24.1 Introduction
24.2 Complex number
24.3 De Moivre’s theorem
24.4 Conjugate complex number
24.5 The logarithm of a complex number
24.6 Functions of complex variable
24.7 Relation of functions of a complex variable to
irrotational flow
24.8 Conformal transformation
24.9 Simple conformal transformation
24.10 Complex potential for a source
24.11 Complex potential for vortex
24.12 Complex potential for a doublet
24.13 Image in two-dimensions
24.13.1 Image of a source with regard to a line
24.14 Source and sink of equal strength
24.15 Steady flow around a circular cylinder
without circulation
24.16 Circulation about a circular cylinder
24.17 Flow past a circular cylinder with circulation
24.18 Milne Thomson method to determine complex
function
24.19 Blasius theorem
24.20 Theorem of Kutta and Joukowski
Summary
Review questions
OBJECTIVE QUESTIONS
ABBREVIATIONS
BIBLIOGRAPHY
INDEX
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