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854 p, Soft Cover,
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About The Book
Table Of Contents
About The Author
The fundamental concepts of continuum mechanics have been widely used at various stages in the study of solid mechanics, fluid mechanics, geomechanics and material engineering. The basic concepts of continuum mechanics are used in their simpler form for initial analysis before preliminary design of engineering structures and the advanced principles are used for complex analysis before final design. Many of the undergraduate and graduate courses employ the concepts of continuum mechanics as the basis for further development of engineering principles. Therefore, it is necessary as a first step to understand clearly the basic principles and corresponding mathematical expressions involved in continuum mechanics. Since the solutions to most of the engineering problems are obtained by solving the governing equations, it is imperative that one should learn the origin of such equations and the basis on which they have been derived. For this reason, attention has been given in this book to present the derivations of various fundamental equations in an extensive manner. Key Features: * Explains the complex theory, in a very lucid way, to enable an average student to understand the basic principles * Key concepts to help the instructor to deliver the lecture in a better way * Large number of worked examples * Objective type questions to test the students' understanding of the subject * Chapter end review questions to enhance problem solving ability.
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 linear 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 2.5 Differential equation of equilibrium in a general three-dimensional stress system 2.6 Stress on a general plane 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 3.8 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 behaviour 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 5.2 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-Venants' principle 6.4 Two-dimensional problems in Cartesian coordinate 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 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 12.4 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 13.4 Determination of factor 'k' for various sections 13.5 Resultant stress in a curved bar subjected to direct stresses and bending stresses Summary Review questions CHAPTER 14 SHEAR CENTRE 14.1 Introduction 14.2 Shear flow 14.3 Principle involved in finding the shear centre 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 17.6 Description of fluid motion 17.7 Fundamentals of flow visualization Summary Review questions CHAPTER 18 FLOW EQUATIONS-CONTINUITY EQUATIONS 18.1 System and control volume 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 Vθ 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) 22.3 Source flow (q or m) 22.4 Sink flow (-q or -m) 22.5 Free vortex flow 22.6 Superimposed flow 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 8 CHAPTER 23 REAL FLUID FLOW 23.1 Introduction 23.2 Navier-Stokes' equation 23.3 Exact solutions of Navier-Stokes' equations 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 OBJECTIVE QUESTIONS ABBREVIATIONS BIBLIOGRAPHY INDEX
Dr. P. N. Chandramouli is Professor in Department of Civil Engineering, The National Institute of Engineering, Mysore. He received his B.E in Civil Engineering from University of Mysore, M.E from Indian Institute of Science, Bangalore and Ph.D from Indian Institute of Technology, Roorkee. He has over 27 years of teaching experience at The National Institute of Engineering. He is a member of ISTE.
Students of Mechanical and Civil Engineering
Mechanical and Civil Engineering
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