Introduction to Continuum Mechanics (4th Edition)
Continuum mechanics is a branch of physical mechanics that describes the macroscopic mechanical behavior of solid or fluid materials considered to be continuously distributed. It is fundamental to the fields of civil, mechanical, chemical and bioengineering. This time-tested text has been used for o...
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| Main Authors | , , |
|---|---|
| Format | eBook Book |
| Language | English |
| Published |
Amsterdam ; Boston ; Tokyo
Elsevier
2010
Butterworth-Heinemann Elsevier Science & Technology |
| Edition | 4 |
| Subjects | |
| Online Access | Get full text |
| ISBN | 9780750685603 0750685603 |
| DOI | 10.1016/B978-0-7506-8560-3.X0001-1 |
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| Abstract | Continuum mechanics is a branch of physical mechanics that describes the macroscopic mechanical behavior of solid or fluid materials considered to be continuously distributed. It is fundamental to the fields of civil, mechanical, chemical and bioengineering. This time-tested text has been used for over 35 years to introduce junior and senior-level undergraduate engineering students, as well as graduate students, to the basic principles of continuum mechanics and their applications to real engineering problems. The text begins with a detailed presentation of the coordinate invariant quantity and the tensor, introduced as a linear transformation. |
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| AbstractList | Continuum Mechanics is a branch of physical mechanics that describes the macroscopic mechanical behavior of solid or fluid materials considered to be continuously distributed. It is fundamental to the fields of civil, mechanical, chemical and bioengineering. This time-tested text has been used for over 35 years to introduce junior and senior-level undergraduate engineering students, as well as graduate students, to the basic principles of continuum mechanics and their applications to real engineering problems. The text begins with a detailed presentation of the coordinate invariant quantity, the tensor, introduced as a linear transformation. This is then followed by the formulation of the kinematics of deformation, large as well as very small, the description of stresses and the basic laws of continuum mechanics. As applications of these laws, the behaviors of certain material idealizations (models) including the elastic, viscous and viscoelastic materials, are presented. This new edition offers expanded coverage of the subject matter both in terms of details and contents, providing greater flexibility for either a one or two-semester course in either continuum mechanics or elasticity. Although this current edition has expanded the coverage of the subject matter, it nevertheless uses the same approach as that in the earlier editions - that one can cover advanced topics in an elementary way that go from simple to complex, using a wealth of illustrative examples and problems. It is, and will remain, one of the most accessible textbooks on this challenging engineering subject.
Significantly expanded coverage of elasticity in Chapter 5, including solutions of some 3-D problems based on the fundamental potential functions approach. New section at the end of Chapter 4 devoted to the integral formulation of the field equations Seven new appendices appear at the end of the relevant chapters to help make each chapter more self-contained Expanded and improved problem sets providing both intellectual challenges and engineering applications Continuum mechanics is a branch of physical mechanics that describes the macroscopic mechanical behavior of solid or fluid materials considered to be continuously distributed. It is fundamental to the fields of civil, mechanical, chemical and bioengineering. This time-tested text has been used for over 35 years to introduce junior and senior-level undergraduate engineering students, as well as graduate students, to the basic principles of continuum mechanics and their applications to real engineering problems. The text begins with a detailed presentation of the coordinate invariant quantity and the tensor, introduced as a linear transformation. Continuum Mechanics is a branch of physical mechanics that describes the macroscopic mechanical behavior of solid or fluid materials considered to be continuously distributed.It is fundamental to the fields of civil, mechanical, chemical and bioengineering. |
| Author | Krempl, Erhard Lai, W. Michael Rubin, David |
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| Copyright | 2010 |
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| Notes | Includes bibliographical references and index |
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| Snippet | Continuum mechanics is a branch of physical mechanics that describes the macroscopic mechanical behavior of solid or fluid materials considered to be... Continuum Mechanics is a branch of physical mechanics that describes the macroscopic mechanical behavior of solid or fluid materials considered to be... |
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| SubjectTerms | Continuum mechanics General References Mechanics & Mechanical Engineering |
| TableOfContents | Title Page
Preface to the Fourth Edition
Table of Contents
1. Introduction
2. Tensors
3. Kinematics of a Continuum
4. Stress and Integral Formulations of General Principles
5. The Elastic Solid
6. Newtonian Viscous Fluid
7. The Reynolds Transport Theorem and Applications
8. Non-Newtonian Fluids
References
Index
Answers to Problems Problems for Chapter 5, Part A, Sections 5.20-5.37 (A.3) -- Problems for Chapter 5, Part A, Sections 5.38-5.46 (A.4) -- Part B: Anisotropic Linearly Elastic Solid -- 5.46 Constitutive Equations for an Anisotropic Linearly Elastic Solid -- 5.47 Plane of Material Symmetry -- 5.48 Constitutive Equation for a Monoclinic Linearly Elastic Solid -- 5.49 Constitutive Equation for an Orthotropic Linearly Elastic Solid -- 5.50 Constitutive Equation for a Transversely Isotropic Linearly Elastic Material -- 5.51 Constitutive Equation for an Isotropic Linearly Elastic Solid -- 5.52 Engineering Constants for an Isotropic Linearly Elastic Solid -- 5.53 Engineering Constants for a Transversely Isotropic Linearly Elastic Solid -- 5.54 Engineering Constants for an Orthotropic Linearly Elastic Solid -- 5.55 Engineering Constants for a Monoclinic Linearly Elastic Solid -- Problems for Part B -- Part C: Isotropic Elastic Solid Under Large Deformation -- 5.56 Change of Frame -- 5.57 Constitutive Equation for an Elastic Medium Under Large Deformation -- 5.58 Constitutive Equation for an Isotropic Elastic Medium -- 5.59 Simple Extension of an Incompressible Isotropic Elastic Solid -- 5.60 Simple Shear of an Incompressible Isotropic Elastic Rectangular Block -- 5.61 Bending of an Incompressible Isotropic Rectangular Bar -- 5.62 Torsion and Tension of an Incompressible Isotropic Solid Cylinder -- Appendix 5C.1: Representation of Isotropic Tensor-Valued Functions -- Problems for Part C -- Chapter 6: Newtonian Viscous Fluid -- 6.1 Fluids -- 6.2 Compressible and Incompressible Fluids -- 6.3 Equations of Hydrostatics -- 6.4 Newtonian Fluids -- 6.5 Interpretation of lambda and mu -- 6.6 Incompressible Newtonian Fluid -- 6.7 Navier-Stokes Equations for Incompressible Fluids -- 6.8 Navier-Stokes Equations for Incompressible Fluids in Cylindrical and Spherical Coordinates Front Cover -- Introduction to Continuum Mechanics -- Copyright Page -- Table of Contents -- Preface to the Fourth Edition -- Chapter 1: Introduction -- 1.1 Introduction -- 1.2 What is Continuum Mechanics? -- Chapter 2: Tensors -- Part A: Indicial Notation -- 2.1 Summation Convention, Dummy Indices -- 2.2 Free Indices -- 2.3 The Kronecker Delta -- 2.4 The Permutation Symbol -- 2.5 Indicial Notation Manipulations -- Problems For Part A -- Part B: Tensors -- 2.6 Tensor: A Linear Transformation -- 2.7 Components of a Tensor -- 2.8 Components of a Transformed Vector -- 2.9 Sum of Tensors -- 2.10 Product of Two Tensors -- 2.11 Transpose of A Tensor -- 2.12 Dyadic Product of Vectors -- 2.13 Trace of A Tensor -- 2.14 Identity Tensor and Tensor Inverse -- 2.15 Orthogonal Tensors -- 2.16 Transformation Matrix Between Two Rectangular Cartesian Coordinate Systems -- 2.17 Transformation Law for Cartesian Components of A Vector -- 2.18 Transformation Law for Cartesian Components of a Tensor -- 2.19 Defining Tensor by Transformation Laws -- 2.20 Symmetric and Antisymmetric Tensors -- 2.21 The Dual Vector of an Antisymmetric Tensor -- 2.22 Eigenvalues and Eigenvectors of a Tensor -- 2.23 Principal Values and Principal Directions of Real Symmetric Tensors -- 2.24 Matrix of a Tensor with Respect to Principal Directions -- 2.25 Principal Scalar Invariants of a Tensor -- Problems for Part B -- Part C: Tensor Calculus -- 2.26 Tensor-Valued Functions of a Scalar -- 2.27 Scalar Field and Gradient of a Scalar Function -- 2.28 Vector Field and Gradient of a Vector Function -- 2.29 Divergence of a Vector Field and Divergence of a Tensor Field -- 2.30 Curl of a Vector Field -- 2.31 Laplacian of a Scalar Field -- 2.32 Laplacian of a Vector Field -- Problems for Part C -- Part D: Curvilinear Coordinates -- 2.33 Polar Coordinates -- 2.34 Cylindrical Coordinates 4.6 Maximum Shearing Stresses -- 4.7 Equations of Motion: Principle of Linear Momentum -- 4.8 Equations of Motion in Cylindrical and Spherical Coordinates -- 4.9 Boundary Condition for the Stress Tensor -- 4.10 Piola Kirchhoff Stress Tensors -- 4.11 Equations of Motion Written with Respect to the Reference Configuration -- 4.12 Stress Power -- 4.13 Stress Power in Terms of the Piola-Kirchhoff Stress Tensors -- 4.14 Rate of Heat Flow into a Differential Element by Conduction -- 4.15 Energy Equation -- 4.16 Entropy Inequality -- 4.17 Entropy Inequality in Terms of the Helmholtz Energy Function -- 4.18 Integral Formulations of the General Principles of Mechanics -- Appendix 4.1: Determination of Maximum Shearing Stress and the Planes on Which It Acts -- Problems for Chapter 4 -- Chapter 5: The Elastic Solid -- 5.1 Mechanical Properties -- 5.2 Linearly Elastic Solid -- Part A: Isotropic Linearly Elastic Solid -- 5.3 Isotropic Linearly Elastic Solid -- 5.4 Young's Modulus, Poisson's Ratio, Shear Modulus, and Bulk Modulus -- 5.5 Equations of the Infinitesimal Theory of Elasticity -- 5.6 Navier Equations of Motion for Elastic Medium -- 5.7 Navier Equations in Cylindrical and Spherical Coordinates -- 5.8 Principle of Superposition -- A.1 Plane Elastic Waves -- 5.9 Plane Irrotational Waves -- 5.10 Plane Equivoluminal Waves -- 5.11 Reflection of Plane Elastic Waves -- 5.12 Vibration of an Infinite Plate -- A.2 Simple Extension, Torsion, and Pure Bending -- 5.13 Simple Extension -- 5.14 Torsion of a Circular Cylinder -- 5.15 Torsion of a Noncircular Cylinder: St. Venant's Problem -- 5.16 Torsion of Elliptical Bar -- 5.17 Prandtl's Formulation of the Torsion Problem -- 5.18 Torsion of a Rectangular Bar -- 5.19 Pure Bending of a Beam -- A.3 Plane Stress and Plane Strain Solutions -- 5.20 Plane Strain Solutions -- 5.21 Rectangular Beam Bent by End Couples 5.22 Plane Stress Problem -- 5.23 Cantilever Beam with End Load -- 5.24 Simply Supported Beam Under Uniform Load -- 5.25 Slender Bar Under Concentrated Forces and St. Venant's Principle -- 5.26 Conversion for Strains Between Plane Strain and Plane Stress Solutions -- 5.27 Two-Dimensional Problems in Polar Coordinates -- 5.28 Stress Distribution Symmetrical About an Axis -- 5.29 Displacements for Symmetrical Stress Distribution in Plane Stress Solution -- 5.30 Thick-Walled Circular Cylinder Under Internal and External Pressure -- 5.31 Pure Bending of a Curved Beam -- 5.32 Initial Stress in a Welded Ring -- 5.33 Airy Stress Function phivf(r)cosntheta and phivf(r)sinntheta -- 5.34 Stress Concentration Due to a Small Circular Hole in a Plate Under Tension -- 5.35 Stress Concentration Due to a Small Circular Hole in a Plate Under Pure Shear -- 5.36 Simple Radial Distribution of Stresses in a Wedge Loaded at the Apex -- 5.37 Concentrated Line Load on a 2-D Half-Space: the Flamont Problem -- A.4 Elastostatic Problems Solved with Potential Functions -- 5.38 Fundamental Potential Functions for Elastostatic Problems -- 5.39 Kelvin Problem: Concentrated Force at the Interior of an Infinite Elastic Space -- 5.40 Boussinesq Problem: Normal Concentrated Load on an Elastic Half-Space -- 5.41 Distributive Normal Load On The Surface Of An Elastic Half-Space -- 5.42 Hollow Sphere Subjected to Uniform Internal and External Pressure -- 5.43 Spherical Hole in a Tensile Field -- 5.44 Indentation by a Rigid Flat-Ended Smooth Indenter on an Elastic Half-Space -- 5.45 Indentation by a Smooth Rigid Sphere on an Elastic Half-Space -- Appendix 5A.1: Solution of the Integral Equation in Section 5.45 -- Problems for Chapter 5, Part A, Sections 5.1-5.8 -- Problems for Chapter 5, Part A, Sections 5.9-5.12 (A.1) -- Problems for Chapter 5, Part A, Sections 5.13-5.19 (A.2) 2.35 Spherical Coordinates -- Problems for Part D -- Chapter 3: Kinematics of a Continuum -- 3.1 Description of Motions of a Continuum -- 3.2 Material Description and Spatial Description -- 3.3 Material Derivative -- 3.4 Acceleration of a Particle -- 3.5 Displacement Field -- 3.6 Kinematic Equation for Rigid Body Motion -- 3.7 Infinitesimal Deformation -- 3.8 Geometrical Meaning of the Components of the Infinitesimal Strain Tensor -- 3.9 Principal Strain -- 3.10 Dilatation -- 3.11 The Infinitesimal Rotation Tensor -- 3.12 Time Rate of Change of a Material Element -- 3.13 The Rate of Deformation Tensor -- 3.14 The Spin Tensor and the Angular Velocity Vector -- 3.15 Equation of Conservation of Mass -- 3.16 Compatibility Conditions for Infinitesimal Strain Components -- 3.17 Compatibility Condition for Rate of Deformation Components -- 3.18 Deformation Gradient -- 3.19 Local Rigid Body Motion -- 3.20 Finite Deformation -- 3.21 Polar Decomposition Theorem -- 3.22 Calculation of Stretch and Rotation Tensors from the Deformation Gradient -- 3.23 Right Cauchy-Green Deformation Tensor -- 3.24 Lagrangian Strain Tensor -- 3.25 Left Cauchy-Green Deformation Tensor -- 3.26 Eulerian Strain Tensor -- 3.27 Change of Area Due to Deformation -- 3.28 Change of Volume Due to Deformation -- 3.29 Components of Deformation Tensors in Other Coordinates -- 3.30 Current Configuration as the Reference Configuration -- Appendix 3.1: Necessary and Sufficient Conditions for Strain Compatibility -- Appendix 3.2: Positive Definite Symmetric Tensors -- Appendix 3.3: The Positive Definite Root of U2 = D -- Problems for Chapter 3 -- Chapter 4: Stress and Integral Formulations of General Principles -- 4.1 Stress Vector -- 4.2 Stress Tensor -- 4.3 Components of Stress Tensor -- 4.4 Symmetry of Stress Tensor: Principle of Moment of Momentum -- 4.5 Principal Stresses 6.9 Boundary Conditions |
| Title | Introduction to Continuum Mechanics (4th Edition) |
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