Theory and Practice of Solid Mechanics

ISBN-13: 9781461342793 / Angielski / Miękka / 2011 / 282 str.

Thomas Dawson

Opis

This book is intended for use by engineers and scientists who have a need for an introduction to advanced topics in solid mechanics. It deals with modern concepts of continuum mechanics as well as with details of the classical theories of elasticity, thermal elasticity, viscous elasticity, and plasticity of solids. The book assumes no prior knowledge of the mechanics of solids and develops the subject entirely from first principles. Rigorous derivations of governing equations are also followed by applications to a number of basic and practical problems. Cartesian tensors are used throughout the book to express mathematical concepts in a clear and concise fashion. Chapter I, accordingly, provides a discussion of this topic for those readers not already familiar with it. This material is then followed by detailed discussions in Chapters 2 and 3 of the kinematics of continuum motion and the fundamental principles of mass conservation and momentum balance. Unlike traditional treatments, this material is first developed for the general large-deformation case and only then restricted to small deformations for use in the usual engineering appli cations. In this way the reader thus gets a fuller picture of the basic governing relations of solid mechanics."

Spis treści

I General Principles.- 1 Vectors and Cartesian Tensors.- 1.1. Scalars and Vectors.- 1.2. Coordinate Transformations.- 1.3. Orthogonality Relations.- 1.4. Addition of Vectors and Multiplication by a Scalar.- 1.5. Scalar and Vector Products of Two Vectors.- 1.6. Definition of Cartesian Tensors.- 1.7. Addition of Cartesian Tensors.- 1.8. Multiplication of Cartesian Tensors.- 1.9. Quotient Rule for Second-Order Tensors.- 1.10. Symmetric and Antisymmetric Tensors.- 1.11. Antisymmetric Tensor Components.- 1.12. Eigenvalues and Eigenvectors of Symmetric Tensors.- 1.13. Principal Axes of a Symmetric Tensor.- Selected Reading.- Exercises.- 2 Kinematics of Continuum Motion.- 2.1. Material and Spatial Variables.- 2.2. Definitions of Displacement, Velocity, and Acceleration.- 2.3. Deformation Gradients.- 2.4. Stretch and Angular Distortion of Line Elements.- 2.5. Condition for Rigid-Body Motion of Material about a Point.- 2.6. Decomposition of Deformation Gradients.- 2.7. General Motion of Material in the Neighborhood of a Point.- 2.8. Approximations Valid for Small Deformations.- 2.9. Motion in the Neighborhood of a Point for Small Deformations.- 2.10. Geometric Interpretation of Strain and Rotation Components of Small Deformation.- 2.11. Examples of Small Deformation.- 2.12. Unabridged Notation.- 2.13. Cylindrical Polar Coordinates.- Selected Reading.- Exercises.- 3 Governing Equations of Motion.- 3.1. Conservation of Mass.- 3.2. Balance of Linear Momentum.- 3.3. Balance of Angular Momentum.- 3.4. Evaluation of Time Derivative of Volume Integral.- 3.5. Green’s Theorem.- 3.6. The Stress Vector.- 3.7. The Stress Tensor.- 3.8. Change of Stress Components with Rigid Rotations.- 3.9. Local Form of Mass Conservation.- 3.10. Local Form of Linear Momentum Balance.- 3.11. Local Form of Angular Momentum Balance.- 3.12. Some Simple Examples of Stress.- 3.13. Stress Boundary Conditions.- 3.14. Approximations Valid for Small Deformations.- 3.15. Unabridged Notation.- 3.16. Cylindrical Polar Coordinates.- Selected Reading.- Exercises.- II Classical Elasticity.- 4 Theory of Elasticity.- 4.1. Constitutive Relations for an Elastic Solid.- 4.2. Restrictions Placed on Constitutive Relations by Principle of Material Indifference.- 4.3. Material Symmetry Restrictions on the Constitutive Relations.- 4.4. Elastic Constitutive Relations Applicable to Small Deformations.- 4.5. Restriction on Elastic Constants Due to Existence of a Strain Energy Function.- 4.6. Restrictions on Elastic Constants Due to Material Symmetries.- 4.7. Constitutive Relations for Isotropic Elastic Materials.- 4.8. Alternate Form of Elastic Constitutive Relations.- 4.9. Governing Equations for Linear Elastic Deformation of an Isotropic Solid.- Selected Reading.- Exercises.- 5 Problems in Elasticity.- 5.1. Longitudinal and Transverse Elastic Waves.- 5.2. Static Twisting of Rods and Bars.- 5.3. Saint-Venant’s Principle.- 5.4. Compatibility Equations.- 5.5. Plane Strain and Plane Stress.- 5.6. Bending of a Thin Beam by Uniform Loading.- 5.7. Equations for Plane Strain and Plane Stress in Polar Coordinates.- 5.8. Thick-Walled Cylinder under Internal Pressure.- 5.9. Circular Hole in a Strained Plate.- 5.10. Strength-of-Material Formulations.- 5.11. Bending and Extension of Beams.- 5.12. Bending and Extension of Thin Rectangular Plates.- 5.13. Axisymmetric Bending and Extension of Thin Cylindrical Shells.- Selected Reading.- Exercises.- III Thermal Elasticity.- 6 Theory of Thermal Elasticity.- 6.1. First Law of Thermodynamics.- 6.2. Second Law of Thermodynamics.- 6.3. Definition of a Thermoelastic Solid.- 6.4. Restrictions Placed on Constitutive Relations by the Second Law of Thermodynamics.- 6.5. Restrictions Placed on Constitutive Relations by Principle of Material Indifference.- 6.6. Restriction to Small Deformations and Small Temperature Changes.- 6.7. Restriction to Isotropic Materials.- 6.8. Governing Equations for Linear Thermoelastic Deformation of an Isotropic Solid.- Selected Reading.- Exercises.- 7 Problems in Thermal Elasticity.- 7.1. Thermoelastic Vibrations.- 7.2. Periodic Temperature Variation on the Boundary of a Thermoelastic Half-Space.- 7.3. Plane Strain and Plane Stress Thermoelastic Problems.- 7.4. Thermal Stresses in a Thin Elastic Strip.- 7.5. Plane Strain and Plane Stress Equations in Polar Coordinates.- 7.6. Hollow Circular Cylinder with Elevated Bore Temperature.- 7.7. Thermal Effects in Beam Deformations.- Selected Reading.- Exercises.- IV Viscous Elasticity.- 8 Theory of Viscous Elasticity.- 8.1. Definition of a Standard Viscoelastic Solid.- 8.2. Restrictions Placed by Principle of Material Indifference.- 8.3. Restriction to Small Deformations.- 8.4. Restriction to Isotropic Materials.- 8.5. Reduction of Constitutive Relations for Special Cases.- 8.6. Governing Equations for Linear Viscoelastic Deformation of an Isotropic Solid.- Selected Reading.- Exercises.- 9 Problems in Viscous Elasticity.- 9.1. Free Vibration of a Standard Viscoelastic Solid.- 9.2. Time-Dependent Uniaxial Response of a Standard Viscoelastic Solid.- 9.3. Hollow Circular Cylinder of Kelvin-Voigt Material Subjected to Periodic Bore Pressure.- 9.4. Viscous Effects in Beam Deformations.- 9.5. Viscoelastic Correspondence Principle.- 9.6. Laterally Constrained Bar.- Selected Reading.- Exercises.- V Plasticity.- 10 Theory of Plasticity.- 10.1. Definition of an Elastic-Plastic Solid.- 10.2. Restrictions Placed by Principle of Material Indifference.- 10.3. Restriction to Quasilinear Response Independent of Mean Stress.- 10.4. Plastic Constitutive Relations Applicable for Negligible Elastic Deformations.- 10.5. Governing Equations.- Selected Reading.- Exercises.- 11 Problems in Plasticity.- 11.1. Initial Yielding of a Thin-Walled Tube under Combined Tension-Torsion Loading.- 11.2. Initial Yielding of a Hollow Cylinder under Internal Pressure Loading.- 11.3. Twisting of a Circular Rod.- 11.4. Plastic Extension of a Cylindrical Bar under Simple Tension Loading.- 11.5. Plane Strain Compression.- 11.6. Plane Strain Deformation of Rigid-Perfectly Plastic Solids.- 11.7. Reduction of Plane Strain Equations.- 11.8. Slip-Line Theory.- 11.9. Numerical Solutions Using Slip-Line Theory.- 11.10. Wedge Penetration in a Rigid-Plastic Material.- Selected Reading.- Exercises.- Appendix A.- Similitude and Scale Modeling in Solid Mechanics.- Appendix B.- to Numerical Methods in Solid Mechanics.