Theory and Practice of Solid Mechanics

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.