Handbook of elasticity solutions

1: Basic Equations of Elasticity. 1.1. Cartesian Coordinates. 1.2. Cylindrical Coordinates. 1.3. Spherical Coordinates. 1.4. Hooke's Law for Anisotropic Materials. 2: Point Forces and Systems of Point Forces in Three-Dimensional Space and Half-Space. 2.1. Point Force in an Infinite Isotropic Solid. 2.2. Systems of Forces Distributed in a Small Volume of an Infinite Isotropic Solid. 2.3. Dynamic Problems of a Suddenly Introduced Point Forces Couples and Dipoles in an Infinite Isotropic Solid. 2.4. Point Force in the Isotropic Half-Space (Mindlin's Problem). 2.5. Point Force Applied at the Boundary of the Isotropic Half-Space. 2.6. Point Force of an Infinite Transverse Isotropic Solid. 2.7. Point Force Applied at the Boundary of the Transversely Isotropic Half-Space. 2.8. Two Joined Isotropic Half-Spaces with Different Moduli: Solution for a Point Force. 3: Selected Two-Dimensional Problems. 3.1. Introductory Material. 3.2. Infinite 2-D Solid. Isotropic and Orthotropic Materials. 3.3. 2-D Isotropic Half-Plane. 3.4. Stress Concentrations near Holes and Inclusions. 3.5. Equilibrium of an Elastic Wedge. 3.6. Circular Ring Loaded by External and Internal Pressures. 4: Three-Dimensional Crack Problems for the Isotropic or Transversely Isotropic Infinite Solid. 4.1. Circular (Penny-Shaped) Crack. 4.2. Half-Plane Crack. 4.3. External Circular Crack. 4.4. Elliptical Crack. 5: A Crack in an Infinite Isotropic Two-Dimensional Solid. 5.1. A Pair of Equal and Opposite Point Forces Applied at an Arbitrary Pointof the Crack. 5.2. Uniform Loading at Crack Faces. 5.3. Crack Tip Fields. 5.4. Far Field Asymptotics. 6: A Crack in an Infinite Anisotropic Two-Dimensional Solid. 6.1. Notations and General Representations for a 2-D Anisotropic Elastic Solid. 6.2. A Pair of Equal and Opposite Point Forces Applied at an Arbitrary Point of the Crack. 6.3. Uniform Loading at Crack Faces. 6.4. Crack Tip Fields. 6.5. Far Field Asymptotics. 6.6. Crack Compliance Tensor. 6.7. Appendix. 7: Thermoelasticity. 7.1. Basic Equations. 7.2. Stationary 3-D Problems. 7.3. Non-Stationary 3-D Problems. 7.4. Stationary 2-D Problems. 7.5. Non-Stationary 2-D Problems. 7.6. Thermal Stresses in Heated Infinite Solid Containing an Inhomogeneity or a Cavity. 8: Contact Problems. 8.1. 2-D Problems for a Rigid Punch on the Isotropic and Anisotropic Elastic Half-Plane. 8.2. 3-D Problems for a Rigid Punch on the Isotropic and Transversely Isotropic Elastic Half-Space. 8.3. Contact of Two Elastic Bodies (Hertz' Problem). 9: Eshelby's Problem and Related Results. 9.1. Inclusion Problem. 9.2. Ellipsoidal Inhomogeneity. 9.3. Eshelby's Tensor for Various Ellipsoidal Shapes. 9.4. Alternative Form of Solution for Ellipsoidal Inhomogeneity. 9.5. Expressions for Tensors P, Q, A and GBPIiGBP. 9.6. Quantities Relevant for Calculation of the Effective Elastic Properties. 10: Elastic Space Containing a Rigid Ellipsoidal Inclusion Subjected to Translation and Rotation. 10.1.