Handbook of Elasticity Solutions

This handbook is a collection of elasticity solutions. Many of the results presented here cannot be found in textbooks and are available in scientific articles only. Some of them were obtained in the closed form quite recently. The solutions have been thoroughly checked and reduced to a "user friendly" form. Every effort has been made to keep the book free of misprints. The theory of elasticity is a mature field and a large number of solutions are ava- able. We had to make choices in selecting material for this book. The emphasis is made on results relevant to general solid mechanics and materials science appli- tions. Solutions related to structural mechanics (beams, plates, shells, etc.) are left out. The content is limited to the linear elasticity. We are grateful to B. Nuller for several clarifications concerning the contact pr- lem and to V. Levin for suggestions on Eshelby's problem. We also appreciate a n- ber of remarks and comments made by L. Germanovich, I. Sevostianov, O. Zharii and R. Zimmerman. We are particularly indebted to E. Karapetian for a substantial help in putting the material together.

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 £Ii£. 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.