Solid Mechanics and Its Applications

Preface; Chapter 1 BASIC EQUATIONS OF ANISOTROPIC ELASTICITY: 1.1 Transformation of Strains and Stresses; 1.2 Basic Equations; 1.2.1 Geometric equations; 1.2.2 Equations of motion; 1.2.3 Constitutive equations; 1.3 Boundary and Initial Conditions; 1.3.1 Boundary conditions; 1.3.2 Initial conditions; 1.4 Thermoelasticity. Chapter 2 GENERAL SOLUTION FOR TRANSVERSELY ISOTROPIC PROBLEMS: 2.1 Governing Equations; 2.1.1 Methods of solution; 2.1.2 Governing equations for the displacement method 2.1.3 Equations for a mixed method -- the state-space method; 2.2 Displacement Method; 2.2.1 General solution in Cartesian coordinates; 2.2.2 General solution in cylindrical coordinates; 2.3 Stress Method for Axisymmetric Problems 2.4 Displacement Method for Spherically Isotropic Bodies; 2.4.1 General solution; 2.4.2 Relationship between transversely isotropic and spherically isotropic solutions. Chapter 3 PROBLEMS FOR INFINITE SOLIDS: 3.1 The Unified Point Force Solution; 3.1.1 A point force perpendicular to the isotropic plane; 3.1.2 A point force within the isotropic plane; 3.2 The Point Force Solution for an Infinite Solid Composed of two Half-Spaces; 3.2. 1 A point force perpendicular to the isotropic plane; 3.2.2 A point force within the isotropic plane; 3.2.3 Some remarks; 3.3 An Infinite Transversely Isotropic Space with an Inclusions; 3.4 Spherically Isotropic Materials; 3.4.1 An infinite space subjected to a point force; 3.4.2 Stress concentration in neighbourhood of a spherical cavity. Chapter 4 HALF-SPACE AND LAYERED MEDIA: 4.1 Unified Solution for a Half-Space Subjected to a Surface Point Force; 4.1.1 A point force normal to the half-space surface; 4.1.2 A point force tangential to the half-space surface; 4.2 A Half-Space Subjected to an Interior Point Force; 4.2. 1 A point force normal to the half-space surface; 4.2.2 A point force tangential to the half-space surface; 4.3 General Solution by Fourier Transform; 4.4 Point Force Solution of an Elastic Layer; 4.5 Layered Elastic Media. Chapter 5 EQUILIBRIUM OF BODIES OF REVOLUTION: 5.1 Some Harmonic Functions; 5.1.1 Harmonic polynomials; 5.1.2 Harmonic functions containing ln(r I ij ); 5.1.3 Harmonic functions containing R; 5.2 An Annular (Circular) Plate Subjected to Axial Tension and Radial Compression; 5.3 An Annular (Circular) Plate Subjected to Pure Bending; 5.4 A Simply-Supported Annular (Circular) Plate Under Uniform Transverse Loading; 5.5 A Uniformly Rotating Annular (Circular) Plate; 5.6 Transversely Isotropic Cones; 5.6.1 Compression of a cone under an axial force; 5.6.2 Bending of a cone under a transverse force; 5.7 Spherically Isotropic Cones; 5.7.1. Equilibrium and boundary conditions; 5.7.2. A cone under tip forces; 5.7.3. A cone under concentrated moments at its apex; 5.7.4. Conical shells. Chapter 6 THERMAL STRESSES: 6.1 Transversely Isotropic Materials; 6.2 A Different General Solution for Transversely Isotropic Thermoelasticity; 6.2. 1 General solution for dynamic problems; 6.2.2 General solution for static problems; 6.3 Spherically Isotropic Materials. Chapter 7 FRICTIONAL CONTACT: 7.1 Two Elastic Bodies in Contact; 7.1.1 Mathematical description of a contact system; 7.1.2 Deformation of transversely isotropic bodies under frictionless contact; 7.1.3 A half-space under point forces; 7.2 Contact of a Sphere with a Half-Space; 7.2.1 Contact with normal loading; 7.2.2 Contact with tangential loading; 7.3 Contact of a Cylindrical Punch with a Half-Space; 7.3.1 Contact with normal loading; 7.3.2 Contact with tangential loading; 7.4 Indentation by a Cone; 7.4.1 Contact with normal loading; 7.4.2 Contact with tangential loading; 7.5 Inclined Contact of a Cylindrical Punch with a Half-Space; 7.5.1 Contact with normal loading; 7.5.2 Contact with tangential loading; 7.6 Discussions on Solutions for Frictional Contact. Chapter 8 BENDING, VIBRATION AND STABILITY OF PLATES: 8.1 General Solution Method; 8.1.1 Rectangular plates; 8.1.2 Circular plates; 8.2 The Sate-Space Method for Laminated Plates; 8.2.1 Laminated rectangular plates; 8.2.2 Laminated circular plates. Chapter 9 VIBRATIONS OF CYLINDERS AND CYLINDRICAL SHELLS OF TRANSVERSELY ISOTROPIC MATERIALS: 9.1 Three Simple Modes of Vibration; 9.1.1 Axisymmetric torsional vibration; 9.1.2 Breathing mode vibration; 9.1.3 Thickness-shear vibration; 9.2 Asymmetric Vibration; 9.3 Vibration of a Layered Cylindrical Shell; 9.3.1 State-space formulations; 9.3.2 Layerwise method and state vector solution; 9.3.3 Free vibration analysis and numerical results; 9.4 Vibration of a Cylindrical Shell Coupled with Fluid; 9.4.1 Coupling effect of fluid; 9.4.2 Free vibration of submerged and/or fluid-filled cylinders and cylindrical shells; 9.4.3 Numerical results of a fluid-filled cylindrical shell; 9.5 Vibration of a Cylindrical Shell Coupled with the Surrounding Elastic Medium; 9.5.1 Elastic waves in an isotropic elastic medium; 9.5.2 Displacements and stresses in the shell; 9.5.3 Vibration of the shell. Chapter 10 SPHERICAL SHELLS OF SPHERICALLY ISOTROPIC MATERIALS: 10.1 Free Vibration; 10.1.1 Basic equations and solution; 10.1.2 Free vibration analysis; 10.2 Frequency Equations and Numerical Results; 10.2.1 Frequency equations of a single-layered hollow sphere; 10.2.2 Some special cases; 10.2.3 An example; 10.3 Vibration Coupled with Fluid 10.3.1 Effect of fluid; 10.3.2 Frequency equations; 10.3.3 Numerical results; 10.4 Vibration Coupled with the Surrounding Elastic Medium; 10.4.1 Pasternak model of elastic foundation; 10.4.2 Frequency equations; 10.4.3 Numerical results; 10.5 Laminated Spherical Shells; 10.5.1 State-space formulations for spherically isotropic elasticity; 10.5.2 Layerwise method and state vector solution; 10.5.3 Frequency equations; 10.5.4 Numerical results. Appendix A ADDITIONAL NOTES AND BIBLIOGRAPHY TO CHAPTERS. Appendix B SPECIAL FUNCTIONS. Appendix C NOMENCLATURE. REFERENCES. INDEX.