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-spacesurface; 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 Solu
This book aims to provide a comprehensive introduction to the theory and applications of the mechanics of transversely isotropic elastic materials. There are many reasons why it should be written. First, the theory of transversely isotropic elastic materials is an important branch of applied mathematics and engineering science; but because of the difficulties caused by anisotropy, the mathematical treatments and descriptions of individual problems have been scattered throughout the technical literature. This often hinders further development and applications. Hence, a text that can present the theory and solution methodology uniformly is necessary. Secondly, with the rapid development of modern technologies, the theory of transversely isotropic elasticity has become increasingly important. In addition to the fields with which the theory has traditionally been associated, such as civil engineering and materials engineering, many emerging technologies have demanded the development of transversely isotropic elasticity. Some immediate examples are thin film technology, piezoelectric technology, functionally gradient materials technology and those involving transversely isotropic and layered microstructures, such as multi-layer systems and tribology mechanics of magnetic recording devices. Thus a unified mathematical treatment and presentation of solution methods for a wide range of mechanics models are of primary importance to both technological and economic progress.
Three-dimensional general solution that can be used to solve problems of three-dimensional elastic bodies
Unified fundamental solutions that are numerically stable for both isotropic and transversely isotropic materials
Three-dimensional analyses of statics and dynamics of plates and shells that can be used as benchmarks for validating numerical methods and approximate theories
State-space formulations that are very efficient for analyzing layered media and laminated structures
Lots of three-dimensional numerical results relevant to coupled vibrations of cylindrical and spherical shells that are seldom found in literature