Elasticity of Transversely Isotropic Materials by Haojiang DingElasticity of Transversely Isotropic Materials by Haojiang Ding

Elasticity of Transversely Isotropic Materials

byHaojiang Ding

Paperback | November 18, 2010

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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.
Title:Elasticity of Transversely Isotropic MaterialsFormat:PaperbackDimensions:435 pagesPublished:November 18, 2010Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9048170184

ISBN - 13:9789048170180

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Table of Contents

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-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

Editorial Reviews

From the reviews:"The authors' main goal is to provide an introduction to the theory and applications of mechanics of transversely isotropic elastic materials. . Additional notes and bibliography to chapters, special functions and nomenclature are included in three appendices. . this book is written to meet the needs of modern topics on mechanics of transversely isotropic elastic solids. . It seems to be a useful reference book on the subject. . the book can be considered as an important contribution to the engineering literature." (Lokenath Debnath, Zentralblatt MATH, Vol. 1101 (3), 2007)"Ideally and emphatically Elasticity of Transversely Isotropic Materials may claim to be the first monograph on mechanics of transversely isotropic materials, which is unique, covers topics of practical importance and provides many references for the reader. Engineers, production and field engineers in engineering disciplines;, designers, and researchers in industry who are interested in the solution of transversely isotropic elastic materials will find this text an inviting study . . a pleasure and an education to read. It is simply brilliant." (Current Engineering Practice, 2007)