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Anisotropic Elasticity : Theory and Applications.

Author: Thomas C T Ting
Publisher: Cary : Oxford University Press, 1996.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
1. Matrix Algebra2. Linear Anisotropic Elastic Materials3. Antiplane Deformations4. The Lekhnitskii Formalism5. The Stroh Formalism6. The Structures and Identities of the Elasticity Matrices7. Transformation of the Elasticity Matrices and Dual Coordinate Systems8. Green's Functions for Infinite Space, Half-Space, and Composite Space9. Particular Solutions, Stress Singularities, and Stress Decay10. Anisotropic  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Ting, Thomas C. T.
Anisotropic Elasticity : Theory and Applications
Cary : Oxford University Press,c1996
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Thomas C T Ting
ISBN: 9780198023845 0198023847
OCLC Number: 936849115
Notes: Description based upon print version of record.
7.3 Sextic Formalism in Dual Coordinate Systems
Description: 1 online resource (591 p.)
Contents: 1. MATRIX ALGEBRA; 1.1 Notations, Definitions, and Identities; 1.2 Eigenvalues and Eigenvectors; 1.3 Diagonalization of Simple and Semisimple Matrices; 1.4 Nonsemisimple Matrices; 1.5 Commutative Matrices; 1.6 Positive Definite Real Matrices; 1.7 Hermitian Matrices; 1.8 Eigenplane; 1.9 Square Roots of a Matrix; 2. LINEAR ANISOTROPIC ELASTIC MATERIALS; 2.1 Elastic Stiffnesses; 2.2 Elastic Compliances; 2.3 Contracted Notations; 2.4 Reduced Elastic Compliances; 2.5 Material Symmetry; 2.6 Matrix C for Materials with Symmetry Planes 2.7 Matrices s and s' for Materials with Symmetry Planes2.8 Transformation of C and s; 2.9 Restrictions on Elastic Constants; 2.10 Determination of Symmetry Planes; 3. ANTIPLANE DEFORMATIONS; 3.1 Uncoupling of Inplane and Antiplane Displacements; 3.2 Plane Stress Deformations; 3.3 General Solutions for Antiplane Deformations; 3.4 The Complex Functions Inz and √z[sup(2)] --
a[sup(2)]; 3.5 Green's Functions for Infinite Space and Half-Space; 3.6 Green's Function for Bimaterials; 3.7 Mapping of an Ellipse to a Circle for z=x[sub(1)]+px[sub(2)] 3.8 Infinite Space with an Elliptic Hole or an Elliptic Rigid Inclusion3.9 Anisotropic Elliptic Body; 3.10 Green's Functions for an Elliptic Inclusion; 3.11 A Crack in an Infinite Space and Bimaterials; 3.12 Infinite Space with a Hole of Arbitrary Shape; 3.13 Remarks; 3.14 A Theorem; 4. THE LEKHNITSKII FORMALISM; 4.1 The Airy Function χ and the Stress Function Ψ; 4.2 Displacements for Two-Dimensional Stresses; 4.3 Differential Equations for χ and Ψ; 4.4 Eigenvalues p; 4.5 Anisotropic Materials with p[sub(1)]=p[sub(2)]=p[sub(3)]; 4.6 Representation of General Solutions 4.7 Dependence of Solutions on Elastic Constants5. THE STROH FORMALISM; 5.1 The Eshelby-Reid-Shockley Formalism; 5.2 Eigenvalues p; 5.3 The Sextic Formalism of Stroh; 5.4 The Stress Function Φ and the Airy Function χ; 5.5 Orthogonality and Closure Relations; 5.6 Positive Definite Hermitian Matrices; 5.7 The Matrix Differential Equation; 5.8 Physical Meanings of p, a, and b; 5.9 Nonsemisimple N; 5.10 Dependence of Solutions on Elastic Constants; 5.11 A. N. Stroh (1926-1962); 6. THE STRUCTURES AND IDENTITIES OF THE ELASTICITY MATRICES; 6.1 The Structure of N[sub(i)] 6.2 The Structure of N[sub(i)][sup(-1)] [sub(i)]6.3 Explicit Expressions of A and B; 6.4 Explicit Expressions of S, H, and L; 6.5 Identities Relating S, H, and L; 6.6 The Structure of S, H, and L; 6.7 Classification of the Eigenvectors e[sub(i)] and e[sup(i)]; 6.8 Commutative 6×6 Matrices; 6.9 Identities Connecting p, A, and B to Real Matrices; 6.10 Eigenvectors of the Extraordinary Semisimple Matrix Ñ; 7. TRANSFORMATION OF THE ELASTICITY MATRICES AND DUAL COORDINATE SYSTEMS; 7.1 Eigenvalues p(θ); 7.2 Elasticity Matrices in a Rotated Coordinate System

Abstract:

1. Matrix Algebra2. Linear Anisotropic Elastic Materials3. Antiplane Deformations4. The Lekhnitskii Formalism5. The Stroh Formalism6. The Structures and Identities of the Elasticity Matrices7. Transformation of the Elasticity Matrices and Dual Coordinate Systems8. Green's Functions for Infinite Space, Half-Space, and Composite Space9. Particular Solutions, Stress Singularities, and Stress Decay10. Anisotropic Materials With an Elliptic Boundary11. Anisotropic Media With a Crack or a Rigid Line Inclusion12. Steady State Motion and Surface Waves13. Degenerate and Near Degenerate Materials14. Gen.

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