Beschreibung
Stroh formalism is a powerful mathematical method developed for the analysis of equations of anisotropic elasticity. This exposition introduces the essence of this formalism and demonstrates its effectiveness in both static and dynamic elasticity. The book gives a succinct introduction to Stroh formalism, discusses several important topics in static elasticity, and examines Rayleigh waves, a key topic in nondestructive evaluation, seismology, and materials science.
Inhaltsverzeichnis
Preface Chapter 1: The Stroh Formalism for Static Elasticity Section 1.1: Basic Elasticity Section 1.2: Stroh''s Eigenvalue Problem Section 1.3: Rotational Invariance of Stroh Eigenvector in Reference Plane Section 1.4: Forms of Basic Solutions When Stroh''s Eigenvalue Problem is Degenerate Section 1.5: Rotational Dependence When Stroh''s Eigenvalue Problem is Degenerate Section 1.6: Angular Average of Stroh''s Eigenvalue Problem: Integral Formalism Section 1.7: Surface Impedance Tensor Section 1.8: Examples Subsection 1.8.1: Isotropic Media Subsection 1.8.2: Transversely Isotropic Media Section 1.9: Justification of the Solutions in the Stroh Formalism Section 1.10: Comments and References Section 1.11: Exercises Chapter 2: Applications in Static Elasticity Section 2.1: Fundamental Solutions Subsection 2.1.1: Fundamental Solution in the Stroh Formalism Subsection 2.1.2: Formulas for Fundamental Solutions: Examples Section 2.2: Piezoelectricity Subsection 2.2.1: Basic Theory Subsection 2.2.2: Extension ofthe Stroh Formalism Subsection 2.2.3: Surface Impedance Tensor of Piezoelectricity Subsection 2.2.4: Formula for Surface Impedance Tensor of Piezoelectricity: Example Section 2.3: Inverse Boundary Value Problem Subsection 2.3.1: Dirichlet to Neumann map Subsection 2.3.2: Reconstruction of Elasticity Tensor Subsubsection 2.3.2.1: Reconstruction of Surface Impedance Tensor from Localized Dirichlet to Neumann Map Subsubsection 2.3.2.2: Reconstruction of Elasticity Tensor from Surface Impedance Tensor Section 2.4: Comments and References Section 2.5: Exercises Chapter 3: Rayleigh waves in the Stroh formalism Section 3.1: The Stroh Formalism for Dynamic Elasticity Section 3.2: Basic Theorems and Integral Formalism Section 3.3: Rayleigh Waves in Elastic Half-space Section 3.4: Rayleigh Waves in Isotropic Elasticity Section 3.5: Rayleigh Waves in Weakly Anisotropic Elastic Media Section 3.6: Rayleigh Waves in Anisotropic Elasticity Subsection 3.6.1: Limiting Wave Solution Subsection 3.6.2: Existence Criterion Based on S_3 Subsection 3.6.3: Existence Criterion Based on Z Subsection 3.6.4: Existence Criterion Based on Slowness Sections Section 3.7: Comments and References Section 3.8: Exercises
