Xie, Longtao: Three-dimensional Green’s function and its derivatives for anisotropic elastic, piezoelectric and magnetoelectroelastic materials. 2016
Inhalt
- Abstract
- Contents
- List of Figures
- List of Tables
- Introduction
- Mathematical preliminaries
- Basic equations of anisotropic linear elasticity
- Basic equations of linear piezoelectricity
- Basic equations of linear magnetoelectroelasticity
- Stroh formalism
- Fundamentals of the Green's function
- Boundary integral equations
- Green's function in anisotropic linear elasticity
- Problem statement
- Line integral Green's function and its derivatives
- Explicit Green's function and its derivatives
- Unified explicit Green's function and its derivatives
- Verifications and comparison of the different methods
- Verification of the numerical integration method
- Verification of the residue calculus method
- Verification of the Stroh formalism method
- Verification of the unified explicit expressions
- Comparison of the efficiency
- Numerical examples
- Numerical results near the degenerated point
- Numerical results for an arbitrary point on a unit sphere
- Concluding remarks
- Green's function in linear piezoelectricity
- Problem statement
- Stroh formalism method
- Representation of the Green's function
- First derivative of the Green's function
- Second derivative of the Green's function
- Residue calculus method
- Representation of the Green's function
- First derivative of the Green's function
- Second derivative of the Green's function
- Numerical procedures
- Numerical examples and discussions
- Concluding remarks
- Green's function in linear magnetoelectroelasticity
- Problem statement
- Stroh formalism method
- Representation of the Green's function
- First derivative of the Green's function
- Second derivative of the Green's function
- Numerical examples and discussions
- Concluding remarks
- Applications of the Green's function and its derivatives in the BEM
- Preliminary remarks
- Description of the BEM for anisotropic linear elasticity
- Numerical examples
- Concluding remarks
- Summary and outlook
- Appendix A - Residue calculus of an improper line integral
- Appendix B - Explicit expressions of Ni and Nij
- Appendix C - Auxiliary functions F(n)m for the second derivative of the Green’s function
- Appendix D - Explicit expression of the Stroh eigenvector
- Bibliography