Fundamental Solutions in Elastodynamics
A Compendium

This work contains fundamental solutions for classical, canonical, elastodynamics problems using common format and notation.

Eduardo Kausel (Author)

9780521375993, Cambridge University Press

Paperback, published 21 July 2011

262 pages
25.4 x 17.8 x 1.4 cm, 0.46 kg

'[This book] presents a concise treatment of fundamental solutions of a variety of problems arising in elastodynamics … It should be useful to students and researchers in applied mathematics, geophysics, engineering and other applied sciences.' Fiazud Din Zaman, Zentralblatt MATH

This work is a compilation of fundamental solutions (or Green's functions) for classical or canonical problems in elastodynamics presented with a common format and notation. These formulas describe the displacements and stresses elicited by dynamic sources in solid elastic media like full spaces, half-spaces, strata and plates in both two and three dimensions, using the three major coordinate systems (Cartesian, cylindrical and spherical), and also for transient and harmonic motions. Such formulas are useful for numerical methods and practical application to problems of wave propagation in elasticity, soil dynamics, earthquake engineering, mechanical vibration, or geophysics. These formulas were heretofore only found scattered throughout the literature. The solutions are tabulated without proof, but giving reference to appropriate modern papers and books containing full derivations. Most formulas in the book have been programmed and tested within the MATLAB environment. The program listings are available for free download on the book's website.

Preface
Part I. Preliminaries: 1. Fundamentals
2. Dipoles
Part II. Full Space Problems: 3. Two-dimensional problems in full, homogeneous spaces
4. Three-dimensional problems in full, homogeneous spaces
Part III. Half-Space Problems: 5. Two-dimensional problems in homogeneous half-spaces
6. Three-dimensional problems in homogeneous half-spaces
Part IV. Plates and Strata: 7. Two-dimensional problems in homogeneous plates and strata
Part V. Analytical and Numerical Methods: 8. Solutions to the Helmholtz and wave equations
9. Integral transform method
10. Stiffness (impedance) matrix method
Part VI. Appendices: 11. Basic properties of mathematical functions
12. Brief table of integral transforms
13. MATLAB(R) program listings.

Subject Areas: Civil engineering, surveying & building [TN]