Fundamental Solutions in Elastodynamics. A Compendium

  • ID: 2128840
  • Book
  • 262 Pages
  • Cambridge University Press
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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.
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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.
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Eduardo Kausel Massachusetts Institute of Technology.
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