Premium
The precise evaluation of derivatives of the anisotropic elastic Green's functions
Author(s) -
Barnett D. M.
Publication year - 1972
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2220490238
Subject(s) - eigenvalues and eigenvectors , anisotropy , elasticity (physics) , mathematics , algebraic equation , algebraic number , tensor (intrinsic definition) , fourier transform , mathematical analysis , simple (philosophy) , green s , geometry , physics , optics , philosophy , epistemology , nonlinear system , quantum mechanics , thermodynamics
Using Fourier transforms a simple scheme for numerically obtaining derivatives of the tensor Green's functions of elasticity with great precision is derived. The technique developed circumvents the need for solving an auxiliary eigenvalue problem and a related sextic algebraic equation common to previous treatments of this problem. Numerical results for the dilatation associated with a “dilatation center” in copper are given. The speed and accuracy of the present technique indicates that a previous suggestion by Lothe is indeed quite practical — namely, that internal stress problems (dislocations, point defects, inclusions, thermal stresses) in anisotropic media may be treated using tabulated data for the Green's functions and their derivatives.