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Elastostatic Green's Function and Its Spatial Derivatives for Cubic Symmetry. Exactly Solvable Cases
Author(s) -
Morawiec A.
Publication year - 1994
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.2221840204
Subject(s) - symmetry (geometry) , function (biology) , mathematics , mathematical analysis , green's function , pure mathematics , geometry , evolutionary biology , biology
The Green's function and its spatial derivatives for a cubic infinite medium in cases when they can be obtained in form of explicit analytic expressions are presented. It is known that the problem reduces to a sextic equation which, in general case, is unsolvable. Symbolic solutions, however, can be given in some special cases. New formulae for directions lying in (001) and (1 1 0) planes are given. Full solutions for [100] and [111] directions are presented as examples. First derivatives of the Green's function with respect to spatial coordinates are also expressed through the roots of the sextic equation and the solutions for the same special directions are given.