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Numerical evaluation of harmonic Green's functions for triclinic half‐space with embedded sources—Part II: a 3D model
Author(s) -
Chen Zhengxiang,
Dravinski Marijan
Publication year - 2006
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1767
Subject(s) - triclinic crystal system , superposition principle , displacement (psychology) , mathematical analysis , matlab , point (geometry) , mathematics , half space , harmonic , fourier transform , geometry , numerical integration , stress (linguistics) , space (punctuation) , physics , computer science , acoustics , psychology , linguistics , philosophy , quantum mechanics , molecule , psychotherapist , operating system
The displacement and stress Green's functions for a 3D triclinic half‐space with embedded harmonic point load is considered. The resulting displacement and stress fields are expressed in terms of triple Fourier integrals. The first integral was evaluated using contour integration and the 3D Green's functions were obtained as a superposition of 2D results over the azimuthal angle. The resulting algorithm developed for evaluation of the Green's functions avoids repeated calculations of the same quantities and it utilizes the vectorized manipulation within MATLAB environment. The algorithm places no restriction on material properties, frequency and location of source and observation points. Extensive testing of the numerical results was performed for both displacement and stress. The tests confirm the accuracy of the numerical results. Copyright © 2006 John Wiley & Sons, Ltd.