Numerical evaluation of harmonic Green's functions for triclinic half‐space with embedded sources—Part I: a 2D model

Abstract

SUMMARYThe Green's functions for a triclinic half-space for embedded harmonic line load are considered. Corresponding displacement and stress fields are expressed in terms of double Fourier integrals. The first integral was evaluated using contour integration while the second one was computed through the Gauss-Legendre quadrature. The resulting Green's functions algorithm avoids repeated calculations of the same quantities and utilizes the vector computational features within MATLAB environment. Extensive testing of the results has been performed for both displacement and stress fields. The tests demonstrate the accuracy of the proposed procedure for evaluating the Green's functions without any restrictions upon material properties, frequency, and location of the source and observation points.

Scattering of plane harmonic P, SV and Rayleigh waves by a completely embedded corrugated elastic inclusion

“…The advantage of using the full-space Green's functions lies in ease of their numerical evaluation when compared to the half-space Green's functions [23][24][25][26][27].…”

Scattering of a plane harmonic SH wave by a completely embedded corrugated scatterer

“…However, the purpose of this study is to facilitate future research of plane-strain and three-dimensional models for both the isotropic and anisotropic half spaces. Since for these general models the corresponding full-space Green's functions are much easier to evaluate numerically than the equivalent half-space Green's functions [20][21][22][23][24], the full-space Green's functions are chosen to be used for this study.…”

Numerical evaluation of harmonic Green's functions for triclinic half‐space with embedded sources—Part II: a 3D model

“…This paper is a continuation of the work reported in Part I [1] where the corresponding 2D model was considered. Thus for the review of the literature the reader is referred to Part I.…”