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

2006 ◽  
Vol 69 (2) ◽  
pp. 347-366 ◽  
Author(s):  
Zhengxiang Chen ◽  
Marijan Dravinski
Keyword(s):  
Half Space ◽  
Numerical Evaluation ◽  
Green's Functions ◽  
Green’S Functions ◽  
2D Model

On the Green's functions for a layered half-space. Part II

1983 ◽  
Vol 73 (4) ◽  
pp. 931-951
Author(s):  
Randy J. Apsel ◽  
J. Enrique Luco
Keyword(s):  
Integral Representation ◽  
Half Space ◽  
Numerical Evaluation ◽  
Green's Functions ◽  
Green’S Functions ◽  
Numerical Procedure ◽  
Number Of Solutions ◽  
Viscoelastic Media ◽  
Layered Half Space

abstract A numerical procedure to obtain the dynamic Green's functions for layered viscoelastic media is presented. The procedure is based on numerical evaluation of certain Hankel-type integrals which appear in an integral representation derived previously by the authors. Comparisons illustrating the accuracy and flexibility of the approach are made with a number of solutions obtained by other methods.

scholarly journals Thermoelastic Diffusion Multicomponent Half-Space under the Effect of Surface and Bulk Unsteady Perturbations

2019 ◽  
Vol 24 (1) ◽  
pp. 26 ◽  
Author(s):  
Sergey Davydov ◽  
Andrei Zemskov ◽  
Elena Akhmetova
Keyword(s):  
Half Space ◽  
Green's Functions ◽  
Green’S Functions ◽  
Local Equilibrium ◽  
Linear Equations ◽  
Integral Form ◽  
External Effects ◽  
Thermoelastic Diffusion ◽  
One Dimensional ◽  
The Laplace Transform

This article presents an algorithm for solving the unsteady problem of one-dimensional coupled thermoelastic diffusion perturbations propagation in a multicomponent isotropic half-space, as a result of surface and bulk external effects. One-dimensional physico-mechanical processes, in a continuum, have been described by a local-equilibrium model, which included the coupled linear equations of an elastic medium motion, heat transfer, and mass transfer. The unknown functions of displacement, temperature, and concentration increments were sought in the integral form, which was a convolution of the surface and bulk Green’s functions and external effects functions. The Laplace transform on time and the Fourier sine and cosine transforms on the coordinate were used to find the Green’s functions. The obtained Green’s functions was analyzed. Test calculations were performed on the examples of some technological processes.

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