Green's functions and response functions in geochemical modelling

1985 ◽  
Vol 123 (2) ◽  
pp. 328-343 ◽  
Author(s):  
I. G. Enting
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Geochemical Modelling ◽  
Response Functions

A Fast and Effective Method for Transient Thermoelastic Displacement Analyses

2000 ◽  
Vol 123 (3) ◽  
pp. 479-485 ◽  
Author(s):  
Shuangbiao Liu ◽  
Michael J. Rodgers ◽  
Qian Wang ◽  
Leon M. Keer
Keyword(s):  
Heat Flux ◽  
Frequency Response ◽  
Frequency Domain ◽  
Green's Functions ◽  
Green’S Functions ◽  
Surface Displacement ◽  
Response Functions ◽  
Normal Surface ◽  
Frequency Response Functions ◽  
Convolution Integrals

Frictional heating due to the relative motion of contacting surfaces causes temperature rise and thermal distortion, which in turn affects the contact geometry and pressure distribution. A fast and effective method is presented for the calculation of the normal surface displacement of an elastic halfspace due to arbitrary transient surface heating. The method uses Fourier-transformed Green’s functions (frequency response functions), found in the closed form by using the approach of Seo and Mura and the heat conduction analyses of Carslaw and Jaeger. The frequency response functions are shown analytically to be the frequency domain representations of the Green’s functions given by Barber. The formulation for the surface normal displacement is in the form of three-dimensional convolution integrals (over surface and time) of the arbitrary transient heat flux and the Green’s functions. Fourier transforms of these convolution integrals are taken, avoiding the Green’s-function singularities and giving a simple multiplication between the transformed heat flux and the (known) frequency response functions. The discrete convolution–fast Fourier transform (DC-FFT) algorithm is applied for accurate and efficient calculations of the normal surface displacement from the frequency response functions for an arbitrary transient heat input. The combination of the frequency-domain formulation and the DC-FFT algorithm makes the solution of transient thermoelastic deformation extremely fast and convenient.

Temperature field evaluation of a two-dimensional partial heat flow problem through Green's Functions

2019 ◽  
Author(s):  
Guilherme Ramalho Costa ◽  
José Aguiar santos junior ◽  
José Ricardo Ferreira Oliveira ◽  
Jefferson Gomes do Nascimento ◽  
Gilmar Guimaraes
Keyword(s):  
Temperature Field ◽  
Heat Flow ◽  
Green's Functions ◽  
Flow Problem ◽  
Green’S Functions ◽  
Field Evaluation ◽  
Two Dimensional
Sign in / Sign up

Export Citation Format

Share Document