Derivations of two-dimensional green's functions for bimaterials by means of complex variable function technique

1993 ◽  
Vol 60 (1) ◽  
pp. R9-R13 ◽  
Author(s):  
Y. Z. Chen
Keyword(s):  
Complex Variable ◽  
Green's Functions ◽  
Green’S Functions ◽  
Function Technique ◽  
Two Dimensional ◽  
Complex Variable Function ◽  
Variable Function

STUDY ON ELASTIC ANALYSIS OF CRACK PROBLEM OF TWO-DIMENSIONAL DECAGONAL QUASICRYSTALS OF POINT GROUP 10, $\overline {10}$

2009 ◽  
Vol 23 (16) ◽  
pp. 1989-1999 ◽  
Author(s):  
WU LI ◽  
TIAN YOU FAN
Keyword(s):  
Complex Variable ◽  
Point Group ◽  
Crack Problem ◽  
Plane Elasticity ◽  
Two Dimensional ◽  
Partial Differential ◽  
Decagonal Quasicrystal ◽  
Complex Variable Function ◽  
Variable Function ◽  
Group 10

By introducing a stress potential function, we transform the plane elasticity equations of two-dimensional quasicrystals of point group 10, [Formula: see text] to a partial differential equation. And then we use the complex variable function method for classical elasticity theory to that of the quasicrystals. As an example, a decagonal quasicrystal in which there is an arc is subjected to a uniform pressure p in the elliptic notch of the decagonal quasicrystal is considered. With the help of conformal mapping, we obtain the exact solution for the elliptic notch problem of quasicrystals. The work indicates that the stress potential and complex variable function methods are very useful for solving the complicated boundary value problems of higher order partial differential equations which originate from quasicrystal elasticity.

Complex Potentials for Plane Problem of Two-Dimensional Quasicrystals with a Lip-Shape Crack

2014 ◽  
Vol 1004-1005 ◽  
pp. 1415-1418
Author(s):  
Qiong He ◽  
Hai Yun Xiong
Keyword(s):  
Conformal Mapping ◽  
Plane Problem ◽  
Complex Variable ◽  
Function Method ◽  
Potential Functions ◽  
Two Dimensional ◽  
Griffith Crack ◽  
Complex Variable Function ◽  
Variable Function ◽  
Complex Variable Function Method

By introducing a conformal mapping and applying the complex variable function method, two potential functions are determined for plane problem of two-dimensional quasicrystals with a lip-shape crack. When the height of the lip-shape crack approaches to zero, the results can be reduced to the solutions of the Griffith crack.

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

Complex-variable-function–Gaussian solitons

2008 ◽  
Vol 34 (1) ◽  
pp. 43 ◽  
Author(s):  
Dongmei Deng ◽  
Qi Guo ◽  
Wei Hu
Keyword(s):  
Complex Variable ◽  
Complex Variable Function ◽  
Variable Function ◽  
Gaussian Solitons

THREE‐DIMENSIONAL INDUCED POLARIZATION AND ELECTROMAGNETIC MODELING

Geophysics ◽  
1975 ◽  
Vol 40 (2) ◽  
pp. 309-324 ◽  
Author(s):  
Gerald W. Hohmann
Keyword(s):  
Integral Equation ◽  
Green's Functions ◽  
Green’S Functions ◽  
Three Dimensional ◽  
Induced Polarization ◽  
The Body ◽  
Scale Model ◽  
Two Dimensional ◽  
Electromagnetic Modeling ◽  
The Earth

The induced polarization (IP) and electromagnetic (EM) responses of a three‐dimensional body in the earth can be calculated using an integral equation solution. The problem is formulated by replacing the body by a volume of polarization or scattering current. The integral equation is reduced to a matrix equation, which is solved numerically for the electric field in the body. Then the electric and magnetic fields outside the inhomogeneity can be found by integrating the appropriate dyadic Green’s functions over the scattering current. Because half‐space Green’s functions are used, it is only necessary to solve for scattering currents in the body—not throughout the earth. Numerical results for a number of practical cases show, for example, that for moderate conductivity contrasts the dipole‐dipole IP response of a body five units in strike length approximates that of a two‐dimensional body. Moving an IP line off the center of a body produces an effect similar to that of increasing the depth. IP response varies significantly with conductivity contrast; the peak response occurs at higher contrasts for two‐dimensional bodies than for bodies of limited length. Very conductive bodies can produce negative IP response due to EM induction. An electrically polarizable body produces a small magnetic field, so that it is possible to measure IP with a sensitive magnetometer. Calculations show that horizontal loop EM response is enhanced when the background resistivity in the earth is reduced, thus confirming scale model results.

2.5D AND 3D GREEN'S FUNCTIONS FOR ACOUSTIC WEDGES: IMAGE SOURCE TECHNIQUE VERSUS A NORMAL MODE APPROACH

2013 ◽  
Vol 21 (01) ◽  
pp. 1250025 ◽  
Author(s):  
A. TADEU ◽  
E. G. A. COSTA ◽  
J. ANTÓNIO ◽  
P. AMADO-MENDES
Keyword(s):  
Wave Propagation ◽  
Normal Mode ◽  
Green's Functions ◽  
Green’S Functions ◽  
Three Dimensional ◽  
Element Formulation ◽  
Two Dimensional ◽  
Image Source ◽  
Point Pressure ◽  
Fluid Channel

2.5D and 3D Green's functions are implemented to simulate wave propagation in the vicinity of two-dimensional wedges. All Green's functions are defined by the image-source technique, which does not account directly for the acoustic penetration of the wedge surfaces. The performance of these Green's functions is compared with solutions based on a normal mode model, which are found not to converge easily for receivers whose distance to the apex is similar to the distance from the source to the apex. The applicability of the image source Green's functions is then demonstrated by means of computational examples for three-dimensional wave propagation. For this purpose, a boundary element formulation in the frequency domain is developed to simulate the wave field produced by a 3D point pressure source inside a two-dimensional fluid channel. The propagating domain may couple different dipping wedges and flat horizontal layers. The full discretization of the boundary surfaces of the channel is avoided since 2.5D Green's functions are used. The BEM is used to couple the different subdomains, discretizing only the vertical interfaces between them.

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