Application of the fast Fourier transform to the computation of the Sommerfeld integral for a vertical electric dipole above a half-space

1992 ◽  
Vol 40 (7) ◽  
pp. 798-805 ◽  
Author(s):  
S.L. Dvorak
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Half Space ◽  
Electric Dipole ◽  
Sommerfeld Integral ◽  
Vertical Electric Dipole

A Fast Method for Solving Contact Plasticity in a Half Space

2011 ◽  
Author(s):  
Zhanjiang Wang ◽  
Xiaoqing Jin ◽  
Shuangbiao Liu ◽  
Leon M. Keer ◽  
Jian Cao ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Residual Stresses ◽  
Fast Fourier Transform ◽  
Half Space ◽  
Three Dimensional ◽  
New Method ◽  
Fast Method ◽  
Discrete Convolution ◽  
Influence Coefficients ◽  
The One

This paper presents a new method of contact plasticity analysis based on Galerkin vectors to solve the eigenstresses due to eigenstrain. The influence coefficients relating eigenstrains to eigenstresses thus can be divided into four terms the one due to the eigenstrains in the full space, others due to the mirrored eigenstrains in the mirror half space. Each term can be solved fast and efficient by using the three-dimensional discrete convolution and fast Fourier transform (DC-FFT) or the three-dimensional discrete correlation and fast Fourier transform (DCR-FFT). The new method is used to analyze the contact plastic residual stresses in half space.

Elastic Fields due to Eigenstrains in a Half-Space

2005 ◽  
Vol 72 (6) ◽  
pp. 871-878 ◽  
Author(s):  
Shuangbiao Liu ◽  
Qian Wang
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Half Space ◽  
Numerical Algorithms ◽  
Elastic Field ◽  
Contact Problems ◽  
Fast Fourier Transform Algorithm ◽  
Elastic Fields ◽  
Influence Coefficients ◽  
Residual Strains

Engineering components inevitably encounter various eigenstrains, such as thermal expansion strains, residual strains, and plastic strains. In this paper, a set of formulas for the analytical solutions to cases of uniform eigenstrains in a cuboidal region-influence coefficients, is presented in terms of derivatives of four key integrals. The linear elastic field caused by arbitrarily distributed eigenstrains in a half-space is thus evaluated by the discrete correlation and fast Fourier transform algorithm, along with the discrete convolution and fast Fourier transform algorithm. By taking advantage of both the convolution and correlation characteristics of the problem, the formulas of influence coefficients and the numerical algorithms are expected to enable efficient and accurate numerical analyses for problems having nonuniform distribution of eigenstrains and for contact problems.

Radiation from a vertical electric dipole in an inhomogeneous half-space

1967 ◽  
Vol 55 (11) ◽  
pp. 2023-2024
Author(s):  
C.J. Lombardo ◽  
S.N. Samaddar
Keyword(s):  
Half Space ◽  
Electric Dipole ◽  
Vertical Electric Dipole
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