A numerical scheme to obtain the RCS of three-dimensional bodies of resonant size using the conjugate gradient method and the fast Fourier transform

1989 ◽  
Vol 37 (5) ◽  
pp. 528-537 ◽  
Author(s):  
M.F. Catedra ◽  
E. Gago ◽  
L. Nuno
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Numerical Scheme ◽  
Three Dimensional

Stress Analysis of Layered Elastic Solids With Cracks Using the Fast Fourier Transform and Conjugate Gradient Techniques

2001 ◽  
Vol 68 (5) ◽  
pp. 708-714 ◽  
Author(s):  
I. A. Polonsky ◽  
L. M. Keer
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Conjugate Gradient ◽  
Protective Coatings ◽  
Three Dimensional ◽  
Numerical Approach ◽  
Multiple Cracks ◽  
Elastic Solids ◽  
Shape Changes ◽  
Stress Analyses

The fast Fourier transform (FFT) technique has recently been applied to stress analyses of layered elastic solids, with a great deal of success. However, the existing FFT-based methods are limited to intact solids. This paper explores the possibility of using FFT for stress analyses of layered elastic solids containing cracks. A new numerical approach is developed by combining three-dimensional FFT with the theory of periodic eigenstrain and the conjugate gradient method. The new method is primarily designed for analyzing complex three-dimensional crack patterns in layered solids, such as those produced in thin protective coatings by roughness-induced contact stresses. The method should be particularly advantageous for studying crack propagation in coatings, as it does not require remeshing when the crack shape changes. Numerical examples illustrating advantages as well as limitations of the method are presented. Some unexpected results that were obtained for multiple cracks in a thin coating are discussed.

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