Analysis of Rubber Friction by the Fast Fourier Transform

1978 ◽  
Vol 6 (2) ◽  
pp. 89-113 ◽  
Author(s):  
R. A. Schapery
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Numerical Method ◽  
Plane Strain ◽  
Contact Problems ◽  
Fast Fourier Transform Algorithm ◽  
Periodic Arrays ◽  
Rubber Friction

Abstract A numerical method for solving contact problems is developed and then used to predict friction (without adhesion) between rubber in plane strain and periodic arrays of parabolic and triangular substrate asperities; the numerical method itself, which is based on the fast Fourier transform algorithm, is not limited to these asperity shapes. Also, effects of superposing two and more scales of texture are described. Some generalizations and related applications, such as analysis of tire traction, are then discussed.

Note on the FFT Based Computational Code and Its Application

2008 ◽  
Author(s):  
Xiaoqing Jin ◽  
Leon M. Keer ◽  
Qian Wang
Keyword(s):  
Numerical Simulation ◽  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Toeplitz Matrix ◽  
Contact Problems ◽  
Point Of View ◽  
Fast Fourier Transform Algorithm ◽  
Discrete Convolution ◽  
Mathematical Point ◽  
Computational Code

The discrete convolution based Fast Fourier Transform algorithm (DC-FFT) has been successfully applied in numerical simulation of contact problems. The algorithm is revisited from a mathematical point of view, equivalent to a Toeplitz matrix multiplied by a vector. The nature of the convolution property permits one to implement the algorithm with fewer constraints in choosing the computational domains. This advantageous feature is explored in the present work, and is expected to be beneficial to many tribological studies.

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.

SNOCRAFT: A Learning-Oriented Shorthand Notation for Creating, Representing, and Analyzing Fast Fourier Transform Algorithms

1980 ◽  
Vol 17 (3) ◽  
pp. 284-284
Author(s):  
Robert J. Meir ◽  
Sathyanarayan S. Rao
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Fourier Transforms ◽  
Reduced Form ◽  
Fast Fourier Transform Algorithm ◽  
Signal Flow Graph ◽  
Shorthand Notation ◽  
The Matrix ◽  
Fourier Algorithm ◽  
Fft Analysis

This paper presents a full and well-developed view of the Fast Fourier Transform (FFT). It is intended for the reader who wishes to learn and develop his own fast Fourier algorithm. The approach presented here utilizes the matrix description of fast Fourier transforms. This approach leads to a systematic method for greatly reducing the complexity and the space required by variety of signal flow graph descriptions. This reduced form is called SNOCRAFT. From this representation, it is then shown how one can derive all possible fast Fourier transform algorithms, including the Weinograd Fourier transform algorithm. It is also shown from the SNOCRAFT representation that one can easily compute the number of multiplications and additions required to perform a specified fast Fourier transform algorithm. After an elementary introduction to matrix representation of fast Fourier transform algorithm, the method of generating all possible fast Fourier transform algorithms is presented in detail and is given in three sections. The first section discusses the Generation of SNOCRAFT and the second section illustrates how Operations on SNOCRAFT are made. These operations include inversion and rotation. The last section deals with the FFT Analysis. In this section, examples are provided to illustrate how one counts the number of multiplications and additions involved in performing the transform that one has developed.

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