During the last years the Fast Fourier Transforms (FFT) technique was applied by many researchers for the calculation of the deformations in contact problems. The use of conventional convolution algorithms however led to the inclusion of a periodicity error that proved hard to correct. The correction procedures that had been suggested so far, involved the extension of the calculation grid and thus negated any time gains that the FFT would provide. In order to overcome the lack of accuracy of the current FFT methods, a new method for the calculation of deformations for line contacts was developed. In the framework of this method the so-called periodicity error has been identified as a discretization error in the Fourier space. The new method imposes a correction on the Fourier transformed kernel function in order to compensate the discretization error and achieve better accuracy. Tests have proven that the new method provides the desired accuracy while having a cost of arithmetic operations of O(N log(N)). Numerical examples are presented showing the improved accuracy of the proposed method.
Corrected FFT-Based Method for the Calculation of Deformations in Line Contacts
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Bakolas, V, Borchers, W, & Liebel, AF. "Corrected FFT-Based Method for the Calculation of Deformations in Line Contacts." Proceedings of the World Tribology Congress III. World Tribology Congress III, Volume 1. Washington, D.C., USA. September 12–16, 2005. pp. 211-212. ASME. https://doi.org/10.1115/WTC2005-63115
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