FFT-Based Methods for Computational Contact Mechanics
| Autor: | Dong Zhu, Shuangbiao Liu, Q. Jane Wang, Xin Zhang, Linlin Sun |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Computer science
lcsh:Mechanical engineering and machinery Fast Fourier transform fast fourier transform contact of materials 02 engineering and technology Industrial and Manufacturing Engineering Convolution symbols.namesake 0203 mechanical engineering Fundamental solution lcsh:TJ1-1570 General Materials Science contact pressure Mechanical Engineering Mathematical analysis FFT algorithms Function (mathematics) 021001 nanoscience & nanotechnology Computer Science Applications contact stress 020303 mechanical engineering & transports Fourier transform Contact mechanics Frequency domain tribology symbols 0210 nano-technology Contact area |
| Zdroj: | Frontiers in Mechanical Engineering, Vol 6 (2020) |
| ISSN: | 2297-3079 |
| DOI: | 10.3389/fmech.2020.00061 |
| Popis: | Computational contact mechanics seeks for numerical solutions to contact area, pressure, deformation, and stresses, as well as flash temperature, in response to the interaction of two bodies. The materials of the bodies may be homogeneous or inhomogeneous, isotropic or anisotropic, layered or functionally graded, elastic, elastoplastic, or viscoelastic, and the physical interactions may be subjected to a single field or multiple fields. The contact geometry can be cylindrical, point (circular or elliptical), or nominally flat-to-flat. With reasonable simplifications, the mathematical nature of the relationship between a surface excitation and a body response for an elastic contact problem is either in the form of a convolution or correlation, making it possible to formulate and solve the contact problem by means of an efficient Fourier-transform algorithm. Green's function inside such a convolution or correlation form is the fundamental solution to an elementary problem, and if explicitly available, it can be integrated over a region, or an element, to obtain influence coefficients (ICs). Either the problem itself or Green's functions/ICs can be transformed into a space-related frequency domain, via a Fourier transform algorithm, to formulate a frequency-domain solution for contact problems. This approach converts the original tedious integration operation into multiplication accompanied by Fourier and inverse Fourier transforms, and thus a great computational efficiency is achieved. The conversion between ICs and frequency-response functions facilitate the solutions to problems with no explicit space-domain Green's function. This paper summarizes different algorithms involving the fast Fourier transform (FFT), developed for different contact problems, error control, as well as solutions to the problems involving different contact geometries, different types of materials, and different physical issues. The related works suggest that (i) a proper FFT algorithm should be used for each of the cylindrical, point, and nominally flat-flat contact problems, and then (ii) the FFT-based algorithms are accurate and efficient. In most cases, the ICs from the 0-order shape function can be applied to achieve satisfactory accuracy and efficiency if (i) is guaranteed. |
| Databáze: | OpenAIRE |
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