Geodesic
The use of wavelets in the mathematical and computer modelling of manufacture of the complex-shaped shells made of composite materials
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 9 (2016) no. 3, pp. 5-16 Cet article a éte moissonné depuis la source Math-Net.Ru

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This article focuses on the application of wavelet theory to the problem of modelling the processes of manufacturing the shells of fibrous composite materials (CM). The basic methods for preparing such shells are two related ones: filament winding, when the strip made of CM is laid out on the outstretched surface, and laying out, when the tape is placed by dint of pressing rollers. In both cases, laying the tape is carried out in accordance with the program of moving spreader. To create such a program the mathematical model of the process of placing the tape is needed. The article describes semi orthogonal wavelet systems on the segment that are based on B-spline of arbitrary order. The matrices which compose the filter bank for such wavelet systems are represented. Some algorithms for geometric modelling are reviewed and summarized from the point of view of the wavelet theory. The results are applied to the mathematical modelling and software of manufacturing process of shells made of fibrous composite materials. As an example, consider the process of making the ventilator blade.
Keywords: wavelet; computer-aided design; the Chaikin's algorithm; a filter bank. 
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Yu. I. Bityukov; V. N. Akmaeva. The use of wavelets in the mathematical and computer modelling of manufacture of the complex-shaped shells made of composite materials. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 9 (2016) no. 3, pp. 5-16. http://geodesic.mathdoc.fr/item/VYURU_2016_9_3_a0/

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