Fourier variant homogenization treatment of single impulse boundary effect behaviour

• Autorzy: Kula D. , Wierzbicki E. , Witkowska-Dobrev J. , Wodzyński Ł.
• Języki publikacji: EN

Abstrakty

EN

Boundary effect behavior understood as near-boundary suppression of boundary fluctuation loads is described in various ways depending on the mathematical representation of solutions and the type of the center. In the case of periodic composites, the homogenization method is decisive here. In the framework of the Tolerance Averaging Approach, developed by prof. Cz. Wo´zniak leading to an approximate model of phenomena related to periodic composites this effect is described by a homogeneous part of differential equation for fluctuation amplitudes and usually this approximate description of the boundary effect behavior is restricted to a single fluctuation. In this paper, contrary to the previous elaborations, the boundary effect is developed in the variant of the tolerance thermal conductivity model in which the temperature field is represented by the Fourier expansions composed by an average temperature with infinite number of Fourier terms imposed on the average temperature as tolerance fluctuation suppressed in the framework of the boundary effect.

Słowa kluczowe

EN

even temperature fluctuations; homogenization; tolerance modelling

PL

fluktuacja temperatury; homogenizacja; modelowanie tolerancyjne

• Wydawca: Wydawnictwo Politechniki Łódzkiej
• Czasopismo: Mechanics and Mechanical Engineering
• Rocznik: 2018
• Tom: Vol. 22, nr 3
• Strony: 683--690
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Kula D.

• Warsaw University of Life Sciences, Faculty of Civil and Enviromental Engineering, Department of Civil Engineering, Warsaw, Poland

autor

Wierzbicki E.

• Warsaw University of Life Sciences, Faculty of Civil and Enviromental Engineering, Department of Civil Engineering, Warsaw, Poland

autor

Witkowska-Dobrev J.

• Warsaw University of Life Sciences, Faculty of Civil and Enviromental Engineering, Department of Civil Engineering, Warsaw, Poland

autor

Wodzyński Ł.

• Warsaw University of Life Sciences, Faculty of Civil and Enviromental Engineering, Department of Civil Engineering, Warsaw, Poland

Bibliografia

• [1] Ariault, J.L.: Effective macroscopic description for heat conduction in periodic composites, International Journal of Heat and Mass Transfer, 26, 6, 861-869, DOI: 10.1016/S0017-9310(83)80110-0, 1983.
• [2] Bensoussan, A., Lions, J.-L. and Papanicolaou, G.: Asymptotic analysis for periodic structures, American Math. Soc., ISBN-10: 0-8218-5324-4, ISBN-13: 978-0-8218-5324-5, 2011.
• [3] Woźniak, Cz. and Wierzbicki, E.: Averaging techniques In thermomechanics of composite solids, Tolerance averaging versus homogenization, Technical University of Czestochowa Press, 2000.
• [4] Woźniak, Cz. (ed.): Thermomechanics of microheterogeneous solids and structures. Tolerance averaging approach, Lodz University of Technology Press, 2009.
• [5] Woźniak, Cz. (ed.): Developments In Mathematical Modeling and Analysis of Microstructured Media, Silesian University Press, Gliwice, 2010.
• [6] Jędrysiak, J.: Termomechanics of laminates, plates and shells with functionally graded properties /in Polish/, Lodz University of Technology Press, 2010.
• [7] Michalak, B.: Termomechanics of solids with a certain nonhonmogeneous microstructure: tolerance approximation technique, /in Polish/, Lodz University of Technology Press, 2010.
• [8] Kula, D.: Assessment of the impact of the geometric structure of periodic composites on the intensity of damping the fluctuation of boundary loads /PhD dissertation in Polish/, Faculty of Civil Engineering, Architecture and Environmental Engineering, Łódź University of Technology, 2016.
• [9] Kula, D. and Wierzbicki, E.: On the Fourier series implementation issue tolerance modeling thermal conductivity of periodic composites, Engineering Transaction, 63, 1, 77-92, 2015.
• [10] Kula, D.: On the existence of the sinusoidal-type temperature fluctuations independently suppressed by the periodic two - phased conducting layer, Acta Scientarum Polonorum, Ser, Arch., 63, 1, 77-92, 2015.
• [11] Woźniak, Cz., Łacińska, L. and Wierzbicki, E.: Boundary and initial fluctuation effect on dynamic behaviour of a laminated solid, Arch. Appl. Mech., 74, 618-628, 2005.
• [12] Woźniak, M., Wierzbicki, E. and Woźniak, Cz.: A macroscopic model of the diffusion and heat transfer processes in a periodically micro-stratified solid layer, Acta Mechanica, 157, 175-185, 2002.
• [13] Szlachetka, O. and Wągrowska, M.: The boundary effect in the layered barier with the longitudinal material gradation, Acta Scientarum Polonorum, Ser.; Architectura, 10, 3, 27-34, 2011.
• [14] Witkowska-Dobrev, J. and Wągrowska, M.: The area of effect of boundary layer for multilayer composites for stationary elastic problems /in Polish/, Acta Scientarum Polonorum, Ser.: Architectura, 14, 2, 3-17, 2015.
• [15] Wierzbicki, E., Kula, D. and Wodzyński, Ł.: Fourier variant homogenization of the heat transfer processes in periodic composites, M&ME, 22, 3, 2018.
• [16] Wodzyński, Ł., Kula, D. and Wierzbicki, E.: Transport of even and odd temperaturę fluctuations across the chess-board type periodic composite, M&ME, 22, 3, 2018.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).