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A new model for the analysis of nonstationary processes in material systems with a periodic structure

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EN
Abstrakty
EN
The main aim of this paper is to outline a new approach to the formulation of approximate mathematical models for the analysis of non-stationary thermomechanical processes in micro-periodic solids and structures. The modelling procedure is realized in two steps. First, a system of finite difference equations is formulated by the periodic FEM discretization of the unit cell for a solid under consideration. Second, by applying some smoothness operations we derive continuum model equations directly from the finite difference equations. In contrast to the known homogenization and tolerance averaging methods, the proposed modeling approach can be formulated on different levels of accuracy which depend on the mesh parameter related to the periodic FEM discretization of the unit cell.
Twórcy
  • Institute of Mathematics and Computer Science, Technical University of Częstochowa
autor
  • Institute of Mathematics and Computer Science, Technical University of Częstochowa
autor
  • Institute of Mathematics and Computer Science, Technical University of Częstochowa
Bibliografia
  • [1] Achenbach J.D., Sun C.T., Herrmann G., Continuum theory for a laminated medium, J. Appl. Mech. 1968, 35, 467-475.
  • [2] Bakhvalov N.C., Panasenko G.P., Averaging processes in periodic media (in Russian), Nauka, Moscow 1984.
  • [3] Bedford A., Stern M., Toward a diffusing continuum theory of composite materials, J. Appl. Mech. 1971, 38, 8-14.
  • [4] Bensoussan A., Lions J.L., Papanicolau G., Asymptotic analysis for periodic structures, North Holland, Amsterdam 1978.
  • [5] Christensen R.M., Wave propagation in layered elastic media, J. Appl. Mech. 1979, 42, 153-344.
  • [6] Fish J., Wen Chen, Higher-order homogenization of initial/boundary - value problem, Journal of Engineering Mechanics, December 2001, 1223-1230.
  • [7] Fichera G., Is the Fourier theory of heat propagation paradoxical?, Rendiconti del Circolo Matematico di Palermo 1992, Serie I 41, 5-28.
  • [8] Hegemeier G.A., On a theory of interacting continua for wave propagation in composites, (in:) Dynamics of Composite Materials, ed. E.H. Lee, Ant Soc. Mech. Engng, New York 1972.
  • [9] Herrmarin G., Kaul R.K., Delph T.J., On continuum mode of the dynamic behaviour of layered composites, Arch. Mech. 1976, 28, 405-421.
  • [10] Hornung D., Homogenization and porous media, Interdisciplinary Appl. Math. 1997, Vol. 6, Springer Verlag.
  • [11] Jędrysiak J., On the stability of thin periodic plates, Eur. J. Mech. 2000, A/ Solids, 19, 487-502.
  • [12] Jikov V.V., Kozlov C.M., Oleinik O.A., Homogenization of differential operators and integral functionals, Springer Verlag, Berlin-Heidelberg 1994.
  • [13] Kohn W., Krumhansl J.A., Lee E.H., Variational methods for dispersion relation and elastic properties of composite materials, J. Appl. Mech. 1972, 39, 327-336.
  • [14] Lee E.H., A survey of variational methods for elastic wave propagation analysis in composites with periodic structures, (in:) Dynamics of Composite Materials, ed. E.H. Lee, Am. Soc. Mech. Engineers, New York 1972.
  • [15] Maewal A., Construction of models of dispersive elastodynamic behavior of periodic composites; a computational approach, Comp. Math. Appl. Mech. 1986, Engng, 57, 191-205.
  • [16] Michalak B., Vibrations of plates with initial geometrical imperfections interacting with a periodic elastic foundations, Arch. Appl. Mech. 2000, 70, 508-518.
  • [17] Oden J.T., Carey G.F., Finite elements, Volume V, Prentice-Hall Inc. Englewood Cliffs, 1984.
  • [18] Rychlewska J., Szymczyk J., Woźniak C., A contribution to dynamics of polyatomic lattices, J. Theor. Appl. Mech. 1999, 37, 799-807.
  • [19] Rychlewska J., Szymczyk J., Woźniak C., A simplicial model for dynamic problems in periodic media, J. Theor. Appl. Mech. 2000, 38, 3-13.
  • [20] Rychlewska J., Modele symplicjalne zagadnień elastodynamiki mikroperiodycznych osrodków ciągłych (Simplicial models for elastodynamic problems in microperiodic continua), Dissertation, Częstochowa University of Technology, Faculty of Mechanical Engineering and Informatics, Czestochowa 2002.
  • [21] Sanchez-Palencia E., Non-homogeneous media and vibration theory, Lecture Notes in Physics, 127, Springer-Verlag, Berlin 1980.
  • [22] Sun C.T., Achenbach J.D., Herrmann D., Continuum theory for a laminated medium, J. Appl. Mech. 1968, 35, 467-475.
  • [23] Szymczyk J., Zmienne wewnętrzne w termosprężystości siatek periodycznych o złożonej strukturze (Internal variables in thermoelasticity of periodic lattice structures), Dissertation, Częstochowa University of Technology, Faculty of Mechanical Engineering and Informatics, Częstochowa 2002.
  • [24] Wierzbicki E., Woźniak C., Woźniak M., On the modelling of transient micro-motions and nearboundary phenomena in a stratified elastic layer, Int. J. of Engng. Sci. 2001, 39, 1429-1441.
  • [25] Woźniak C., Macroscopic modelling of multiperiodic composites, C.R. Mecanique 2002, 330, 267-272.
  • [26] Woźniak C., Wierzbicki E., Averaging techniques in thermomechanics of composite solids, Wydawnictwo Politechniki Częstochowskiej, Częstochowa 2000.
  • [27] Woźniak C., Wierzbicki E., Woźniak M., A macroscopic model for the heat propagation in the microperiodic composite solids, Journ. of Thermal Stresses 2002, 25, 283-293.
  • [28] Woźniak M., Wierzbicki E., Woźniak C., A macroscopic model of the diffusion and heat transfer processes in a periodically micro-stratified solid layer, Acta Mechanica 2002, 157, 175-185.
  • [29] Zeeman B.C., The topology of the brain, in: Biology and medicine, Medical Research Council 1965, 227-292.
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Bibliografia
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bwmeta1.element.baztech-657d6320-13d4-471e-a49c-5ae1947502bb
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