Simplicial modelling of dynamic problems in a micro-periodic composite material

• Autorzy: Rychlewska J. , Woźniak C.
• Języki publikacji: EN

Abstrakty

EN

The aim of this paper is to propose a certain new approach to the formulation of both discrete and continuum models for the analysis of dynamic problems in elastic composite solids with a periodic microstructure. The proposed approach is based on a periodic simplicial division of the unit cell and on the assumption of a uniform strain in every simplex. The main feature of the obtained discrete model is the finite-difference form of the governing equations. By applying smoothing operation the continuum models are derived directly from the discrete ones.

Słowa kluczowe

EN

composite materials; periodic microstructure; simplified finite difference models

PL

materiały kompozytowe; mikrostruktura periodyczna

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
• Rocznik: 2003
• Tom: Vol. 2, nr 1
• Strony: 159--168
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Rychlewska J.

• Institute of Mathematics and Computer Science, Czestochowa University of Technology

autor

Woźniak C.

• Institute of Mathematics and Computer Science, Czestochowa University of Technology

Bibliografia

• [1] Achenbach J.D., Sun C.T., The Directionally Reinforced Composite as a Homogeneous Continuum with Microstructure, (in:) E.H. Lee (ed.), Dynamics of Composite Materials, Am. Soc. Mech. Eng., New York 1972.
• [2] Bedford A., Stern M., Toward a Diffusing Continuum Theory of Composite Materials, J. Appl. Mech. 1971, 38, 8-14.
• [3] Bensoussan A., Lions J.L., Papanicolau G., Asymptotic analysis for periodic structures, North-Holland, Amsterdam 1978.
• [4] Boutin C., Auriault J.L., Rayleigh Scattering in Elastic Composite Materials, Int. J. Engng Sci. 1993, 12, 1669-1689.
• [5] Hegemeier G.A., On a Theory of Interacting Continua for Wave Propagation in Composites, (in:) E.H. Lee (ed.), Dynamics of Composite Materials, Am. Soc. Mech. Eng., New York 1972.
• [6] Jikov V.V., Kozlov S.M., Oleinik O.A., Homogenization of Differential Operators and Integral Functionals, Springer-Verlag, Berlin 1994.
• [7] Lee E.H., A Survey of Variational Methods for Elastic Wave Propagation Analysis in Composites with Period Structures, (in:) E.H. Lee (ed.), Dynamics of Composite Materials, Am. Soc. Mech. Eng., New York 1972.
• [8] Rychlewska J., Modele symplicjalne zagadnień elastodynamiki mikroperiodycznych ośrodków ciągłych (Simplicial models for elastodynamic problems in microperiodic continua), Dissertation, Faculty of Mechanical Engineering and Informatics, Częstochowa University of Technology, Częstochowa 2002.
• [9] Rychlewska J., Szymczyk J., Woźniak C., A Simplicial Model for Dynamic Problems in Periodic Media, J. Theor. Appl. Mech. 2000, 38, 3-13.
• [10] Sanchez-Palencia E., Non-homogeneous media and vibration theory, Lecture Notes in Physics, 127, Springer-Verlag, Berlin 1980.
• [11] Woźniak C., Wierzbicki E., Averaging Techniques in Thermomechanics of Composite Solids, Wydawnictwo Politechniki Częstochowskiej, Częstochowa 2000.
• [12] Woźniak C., Discrete Elasticity, Arch. Mech. 1971, 23, 801-816.

Uwagi

EN

The papers have been presented during the session devoted to application of mathematics (as part of International Conference on Parallel Processing and Applied Mathematics).