Two approaches to the formation of a tolerance averaged equations for elastodynamics of periodic solids

• Autorzy: Augustowska, L. , Wierzbicki, E.
• Języki publikacji: EN

Abstrakty

EN

The aim of this contribution is to formulate two different approaches to the computation of averaged moduli in the equations of the tolerance averaged model of microperiodic linear-elastic composites. In the first approach, which will be called basis function approach, we shall use some of the FEM concepts in order to establish the basis functions in the Galerkin approximation to the non-stationary periodic cell problem of elastodynamics. In the second approach, which will be called mode shape function approach, we shall also use FEM concepts in order to determine functions describing the character of free vibrations of the periodicity cell. This approach makes it possible to reduce a large number of unknowns occuring in the first approach.

Słowa kluczowe

PL

materiały kompozytowe; elastodynamika; tolerancja; modelowanie

EN

composite materials; elastodynamics; tolerance; modelling

• Czasopismo: Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
• Rocznik: 2002
• Tom: Vol. 1, nr 1
• Strony: 5--13
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Augustowska, L.

• Institute of Mathematics and Computer Science, Technical University of Częstochowa

autor

Wierzbicki, E.

• Institute of Mathematics and Computer Science, Technical University of Częstochowa

Bibliografia

• [1] Woźniak C., Wierzbicki E., Averaging technique in thermomechanics of composite solids, Wydawnictwo Politechniki Częstochowskiej, Częstochowa 2000.
• [2] Żmijewski K.H., Numeryczna realizacja metody parametrów mikrolokalnych, VIII Konferencja Metody komputerowe w mechanice konstrukcji, Jadwisin 1987, 471-480.
• [3] Woźniak C., Tolerance systems and composite media, (in:) Structure and Media, ed. B.T. Maruszewski, Publishing House of Poznań University of Technology, Poznań 2002, 325-340.
• [4] Oden J.J., Reddy J.N., An introduction to the mathematical theory of finite elements, John Willey & Sons, New York 1976.
• [5] Bensoussan A., Lions J.L., Papanicolau G., Aymptotic analysis for periodic structures, North-Holland, Amsterdam 1978.