Continuum modelling of laminates with a slowly graded microstructure

• Autorzy: Szymczyk J. , Woźniak Cz.
• Konferencja: International Conference on Continuous and Discrete Modelling in Mechanics (05-09.09.2005 ; Warsaw ; Poland)
• Języki publikacji: EN

Abstrakty

EN

The considerations are concerned with modelling and analysis of the dynamic response for micro-laminated two-phased solids. The main attention is focussed on modelling of the laminates which have a slowly graded microstructure in the direction normal to the layering (slowly graded laminates, SGL). Periodic and functionally graded laminates can be treated as special cases of SGL. A new mathematical model which couples micro- and macro-response of the linear elastic SGL is proposed. It is shown that for laminates with a weak transversal inhomogeneity, the derived model equations can be decomposed into asymptotic equations which describe the behavior of a laminate independently on the macro- and micro-level. This decomposition is estimated on the example of a specific vibration problem.

Słowa kluczowe

EN

slowly graded laminates SGL; dynamic response; two-phase linear elastic SGL; asymptotic approximation; mathematical model

PL

laminaty o stopniowanej zmianie własności typu SGL; charakterystyka dynamiczna; liniowo sprężysty dwufazowy laminat SGL; aproksymacja asymptotyczna; model matematyczny

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2006
• Tom: Vol. 58, nr 4-5
• Strony: 445--458
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Szymczyk J.

autor

Woźniak Cz.

• Institute of Mathematics and Computer Sciences, Częstochowa University of Technology, Dąbrowskiego 73, 42-200 Częstochowa

Bibliografia

• 1. J. ABOUDI, M.-J. PINDERA S. M, ARNOLD, Higher-order theory for functionally graded materiale, Composites: Part B, 30, 777-832, 1999.
• 2. N. C. BAKHVALOV, G. P. PANASENKO, Averaging processes in periodic media [in Russian), Nauka, Moscow 1984.
• 3. Ł. ŁACIŃSKI, Numerical verification of two mathematical models for the heat transfer in a laminated rigid conductor, J. Theor. Appl. Mech., 2, 43, 367-384, 2005.
• 4. T. REITER, G. J. DVORAK, V. TVERGAARD, Micromechanical models for graded composite materials, J. Mech. Phys. Solids, 45, 1281-1302, 1997.
• 5. S. SURESH, A. MORTENSEN, Fundamentals of functionally graded materials, The University Press, Cambridge 1998.
• 6. E. WIERZBICKI, Cz. WOŹNIAK, L. ŁACIŃSKA, Boundary and initial fluctuation effect on dynamic behavior of a laminated solid, Arch. Appl. Mech., 74, 618-628, 2005.
• 7. Cz. WOŹNIAK, E. WIERZBICKI, Averaging techniques in thermomechanics of composite solids, Wyd. Politechniki Częstochowskiej, Częstochowa 2000.