On the Effect of Material Properties Uncertainty on the Magnitude of Temperature Oscillations in Two-Component Periodic Laminate: Tolerance Averaging Modelling

Abstract:

Over last decades composite materials gained even more interests in many industries due to theirs effective properties which may be apparently different (better) then constituents itself. By specific layout and distribution of composite components we can achieve desired properties in macro scale, e.g. high elasticity and low conductivity at the same time. On all interfaces, by perfect contact between phases, there will appear jump of gradient field (displacement or temperature) of unknown magnitude. This magnitude depends in fact, for the heat transfer problem, inter alia on the ratio of conductivities of composite constituents lying next to interface. Values of these oscillation magnitudes are case of our study here. The conductor under considerations is a two-phase, periodic laminate subjected to initial-boundary conditions assuring unidirectional heat flow, perpendicular to the laminas. Ratios of material properties are assumed as random variables of known probabilistic distribution. We will give an answer to the question: is the jump function of temperature gradient a random variable of Gaussian distribution In order to have a good description to considered problem we have decided on the use of tolerance averaging technique.

• Periodical: Key Engineering Materials (Volume 843)
• Pages: 19-25
• DOI: https://doi.org/10.4028/www.scientific.net/KEM.843.19
• Online since: May 2020
• Authors: Piotr Ostrowski*, Jarosław Jędrysiak
• Keywords: Heat Transfer, Periodic Laminate, Tolerance Averaging Technique, Uncertain Material Properties

References

[1] A. Bensoussan, J.L. Lions, G. Papanicolaou, Asymptotic Analysis for Periodic Structures, North-Holland Publishing Co., Amsterdam, New York, (1978).

[2] V.V. Jikov, S.M. Kozlov, O.A. Oleinik, Homogenization of Differential Operators and Integral Functionals, Springer-Verlag, Berlin, Heidelberg, (1994).

DOI: 10.1007/978-3-642-84659-5

[3] S.J. Matysiak, A.A. Yevtushenko, Influence of microstructure on temperature distribution for some mixed problem of composite half-space, Int. Commun. Heat Mass Transf. 35 (2008) 704-709.

DOI: 10.1016/j.icheatmasstransfer.2008.02.005

[4] S.J. Matysiak, D.M. Perkowski, Temperature distribution in a periodically stratified layer with slant lamination, Heat Mass Transf. 50 (2014) 75-83.

DOI: 10.1007/s00231-013-1225-9

[5] R. Hill, Elastic properties of reinforced solids: some theoretical principles, J. Mech. Phys. Solids 11 (1963) 357-372.

DOI: 10.1016/0022-5096(63)90036-x

[6] Cz. Woźniak, E. Wierzbicki, Averaging Techniques in Thermomechanics of Composite Solids, Częstochowa University Press, Częstochowa, (2000).

[7] Cz. Woźniak, B. Michalak, J. Jędrysiak (Eds.), Thermomechanics of Microheterogeneous Solids and Structures, Monographs of Lodz University of Technology, Łódź, (2008).

[8] P. Ostrowski, Tolerance Modelling of Thermoelasticity in Microstructured Media, Monographs of Lodz University of Technology, Łódź, (2017).

[9] B. Michalak, Vibrations of plates with initial geometrical imperfections interacting with a periodic elastic foundation, Arch. Appl. Mech. 70 (2000) 508-518.

DOI: 10.1007/s004190000081

[10] E. Pazera, J. Jędrysiak, Thermoelastic phenomena in transversally gradedlaminates, Comp. Struc. 134 (2015) 663-671.

DOI: 10.1016/j.compstruct.2015.08.081

[11] P. Ostrowski, Thermoelasticity in a two-phase hollow cylinder with longitudinally graded material properties, in: W. Pietraszkiewicz, J. Górski (Eds.), Shell Structures: Theory and Applications – Proceedings of the 10th SSTA 2013 Conference, Vol. 3, Taylor & Francis Group, London, 2014, pp.133-136.

DOI: 10.1201/b15684-31

[12] J. Ignaczak, Z.F. Baczyński, On a refined heat conduction theory for microperiodic layered solids, J. Therm. Stresses 20 (1997) 749-771.

DOI: 10.1080/01495739708956127

[13] M. Kamiński, Monte-Carlo simulation of effective conductivity for fiber composites, Int. Commun. Heat Mass Tranf. 26 (1999) 791-800.

DOI: 10.1016/s0735-1933(99)00067-6

[14] P. Ostrowski, J. Jędrysiak, Heat conduction in periodic laminates with probabilistic distribution of material properties, Heat Mass Transf. 53 (2017) 1425-1437.

DOI: 10.1007/s00231-016-1908-0