On thermoelasticity in FGL - tolerance averaging technique

• Autorzy: Pazera E. , Ostrowski P. , Jędrysiak J.
• Języki publikacji: EN

Abstrakty

EN

In this paper the problem of linear thermoelasticity in a laminate with functional gradation of properties is considered. In micro level this laminate is made of two different materials, microlaminas, distributed non-periodically but also not randomly along one of directions, what in macro level results in aforementioned functionally gradation of laminate properties. In order to describe behavior of such structure, equations of two models are here presented - the tolerance and the tolerance-asymptotic model. Both are obtained by the tolerance averaging technique. The basic aim of this work is to analyse the influence of some terms from these averaged equations on the distribution and the values of the displacements and the temperature functions. To solve the equations of two proposed models the finite difference method is used.

Słowa kluczowe

EN

functionally graded laminates; thermoelasticity; tolerance modelling; finite difference method

PL

laminaty o strukturze gradientowej; termosprężystość; modelowanie tolerancyjne; metoda różnic skończonych

• Wydawca: Wydawnictwo Politechniki Łódzkiej
• Czasopismo: Mechanics and Mechanical Engineering
• Rocznik: 2018
• Tom: Vol. 22, nr 3
• Strony: 703--717
• Opis fizyczny: Bibliogr. 23 poz., 1 rys., wykr.

Twórcy

autor

Pazera E.

• Department of Structural Mechanics, Łódź University of Technology, Politechniki 6, 90-924 Łódź, Poland

autor

Ostrowski P.

• Department of Structural Mechanics, Łódź University of Technology, Politechniki 6, 90-924 Łódź, Poland

autor

Jędrysiak J.

• Department of Structural Mechanics, Łódź University of Technology, Politechniki 6, 90-924 Łódź, Poland

Bibliografia

• [1] Suresh, S. and Mortensen, A.: Fundamentals of functionally graded materials, The University Press, Cambridge, 1998.
• [2] Bensoussan, A., Lions, J.L. and Papanicolau, G.: Asymptotic analysis for periodic structures, North-Holland, Amsterdam, 1978.
• [3] Wojnar, R.: Thermoelasticity and homogenization. J. Theor. Appl. Mech., 33, 322-335, 1990.
• [4] Jikov, V.V., Kozlov, C.M. and Oleinik, O.A.: Homogenization of differentia operators and integral functionals, Springer-Verlag, Berlin-Heidelberg, 1994.
• [5] Matysiak, S.J.: Application of the method of microlocal parameters to problems of periodic thermoelastic composites, Materials Science, 35, 4, 521-526, 1999.
• [6] Aboudi, J., Pindera, M.J. and Arnold, S.M.: Higher-order theory for functionally graded materials. Composites Part B: Engineering, 30, 777-832, 1999.
• [7] Goldberg, R.K. and Hopkins, D.A.: Thermal Analysis of a functionally graded material subject to a thermal gradient using the boundary element method, Composites Engineering, 5, 793-806, 1995.
• [8] Woźniak, C., Michalak, B. and Jędrysiak, J.: Thermomechanics of heterogeneous solids and structures. Tolerance Averaging Approach, Publishing House of Łódź University of Technology, Łódź, 2008.
• [9] Woźniak, C., Wierzbicki, E. and Woźniak, M.: A macroscopic model for the heat propagation in the microperiodic composite solids, J. Therm. Stresses, 25, 283-293, 2002.
• [10] Pazera, E. and Jędrysiak, J.: Thermoelastic phenomena in the transversally graded laminates, Composite Structures, 134, 663-671, 2015.
• [11] Pazera, E. and Jędrysiak, J.: Effect of microstructure in thermoelasticity problems of functionally graded laminates, Composite Structures, 202, 296-303, 2018.
• [12] Jędrysiak, J. and Pazera, E.: Vibrations of non-periodic thermoelastic laminates. Vibrations in Physical Systems, 27, 175-180, 2016.
• [13] Ostrowski, P. and Michalak, B.: The combined asymptotic-tolerance model of heat conduction in a skeletal micro-heterogeneous hollow cylinder, Composite Structures, 134, 343-352, 2015.
• [14] Ostrowski, P.: Thermoelasticity in a two-phase hollow cylinder with longitudinally graded material properties, in: W. Pietraszkiewicz, et. al. (eds), Shell Structures. Theory and Applications Volume 3, Taylor&Francis, London, 133-136, 2016.
• [15] Ostrowski, P. and Michalak, B.: A contribution to the modelling of heat conduction for cylindrical composite conductors with non-uniform distribution of constituents. International Journal of Heat and Mass Transfer, 92, 435-448, 2016.
• [16] Marczak, J. and Jędrysiak, J.: Tolerance modelling of vibrations of periodic threelayered plates with inert core. Composite Structures, 134, 854-861, 2015.
• [17] Tomczyk, B. and Szczerba, P.: Tolerance and asymptotic modelling of dynamics problems for thin microstructured transversally graded shells, Composite Structures, 162, 365-373, 2017.
• [18] Domagalski, L. and Jędrysiak, J.: Geometrically nonlinear vibrations of slender meso-periodic beams. The tolerance modeling approach, Composite Structures, 136, 270-277, 2016.
• [19] Jędrysiak, J.: Tolerance modelling of free vibration frequencies of thin functionally graded plates with one-directional microstructure, Composite Structures, 161, 453-468, 2017.
• [20] Wirowski, A., Michalak, B. and Gajdzicki, M.: Dynamic Modelling of Annular Plates of Functionally Graded Structure Resting on Elastic Heterogeneous Foundation with Two Modules, Journal of Mechanics, 31, 5, 493-504, 2015.
• [21] Perliński, W., Gajdzicki, M. and Michalak, B.: Modelling of annular plates stability with functionally graded structure interacting with elastic heterogeneous subsoil, Journal of Theoretical and Applied Mechanics, 52, 2, 485-498, 2014.
• [22] Pawlus, D.: Stability of three-layered annular plate with composite facings, Appl. Compos. Mater., 24, 1, 141-158, 2017.
• [23] Liu, B., Ferreira, A.J.M., Xing, Y.F. and Neves, A.M.A.: Analysis of composite plates using a layerwise theory and a differential quadrature finite element method, Composite Structures, 156, 393-398, 2016.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).