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The role of micromechanical models in the mechanical response of elastic foundation FG sandwich thick beams

  • Yahiaoui, Mohammed (Department of Civil Engineering, Material and Hydrology Laboratory, Faculty of Technology, University of Sidi Bel Abbes) ;
  • Tounsi, Abdelouahed (Department of Civil Engineering, Material and Hydrology Laboratory, Faculty of Technology, University of Sidi Bel Abbes) ;
  • Fahsi, Bouazza (Laboratoire de Modelisation et Simulation Multi-echelle, Faculte des Sciences Exactes, Universite de Sidi Bel Abbes) ;
  • Bouiadjra, Rabbab Bachir (Department of Civil Engineering, University Mustapha Stambouli of Mascara) ;
  • Benyoucef, Samir (Department of Civil Engineering, Material and Hydrology Laboratory, Faculty of Technology, University of Sidi Bel Abbes)
  • 투고 : 2018.01.04
  • 심사 : 2018.07.18
  • 발행 : 2018.10.10

초록

This paper presents an analysis of the bending, buckling and free vibration of functionally graded sandwich beams resting on elastic foundation by using a refined quasi-3D theory in which both shear deformation and thickness stretching effects are included. The displacement field contains only three unknowns, which is less than the number of parameters of many other shear deformation theories. In order to homogenize the micromechanical properties of the FGM sandwich beam, the material properties are derived on the basis of several micromechanical models such as Tamura, Voigt, Reuss and many others. The principle of virtual works is used to obtain the equilibrium equations. The elastic foundation is modeled using the Pasternak mathematical model. The governing equations are obtained through the Hamilton's principle and then are solved via Navier solution for the simply supported beam. The accuracy of the proposed theory can be noticed by comparing it with other 3D solution available in the literature. A detailed parametric study is presented to show the influence of the micromechanical models on the general behavior of FG sandwich beams on elastic foundation.

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참고문헌

  1. Abdelaziz, H.H., Atmane, H.A., Mechab, I., Boumia, L., Tounsi, A. and Adda Bedia, E.A. (2011), "Static analysis of functionally graded sandwich plates using an efficient and simple refined theory", Chin. J. Aeronaut., 24, 434-448. https://doi.org/10.1016/S1000-9361(11)60051-4
  2. Abdelaziz, H.H., Ait Amar Meziane, M., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. and Alwabli, A.S. (2017), "An efficient hyperbolic shear deformation theory for bending, buckling and free vibration of FGM sandwich plates with various boundary conditions", Steel Compos. Struct., 25(6), 693-704. https://doi.org/10.12989/SCS.2017.25.6.693
  3. Ait Yahia, S., Ait Atmane, H., Houari, M.S.A. and Tounsi, A. (2015), "Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories", Struct. Eng. Mech, Int. J., 53(6), 1143-1165. https://doi.org/10.12989/sem.2015.53.6.1143
  4. Akbarzadeh, A.H., Abedini, A., Chen, Z.T. (2015), "Effect of micromechanical models on structural responses of functionally graded plates", Compos. Struct., 119, 598-609. https://doi.org/10.1016/j.compstruct.2014.09.031
  5. Armagan Karamanli. (2017), "Bending behaviour of two directional functionally graded sandwich beams by using a quasi-3d shear deformation theory", Compos. Struct., 174, 70-68. https://doi.org/10.1016/j.compstruct.2017.04.046
  6. Attia, A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R., Alwabli, A.S. (2018), "A refined four variable plate theory for thermoelastic analysis of FGM plates resting on variable elastic foundations", Struct. Eng. Mech., 65(4), 453-464. https://doi.org/10.12989/SEM.2018.65.4.453
  7. Bachir Bouiadjra, R., Adda Bedia, E.A. and Tounsi, A. (2013), "Nonlinear thermal buckling behavior of functionally graded plates using an efficient sinusoidal shear deformation theory", Struct. Eng. Mech., 48(4), 547-567. https://doi.org/10.12989/sem.2013.48.4.547
  8. Bachir Bouiadjra, R., Mahmoudi, A., Benyoucef, S., Tounsi, A. and Bernard, F. (2018), "Analytical investigation of bending response of FGM plate using a new quasi 3D shear deformation theory: Effect of the micromechanical models", Struct. Eng. Mech., 66(3), 317-328. https://doi.org/10.12989/SEM.2018.66.3.317
  9. Belabed, Z., Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2018), "A new 3-unknown hyperbolic shear deformation theory for vibration of functionally graded sandwich plate", Earthq. Struct., 14(2), 103-115. https://doi.org/10.12989/EAS.2018.14.2.103
  10. Bellifa, H., Bakora, A., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2017), "An efficient and simple four variable refined plate theory for buckling analysis of functionally graded plates", Steel Compos. Struct., 25(3), 257-270. https://doi.org/10.12989/SCS.2017.25.3.257
  11. Benachour, A., Daouadji, H. T., Ait Atmane, H., Tounsi, A. and Meftah, S.A. (2011), "A four variable refined plate theory for free vibrations of functionally graded plates with arbitrary gradient", Compos. Part B-Eng., 42, 1386-1394. https://doi.org/10.1016/j.compositesb.2011.05.032
  12. Benahmed, A., Houari, M.S.A., Benyoucef, S., Belakhdar, K. and Tounsi, A. (2017), "A novel quasi-3D hyperbolic shear deformation theory for functionally graded thick rectangular plates on elastic foundation", Geomech. Eng., 12(1), 9-34. https://doi.org/10.12989/gae.2017.12.1.009
  13. Bennai, R., Ait Atmane, H. and Tounsi, A. (2015), "A new higher-order shear and normal deformation theory for functionally graded sandwich beams", Steel Compos. Struct., 19(3), 521-546. https://doi.org/10.12989/scs.2015.19.3.521
  14. Bennoun, M., Houari, M.S.A. and Tounsi, A. (2016), "A novel five variable refined plate theory for vibration analysis of functionally graded sandwich plates", Mech. Adv. Mater. Struct., 23(4), 423-431. https://doi.org/10.1080/15376494.2014.984088
  15. Benveniste, Y. (1987), "A new approach to the application of Mori-Tanaka's theory in composite materials", Mech. Mater., 6, 147-157. https://doi.org/10.1016/0167-6636(87)90005-6
  16. Bessaim, A., Houari, M.S.A., Tounsi, A., Mahmoud, S.R. and Adda Bedia, E.A. (2013), "A new higher-order shear and normal deformation theory for the static and free vibration analysis of sandwich plates with functionally graded isotropic face sheets", Sandw. Struct. Mater., 15(6), 671-703. https://doi.org/10.1177/1099636213498888
  17. Bouderba, B., Houari, M.S.A. and Tounsi, A. (2013), "Thermomechanical bending response of FGM thick plates resting on Winkler-Pasternak elastic foundations", Steel. Compos. Struct., 14(1), 85-104. https://doi.org/10.12989/scs.2013.14.1.085
  18. Bounouara, F., Benrahou, K.H., Belkorissat, I. and Tounsi, A. (2016), "A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation", Steel Compos. Struct., 20(2), 227-249. https://doi.org/10.12989/scs.2016.20.2.227
  19. Bourada, M., Kaci, A., Houari, M.S.A. and Tounsi, A. (2015), "A new simple shear and normal deformations theory for functionally graded beams", Compos. Struct., 18(2), 409-423. https://doi.org/10.12989/scs.2015.18.2.409
  20. Bourada, M., Tounsi, A., Houari, M.S.A. and Adda Bedia, E.A. (2012), "A new four-variable refined plate theory for thermal buckling analysis of functionally graded sandwich plates", J. Sandw. Struct. Mater., 14(1), 5-33. https://doi.org/10.1177/1099636211426386
  21. Bousahla, A.A., Benyoucef, S., Tounsi, A. and Mahmoud, S.R. (2016), "On thermal stability of plates with functionally graded coefficient of thermal expansion", Struct. Eng. Mech., 60(2), 313-335. https://doi.org/10.12989/sem.2016.60.2.313
  22. Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Adda Bedia, E.A. (2014), "A novel higher order shear and normal deformation theory based on neutral surface position for bending analysis of advanced composite plates", Int. J. Computat. Meth., 11(6), 1350082. https://doi.org/10.1142/S0219876213500825
  23. Carrera, E., Giunta, G. and Petrolo, M. (2011), Beam Structures: Classical and Advanced Theories, John Wiley & Sons.
  24. Chakraborty, A., Gopalakrishnan, S. and Reddy, J.N. (2003), "A new beam finite element for the analysis of functionally graded materials", Int. J. Mech. Sci., 45(3), 519-539. https://doi.org/10.1016/S0020-7403(03)00058-4
  25. Fekrar, A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2014), "A new five-unknown refined theory based on neutral surface position for bending analysis of exponential graded plates", Meccan., 49, 795-810. https://doi.org/10.1007/s11012-013-9827-3
  26. Fourn, H., Ait Atmane, H., Bourada, M., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "A novel four variable refined plate theory for wave propagation in functionally graded material plates material plates|", Steel Compos. Struct., 27(1), 109-122. https://doi.org/10.12989/SCS.2018.27.1.109
  27. Hadji, L., Atmane, H. A., Tounsi, A., Mechab, I. and Adda Bedia, E.A. (2011), "Free vibration of functionally graded sandwich plates using four variable refined plate theory", Appl. Math. Mech., 32, 925-942. https://doi.org/10.1007/s10483-011-1470-9
  28. Hamidi, A., Houari, M.S.A., Mahmoud, S.R. and Tounsi, A. (2015), "A sinusoidal plate theory with 5-unknowns and stretching effect for thermomechanical bending of functionally graded sandwich plates", Steel Compos. Struct., 18(1), 235-253. https://doi.org/10.12989/scs.2015.18.1.235
  29. Hebali, H., Tounsi, A., Houari, M.S.A., Bessaim, A. and Adda Bedia, E.A. (2014), "New quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", J. Eng. Mech., 140, 374-383. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000665
  30. Houari, M.S.A., Benyoucef, S., Mechab, I., Tounsi, A. and Adda Bedia, E.A. (2011), "Two variable refined plate theory for thermoelastic bending analysis of functionally graded sandwich plates", J. Therm. Stress., 34, 315-334. https://doi.org/10.1080/01495739.2010.550806
  31. Jha, D.K., Kant, T. and Singh, R.K. (2013), "critical review of recent research on functionally graded plates", Compos. Struct., 96, 833-849. https://doi.org/10.1016/j.compstruct.2012.09.001
  32. Ju, J. and Chen, T.M. (1994), "Micromechanics and effective moduli of elastic composites containing randomly dispersed ellipsoidal inhomogeneities", Acta. Mech., 103, 103-121.
  33. Kadoli, R., Akhtar, K. and Ganesan, N. (2008), "Static analysis of functionally graded beams using higher order shear deformation theory", Appl. Math. Mod., 32(12), 2509-2525. https://doi.org/10.1016/j.apm.2007.09.015
  34. Kapuria, S., Bhattacharyya, M. and Kumar, A.N. (2008), "Bending and free vibration response of layered functionally graded beams: A theoretical model and its experimental validation", Compos. Struct., 82(3), 390-402. https://doi.org/10.1016/j.compstruct.2007.01.019
  35. Kerr, A.D. (1964), "Elastic and viscoelastic foundation models", ASME J. Appl. Mech., 31(3), 491-498.
  36. Koizumi, M. (1993), "The concept of FGM", Ceram. Trans. Funct. Gradient Mater., 34, 3-10.
  37. Li, X.F. (2008), "A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler- Bernoulli beams", J. Sound Vibr., 318(4-5), 1210-1229. https://doi.org/10.1016/j.jsv.2008.04.056
  38. Mahmoudi, A., Benyoucef, S., Tounsi, A., Benachour, A., Adda Bedia, E.A. and Mahmoud, S.R. (2017), "A refined quasi-3D shear deformation theory for thermo-mechanical behavior of functionally graded sandwich plates on elastic foundations", J. Sandw. Struct. Mater., In Press.
  39. Mantari, J.L. (2015), "A refined theory with stretching effect for the dynamics analysis of advanced composites on elastic foundation", Mech. Mater., 86, 31-43. https://doi.org/10.1016/j.mechmat.2015.02.010
  40. Merdaci, S., Tounsi, A., Houari, M.S.A., Mechab, I., Hebali, H. and Benyoucef, S. (2011), "Two new refined shear displacement models for functionally graded sandwich plates", Arch. Appl. Mech., 81, 1507-1522. https://doi.org/10.1007/s00419-010-0497-5
  41. Mishnaevsky, Jr. L. (2007), Computational Mesomechanics of Composites, John Wiley & Sons, U.K.
  42. Mori, T. and Tanaka, K. (1973), "Average stress in matrix and average elastic energy of materials with misfitting inclusions", Acta. Metall., 21, 571-574. https://doi.org/10.1016/0001-6160(73)90064-3
  43. Nguyen, T.K. and Nguyen, B.D. (2017), "A new higher-order shear deformation theory for static, buckling and free vibration analysis of functionally graded sandwich beams", J. Sandw. Struct. Mater., 17(6), 613-631. https://doi.org/10.1177/1099636215589237
  44. Pasternak, P.L. (1954), On a New Method of Analysis of an Elastic Foundation by Means of Two Foundation Constants, Gosudarstvennoe Izdatelstvo Literaturi po Stroitelstvu i Arkhitekture, Moscow, USSR, 1-56.
  45. Simsek, M. and Kocaturk, T. (2009), "Free and forced vibration of a functionally graded beam subjected to a concentrated moving harmonic load", Compos. Struct., 90(4), 465-473. https://doi.org/10.1016/j.compstruct.2009.04.024
  46. Sina, S.A., Navazi, H.M. and Haddadpour, H. (2009), "An analytical method for free vibration analysis of functionally graded beams", Mater. Des., 30(3), 741-747. https://doi.org/10.1016/j.matdes.2008.05.015
  47. Taibi, F.Z., Benyoucef, S., Tounsi, A., Bachir Bouiadjra, R., Adda Bedia, E.A. and Mahmoud, S.R. (2015), "A simple shear deformation theory for thermo-mechanical behaviour of functionally graded sandwich plates on elastic foundations". J. Sandw. Struct. Mater., 17(2) ,99-129. https://doi.org/10.1177/1099636214554904
  48. Tamura, I., Tomota, Y. and Ozawa, M. (1973), "Strength and ductility of Fe-Ni-C alloys composed of austenite and martensite with various strength", Proceedings of the 3rd International Conference on Strength of Metals and Alloys, Cambridge, 1, 611-615.
  49. Tounsi, A., Houari, M.S.A., Benyoucef, S. and Adda Bedia, E.A. (2013), "A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates", Aerosp. Sci. Technol., 24(1), 209-220. https://doi.org/10.1016/j.ast.2011.11.009
  50. Vo, T.P., Thai, H.T., Nguyen, T.K., Maheri, A. and Lee, J. (2014), "Finite element model for vibration and buckling of functionally graded sandwich beams based on a refined shear deformation theory", Eng. Struct., 64, 12-22.
  51. Voigt, W. (1889), "Uber die beziehung zwischen den beiden elastizitatskonstanten isotroper korper", Wied. Ann. Phys., 38, 573-587.
  52. WANG, X., LI, S., (2016),"Free vibration analysis of functionally graded material beams based on Levinson beam theory", Appl. Math. Mech. -Engl. Ed., 37(7), 861-878. https://doi.org/10.1007/s10483-016-2094-9
  53. Williamson, RL., Rabin, BH., Drake, JT. (1993), "Finite element analysis of thermal residual stresses at graded ceramic-metal interfaces. Part I. Model description and geometrical effects", J. Appl. Phys. 74: 1310-20.
  54. Winkler, E. (1867), Die Lehre von der Elasticitaet und Festigkeit, Prag, Dominicus.
  55. Yaghoobi, H. and Torabi, M. (2013), "Post-buckling and nonlinear free vibration analysis of geometrically imperfect functionally graded beams resting on nonlinear elastic foundation", Appl. Math. Model., 37(18-19), 8324-8340. https://doi.org/10.1016/j.apm.2013.03.037
  56. Yas, M.H., Kamarian, S. and Pourasghar, A. (2017), "Free vibration analysis of functionally graded beams resting on variable elastic foundations using a generalized power-law distribution and GDQ method", Ann. Sol. Struct. Mech.
  57. Zenkour, A.M. (2013), "Bending analysis of functionally graded sandwich plates using a simple four-unknown shear and normal deformations theory", J. Sandw. Struct. Mater, 15(6), 629-659. https://doi.org/10.1177/1099636213498886
  58. Zidi, M., Tounsi, A., Houari M.S.A., Adda Bedia, E.A. and Anwar Beg, O. (2014), "Bending analysis of FGM plates under hygro-thermo-mechanical loading using a four variable refined plate theory", Aerosp. Sci. Technol., 34, 24-34. https://doi.org/10.1016/j.ast.2014.02.001
  59. Zimmerman, R.W. (1994), "Behavior of the Poisson ratio of a two-phase composite material in the high-concentration limit", Appl. Mech. Rev., 47(1),38-44.

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