Steel and Composite Structures

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Mechanical and hygrothermal behaviour of functionally graded plates using a hyperbolic shear deformation theory

  • Laoufi, Imene (Laboratoire des Materiaux et Hydrologie, Universite de Sidi Bel Abbes) ;
  • Ameur, Mohammed (Laboratoire des Materiaux et Hydrologie, Universite de Sidi Bel Abbes) ;
  • Zidi, Mohamed (Laboratoire des Materiaux et Hydrologie, Universite de Sidi Bel Abbes) ;
  • Bedia, El Abbes Adda (Laboratoire des Materiaux et Hydrologie, Universite de Sidi Bel Abbes) ;
  • Bousahla, Abdelmoumen Anis (Laboratoire des Materiaux et Hydrologie, Universite de Sidi Bel Abbes)
  • Received : 2015.08.17
  • Accepted : 2015.12.21
  • Published : 2016.03.20
⟨ Previous Next ⟩

Abstract

Using the hyperbolic shear deformation plate model and including plate-foundation interaction (Winkler and Pasternak model), an analytical method in order to determine the deflection and stress distributions in simply supported rectangular functionally graded plates (FGP) subjected to a sinusoidal load, a temperature and moisture fields. The present theory exactly satisfies stress boundary conditions on the top and the bottom of the plate. No transversal shear correction factors are needed because a correct representation of the transversal shearing strain is given. Materials properties of the plate (elastic, thermal and moisture expansion coefficients) are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. Numerical examples are presented and discussed for verifying the accuracy of the present theory in predicting the bending response of FGM plates under sinusoidal load and a temperature field as well as moisture concentration. The effects of material properties, temperature, moisture, plate aspect ratio, side-to-thickness ratio, ratio of elastic coefficients (ceramic-metal) and three distributions for both temperature and moisture on deflections and stresses are investigated.

Keywords

References

  1. Ait Amar Meziane, M., Abdelaziz, H.H. and Tounsi, A. (2014), "An efficient and simple refined theory for buckling and free vibration of exponentially graded sandwich plates under various boundary conditions", J. Sandw. Struct. Mater., 16(3), 293-318. https://doi.org/10.1177/1099636214526852
  2. Ait Atmane, H., Tounsi, A. and Bernard, F. (2016), "Effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations", Int. J. Mech. Mater. Des. [In Press]
  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. Bahrami, A. and Nosier, A. (2007), "Interlaminar hygrothermal stresses in laminated plates", Int. J. Solids Struct., 44(25-26), 8119-8142. https://doi.org/10.1016/j.ijsolstr.2007.06.004
  5. Belabed, Z., Houari, M.S.A., Tounsi, A., Mahmoud, S.R. and Anwar Beg, O. (2014), "An efficient and simple higher order shear and normal deformation theory for functionally graded material (FGM) plates", Composites: Part B, 60, 274-283. https://doi.org/10.1016/j.compositesb.2013.12.057
  6. Benachour, A., Tahar, H.D., 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", Composites, Part B, 42(6), 1386-1394. https://doi.org/10.1016/j.compositesb.2011.05.032
  7. 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
  8. Benkhedda, A., Tounsi, A. and Adda bedia, E.A. (2008), "Effect of temperature and humidity on transient hygrothermal stresses during moisture desorption in laminated composite plates", Compos. Struct., 82(4), 629-635. https://doi.org/10.1016/j.compstruct.2007.04.013
  9. Bessaim, A., Houari, M.S.A., Tounsi, A., Mahmoud, S.R. and Adda Bedia, E.A. (2013), "A new higherorder shear and normal deformation theory for the static and free vibration analysis of sandwich plates with functionally graded isotropic face sheets", J. Sandw. Struct. Mater., 15(6), 671-703. https://doi.org/10.1177/1099636213498888
  10. Birman, V. and Byrd, L.W. (2007), "Modeling and analysis of functionally graded materials and structures", Appl. Mech. Rev., 60(1-6), 195-216. https://doi.org/10.1115/1.2777164
  11. Bouchafa, A., Bachir Bouiadjra, M., Houari, M.S.A. and Tounsi, A. (2015), "Thermal stresses and deflections of functionally graded sandwich plates using a new refined hyperbolic shear deformation theory", Steel Compos. Struct., Int. J., 18(6), 1493-1515. https://doi.org/10.12989/scs.2015.18.6.1493
  12. 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., Int. J., 14(1), 85-104. https://doi.org/10.12989/scs.2013.14.1.085
  13. 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
  14. Bourada, M., Kaci, A., Houari, M.S.A. and Tounsi, A. (2015), "A new simple shear and normal deformations theory for functionally graded beams", Steel Compos. Struct., Int. J., 18(2), 409-423. https://doi.org/10.12989/scs.2015.18.2.409
  15. 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. Comput. Method., 11(6), 1350082. https://doi.org/10.1142/S0219876213500825
  16. Dai, K.Y., Liu, G.R., Han, X. and Lim, K.M. (2005), "Thermomechanical analysis of functionally graded material (FGM) plates using element-free Galerkin method", Comput. Struct., 83(17-18), 1487-1502. https://doi.org/10.1016/j.compstruc.2004.09.020
  17. 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", Meccanica, 49(4), 795-810. https://doi.org/10.1007/s11012-013-9827-3
  18. 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., Int. J., 18(1), 235-253. https://doi.org/10.12989/scs.2015.18.1.235
  19. Hebali, H., Tounsi, A., Houari, M.S.A., Bessaim, A. and Adda Bedia, E.A. (2014), "A new quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", ASCE J. Eng. Mech., 140(2), 374-383. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000665
  20. Houari, M.S.A., Tounsi, A. and Anwar Beg, O. (2013), "Thermoelastic bending analysis of functionally graded sandwich plates using a new higher order shear and normal deformation theory", Int. J. Mech. Sci., 76, 467-479.
  21. Javaheri, R. and Eslami, M.R. (2002), "Thermal buckling of functionally graded plates", AIAA J., 40 162-168. https://doi.org/10.2514/2.1626
  22. Khalfi, Y., Houari, M.S.A. and Tounsi, A. (2014), "A refined and simple shear deformation theory for thermal buckling of solar functionally graded plates on elastic foundation", Int. J. Comput. Method., 11(5), 1350077. https://doi.org/10.1142/S0219876213500771
  23. Koizumi, M. (1993), "The concept of FGM, ceramic transactions", Function. Grad. Mater., 34, 3-10.
  24. Liu, G.R. and Tani, J. (1994), "Surface-waves in functionally gradient piezoelectric plates", J. Vib. Acoust., 116(4), 440-448. https://doi.org/10.1115/1.2930447
  25. Liu, G.R., Han, X. and Lam, K.Y. (1999), "Stress waves in functionally gradient materials and its use for material characterization", Compos. Part B-Eng., 30(4), 383-394. https://doi.org/10.1016/S1359-8368(99)00010-4
  26. Liu, G.R., Han, X. and Lam, K.Y. (2001), "An integration technique for evaluating confluent hypergeometric functions and its application to functionally graded materials", Comput. Struct., 79(10), 1039-1047. https://doi.org/10.1016/S0045-7949(00)00197-8
  27. Liu, G.R., Dai, K.Y., Han, X. and Ohyoshi, T. (2003), "Dispersion of waves and characteristic wave surfaces in functionally graded piezoelectric plates", J. Sound Vib., 268(1), 131-147. https://doi.org/10.1016/S0022-460X(02)01494-3
  28. Lo, S.H., Zhen, W., Cheung, Y.K. and Wanji, C. (2010), "Hygrothermal effects on multilayered composite plates using a refined higher order theory", Compos. Struct., 92(3), 633-646. https://doi.org/10.1016/j.compstruct.2009.09.034
  29. Mahi, A., Adda Bedia, E.A. and Tounsi, A. (2015), "A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates", Appl. Math. Model., 39(9), 2489-2508. https://doi.org/10.1016/j.apm.2014.10.045
  30. Patel, B.P., Ganapathi, M. and Makhecha, D.P. (2002), "Hygrothermal effects on the structural behavior of thick composite laminates using higher-order theory", Compos. Struct., 56(1), 25-34. https://doi.org/10.1016/S0263-8223(01)00182-9
  31. Rao, V.V.S. and Sinha, P.K. (2004), "Bending characteristic of thick multidirectional composite plates under hygrothermal environment", J. Reinf. Plast. Compos., 23(14), 1481-1495. https://doi.org/10.1177/0731684404038595
  32. Reddy, J.N. (2000), "Analysis of functionally graded plates", Int. J. Numer. Method. Eng., 47(1-3), 663-684. https://doi.org/10.1002/(SICI)1097-0207(20000110/30)47:1/3<663::AID-NME787>3.0.CO;2-8
  33. Said, A., Ameur, M., Bousahla, A.A. and Tounsi, A. (2014), "A new simple hyperbolic shear deformation theory for functionally graded plates resting on Winkler-Pasternak elastic foundations", Int. J. Comput. Methods, 11(6), 1350098. https://doi.org/10.1142/S0219876213500989
  34. Shen, H.S. (2001), "Hygrothermal effects on the postbuckling of shear deformable laminated plates", Int. J. Mech. Sci., 43(5), 1259-1281. https://doi.org/10.1016/S0020-7403(00)00058-8
  35. Suresh, S. and Mortensen, A. (1998), Fundamentals of Functionally Graded Materials, Institute of Materials (IOM) Communications Limited, London, UK.
  36. Tani, J. and Liu, G.R. (1993), "SH surface-waves in functionally gradient piezoelectric plates", JSME Int. J Series A-Mech. Mater. Eng., 36(2), 152-155. https://doi.org/10.1299/jsmea1993.36.2_152
  37. Thai, H.T. and Choi, D.H. (2013), "A simple first-order shear deformation theory for the bending and free vibration analysis of functionally graded plates", Compos. Struct., 101, 332-340. https://doi.org/10.1016/j.compstruct.2013.02.019
  38. 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
  39. Wang, X., Dong, K. and Wang, X.Y. (2005), "Hygrothermal effect on dynamic interlaminar stresses in laminated plates with piezoelectric actuators", Compos. Struct., 71(2), 220-228. https://doi.org/10.1016/j.compstruct.2004.10.004
  40. Whitney, J.M. and Ashton, J.E. (1971), "Effect of environment on the elastic response of layered composite plates", AIAA J., 9(9), 1708-1713. https://doi.org/10.2514/3.49976
  41. Zenkour, A.M. (2006), "Generalized shear deformation theory for bending analysis of functionally graded plates", Appl. Math. Model., 30(1), 67-84. https://doi.org/10.1016/j.apm.2005.03.009
  42. Zenkour, A.M. (2010), "Hygro-thermo-mechanical effects on FGM plates resting on elastic foundations", Compos. Struct., 93, 234-238. https://doi.org/10.1016/j.compstruct.2010.04.017
  43. Zhang, W., Hao, Y.X. and Yang, J. (2012), "Nonlinear dynamics of FGM circular cylindrical shell with clamped-clamped edges", Compos. Struct., 94(3), 1075-1086. https://doi.org/10.1016/j.compstruct.2011.11.004
  44. 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

Cited by

  1. Hygro-thermo-mechanical bending of S-FGM plates resting on variable elastic foundations using a four-variable trigonometric plate theory vol.18, pp.4, 2016, https://doi.org/10.12989/sss.2016.18.4.755
  2. A simple hyperbolic shear deformation theory for vibration analysis of thick functionally graded rectangular plates resting on elastic foundations vol.11, pp.2, 2016, https://doi.org/10.12989/gae.2016.11.2.289
  3. Thermal post-buckling behavior of imperfect temperature-dependent sandwich FGM plates resting on Pasternak elastic foundation vol.22, pp.1, 2016, https://doi.org/10.12989/scs.2016.22.1.091
  4. An analytical approach for buckling of functionally graded plates vol.5, pp.3, 2016, https://doi.org/10.12989/amr.2016.5.3.141
  5. A novel quasi-3D hyperbolic shear deformation theory for functionally graded thick rectangular plates on elastic foundation vol.12, pp.1, 2016, https://doi.org/10.12989/gae.2017.12.1.009
  6. Non-linear study of mode II delamination fracture in functionally graded beams vol.23, pp.3, 2016, https://doi.org/10.12989/scs.2017.23.3.263
  7. A novel and simple HSDT for thermal buckling response of functionally graded sandwich plates vol.62, pp.4, 2017, https://doi.org/10.12989/sem.2017.62.4.401
  8. A new shear deformation plate theory with stretching effect for buckling analysis of functionally graded sandwich plates vol.24, pp.5, 2017, https://doi.org/10.12989/scs.2017.24.5.569
  9. A simple analytical approach for thermal buckling of thick functionally graded sandwich plates vol.63, pp.5, 2016, https://doi.org/10.12989/sem.2017.63.5.585
  10. An efficient shear deformation theory for wave propagation in functionally graded material beams with porosities vol.13, pp.3, 2016, https://doi.org/10.12989/eas.2017.13.3.255
  11. A four variable refined nth-order shear deformation theory for mechanical and thermal buckling analysis of functionally graded plates vol.13, pp.3, 2016, https://doi.org/10.12989/gae.2017.13.3.385
  12. Vibration analysis of nonlocal advanced nanobeams in hygro-thermal environment using a new two-unknown trigonometric shear deformation beam theory vol.20, pp.3, 2016, https://doi.org/10.12989/sss.2017.20.3.369
  13. A new and simple HSDT for thermal stability analysis of FG sandwich plates vol.25, pp.2, 2016, https://doi.org/10.12989/scs.2017.25.2.157
  14. A novel simple two-unknown hyperbolic shear deformation theory for functionally graded beams vol.64, pp.2, 2016, https://doi.org/10.12989/sem.2017.64.2.145
  15. Free vibration of functionally graded plates resting on elastic foundations based on quasi-3D hybrid-type higher order shear deformation theory vol.20, pp.4, 2017, https://doi.org/10.12989/sss.2017.20.4.509
  16. An efficient and simple four variable refined plate theory for buckling analysis of functionally graded plates vol.25, pp.3, 2016, https://doi.org/10.12989/scs.2017.25.3.257
  17. A novel and simple higher order shear deformation theory for stability and vibration of functionally graded sandwich plate vol.25, pp.4, 2017, https://doi.org/10.12989/scs.2017.25.4.389
  18. A new quasi-3D HSDT for buckling and vibration of FG plate vol.64, pp.6, 2016, https://doi.org/10.12989/sem.2017.64.6.737
  19. An efficient hyperbolic shear deformation theory for bending, buckling and free vibration of FGM sandwich plates with various boundary conditions vol.25, pp.6, 2016, https://doi.org/10.12989/scs.2017.25.6.693
  20. An original HSDT for free vibration analysis of functionally graded plates vol.25, pp.6, 2016, https://doi.org/10.12989/scs.2017.25.6.735
  21. Vibration analysis of thick orthotropic plates using quasi 3D sinusoidal shear deformation theory vol.16, pp.2, 2016, https://doi.org/10.12989/gae.2018.16.2.141
  22. Novel quasi-3D and 2D shear deformation theories for bending and free vibration analysis of FGM plates vol.14, pp.6, 2016, https://doi.org/10.12989/gae.2018.14.6.519
  23. Hygro-thermal post-buckling analysis of a functionally graded beam vol.8, pp.5, 2019, https://doi.org/10.12989/csm.2019.8.5.459
  24. Dynamic and wave propagation investigation of FGM plates with porosities using a four variable plate theory vol.28, pp.1, 2016, https://doi.org/10.12989/was.2019.28.1.049
  25. Vibration response and wave propagation in FG plates resting on elastic foundations using HSDT vol.69, pp.5, 2016, https://doi.org/10.12989/sem.2019.69.5.511
  26. Thermoelastic static and vibrational behaviors of nanocomposite thick cylinders reinforced with graphene vol.31, pp.5, 2019, https://doi.org/10.12989/scs.2019.31.5.529
  27. A study on the structural behaviour of functionally graded porous plates on elastic foundation using a new quasi-3D model: Bending and free vibration analysis vol.25, pp.1, 2020, https://doi.org/10.12989/cac.2020.25.1.037
  28. Bending behaviour of FGM plates via a simple quasi-3D and 2D shear deformation theories vol.9, pp.3, 2020, https://doi.org/10.12989/csm.2020.9.3.237
  29. 3D Stress Analysis of Multilayered Functionally Graded Plates and Shells under Moisture Conditions vol.12, pp.1, 2016, https://doi.org/10.3390/app12010512