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A four variable trigonometric integral plate theory for hygro-thermo-mechanical bending analysis of AFG ceramic-metal plates resting on a two-parameter elastic foundation

  • Tounsi, Abdelouahed (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals) ;
  • Al-Dulaijan, S.U. (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals) ;
  • Al-Osta, Mohammed A. (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals) ;
  • Chikh, Abdelbaki (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Al-Zahrani, M.M. (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals) ;
  • Sharif, Alfarabi (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals) ;
  • Tounsi, Abdeldjebbar (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
  • 투고 : 2019.08.04
  • 심사 : 2019.12.26
  • 발행 : 2020.02.25

초록

In this research, a simple four-variable trigonometric integral shear deformation model is proposed for the static behavior of advanced functionally graded (AFG) ceramic-metal plates supported by a two-parameter elastic foundation and subjected to a nonlinear hygro-thermo-mechanical load. The elastic properties, including both the thermal expansion and moisture coefficients of the plate, are also supposed to be varied within thickness direction by following a power law distribution in terms of volume fractions of the components of the material. The interest of the current theory is seen in its kinematics that use only four independent unknowns, while first-order plate theory and other higher-order plate theories require at least five unknowns. The "in-plane displacement field" of the proposed theory utilizes cosine functions in terms of thickness coordinates to calculate out-of-plane shear deformations. The vertical displacement includes flexural and shear components. The elastic foundation is introduced in mathematical modeling as a two-parameter Winkler-Pasternak foundation. The virtual displacement principle is applied to obtain the basic equations and a Navier solution technique is used to determine an analytical solution. The numerical results predicted by the proposed formulation are compared with results already published in the literature to demonstrate the accuracy and efficiency of the proposed theory. The influences of "moisture concentration", temperature, stiffness of foundation, shear deformation, geometric ratios and volume fraction variation on the mechanical behavior of AFG plates are examined and discussed in detail.

키워드

과제정보

The authors would like to acknowledge the support provided by the Deanship of Scientific Research (DSR) at King Fahd University of Petroleum & Minerals (KFUPM), Saudi Arabia for funding this work through Project No. DF181032. The support provided by the Department of Civil and Environmental Engineering is also acknowledged.

참고문헌

  1. Aliaga, J.W. and Reddy, J.N. (2004), "Nonlinear thermoelastic analysis of functionally graded plates using the third-order shear deformation theory", Int. J. Comp. Eng. Sci., 5(4), 753-779. https://doi.org/10.1142/S146587630400266.
  2. Alibeigloo, A. (2010), "Exact solution for thermo-elastic response of functionally graded rectangular plates", Compos. Struct., 92(1), 113-121. https://doi.org/10.1016/j.compstruct.2009.07.003.
  3. Avcar, M. (2019), "Free vibration of imperfect sigmoid and power law functionally graded beams", Steel Compos. Struct., 30(6), 603-615. https://doi.org/10.12989/scs.2019.30.6.603.
  4. Avcar, M. and Mohammed, W.K.M. (2018), "Free vibration of functionally graded beams resting on Winkler-Pasternak foundation", Arabian J. Geosci., 11(10), 232. https://doi.org/10.1007/s12517-018-3579-2.
  5. Avcar, M. (2016), "Effects of material non-homogeneity and two parameter elastic foundation on fundamental frequency parameters of Timoshenko beams", Acta Physica Polonica A, 130(1), 375-378. DOI: 10.12693/APhysPolA.130.375.
  6. Benferhat, R., HassaineDaouadji, T., Hadji, L. and Said Mansour, M. (2016), "Static analysis of the FGM plate with porosities", Steel Compos. Struct., 21(1), 123 -136. https://doi.org/10.12989/scs.2016.21.1.123.
  7. Bouderba, B. (2018), "Bending of FGM rectangular plates resting on non-uniform elastic foundations in thermal environment using an accurate theory", Steel Compos. Struct., 27(3), 311-325. https://doi.org/10.12989/scs.2018.27.3.311.
  8. Chavan, S.G. and Lal, A. (2017), "Dynamic bending response of SWCNT reinforced composite plates subjected to hygro-thermo-mechanical loading", Comput. Concrete, 20(2), 229-246. https://doi.org/10.12989/cac.2017.20.2.229.
  9. Chen, W.Q., Bian, Z. and Ding, H. (2003), "Three-dimensional analysis of a thick FGM rectangular plate in thermal environment", J. Zhejiang Univ. Sci., 4(1), 1-7. https://doi.org/10.1007/BF02841071.
  10. Chi, S.H. and Chung, Y.L. (2006a), "Mechanical behavior of functionally graded material plates under transverse load-Part I: analysis", Int. J. Solids Struct., 43(13), 3657-3674. https://doi.org/10.1016/j.ijsolstr.2005.04.011.
  11. Chi, S.H. and Chung, Y.L. (2006b), "Mechanical behavior of functionally graded material plates under transverse load -Part II: numerical results", Int. J. Solids Struct., 43(13), 3675-3691. https://doi.org/10.1016/j.ijsolstr.2005.04.010
  12. Civalek, O. and Ozturk, B. (2010), "Free vibration analysis of tapered beam-column with pinned ends embedded in Winkler-Pasternak elastic foundation", Geomech. Eng., 2(1), 45-56. https://doi.org/10.12989/gae.2010.2.1.045.
  13. Daouadji, T.H., Adim, B. and Benferhat, R. (2016), "Bending analysis of an imperfect FGM plates under hygro-thermo-mechanical loading with analytical validation", Adv. Mater. Res., 5(1), 35-53. https://doi.org/10.12989/amr.2016.5.1.035.
  14. Eltaher, M.A., Fouda, N., El-midany, T. and Sadoun, A.M. (2018), "Modified porosity model in analysis of functionally graded porous nanobeams", J. Brazilian Soc. Mech. Sci. Eng., 40, 141. https://doi.org/10.1007/s40430-018-1065-0.
  15. Fadoun, O.O. (2019), "Analysis of axisymmetric fractional vibration of an isotropic thin disc in finite deformation", Comput. Concrete, 23(5), 303-309. https://doi.org/10.12989/cac.2019.23.5.303.
  16. Faleh, N.M., Ahmed, R.A. and Fenjan, R.M. (2018), "On vibrations of porous FG nanoshells", Int. J. Eng. Sci., 133, 1-14. ttps://doi.org/10.1016/j.ijengsci.2018.08.007.
  17. Fazzolari, F.A. (2016), "Modal characteristics of P- and S-FGM plates with temperature-dependent materials in thermal environment", J. Therm. Stresses, 39(7), 854-873. https://doi.org/10.1080/01495739.2016.1189772.
  18. Gulshan Taj, M.N.A., Chakrabarti, A. and Sheikh, A.H. (2013), "Analysis of functionally graded plates using higher order shear deformation theory", Appl. Math. Model., 37(18-19), 8484-8494. https://doi.org/10.1016/j.apm.2013.03.058.
  19. Hirwani, C.K., Biswash, S.,Mehar, K. and Panda, S.K. (2018), "Numerical flexural strength analysis of thermally stressed delaminated composite structure under sinusoidal loading", IOP Conf. Series: Materials Science and Engineering, 338, 012019. doi:10.1088/1757-899X/338/1/012019
  20. Hussain, M. and Naeem, M.N. (2019), "Rotating response on the vibrations of functionally graded zigzag and chiral single walled carbon nanotubes", Appl. Math. Model., 75, 506-520. https://doi.org/10.1016/j.apm.2019.05.039
  21. Kar, V.R. and Panda, S.K. (2015), "Free vibration responses of temperature dependent functionally graded curved panels under thermal environment", Latin Am. J. Solids Struct., 12, 2006-2024. http://dx.doi.org/10.1590/1679-78251691.
  22. Kar, V.R., Mahapatra, T.R. and Panda, S.K. (2015), "Nonlinear flexural analysis of laminated composite flat panel under hygro-thermo-mechanical loading", Steel Compos. Struct., 19(4), 1011-1033. https://doi.org/10.12989/scs.2015.19.4.1011.
  23. Mahapatra, T.R., Panda, S.K. and Dash, S. (2016a), "Effect of hygrothermal environment on the nonlinear free vibration responses of laminated composite plates: A nonlinear Unite element micromechanical approach", IOP CONFERENCE SERIES: MATERIALS SCIENCE and Engineering, 149(1), 012151. https://doi.org/10.1088/1757-899X/149/1/012151
  24. Mahapatra, T.R., Panda, S.K. and Kar, V.R. (2016b), "Nonlinear flexural analysis of laminated composite panel under hygro-thermo-mechanical loading - A Micromechanical Approach", Int. J. Comput. Methods, 13(3), 1650015. https://doi.org/10.1142/S0219876216500158
  25. Mahapatra, T.R., Panda, S.K. and Kar, V.R. (2016c), "Geometrically nonlinear flexural analysis of hygro-thermo-elastic laminated composite doubly curved shell panel", Int. J. Mech. Mater. Design, 12(2), 153-171. https://doi.org/10.1007/s10999-015-9299-9
  26. Mahapatra, T.R., Panda, S.K. (2016), "Hygrothermal effects on the flexural strength of laminated composite cylindrical panels", IOP Conference Series: Materials Science and Engineering, 115(1), 012040. https://doi.org/10.1088/1757-899X/115/1/012040
  27. Mahapatra, T.R. and Panda, S.K. (2015), "Effects of hygrothermal conditions on free vibration behaviour of laminated composite structures", IOP CONFERENCE SERIES: MATERIALS SCIENCE and Engineering, 75(1), 012016. https://doi.org/10.1088/1757-899X/75/1/012016
  28. Mehar, K., Panda, S.K. and Patle, B.K. (2017), "Thermoelastic vibration and flexural behavior of FG-CNT reinforced composite curved panel", Int. J. Appl. Mech., 9(4), 1750046. https://doi.org/10.1142/S1758825117500466.
  29. Mehar, K. and Panda, S.K. (2018), "Nonlinear finite element solutions of thermoelastic flexural strength and stress values of temperature dependent graded CNT-reinforced sandwich shallow shell structure", Struct. Eng. Mech., 67(6), 565-578. https://doi.org/10.12989/sem.2018.67.6.565.
  30. Mindlin, R.D. (1951), "Influence of rotatory inertia and shear on flexural motions of isotropic elastic plates", ASME J. Appl. Mech., 18, 31-38. https://doi.org/10.1115/1.4010217
  31. Nguyen, T.K., Sab, K. and Bonnet, G. (2008), "First-order shear deformation plate models for functionally graded materials", Compos. Struct., 83(1), 25-36. https://doi.org/10.1016/j.compstruct.2007.03.004.
  32. Reddy, J.N. (2000), "Analysis of functionally graded plates", Int. J. Numer. Meth. 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. Panjehpour, M., Woo, E., Loh, K. and Deepak, T.J. (2018), "Structural Insulated Panels: State-of-the-Art", Trends in civil Engineering and its architecture, 3(1) 336-340.
  34. Sahoo, S.S., Panda, S.K. and Singh, V.K. (2016), "Nonlinear flexural analysis of shallow carbon/epoxy laminated composite curved panels: experimental and numerical investigation", J. Eng. Mech., 142(4), 04016008. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001040
  35. Sahoo, S.S., Panda, S.K., Singh, V.K., Mahapatra, T.R. (2017), "Numerical investigation on the nonlinear flexural behaviour of wrapped glass/epoxy laminated composite panel and experimental validation", Arch. Appl. Mech., 87(2), 315-333. https://doi.org/10.1007/s00419-016-1195-8.
  36. Sayyad, A.S. and Ghugal, Y.M. (2019), "Effects of nonlinear hygrothermomechanical loading on bending of FGM rectangular plates resting on two-parameter elastic foundation using four-unknown plate theory", J. Therm. Stresses, 42(2), 213-232. https://doi.org/10.1080/01495739.2018.1469962.
  37. Sayyad, A.S. and Ghugal, Y.M. (2017a), "A unified shear deformation theory for the bending of isotropic, functionally graded, laminated and sandwich beams and plates", Int. J. Appl. Mech., 9(1), 1-36. https://doi.org/10.1142/S1758825117500077.
  38. Sayyad, A.S. and Ghugal, Y.M. (2017b), "Bending, buckling and free vibration of laminated composite and sandwich beams: a critical review of literature", Compos. Struct., 171, 486-504. s://doi.org/10.1016/j.compstruct.2017.03.053.
  39. Sayyad, A.S. and Ghugal, Y.M. (2015), "On the free vibration analysis of laminated composite and sandwich plates: a review of recent literature with some numerical results", Compos. Struct., 129, 177-201. https://doi.org/10.1016/j.compstruct.2015.04.007.
  40. Selmi, A. and Bisharat, A. (2018), "Free vibration of functionally graded SWNT reinforced aluminum alloy beam", J. Vibroeng., 20(5), 2151-2164. https://doi.org/10.21595/jve.2018.19445.
  41. Shahadat, M.R.B., Alam, M.F., Mandal, M.N.A. and Ali, M.M. (2018), "Thermal transportation behaviour prediction of defective graphene sheet at various temperature: A Molecular Dynamics Study", Am. J. Nanomater., 6(1), 34-40.
  42. Sharma, N., Mahapatra, T.R. and Panda, S.K. (2018), "Numerical analysis of acoustic radiation responses of shear deformable laminated composite shell panel in hygrothermal environment", J. Sound Vib., 431, 346-366. tps://doi.org/10.1016/j.jsv.2018.06.007.
  43. Sharma, N., Mahapatra, T.R. and Panda, S.K. (2019), "Hygrothermal effect on vibroacoustic behaviour of higher-order sandwich panel structure with laminated composite face sheets", Eng. Struct., 197, 109355. https://doi.org/10.1016/j.engstruct.2019.109355.
  44. Touratier, M. (1991), "An efficient standard plate theory", Int. J. Eng. Sci., 29(8), 901-916. https://doi.org/10.1016/0020-7225(91)90165-Y.
  45. Vel, S., Batra, R. (2002), "Exact solution for thermoelastic deformations of functionally graded thick rectangular plates", AIAA J., 40(7), 1421-1433. https://doi.org/10.2514/2.1805.
  46. Yaghoobi, H., Valipour, M.S., Fereidoon, A. and Khoshnevisrad, P. (2014), "Analytical study on post-buckling and nonlinear free vibration analysis of FG beams resting on nonlinear elastic foundation under thermo-mechanical loadings using VIM", Steel Compos. Struct., 17(5), 753-776. http://dx.doi.org/10.12989/scs.2014.17.5.753.
  47. Zenkour, A.M. (2006), "Generalized shear deformation theory for bending analysis of functionally graded plates", Appl. Math. Model., 30(1), 67-84. ttps://doi.org/10.1016/j.apm.2005.03.009.
  48. Zidi, M., Tounsi, A., Houari, M.S.A., Adda Bedia, E.A. and Beg, O.A. (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.

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