Structural Engineering and Mechanics

  • 제67권4호
  • /
  • Pages.369-383
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  • 2018
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

A new plate model for vibration response of advanced composite plates in thermal environment

  • Taleb, Ouahiba (University Mustapha Stambouli of Mascara, Department of Civil Engineering) ;
  • Houari, Mohammed Sid Ahmed (University Mustapha Stambouli of Mascara, Department of Civil Engineering) ;
  • Bessaim, Aicha (University Mustapha Stambouli of Mascara, Department of Civil Engineering) ;
  • Tounsi, Abdelouahed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Mahmoud, S.R. (Department of Mathematics, Faculty of Science, King Abdulaziz University)
  • 투고 : 2018.04.11
  • 심사 : 2018.06.01
  • 발행 : 2018.08.25
⟨ 이전 논문 다음 논문 ⟩

초록

In this work, a novel hyperbolic shear deformation theory is developed for free vibration analysis of the simply supported functionally graded plates in thermal environment and the FGM having temperature dependent material properties. This theory has only four unknowns, which is even less than the other shear deformation theories. The theory presented is variationally consistent, without the shear correction factor. The present one has a new displacement field which introduces undetermined integral variables. Equations of motion are obtained by utilizing the Hamilton's principles and solved via Navier's procedure. The convergence and the validation of the proposed theoretical model are performed to demonstrate the efficacy of the model.

키워드

참고문헌

  1. Abualnour, M., Houari, M.S.A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2018), "A novel quasi-3D trigonometric plate theory for free vibration analysis of advanced composite plates", Compos. Struct., 184, 688-697. https://doi.org/10.1016/j.compstruct.2017.10.047
  2. Ahmed, A. (2014), "Post buckling analysis of sandwich beams with functionally graded faces using a consistent higher order theory", Int. J. Civil Struct. Environ., 4(2), 59-64.
  3. Abdelaziz, H.H., Meziane, M.A.A., 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
  4. Akbas, S.D. (2015), "Wave propagation of a functionally graded beam in thermal environments", Steel Compos. Struct., 19(6), 1421-1447. https://doi.org/10.12989/scs.2015.19.6.1421
  5. Alijani, F., Bakhtiari-Nejad, F. and Amabili, M. (2011), "Nonlinear vibrations of FGM rectangular plates in thermal environments", Nonlin. Dyn., 66(3), 251-270. https://doi.org/10.1007/s11071-011-0049-8
  6. Allahverdizadeh, A., Naei, M.H. and Bahrami, M.N. (2008), "Nonlinear free and forced vibration analysis of thin circular functionally graded plates", J. Sound Vibr., 310(4), 966-984. https://doi.org/10.1016/j.jsv.2007.08.011
  7. Amnieh, H.B., Zamzam, M.S. and Kolahchi, R. (2018), "Dynamic analysis of non-homogeneous concrete blocks mixed by SiO2 nanoparticles subjected to blast load experimentally and theoretically", Constr. Build. Mater., 174, 633-644. https://doi.org/10.1016/j.conbuildmat.2018.04.140
  8. Arani, A.G., Cheraghbak, A. and Kolahchi, R. (2016), "Dynamic buckling of FGM viscoelastic nano-plates resting on orthotropic elastic medium based on sinusoidal shear deformation theory", Struct. Eng. Mech., 60(3), 489-505. https://doi.org/10.12989/sem.2016.60.3.489
  9. Arani, A.J. and Kolahchi, R. (2016), "Buckling analysis of embedded concrete columns armed with carbon nanotubes", Comput. Concrete, 17(5), 567-578. https://doi.org/10.12989/cac.2016.17.5.567
  10. Attia, A., Tounsi, A., Bedia, E.A. and Mahmoud, S.R. (2015), "Free vibration analysis of functionally graded plates with temperature-dependent properties using various four variable refined plate theories", Steel Compos. Struct., 18(1), 187-212. https://doi.org/10.12989/scs.2015.18.1.187
  11. Behravan Rad, A. (2015), "Thermo-elastic analysis of functionally graded circular plates resting on a gradient hybrid foundation", Appl. Math. Comput., 256, 276-298.
  12. Belabed, Z., Houari, M.S.A., Tounsi, A., Mahmoud, S.R. and Beg, O.A. (2014), "An efficient and simple higher order shear and normal deformation theory for functionally graded material (FGM) plates", Compos. Part B: Eng., 60, 274-283. https://doi.org/10.1016/j.compositesb.2013.12.057
  13. 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
  14. Beldjelili, Y., Tounsi, A. and Mahmoud, S.R. (2016), "Hygro-thermo-mechanical bending of S-FGM plates resting on variable elastic foundations using a four-variable trigonometric plate theory", Smart Struct. Syst., 18(4), 7 55-786. https://doi.org/10.12989/sss.2016.18.4.755
  15. 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
  16. Bessaim, A., Houari, M.S.A., Bernard, F. and Tounsi, A. (2015), "A nonlocal quasi-3D trigonometric plate model for free vibration behaviour of micro/nanoscale plates", Struct. Eng. Mech., 56(2), 223-240. https://doi.org/10.12989/sem.2015.56.2.223
  17. Besseghier, A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2017), "Free vibration analysis of embedded nanosize FG plates using a new nonlocal trigonometric shear deformation theory", Smart Struct. Syst., 19(6), 601-614. https://doi.org/10.12989/SSS.2017.19.6.601
  18. Bouderba, B., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2016), "Thermal stability of functionally graded sandwich plates using a simple shear deformation theory", Struct. Eng. Mech., 58(3), 397-422. https://doi.org/10.12989/sem.2016.58.3.397
  19. 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
  20. Chakraverty, S. and Pradhan, K.K. (2014), "Free vibration of exponential functionally graded rectangular plates in thermal environment with general boundary conditions", Aerosp. Sci. Technol., 36, 132-156. https://doi.org/10.1016/j.ast.2014.04.005
  21. Chikh, A., Tounsi, A., Hebali, H. and Mahmoud, S.R. (2017), "Thermal buckling analysis of cross-ply laminated plates using a simplified HSDT", Smart Struct. Syst., 19(3), 289-297. https://doi.org/10.12989/sss.2017.19.3.289
  22. Cui, D. and Hu, H. (2016), "Thermal buckling and natural vibration of a rectangular thin plate with in-plane stick-slip-stop boundaries", J. Vibr. Contr., 22(7), 1950-1966. https://doi.org/10.1177/1077546314546394
  23. Darilmaz, K. (2015), "Vibration analysis of functionally graded material (FGM) grid systems", Steel Compos. Struct., 18(2), 395-408. https://doi.org/10.12989/scs.2015.18.2.395
  24. Darilmaz, K., Aksoylu, M.G. and Durgun, Y. (2015), "Buckling analysis of functionally graded material grid systems", Struct. Eng. Mech., 54(5), 877-890. https://doi.org/10.12989/sem.2015.54.5.877
  25. Dinh Due, N. and Hong Cong, P. (2015), "Nonlinear vibration of thick FGM plates on elastic foundation subjected to thermal and mechanical loads using the first-order shear deformation plate theory", Cogent Eng., 2(1), 1045222.
  26. Ebrahimi, F. (2013), "Analytical investigation on vibrations and dynamic response of functionally graded plate integrated with piezoelectric layers in thermal environment", Mech. Adv. Mater. Struct., 20(10), 854-870. https://doi.org/10.1080/15376494.2012.677098
  27. Ebrahimi, F. and Dashti, S. (2015), "Free vibration analysis of a rotating non-uniform functionally graded beam", Steel Compos. Struct., 19(5), 1279-1298. https://doi.org/10.12989/scs.2015.19.5.1279
  28. Ebrahimi, F. and Habibi, S. (2016), "Deflection and vibration analysis of higher-order shear deformable compositionally graded porous plate", Steel Compos. Struct., 20(1), 205-225. https://doi.org/10.12989/scs.2016.20.1.205
  29. Ebrahimi, F. and Jafari, A. (2016), "Thermo-mechanical vibration analysis of temperature-dependent porous FG beams based on Timoshenko beam theory", Struct. Eng. Mech., 59(2), 343-371. https://doi.org/10.12989/sem.2016.59.2.343
  30. El-Haina, F., Bakora, A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2017), "A simple analytical approach for thermal buckling of thick functionally graded sandwich plates", Struct. Eng. Mech., 63(5), 585-595. https://doi.org/10.12989/SEM.2017.63.5.585
  31. Ferreira, A.J.M., Castro, L.M. and Bertoluzza, S. (2009), "A high order collocation method for the static and vibration analysis of composite plates using a first-order theory", Compos. Struct., 89(3), 424-432. https://doi.org/10.1016/j.compstruct.2008.09.006
  32. Hachemi, H., Kaci, A., Houari, M.S.A., Bourada, M., Tounsi, A. and Mahmoud, S.R. (2017), "A new simple three-unknown shear deformation theory for bending analysis of FG plates resting on elastic foundations", Steel Compos. Struct., 25(6), 717-726. https://doi.org/10.12989/SCS.2017.25.6.717
  33. Hajmohammad, M.H., Zarei, M.S., Nouri, A. and Kolahchi, R. (2017), "Dynamic buckling of sensor/functionally graded-carbon nanotube-reinforced laminated plates/actuator based on sinusoidal-visco-piezoelasticity theories", J. Sandw. Struct. Mater., 1099636217720373.
  34. Hajmohammad, M.H., Maleki, M. and Kolahchi, R. (2018), "Seismic response of underwater concrete pipes conveying fluid covered with nano-fiber reinforced polymer layer", Soil Dyn. Earthq. Eng., 110, 18-27. https://doi.org/10.1016/j.soildyn.2018.04.002
  35. Hirwani, C.K., Panda, S.K., Mahapatra, T.R. and Mahapatra, S.S. (2017), "Numerical study and experimental validation of dynamic characteristics of delaminated composite flat and curved shallow shell structure", J. Aerosp. Eng., 30(5), 04017045. https://doi.org/10.1061/(ASCE)AS.1943-5525.0000756
  36. Hirwani, C.K. and Panda, S.K. (2018), "Numerical nonlinear frequency analysis of pre-damaged curved layered composite structure using higher-order finite element method", Int. J. Non-Lin. Mech., 102, 14-24. https://doi.org/10.1016/j.ijnonlinmec.2018.03.005
  37. Hirwani, C.K., Panda, S.K. and Mahapatra, T.R. (2018a), "Thermomechanical deflection and stress responses of delaminated shallow shell structure using higher-order theories", Compos. Struct., 184, 135-145. https://doi.org/10.1016/j.compstruct.2017.09.071
  38. Hirwani, C.K., Panda, S.K. and Mahapatra, T.R. (2018b), "Nonlinear finite element analysis of transient behavior of delaminated composite plate", J. Vibr. Acoust., 140(2), 021001.
  39. Hirwani, C.K., Biswash, S., Mehar, K. and Panda, S.K. (2018c), "Numerical flexural strength analysis of thermally stressed delaminated composite structure under sinusoidal loading", In IOP Conference Series: Materials Science and Engineering, 22(1), 012019. https://doi.org/10.1088/1755-1315/22/1/012019
  40. Houari, M.S.A., Tounsi, A. and Beg, O.A. (2013), "Thermoelastic bending analysis of functionally graded sandwich plates using a new higher order shear and normal deformation theory", Int. J. Mech. Sci., 76, 102-111. https://doi.org/10.1016/j.ijmecsci.2013.09.004
  41. Houari, M.S.A., Tounsi, A., Bessaim, A. and Mahmoud, S.R. (2016), "A new simple three-unknown sinusoidal shear deformation theory for functionally graded plates", Steel Compos. Struct., 22(2), 257-276. https://doi.org/10.12989/scs.2016.22.2.257
  42. Huang, X.L. and Shen, H.S. (2004), "Nonlinear vibration and dynamic response of functionally graded plates in thermal environments", Int. J. Sol. Struct., 41(9), 2403-2427. https://doi.org/10.1016/j.ijsolstr.2003.11.012
  43. Joshi, P.V., Jain, N.K., Ramtekkar, G.D. and Virdi, G.S. (2016), "Vibration and buckling analysis of partially cracked thin orthotropic rectangular plates in thermal environment", Thin-Wall. Struct., 109, 143-158. https://doi.org/10.1016/j.tws.2016.09.020
  44. Joshi, P.V., Gupta, A., Jain, N.K., Salhotra, R., Rawani, A.M. and Ramtekkar, G.D. (2017), "Effect of thermal environment on free vibration and buckling of partially cracked isotropic and FGM micro plates based on a non-classical Kirchhoff's plate theory: An analytical approach", Int. J. Mech. Sci., 131, 155-170.
  45. Kaci, A., Houari, M.S.A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "Post-buckling analysis of shear-deformable composite beams using a novel simple two-unknown beam theory", Sturct. Eng. Mech., 65(5), 621-631.
  46. Kar, V.R. and Panda, S.K. (2014), "Large deformation bending analysis of functionally graded spherical shell using FEM", Struct. Eng. Mech., 53(4), 661-679. https://doi.org/10.12989/SEM.2015.53.4.661
  47. Kar, V.R. and Panda, S.K. (2015a), "Nonlinear flexural vibration of shear deformable functionally graded spherical shell panel", Steel Compos. Struct., 18(3), 693-709. https://doi.org/10.12989/scs.2015.18.3.693
  48. Kar, V. R. and Panda, S.K. (2015b), "Free vibration responses of temperature dependent functionally graded curved panels under thermal environment", Lat. Am. J. Sol. Struct., 12(11), 2006-2024. https://doi.org/10.1590/1679-78251691
  49. Kar, V.R., Mahapatra, T.R. and Panda, S.K. (2017), "Effect of different temperature load on thermal postbuckling behaviour of functionally graded shallow curved shell panels", Compos. Struct., 160, 1236-1247. https://doi.org/10.1016/j.compstruct.2016.10.125
  50. Karami, B., Janghorban, M. and Tounsi, A. (2018), "Nonlocal strain gradient 3D elasticity theory for anisotropic spherical nanoparticles", Steel Compos. Stntct., 27(2), 201-216.
  51. Karami, B., Janghorban, M. and Tounsi, A. (2018), "Variational approach for wave dispersion in anisotropic doubly-curved nanoshells based on a new nonlocal strain gradient higher order shell theory", Thin-Wall. Struct., 129, 251-264. https://doi.org/10.1016/j.tws.2018.02.025
  52. Kant, T. (1993), "A critical review and some results of recently developed refined theories of fiber-reinforced laminated composites and sandwiches", Compos. Struct., 23(4), 293-312. https://doi.org/10.1016/0263-8223(93)90230-N
  53. Kant, T. and Swaminathan, K. (2001), "Free vibration of isotropic, orthotropic, and multilayer plates based on higher order refined theories", J. Sound Vibr., 241(2), 319-327. https://doi.org/10.1006/jsvi.2000.3232
  54. Khetir, H., Bachir Bouiadjra, M., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2017), "A new nonlocal trigonometric shear deformation theory for them1al buckling analysis of embedded nanosize FG plates", Struct. Eng. Mech., 64(4), 391-402. https://doi.org/10.12989/SEM.2017.64.4.391
  55. Kim, Y.W. (2005), "Temperature dependent vibration analysis of functionally graded rectangular plates", J. Sound Vibr., 284(3), 531-549. https://doi.org/10.1016/j.jsv.2004.06.043
  56. Kirchhoff, G.R. (1850), Uber Das Gleichgewicht Und Die Bewegung Einer Elastischen Scheibe.
  57. Kolahchi, R., Safari, M. and Esmailpour, M. (2016a), "Dynamic stability analysis of temperature-dependent functionally graded CNT-reinforced visco-plates resting on orthotropic elastomeric medium", Compos. Struct., 150, 255-265. https://doi.org/10.1016/j.compstruct.2016.05.023
  58. Kolahchi, R. and Bidgoli, A.M. (2016), "Size-dependent sinusoidal beam model for dynamic instability of single-walled carbon nanotubes", Appl. Math. Mech., 37(2), 265-274. https://doi.org/10.1007/s10483-016-2030-8
  59. Kolahchi, R., Zarei, M.S., Hajmohammad, M.H. and Nouri, A. (2017a), "Wave propagation of embedded viscoelastic FG-CNT-reinforced sandwich plates integrated with sensor and actuator based on refined zigzag theory", Int. J. Mech. Sci., 130, 534-545. https://doi.org/10.1016/j.ijmecsci.2017.06.039
  60. Kolahchi, R., Zarei, M.S., Hajmohammad, M.H. and Oskouei, A.N. (2017b), "Visco-nonlocal-refined zigzag theories for dynamic buckling of laminated nanoplates using differential cubature-Bolotin methods", Thin-Wall. Struct., 113, 162-169. https://doi.org/10.1016/j.tws.2017.01.016
  61. Lei, Z.X., Liew, K.M. and Yu, J.L. (2013), "Free vibration analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method in thermal environment", Compos. Struct., 106, 128-138. https://doi.org/10.1016/j.compstruct.2013.06.003
  62. Li, Q., Iu, V.P. and Kou, K.P. (2008), "Three-dimensional vibration analysis of functionally graded material sandwich plates", J. Sound Vibr., 311(1), 498-515. https://doi.org/10.1016/j.jsv.2007.09.018
  63. Li, Q., Iu, V.P. and Kou, K.P. (2009), "Three-dimensional vibration analysis of functionally graded material plates in thermal environment", J. Sound Vibr., 324(3), 733-750. https://doi.org/10.1016/j.jsv.2009.02.036
  64. Li, S.R. and Cheng, C.J. (2009), "Free vibration of functionally graded material beams with surface-bonded piezoelectric layers in thermal environment", Appl. Math. Mech., 30(8), 969-982. https://doi.org/10.1007/s10483-009-0803-7
  65. Lim, C.W., Yang, Q. and Lu, C.F. (2009), "Two-dimensional elasticity solutions for temperature-dependent in-plane vibration of FGM circular arches", Compos. Struct., 90(3), 323-329. https://doi.org/10.1016/j.compstruct.2009.03.014
  66. Lim, T.K. and Kim, J.H. (2017), "Thermo-micromechanical vibration behaviors of FGM structures with neutral surface", Appl. Mech. Mater., 864, 162-166. https://doi.org/10.4028/www.scientific.net/AMM.864.162
  67. Madani, H., Hosseini, H. and Shokravi, M. (2016), "Differential cubature method for vibration analysis of embedded FG-CNT-reinforced piezoelectric cylindrical shells subjected to uniform and non-uniform temperature distributions", Steel Compos. Struct., 22(4), 889-913. https://doi.org/10.12989/scs.2016.22.4.889
  68. Mahapatra, T.R. and Panda, S.K. (2015), "Thermoelastic vibration analysis of laminated doubly curved shallow panels using nonlinear FEM", J. Therm. Stress., 38(1), 39-68. https://doi.org/10.1080/01495739.2014.976125
  69. Mahapatra, T.R., Kar, V.R. and Panda, S.K. (2015), "Nonlinear free vibration analysis of laminated composite doubly curved shell panel in hygrothermal environment", J. Sandw. Struct. Mater., 17(5), 511-545. https://doi.org/10.1177/1099636215577363
  70. Mahapatra, T.R. and Panda, S.K. (2016), "Nonlinear free vibration analysis of laminated composite spherical shell panel under elevated hygrothermal enviromnent: A micromechanical approach", Aerosp. Sci. Technol., 49, 276-288. https://doi.org/10.1016/j.ast.2015.12.018
  71. Mahapatra, T.R., Kar, V.R. and Panda, S.K. (2016a), "Large amplitude vibration analysis of laminated composite spherical panels under hygrothermal environment", Int. J. Struct. Stab. Dyn., 16(3), 1450105. https://doi.org/10.1142/S0219455414501053
  72. Mahapatra, T.R., Panda, S.K. and Kar, V.R. (2016b), "Nonlinear hygro-thermo-elastic vibration analysis of doubly curved composite shell panel using finite element micromechanical model", Mech. Adv. Mater. Struct., 23(11), 1343-1359. https://doi.org/10.1080/15376494.2015.1085606
  73. Mahapatra, T.R., Panda, S.K. and Kar, V.R. (2016c), "Nonlinear flexural analysis of laminated composite panel under hygro-thermo- mechanical loading-a micromechanical approach", Int. J. Comput. Meth., 13(3), 1650015. https://doi.org/10.1142/S0219876216500158
  74. Mahapatra, T.R., Kar, V.R. , Panda, S.K. and Mehar, K. (2017), "Nonlinear thermoelastic deflection of temperature-dependent FGM curved shallow shell under nonlinear thermal loading", J. Therm. Stress., 40(9), 1184-1199. https://doi.org/10.1080/01495739.2017.1302788
  75. 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, 2489-2508. https://doi.org/10.1016/j.apm.2014.10.045
  76. Malekzadeh, P., Shahpari, S.A. and Ziaee, H.R. (2010), "Three-dimensional free vibration of thick functionally graded annular plates in them1al environment", J. Sound Vibr., 329(4), 425-442. https://doi.org/10.1016/j.jsv.2009.09.025
  77. Malekzadeh, P. and Heydarpour, Y. (2012), "Free vibration analysis of rotating functionally graded cylindrical shells in thermal environment", Compos. Struct., 94(9), 2971-2981. https://doi.org/10.1016/j.compstruct.2012.04.011
  78. Malekzadeh, P. and Monajjemzadeh, S.M. (2016), "Dynamic response of functionally graded beams in a thermal environment under a moving load", Mech. Adv. Mater. Struct., 23(3), 248-258. https://doi.org/10.1080/15376494.2014.949930
  79. Mehar, K., Panda, S.K., Dehengia, A. and Kar, V.R. (2016), "Vibration analysis of functionally graded carbon nanotube reinforced composite plate in thermal environment", J. Sandw. Struct. Mater., 18(2), 151-173. https://doi.org/10.1177/1099636215613324
  80. Mehar, K., Panda, S.K. and Mahapatra, T.R. (2017a), "Thermoelastic nonlinear frequency analysis of CNT reinforced functionally graded sandwich structure", Eur. J. Mech.-A/Sol., 65, 384-396.
  81. Mehar, K., Panda, S.K., Bui, T.Q. and Mahapatra, T.R. (2017b), "Nonlinear thermoelastic frequency analysis of functionally graded CNT-reinforced single/doubly curved shallow shell panels by FEM", J. Therm. Stress., 40(7), 899-916. https://doi.org/10.1080/01495739.2017.1318689
  82. Menasria, A., Bouhadra, A., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2017), "A new and simple HSDT for thermal stability analysis of FG sandwich plates", Steel Compos. Struct., 25(2), 157-175. https://doi.org/10.12989/SCS.2017.25.2.157
  83. Mouffoki, A., Adda Bedia, E.A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2017), "Vibration analysis of nonlocal advanced nanobeams in hygro-thermal environment using a new two-unknown trigonometric shear deformation beam theory", Smart Struct. Syst., 20(3), 369-383. https://doi.org/10.12989/SSS.2017.20.3.369
  84. Nguyen, T.K. (2015), "A higher-order hyperbolic shear deformation plate model for analysis of functionally graded materials", Int. J. Mech. Mater. Des., 11(2), 203-219. https://doi.org/10.1007/s10999-014-9260-3
  85. Panda, S.K. and Mahapatra, T.R. (2014), "Nonlinear finite element analysis of laminated composite spherical shell vibration under uniform thermal loading", Meccan., 49(1), 191-213. https://doi.org/10.1007/s11012-013-9785-9
  86. Pandey, S. and Pradyumna, S. (2015), "Free vibration of functionally graded sandwich plates in thermal environment using a layerwise theory", Eur. J. Mech.-A/Sol., 51, 55-66. https://doi.org/10.1016/j.euromechsol.2014.12.001
  87. Parandvar, H. and Farid, M. (2016), "Nonlinear dynamic response of functionally graded shallow shells under harmonic excitation in thermal environment using finite element method", Compos. Struct., 149, 351-361. https://doi.org/10.1016/j.compstruct.2016.04.018
  88. Praveen, G.N. and Reddy, J.N. (1998), "Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates", Int. J. Sol. Struct., 35(33), 4457-4476. https://doi.org/10.1016/S0020-7683(97)00253-9
  89. Reddy, J.N. (1984), "A simple higher-order theory for laminated composite plates", J. Appl. Mech., 51(4), 745-752. https://doi.org/10.1115/1.3167719
  90. Reissner, E. (1945), "The effect of transverse shear deformation on the bending of elastic plates".
  91. Sahoo, S.S., Panda, S.K. and Mahapatra, T.R. (2016), "Static, free vibration and transient response of laminated composite curved shallow panel-an experimental approach", Eur. J. Mech.-A/Sol., 59, 95-113. https://doi.org/10.1016/j.euromechsol.2016.03.014
  92. Sahoo, S.S., Hirwani, C.K., Panda, S.K. and Sen, D. (2017), "Numerical analysis of vibration and transient behaviour of laminated composite curved shallow shell structure: An experimental validation", Sci. Iran.
  93. Shahrjerdi, A., Mustapha, F., Bayat, M. and Majid, D.L.A. (2011), "Free vibration analysis of solar functionally graded plates with temperature-dependent material properties using second order shear deformation theory", J. Mech. Sci. Techol., 25(9), 2195-2209. https://doi.org/10.1007/s12206-011-0610-x
  94. Shi, G. (2007), "A new simple third-order shear deformation theory of plates", Int. J. Sol. Struct., 44(13), 4399-4417. https://doi.org/10.1016/j.ijsolstr.2006.11.031
  95. Setoodeh, A.R., Ghorbanzadeh, M. and Malekzadeh, P. (2012), "A two-dimensional free vibration analysis of functionally graded sandwich beams under thermal environment", J. Mech. Eng. Sci., 226(12), 2860-2873. https://doi.org/10.1177/0954406212440669
  96. Shokravi, M. (2017), "Buckling of sandwich plates with FG-CNT-reinforced layers resting on orthotropic elastic medium using Reddy plate theory", Steel Compos. Struct., 23(6), 623-631. https://doi.org/10.12989/SCS.2017.23.6.623
  97. Srinivas, S., Rao, C.J. and Rao, A.K. (1970), "An exact analysis for vibration of simply-supported homogeneous and laminated thick rectangular plates", J. Sound Vibr., 12(2), 187-199. https://doi.org/10.1016/0022-460X(70)90089-1
  98. Sofiyev, A.H. and Kuruoglu, N. (2015), "Buckling of nonhomogeneous orthotropic conical shells subjected to combined load", Steel Compos. Struct., 19(1), 1-19. https://doi.org/10.12989/scs.2015.19.1.001
  99. Sofiyev, A.H. and Osmancelebioglu, E. (2017), "The free vibration of sandwich truncated conical shells containing functionally graded layers within the shear deformation theory", Compos. Part B: Eng., 120, 197-211. https://doi.org/10.1016/j.compositesb.2017.03.054
  100. Sundararajan, N., Prakash, T. and Ganapathi, M. (2005), "Nonlinear free flexural vibrations of functionally graded rectangular and skew plates under thermal environments", Fin. Elem. Analy. Des., 42(2), 152-168. https://doi.org/10.1016/j.finel.2005.06.001
  101. Tounsi, A., Houari, M.S.A. and Bessaim, A. (2016), "A new 3- unknowns non-polynomial plate theory for buckling and vibration of functionally graded sandwich plate", Struct. Eng. Mech., 60(4), 547-565. https://doi.org/10.12989/sem.2016.60.4.547
  102. Wattanasakulpong, N., Prusty, G.B. and Kelly, D.W. (2013), "Free and forced vibration analysis using improved third-order shear deformation theory for functionally graded plates under high temperature loading", J. Sandw. Struct. Mater., 15(5), 583-606. https://doi.org/10.1177/1099636213495751
  103. Woo, J., Meguid, S.A. and Ong, L.S. (2006), "Nonlinear free vibration behavior of functionally graded plates", J. Sound Vibr., 289(3), 595-611. https://doi.org/10.1016/j.jsv.2005.02.031
  104. Wu, Z., Cheung, Y.K., Lo, S.H. and Chen, W. (2008), "Effects of higher-order global-local shear deformations on bending, vibration and buckling of multilayered plates", Compos. Struct., 82(2), 277-289. https://doi.org/10.1016/j.compstruct.2007.01.017
  105. Xiao, J.R., Batra, R.C., Gilhooley, D.F., Gillespie, J.W. and McCarthy, M.A. (2007), "Analysis of thick plates by using a higher-order shear and normal deformable plate theory and MLPG method with radial basis functions", Comput. Meth. Appl. Mech. Eng., 196(4), 979-987. https://doi.org/10.1016/j.cma.2006.08.002
  106. Yang, J. and Shen, H.S. (2002), "Vibration characteristics and transient response of shear-deformable functionally graded plates in thermal environments", J. Sound Vibr., 255(3), 579-602. https://doi.org/10.1006/jsvi.2001.4161
  107. Yang, J. and Shen, H.S. (2003), "Nonlinear bending analysis of shear deformable functionally graded plates subjected to thermo-mechanical loads under various boundary conditions", Compos. Part B: Eng., 34(2), 103-115. https://doi.org/10.1016/S1359-8368(02)00083-5
  108. 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 loading using VIM", Steel Compos. Struct., 17(5), 753-776. https://doi.org/10.12989/scs.2014.17.5.753
  109. Younsi, A., Tounsi, A., Zaoui, F.Z., Bousahla, A.A. and Mahmoud, S.R. (2018), "Novel quasi-3D and 2D shear deformation theories for bending and free vibration analysis of FGM plates", Geomech. Eng., 14(6), 519-532. https://doi.org/10.12989/GAE.2018.14.6.519
  110. Zamanian, M., Kolahchi, R. and Bidgoli, M.R. (2017), "Agglomeration effects on the buckling behaviour of embedded concrete columns reinforced with SiO2 nano-particles", Wind Sytruct., 24(1), 43-57. https://doi.org/10.12989/was.2017.24.1.043

피인용 문헌

  1. On the finite element analysis of functionally graded sandwich curved beams via a new refined higher order shear deformation theory vol.279, pp.None, 2022, https://doi.org/10.1016/j.compstruct.2021.114715