Steel and Composite Structures

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

A new simple three-unknown shear deformation theory for bending analysis of FG plates resting on elastic foundations

  • Hachemi, Houari (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes) ;
  • Kaci, Abdelhakim (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes) ;
  • Houari, Mohammed Sid Ahmed (Department of Civil Engineering, Universite Mustapha Stambouli de Mascara) ;
  • Bourada, Mohamed (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes) ;
  • Tounsi, Abdelouahed (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes) ;
  • Mahmoud, S.R. (Department of Mathematics, Faculty of Science, King Abdulaziz University)
  • Received : 2017.04.24
  • Accepted : 2017.09.16
  • Published : 2017.12.30
⟨ Previous Next ⟩

Abstract

In this paper, a new simple shear deformation theory for bending analysis of functionally graded plates is developed. The present theory involves only three unknown and three governing equation as in the classical plate theory, but it is capable of accurately capturing shear deformation effects, instead of five as in the well-known first shear deformation theory and higher-order shear deformation theory. A shear correction factor is, therefore, not required. The material properties of the functionally graded plates are assumed to vary continuously through the thickness, according to a simple power law distribution of the volume fraction of the constituents. Equations of motion are obtained by utilizing the principle of virtual displacements and solved via Navier's procedure. The elastic foundation is modeled as two parameter elastic foundation. The results are verified with the known results in the literature. The influences played by transversal shear deformation, plate aspect ratio, side-to-thickness ratio, elastic foundation, and volume fraction distributions are studied. Verification studies show that the proposed theory is not only accurate and simple in solving the bending behaviour of functionally graded plates, but also comparable with the other higher-order shear deformation theories which contain more number of unknowns.

Keywords

References

  1. Abrate, S. (2008), "Functionally graded plates behave like homogeneous plates", Compos. Part B: Eng., 39(1), 151-158. https://doi.org/10.1016/j.compositesb.2007.02.026
  2. Adda Bedia, W., Benzair, A., Semmah, A., Tounsi, A. and Mahmoud, S.R. (2015), "On the thermal buckling characteristics of armchair single-walled carbon nanotube embedded in an elastic medium based on nonlocal continuum elasticity", Brazil. J. Phys., 45(2), 225-233. https://doi.org/10.1007/s13538-015-0306-2
  3. Ahouel, M., Houari, M.S.A., Adda Bedia, E.A. and Tounsi, A. (2016) "Size-dependent mechanical behavior of functionally graded trigonometric shear deformable nanobeams including neutral surface position concept", Steel Compos. Struct., 20(5), 963-981. https://doi.org/10.12989/scs.2016.20.5.963
  4. 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
  5. Ait Atmane, H., Tounsi, A. and Mechab, I. (2010), "Free vibration analysis of functionally graded plates resting on Winkler-Pasternak elastic foundations using a new shear deformation theory", Int. J. Mech. Mater. Des., 6(2), 113-121. https://doi.org/10.1007/s10999-010-9110-x
  6. Ait Atmane, H., Tounsi, A., Bernard, F. and Mahmoud, S.R. (2015), "A computational shear displacement model for vibrational analysis of functionally graded beams with porosities", Steel Compos. Struct., 19(2), 369-384. https://doi.org/10.12989/scs.2015.19.2.369
  7. 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., 53(6), 1143-1165. https://doi.org/10.12989/sem.2015.53.6.1143
  8. Arefi, M. (2015), "The effect of different functionalities of FGM and FGPM layers on free vibration analysis of the FG circular plates integrated with piezoelectric layers", Smart Struct. Syst., 15(5), 1345-1362. https://doi.org/10.12989/sss.2015.15.5.1345
  9. Attia, A., Tounsi, A., Adda 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
  10. 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", Compos. Part B, 60, 274-283. https://doi.org/10.1016/j.compositesb.2013.12.057
  11. Beldjelili, Y., Tounsi, A. and Mahmoud, S.R. (2016), "Hygrothermo-mechanical bending of S-FGM plates resting on variable elastic foundations using a four-variable trigonometric plate theory", Smart Struct. Syst., 18(4), 755-786. https://doi.org/10.12989/sss.2016.18.4.755
  12. Belkorissat, I., Houari, M.S.A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2015), "On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model", Steel Compos. Struct., 18(4), 1063-1081. https://doi.org/10.12989/scs.2015.18.4.1063
  13. Bellifa, H., Benrahou, K.H., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2017), "A nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams", Struct. Eng. Mech., 62(6), 695-702. https://doi.org/10.12989/SEM.2017.62.6.695
  14. Bellifa, H., Benrahou, K.H., Hadji, L., Houari, M.S.A. and Tounsi, A. (2016), "Bending and free vibration analysis of functionally graded plates using a simple shear deformation theory and the concept the neutral surface position", J. Braz. Soc. Mech. Sci. Eng., 38(1), 265-275. https://doi.org/10.1007/s40430-015-0354-0
  15. Benchohra, M., Driz, H., Bakora, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2017), "A new quasi-3D sinusoidal shear deformation theory for functionally graded plates", Struct. Eng. Mech. (Accepted)
  16. 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
  17. Benyoucef, S., Mechab, I., Tounsi, A., Fekrar, A. and Atmane, H. A. (2010), "Bending of thick functionally graded plates resting on Winkler-Pasternak elastic foundations", Mech. Compos. Mater., 46(4), 425-434. https://doi.org/10.1007/s11029-010-9159-5
  18. 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", J. Sandw. Struct. Mater., 15, 671-703. https://doi.org/10.1177/1099636213498888
  19. 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
  20. Bouafia, K., Kaci, A., Houari, M.S.A., Benzair, A. and Tounsi, A. (2017), "A nonlocal quasi-3D theory for bending and free flexural vibration behaviors of functionally graded nanobeams", Smart Struct. Syst., 19(2), 115-126. https://doi.org/10.12989/sss.2017.19.2.115
  21. 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
  22. 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
  23. Boukhari, A., Ait Atmane, H., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2016), "An efficient shear deformation theory for wave propagation of functionally graded material plates", Struct. Eng. Mech., 57(5), 837-859. https://doi.org/10.12989/sem.2016.57.5.837
  24. 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
  25. Bourada, M., Kaci, A., Houari, M.S.A. and Tounsi, A. (2015), "Anew simple shear and normal deformations theory for functionally graded beams", Steel Compos. Struct., 18(2), 409-423. https://doi.org/10.12989/scs.2015.18.2.409
  26. 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, 5-33. https://doi.org/10.1177/1099636211426386
  27. 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
  28. Bousahla, A.A., Houari, M.S.A., Tounsi, A. and AddaBedia, 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. Meth., 11(6), 1350082. https://doi.org/10.1142/S0219876213500825
  29. Castellazzi, G., Krysl, P. and Bartoli, I. (2013), "A displacement-based finite element formulation for the analysis of laminated composite plates", Compos. Struct., 95, 518-527. https://doi.org/10.1016/j.compstruct.2012.08.029
  30. Chen, C.S., Liu, F.H. and Chen, W.R. (2017), "Vibration and stability of initially stressed sandwich plates with FGM face sheets in thermal environments", Steel Compos. Struct., 23(3), 251-261. https://doi.org/10.12989/scs.2017.23.3.251
  31. 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
  32. Draiche, K., Tounsi, A. and Mahmoud, S.R. (2016), "A refined theory with stretching effect for the flexure analysis of laminated composite plates", Geomech. Eng., 11(5), 671-690. https://doi.org/10.12989/gae.2016.11.5.671
  33. 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
  34. Fahsi, A., Tounsi, A., Hebali, H.,Chikh, A., Adda Bedia, E.A. and Mahmoud, S.R. (2017), "A four variable refined nth-order shear deformation theory for mechanical and thermal buckling analysis of functionally graded plates", Geomech. Eng., 13(3), 385-410. https://doi.org/10.12989/GAE.2017.13.3.385
  35. 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, 795-810. https://doi.org/10.1007/s11012-013-9827-3
  36. 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
  37. Ghugal, Y.M. and Shimpi, R.P. (2002), "A review of refined shear deformation theories of isotropic and anisotropic laminated plates", J. Reinf. Plast. Compos., 21(9), 775-813. https://doi.org/10.1177/073168402128988481
  38. 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
  39. 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., ASCE, 140, 374-383. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000665
  40. Hosseini-Hashemi, S., Taher, H.R.D., Akhavan, H. and Omidi, M. (2010), "Free vibration of functionally graded rectangular plates using first-order shear deformation plate theory", Appl. Math. Model., 34(5), 1276-1291. https://doi.org/10.1016/j.apm.2009.08.008
  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, Z.Y., Lu, C.F. and Chen, W.Q., (2008), "Benchmark solutions for functionally graded thick plates resting on Winkler-Pasternak elastic foundations", Compos. Struct., 85(2), 95-104. https://doi.org/10.1016/j.compstruct.2007.10.010
  43. Kar, V.R., Mahapatra, T.R. and Panda, S.K. (2015), "Nonlinear flexural analysis of laminated composite flat panel under hygrothermo-mechanical loading", Steel Compos. Struct., 19(4), 1011-1033. https://doi.org/10.12989/scs.2015.19.4.1011
  44. Khetir, H., Bachir Bouiadjra, M., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2017), "A new nonlocal trigonometric shear deformation theory for thermal buckling analysis of embedded nanosize FG plates", Struct. Eng. Mech., 64(4), 391-402. https://doi.org/10.12989/SEM.2017.64.4.391
  45. Klouche, F., Darcherif, L., Sekkal, M., Tounsi, A. and Mahmoud, S.R. (2017), "An original single variable shear deformation theory for buckling analysis of thick isotropic plates", Struct. Eng. Mech., 63(4), 439-446. https://doi.org/10.12989/SEM.2017.63.4.439
  46. Lam, K.Y., Wang, C.M. and He, X.Q. (2000), "Canonical exact solutions for Levy-plates on two-parameter foundation using Green's functions", Eng. Struct., 22(4), 364-378. https://doi.org/10.1016/S0141-0296(98)00116-3
  47. Larbi Chaht, F., Kaci, A., Houari, M.S.A., Tounsi, A., Anwar Beg, O. and Mahmoud, S.R. (2015), "Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect", Steel Compos. Struct., 18(2), 425-442. https://doi.org/10.12989/scs.2015.18.2.425
  48. Li, D., Deng, Z. and Xiao, H. (2016), "Thermomechanical bending analysis of functionally graded sandwich plates using fourvariable refined plate theory", Compos. Part B: Eng., 106, 107-119. https://doi.org/10.1016/j.compositesb.2016.08.041
  49. Li, Q., Iu, V.P. and Kou, K.P. (2008), "Three-dimensional vibration analysis of functionally graded material sandwich plates", J. Sound Vib., 311(1), 498-515. https://doi.org/10.1016/j.jsv.2007.09.018
  50. 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), 1-16. https://doi.org/10.1080/01495739.2016.1267955
  51. 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
  52. Mehar, K. and Panda, S.K. (2016), "Nonlinear static behavior of FG-CNT reinforced composite flat panel under thermomechanical load", J. Aerosp. Eng., 30(3), 04016100.
  53. Mehar, K. and Panda, S.K. (2017a), "Thermoelastic analysis of FG-CNT reinforced shear deformable composite plate under various loadings", Int. J. Comput. Meth., 14 (2), 1750019. https://doi.org/10.1142/S0219876217500190
  54. Mehar, K. and Panda, S.K. (2017b), "Numerical investigation of nonlinear thermomechanical deflection of functionally graded CNT reinforced doubly curved composite shell panel under different mechanical loads", Compos. Struct., 161, 287-298. https://doi.org/10.1016/j.compstruct.2016.10.135
  55. 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., 09(4), 1750046. https://doi.org/10.1142/S1758825117500466
  56. 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
  57. Meksi, A., Benyoucef, S., Houari, M.S.A. and Tounsi, A. (2015), "A simple shear deformation theory based on neutral surface position for functionally graded plates resting on Pasternak elastic foundations", Struct. Eng. Mech., 53(6), 1215-1240. https://doi.org/10.12989/sem.2015.53.6.1215
  58. Meksi, R, Benyoucef, S., Mahmoudi, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, SR. (2017), "An analytical solution for bending, buckling and vibration responses of FGM sandwich plates", J. Sandw. Struct. Mater., 1099636217698443.
  59. 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
  60. Meradjah, M., Kaci, A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2015), "A new higher order shear and normal deformation theory for functionally graded beams", Steel Compos. Struct., 18(3), 793-809. https://doi.org/10.12989/scs.2015.18.3.793
  61. 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
  62. Nguyen, T.K., Nguyen, T.T.P., Vo, T.P. and Thai, H.T. (2015), "Vibration and buckling analysis of functionally graded sandwich beams by a new higher-order shear deformation theory", Compos. Part B: Eng., 76, 273-285. https://doi.org/10.1016/j.compositesb.2015.02.032
  63. Nguyen, V.H., Nguyen, T.K., Thai, H.T. and Vo, T.P. (2014), "A new inverse trigonometric shear deformation theory for isotropic and functionally graded sandwich plates", Compos. Part B: Eng., 66, 233-246. https://doi.org/10.1016/j.compositesb.2014.05.012
  64. Pradhan, K.K. and Chakraverty, S. (2015a), "Free vibration of functionally graded thin elliptic plates with various edge supports", Struct. Eng. Mech., 53(2), 337-354. https://doi.org/10.12989/sem.2015.53.2.337
  65. Pradhan, K.K. and Chakraverty, S. (2015b), "Transverse vibration of isotropic thick rectangular plates based on new inverse trigonometric shear deformation theories", Int. J. Mech. Sci., 94, 211-231.
  66. 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
  67. 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. Meth., 11(06), 1350098. https://doi.org/10.1142/S0219876213500989
  68. Sayyad, A.S. and Ghugal, Y.M. (2016), "A unified shear deformation theory for the bending of isotropic, functionally graded, laminated and sandwich beams and plates", Int. J. Appl. Mech., 1750007.
  69. Sekkal, M., Fahsi, B., Tounsi, A. and Mahmoud, S.R. (2017), "A novel and simple higher order shear deformation theory for stability and vibration of functionally graded sandwich plate", Steel Compos. Struct., 25(4), 389-401. https://doi.org/10.12989/SCS.2017.25.4.389
  70. 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
  71. 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
  72. Yaghoobi, H. and Yaghoobi, P. (2013)," Buckling analysis of sandwich plates with FGM face sheets resting on elastic foundation with various boundary conditions: an analytical approach", Meccanica, 48(8), 2019-2035. https://doi.org/10.1007/s11012-013-9720-0
  73. 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
  74. Zidi, M., Houari, M.S.A., Tounsi, A., Bessaim, A. and Mahmoud, S.R. (2017), "A novel simple two-unknown hyperbolic shear deformation theory for functionally graded beams", Struct. Eng. Mech., Int. J., 64(2), 145-153.
  75. Zidi, M., Tounsi, A., Houari, M.S.A., Adda Bedia, E.A. and Anwar Beg, O. (2014), "Bending analysis of FGM plates under hygrothermo-mechanical loading using a four variable refined plate theory", Aerosp. Sci. Tech., 34, 24-34. https://doi.org/10.1016/j.ast.2014.02.001

Cited by

  1. Surface effects on nonlinear vibration and buckling analysis of embedded FG nanoplates via refined HOSDPT in hygrothermal environment considering physical neutral surface position vol.5, pp.6, 2017, https://doi.org/10.12989/aas.2018.5.6.691
  2. A simple quasi-3D HSDT for the dynamics analysis of FG thick plate on elastic foundation vol.31, pp.5, 2017, https://doi.org/10.12989/scs.2019.31.5.503
  3. A new higher-order shear and normal deformation theory for the buckling analysis of new type of FGM sandwich plates vol.72, pp.5, 2019, https://doi.org/10.12989/sem.2019.72.5.653
  4. On the modeling of dynamic behavior of composite plates using a simple nth-HSDT vol.29, pp.6, 2017, https://doi.org/10.12989/was.2019.29.6.371
  5. A numerical method for dynamic characteristics of nonlocal porous metal-ceramic plates under periodic dynamic loads vol.7, pp.1, 2020, https://doi.org/10.12989/smm.2020.7.1.027