Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Bending analysis of functionally graded thick plates with in-plane stiffness variation

  • Mazari, Ali (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes) ;
  • Attia, Amina (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes) ;
  • Sekkal, Mohamed (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) ;
  • Tounsi, Abdelouahed (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes) ;
  • Bousahla, Abdelmoumen Anis (Laboratoire de Modelisation et Simulation Multi-echelle, Departement de Physique, Faculte des Sciences Exactes, Departement de Physique, Universite de Sidi Bel Abbes) ;
  • Mahmoud, S.R. (Department of Mathematics, Faculty of Science, King Abdulaziz University)
  • Received : 2018.05.13
  • Accepted : 2018.09.29
  • Published : 2018.11.25
⟨ Previous Next ⟩

Abstract

In the present paper, functionally graded (FG) materials are presented to investigate the bending analysis of simply supported plates. It is assumed that the material properties of the plate vary through their length according to the power-law form. The displacement field of the present model is selected based on quasi-3D hyperbolic shear deformation theory. By splitting the deflection into bending, shear and stretching parts, the number of unknowns and equations of motion of the present formulation is reduced and hence makes them simple to use. Governing equations are derived from the principle of virtual displacements. Numerical results for deflections and stresses of powerly graded plates under simply supported boundary conditions are presented. The accuracy of the present formulation is demonstrated by comparing the computed results with those available in the literature. As conclusion, this theory is as accurate as other shear deformation theories and so it becomes more attractive due to smaller number of unknowns. Some numerical results are provided to examine the effects of the material gradation, shear deformation on the static behavior of FG plates with variation of material stiffness through their length.

Keywords

References

  1. 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
  2. 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.
  3. 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.
  4. 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
  5. 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
  6. Ait Atmane, H., Tounsi, A. and Adda Bedia, E.A. (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
  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. Akavci, S. (2010), "Two new hyperbolic shear displacement models for orthotropic laminated composite plates", Mech. Compos.Mater.,46(2), 215-226. https://doi.org/10.1007/s11029-010-9140-3
  9. Akavci, S.S. and Tanrikulu, A.H. (2015), "Static and free vibration analysis of functionally graded plates based on a new quasi-3D and 2D shear deformation theories", Compos. Part B, 83, 203-215. https://doi.org/10.1016/j.compositesb.2015.08.043
  10. Aldousari, S.M. (2017), "Bending analysis of different material distributions of functionally graded beam", Appl. Phys. A, 123, 296. https://doi.org/10.1007/s00339-017-0854-0
  11. Amirpour, M.R. Das, E.I. and Flores, S. (2016), "Analytical solutions for elastic deformation of functionally graded thick plates with in-plane stiffness variation using higher order shear deformation theory", Compos. Part B., 94, 109-121. https://doi.org/10.1016/j.compositesb.2016.03.040
  12. 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
  13. Attia, A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. and 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
  14. Bachir Bouiadjra, M, Houari, M.S.A. and Tounsi, A. (2012), "Thermal buckling of functionally graded plates according to a four-variable refined plate theory", J. Therm. Stress., 35, 677-694. https://doi.org/10.1080/01495739.2012.688665
  15. Bakhadda, B., Bachir Bouiadjra, M., Bourada, F., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "Dynamic and bending analysis of carbon nanotube-reinforced composite plates with elastic foundation", Wind Struct., 27(5), 311-324. https://doi.org/10.12989/WAS.2018.27.5.311
  16. 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
  17. 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
  18. 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
  19. 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
  20. Bellifa, H., Bakora, A., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2017a), "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
  21. Bellifa, H., Benrahou, K.H., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2017b), "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
  22. 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
  23. Benadouda, M., Ait Atmane, H., Tounsi, A., Bernard, F. and Mahmoud, S.R. (2017), "An efficient shear deformation theory for wave propagation in functionally graded material beams with porosities", Earthq. Struct., 13(3), 255-265. https://doi.org/10.12989/EAS.2017.13.3.255
  24. 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
  25. Benchohra, M., Driz, H., Bakora, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2018), "A new quasi-3D sinusoidal shear deformation theory for functionally graded plates", Struct. Eng. Mech., 65(1), 19-31. https://doi.org/10.12989/SEM.2018.65.1.019
  26. 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
  27. 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
  28. Bilouei, B.S., Kolahchi, R. and Bidgoli, M.R. (2016), "Buckling of concrete columns retrofitted with Nano-Fiber Reinforced Polymer (NFRP)", Comput. Concrete, 18(5), 1053-1063. https://doi.org/10.12989/cac.2016.18.5.1053
  29. Bouadi, A., Bousahla, A.A., Houari, M.S.A., Heireche, H. and Tounsi, A. (2018), "A new nonlocal HSDT for analysis of stability of single layer graphene sheet", Adv. Nano Res., 6(2), 147-162. https://doi.org/10.12989/ANR.2018.6.2.147
  30. 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
  31. 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
  32. Bouderba, B., Houari, M.S.A. and 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
  33. Bouhadra, A., Tounsi, A., Bousahla, A.A., Benyoucef, S. and Mahmoud, S.R. (2018), "Improved HSDT accounting for effect of thickness stretching in advanced composite plates", Struct. Eng. Mech., 66(1), 61-73. https://doi.org/10.12989/SEM.2018.66.1.061
  34. Boukhari, A., Ait Atmane, H., Houari, M.S.A., 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
  35. 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
  36. Bourada, F., Amara, K. and Tounsi, A. (2016), "Buckling analysis of isotropic and orthotropic plates using a novel four variable refined plate theory", Steel Compos. Struct., 21(6), 1287-1306. https://doi.org/10.12989/scs.2016.21.6.1287
  37. 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., 18(2), 409-423. https://doi.org/10.12989/SCS.2015.18.2.409
  38. 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
  39. 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
  40. 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
  41. Carrera, E, Brischetto, S, Cinefra, M. and Soave, M. (2011), "Effects of thickness stretching in functionally graded plates and shells", Compos. Part B, 42(2), 123-133. https://doi.org/10.1016/j.compositesb.2010.10.005
  42. Cherif, R.H., Meradjah, M., Zidour, M., Tounsi, A., Belmahi, H. and Bensattalah, T. (2018), "Vibration analysis of nano beam using differential transform method including thermal effect", J. Nano Res., 54, 1-14.
  43. 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
  44. Dash, S., Sharma, N., Mahapatra, T.R., Panda, S.K. and Sahu, P. (2018), "Free vibration analysis of functionally graded sandwich flat panel", IOP Conf. Ser.: Mater. Sci. Eng., 377, 012140. https://doi.org/10.1088/1757-899X/377/1/012140
  45. 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
  46. Dutta, G., Panda, S.K., Mahapatra, T.R. and Singh, V.K. (2017), "Electro-magneto-elastic response of laminated composite plate: A finite element approach", Int. J. Appl. Comput. Math., 3(3), 2573-2592. https://doi.org/10.1007/s40819-016-0256-6
  47. 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
  48. 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
  49. Fakhar, A. and Kolahchi, R. (2018), "Dynamic buckling of magnetorheological fluid integrated by visco-piezo-GPL reinforced plates", Int. J. Mech. Sci., 144, 788-799. https://doi.org/10.1016/j.ijmecsci.2018.06.036
  50. 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", Steel Compos. Struct., 27(1), 109-122. https://doi.org/10.12989/SCS.2018.27.1.109
  51. Golabchi, H., Kolahchi, R. and Rabani Bidgoli, M. (2018), "Vibration and instability analysis of pipes reinforced by SiO2 nanoparticles considering agglomeration effects", Comput. Concrete, 21(4), 431-440. https://doi.org/10.12989/CAC.2018.21.4.431
  52. Grover, N., Maiti, D.K. and Singh, B.N. (2013), "A new inverse hyperbolic shear deformation theory for static and buckling analysis of laminated composite and sandwich plates", Compos. Struct., 95, 667-675. https://doi.org/10.1016/j.compstruct.2012.08.012
  53. Hachemi, H., Kaci, A., Houari, M.S.A., Bourada, A., 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
  54. Hajmohammad, M.H., Azizkhani, M.B. and Kolahchi, R. (2018a), "Multiphase nanocomposite viscoelastic laminated conical shells subjected to magneto-hygrothermal loads: Dynamic buckling analysis", Int. J. Mech. Sci., 137, 205-213. https://doi.org/10.1016/j.ijmecsci.2018.01.026
  55. Hajmohammad, M.H., Farrokhian, A. and Kolahchi, R. (2018b), "Smart control and vibration of viscoelastic actuator-multiphase nanocomposite conical shells-sensor considering hygrothermal load based on layerwise theory", Aerosp. Sci. Technol., 78, 260-270. https://doi.org/10.1016/j.ast.2018.04.030
  56. Hajmohammad, M.H., Kolahchi, R., Zarei, M.S. and Maleki, M. (2018d), "Earthquake induced dynamic deflection of submerged viscoelastic cylindrical shell reinforced by agglomerated CNTs considering thermal and moisture effects", Compos. Struct., 187, 498-508. https://doi.org/10.1016/j.compstruct.2017.12.004
  57. Hajmohammad, M.H., Maleki, M. and Kolahchi, R. (2018c), "Seismic response of underwater concrete pipes conveying fluid covered with nano-fiber reinforced polymer layer", Soil Dyn. Earthq. Eng., 110, 18-27.
  58. Hajmohammad, M.H., Maleki, M. and Kolahchi, R. (2018e), "Seismic response of underwater concrete pipes conveying fluid covered with nano-fiber reinforced polymer layer", Soil Dyn. Earthq. Eng., 110, 18-27.
  59. Hajmohammad, M.H., Zarei, M.S., Nouri, A. and Kolahchi, R. (2017), "Dynamic buckling of sensor/functionally gradedcarbon nanotube-reinforced laminated plates/actuator based on sinusoidal-visco-piezoelasticity theories", J. Sandw. Struct. Mater., In Press.
  60. 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
  61. 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
  62. Henderson, J.P., Plummer, A. and Johnston, N. (2018), "An electro-hydrostatic actuator for hybrid active-passive vibration isolation", Int. J. Hydromechatron., 1(1), 47-71. https://doi.org/10.1504/IJHM.2018.090305
  63. Hirwani, C.K. and Panda, S.K. (2018), "Numerical and experimental validation of nonlinear deflection and stress responses of pre-damaged glass-fibre reinforced composite structure", Ocean Eng., 159, 237-252.
  64. Hirwani, C.K. and Panda, S.K. (2019), "Nonlinear finite element solutions of thermoelastic deflection and stress responses of internally damaged curved panel structure", Appl. Math. Modell., 65, 303-317.
  65. 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. Ser.: Mater. Sci. Eng., 338, 012019. https://doi.org/10.1088/1757-899X/338/1/012019
  66. 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
  67. Janghorban, M. and Zare, A. (2011), "Free vibration analysis of functionally graded carbon nanotubes with variable thickness by differential quadrature method", Phys. E: Low-Dimens. Syst. Nanostruct., 43(9), 1602-1604. https://doi.org/10.1016/j.physe.2011.05.002
  68. Kaci, A., Houari, M.S.A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "Post-buckling analysis of sheardeformable composite beams using a novel simple twounknown beam theory", Struct. Eng. Mech., 65(5), 621-631. https://doi.org/10.12989/SEM.2018.65.5.621
  69. Kadari, B., Bessaim, A., Tounsi, A., Heireche, H., Bousahla, A.A. and Houari, M.S.A. (2018), "Buckling analysis of orthotropic nanoscale plates resting on elastic foundations", J. Nano Res., Accepted.
  70. Kar, V.R. and Panda, S.K. (2015a), "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
  71. Kar, V.R. and Panda, S.K. (2015b), "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
  72. Kar, V.R. and Panda, S.K. (2016a), "Nonlinear thermomechanical deformation behaviour of P-FGM shallow spherical shell panel", Chin. J. Aeronaut., 29(1), 173-183. https://doi.org/10.1016/j.cja.2015.12.007
  73. Kar, V.R. and Panda, S.K. (2016b), "Nonlinear thermomechanical behavior of functionally graded material cylindrical/hyperbolic/elliptical shell panel with temperaturedependent and temperature-independent properties", J. Press. Vess. Technol., 138(6), 061202.
  74. Karama, M., Afaq, K.S. and Mistou, S. (2003), "Mechanical behaviour of laminated composite beam by the new multilayered laminated composite structures model with transverse shear stress continuity", Int. J. Sol. Struct., 40(6), 1525-1546. https://doi.org/10.1016/S0020-7683(02)00647-9
  75. Karami, B. and Janghorban, M. (2016), "Effect of magnetic field on the wave propagation in nanoplates based on strain gradient theory with one parameter and two-variable refined plate theory", Mod. Phys. Lett. B., 30(36), 1650421. https://doi.org/10.1142/S0217984916504212
  76. Karami, B., Janghorban, M. and Li, L. (2018c), "On guided wave propagation in fully clamped porous functionally graded nanoplates", Acta Astronaut., 143, 380-390.
  77. Karami, B., Janghorban, M. and Tounsi, A. (2018g), "Nonlocal strain gradient 3D elasticity theory for anisotropic spherical nanoparticles", Steel Compos. Struct., 27(2), 201-216. https://doi.org/10.12989/SCS.2018.27.2.201
  78. Karami, B., Janghorban, M. and Tounsi, A. (2018i), "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
  79. Karami, B., Janghorban, M., Shahsavari, D. and Tounsi, A. (2018h), "A size-dependent quasi-3D model for wave dispersion analysis of FG nanoplates", Steel Compos. Struct., 28(1), 99-110. https://doi.org/10.12989/SCS.2018.28.1.099
  80. Karami, B., Shahsavari, D. and Janghorban, M. (2018f), "Wave propagation analysis in functionally graded (FG) nanoplates under in-plane magnetic field based on nonlocal strain gradient theory and four variable refined plate theory", Mech. Adv. Mater. Struct., 25(12), 1047-1057.
  81. Karami, B., Shahsavari, D. and Li, L. (2018b), "Temperaturedependent flexural wave propagation in nanoplate-type porous heterogenous material subjected to in-plane magnetic field", J. Therm. Stress., 41(4), 483-499. https://doi.org/10.1080/01495739.2017.1393781
  82. Karami, B., Shahsavari, D. and Janghorban, M. (2018a), "A sizedependent quasi-3D model for wave dispersion analysis of FG nanoplates", Steel Compos. Struct., 28(1), 99-110. https://doi.org/10.12989/SCS.2018.28.1.099
  83. Karami, B., Shahsavari, D., Karami, M. and Li, L. (2018e), "Hygrothermal wave characteristic of nanobeam-type inhomogeneous materials with porosity under magnetic field", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, In Press.
  84. Karami, B., Shahsavari, D., Li, L., Karami, M. and Janghorban, M. (2018d), "Thermal buckling of embedded sandwich piezoelectric nanoplates with functionally graded core by a nonlocal second-order shear deformation theory", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, In Press.
  85. Katariya, P.V., Hirwani, C.K. and Panda, S.K. (2018), "Geometrically nonlinear deflection and stress analysis of skew sandwich shell panel using higher-order theory", Eng. Comput., In Press.
  86. Katariya, P.V., Panda, S.K. and Mahapatra, T.R. (2017b), "Nonlinear thermal buckling behaviour of laminated composite panel structure including the stretching effect and higher-order finite element", Adv. Mater. Res., 6(4), 349-361. https://doi.org/10.12989/AMR.2017.6.4.349
  87. Katariya, P.V., Panda, S.K., Hirwani, C.K., Mehar, K. and Thakare, O. (2017a), "Enhancement of thermal buckling strength of laminated sandwich composite panel structure embedded with shape memory alloy fibre", Smart Struct. Syst., 20(5), 595-605. https://doi.org/10.12989/SSS.2017.20.5.595
  88. Kettaf, F.Z., Houari, M.S.A., Benguediab, M. and Tounsi, A. (2013), "Thermal buckling of functionally graded sandwich plates using a new hyperbolic shear displacement model", Steel Compos. Struct., 15(4), 399-423. https://doi.org/10.12989/scs.2013.15.4.399
  89. 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
  90. Kitipornchai, S., Yang, J. and Liew, K.M. (2006), "Random vibration of the functionally graded laminates in thermal environments", Comput. Meth. Appl. Mech. Eng., 195(9-12), 1075-1095. https://doi.org/10.1016/j.cma.2005.01.016
  91. 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
  92. Koizumi, M. (1993), "The concept of FGM, ceramic transactions", Function. Grad. Mater., 34, 3-10.
  93. Kolahchi, R. (2017), "A comparative study on the bending, vibration and buckling of viscoelastic sandwich nano-plates based on different nonlocal theories using DC, HDQ and DQ methods", Aerosp. Sci. Technol., 66, 235-248. https://doi.org/10.1016/j.ast.2017.03.016
  94. Kolahchi, R. and Moniri 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
  95. Kolahchi, R., Bidgoli, A.M.M. and Heydari, M.M. (2015), "Size dependent bending analysis of FGM nano-sinusoidal plates resting on orthotropic elastic medium", Struct. Eng. Mech., 55(5), 1001-1014. https://doi.org/10.12989/sem.2015.55.5.1001
  96. Kolahchi, R., Hosseini, H. and Esmailpour, M. (2016a), "Differential cubature and quadrature-Bolotin methods for dynamic stability of embedded piezoelectric nanoplates based on visco-nonlocal-piezoelasticity theories", Compos. Struct., 157, 174-186. https://doi.org/10.1016/j.compstruct.2016.08.032
  97. Kolahchi, R., Keshtegar, B. and Fakhar, M.H. (2017c), "Optimization of dynamic buckling for sandwich nanocomposite plates with sensor and actuator layer based on sinusoidal-visco-piezoelasticity theories using Grey Wolf algorithm", J. Sandw. Struct. Mater., In Press.
  98. Kolahchi, R., Safari, M. and Esmailpour, M. (2016b), "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
  99. Kolahchi, R., Zarei, M.S., Hajmohammad, M.H. and Nouri, A. (2017b), "Wave propagation of embedded viscoelastic FGCNT-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
  100. Kolahchi, R., Zarei, M.S., Hajmohammad, M.H. and Oskouei, A.N. (2017a), "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
  101. Kolahchi, R. and Cheraghbak, A. (2017), "Agglomeration effects on the dynamic buckling of viscoelastic microplates reinforced with SWCNTs using Bolotin method", Nonlin. Dyn., 90, 479-492. https://doi.org/10.1007/s11071-017-3676-x
  102. 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
  103. 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
  104. Mahapatra, T.R., Kar, V.R., Panda, S.K. and Mehar, K. (2017a), "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
  105. Mahapatra, T.R., Mehar, K., Panda, S.K., Dewangan, S. and Dash, S. (2017b), "Flexural strength of functionally graded nanotube reinforced sandwich spherical panel", IOP Conf. Ser.: Mater. Sci. Eng., 178, 012031. https://doi.org/10.1088/1757-899X/178/1/012031
  106. 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
  107. Mantari, J.L. and GuedesSoares, C. (2013), "A novel higher-order shear deformation theory with stretching effect for functionally graded plates", Compos. Part B: Eng., 45(1), 268-281. https://doi.org/10.1016/j.compositesb.2012.05.036
  108. Mantari, J.L., Oktem, A.S. and GuedesSoares, C. (2012), "A new trigonometric shear deformation theory for isotropic, laminated composite and sandwich plates", Int. J. Sol. Struct., 49(1), 43-53. https://doi.org/10.1016/j.ijsolstr.2011.09.008
  109. Mehar, K. and Panda, S.K. (2017a), "Thermoelastic analysis of FG-CNT reinforced shear deformable composite plate under various loadings", Int. J. Appl. Mech., 14(2), 1750019.
  110. 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
  111. Mehar, K. and Panda, S.K. (2018), "Thermoelastic flexural analysis of FG-CNT doubly curved shell panel", Aircr. Eng. Aerosp. Technol., 90(1), 11-23.
  112. Mehar, K., Panda, S.K. and Mahapatra, T.R. (2017a), "Thermoelastic deflection responses of CNT reinforced sandwich shell structure using finite element method", Scientia Iranic., In Press.
  113. Mehar, K., Panda, S.K. and Mahapatra, T.R. (2018), "Large deformation bending responses of nanotube-reinforced polymer composite panel structure: Numerical and experimental analyses", Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, In Press.
  114. Mehar, K., Panda, S.K. and Patle, B.K. (2017b), "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
  115. Mehar, K., Panda, S.K. and Patle, B.K. (2017c), "Stress, deflection, and frequency analysis of CNT reinforced graded sandwich plate under uniform and linear thermal environment: A finite element approach", Polym. Compos., In Press.
  116. Meksi, R, Benyoucef, S., Mahmoudi, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, SR. (2019), "An analytical solution for bending, buckling and vibration responses of FGM sandwich plates", J. Sandw. Struct. Mater., 1099636217698443.
  117. 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
  118. Mindlin, R.D. (1951), "Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates", J. Appl. Mech., 18(1), 31-38.
  119. Mokhtar, Y., Heireche, H., Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2018), "A novel shear deformation theory for buckling analysis of single layer graphene sheet based on nonlocal elasticity theory", Smart Struct. Syst., 21(4), 397-405. https://doi.org/10.12989/SSS.2018.21.4.397
  120. 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
  121. Nami, M.R. and Janghorban, M. (2014), "Resonance behavior of FG rectangular micro/nano plate based on nonlocal elasticity theory and strain gradient theory with one gradient constant", Compos. Struct., 111, 349-353. https://doi.org/10.1016/j.compstruct.2014.01.012
  122. Pradyumna, S. and Bandyopadhyay, J.N. (2008), "Free vibration analysis of functionally graded curved panels using a higherorder finite element formulation", J. Sound Vibr., 318(1-2), 176-192. https://doi.org/10.1016/j.jsv.2008.03.056
  123. 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
  124. 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
  125. Reissner, E. (1945), "The effect of transverse shear deformation on the bending of elastic plates", J. Appl. Mech., 12(2), 69-72.
  126. Ren, J.G. (1986), "A new theory of laminated plate", Compos. Sci. Technol., 26(3), 225-239. https://doi.org/10.1016/0266-3538(86)90087-4
  127. Sahoo, S.S., Panda, S.K. and Singh, V.K. (2017), "Experimental and numerical investigation of static and free vibration responses of woven glass/epoxy laminated composite plate", Proceedings of the Institution of Mechanical Engineers, Part L: J. Mater.: Des. Appl., 231(5), 463-478. https://doi.org/10.1177/1464420715600191
  128. Sekkal, M., Fahsi, B., Tounsi, A. and Mahmoud, S.R. (2017a), "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
  129. Sekkal, M., Fahsi, B., Tounsi, A. and Mahmoud, S.R. (2017b), "A new quasi-3D HSDT for buckling and vibration of FG plate", Struct. Eng. Mech., 64(6), 737-749. https://doi.org/10.12989/SEM.2017.64.6.737
  130. Shahsavari, D., Karami, B., Fahham, H.R. and Li, L. (2018c), "On the shear buckling of porous nanoplates using a new sizedependent quasi-3D shear deformation theory", Acta Mech., In Press.
  131. Shahsavari, D., Karami, B., Janghorban, M. and Li, L. (2017), "Dynamic characteristics of viscoelastic nanoplates under moving load embedded within visco-Pasternak substrate and hygrothermal environment", Mater. Res. Expr., 4(8), 085013. https://doi.org/10.1088/2053-1591/aa7d89
  132. Shahsavari, D., Karami, B. and Mansouri, S. (2018a), "Shear buckling of single layer graphene sheets in hygrothermal environment resting on elastic foundation based on different nonlocal strain gradient theories", Eur. J. Mech.-A/Sol., 67, 200-214. https://doi.org/10.1016/j.euromechsol.2017.09.004
  133. Shahsavari, D., Shahsavarib, M., Li, L. and Karami, B. (2018b), "A novel quasi-3D hyperbolic theory for free vibration of FG plates with porosities resting on Winkler/Pasternak/Kerr foundation", Aerosp. Sci. Technol., 72, 134-149. https://doi.org/10.1016/j.ast.2017.11.004
  134. Shokravi, M. (2017a), "Vibration analysis of silica nanoparticlesreinforced concrete beams considering agglomeration effects", Comput. Concrete, 19(3), 333-338. https://doi.org/10.12989/cac.2017.19.3.333
  135. Shokravi, M. (2017b), "Buckling analysis of embedded laminated plates with agglomerated CNT-reinforced composite layers using FSDT and DQM", Geomech. Eng., 12(2), 327-346. https://doi.org/10.12989/gae.2017.12.2.327
  136. Shokravi, M. (2017c), "Dynamic pull-in and pull-out analysis of viscoelastic nanoplates under electrostatic and Casimir forces via sinusoidal shear deformation theory", Microelectron. Reliab., 71, 17-28.
  137. Shokravi, M. (2017d), "Buckling of sandwich plates with FGCNT-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
  138. Singh, V.K. and Panda, S.K. (2017), "Geometrical nonlinear free vibration analysis of laminated composite doubly curved shell panels embedded with piezoelectric layers", J. Vibr. Contr., 23(13), 2078-2093. https://doi.org/10.1177/1077546315609988
  139. Soldatos, K.P. (1992), "A transverse shear deformation theory for homogeneous monoclinic plates", Acta Mech., 94(3), 195-220. https://doi.org/10.1007/BF01176650
  140. Tornabene, F. (2009), "Free vibration analysis of functionally graded conical, cylindrical shell and annular plate structures with a four-parameter power-law distribution", Comput. Meth. Appl. Mech. Eng., 198(37-40), 2911-2935. https://doi.org/10.1016/j.cma.2009.04.011
  141. Tounsi, A., Houari, M.S.A. and Benyoucef, S. (2013), "A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates", Aerosp. Sci. Technol., 24, 209-220. https://doi.org/10.1016/j.ast.2011.11.009
  142. 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
  143. Xiang, S., Wang, K.M., Ai, Y.T., Sha, Y.D. and Shi, H. (2009), "Analysis of isotropic, sandwich and laminated plates by a meshless method and various shear deformation theories", Compos.Struct., 91(1), 31-37. https://doi.org/10.1016/j.compstruct.2009.04.029
  144. Yamanouchi, M., Koizumi, M., Hirai, T. and Shiota, I. (1990), Proceedings of the 1st International Symposium on Functionally Gradient Materials, Sendai, Japan,
  145. Yang, J., Liew, K.M. and Kitipornchai, S. (2005), "Stochastic analysis of compositionally graded plates with system randomness under static loading", Int. J. Mech. Sci., 47(10), 1519-1541. https://doi.org/10.1016/j.ijmecsci.2005.06.006
  146. Yazid, M., Heireche, H., Tounsi, A., Bousahla, A.A. and Houari, M.S.A. (2018), "A novel nonlocal refined plate theory for stability response of orthotropic single-layer graphene sheet resting on elastic medium", Smart Struct. Syst., 21(1), 15-25. https://doi.org/10.12989/SSS.2018.21.1.015
  147. Youcef, D.O., Kaci, A., Benzair, A., Bousahla, A.A. and Tounsi, A. (2018), "Dynamic analysis of nanoscale beams including surface stress effects", Smart Struct. Syst., 21(1), 65-74. https://doi.org/10.12989/SSS.2018.21.1.065
  148. 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
  149. Zamanian, M., Kolahchi, R. and Bidgoli, M.R. (2017), "Agglomeration effects on the buckling behaviour of embedded concrete columns reinforced with $SiO_{2}$nano-particles", Wind Struct., 24(1), 43-57. https://doi.org/10.12989/was.2017.24.1.043
  150. Zaoui, F.Z., Ouinas, D. and Tounsi, A. (2019), "New 2D and quasi-3D shear deformation theories for free vibration of functionally graded plates on elastic foundations", Compos. Part B, 159, 231-247.
  151. Zarei, M.S., Kolahchi, R., Hajmohammad, M.H. and Maleki, M. (2017), "Seismic response of underwater fluid-conveying concrete pipes reinforced with SiO2 nanoparticles and fiber reinforced polymer (FRP) layer", Soil Dyn. Earthq. Eng., 103, 76-85. https://doi.org/10.1016/j.soildyn.2017.09.009
  152. Zemri, A., Houari, M.S.A., Bousahla, A.A. and Tounsi, A. (2015), "A mechanical response of functionally graded nanoscale beam: an assessment of a refined nonlocal shear deformation theory beam theory", Struct. Eng. Mech., 54(4), 693-710. https://doi.org/10.12989/sem.2015.54.4.693
  153. Zenkour, A.M. (2013), "A simple four-unknown refined theory for bending analysis of functionally graded plates", Appl. Math. Model., 37(20-21), 9041-9051. https://doi.org/10.1016/j.apm.2013.04.022
  154. Zenkour, A.M. (2006), "Generalized shear deformation theory for bending analysis of functionally graded plates", Appl. Math. Modell., 30, 67-84. https://doi.org/10.1016/j.apm.2005.03.009
  155. 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., 64(2), 145-153. https://doi.org/10.12989/sem.2017.64.2.145
  156. Zidi, M., Tounsi, A., Houari, M.S.A. and Beg, O.A. (2014), "Bending analysis of FGM plates under hygro-thermomechanical loading using a four variable refined plate theory", Aerosp. Sci. Technol., 34, 24-34. https://doi.org/10.1016/j.ast.2014.02.001
  157. Zine, A., Tounsi, A., Draiche, K., Sekkal, M. and Mahmoud, S.R. (2018), "A novel higher-order shear deformation theory for bending and free vibration analysis of isotropic and multilayered plates and shells", Steel Compos. Struct., 26(2), 125-137. https://doi.org/10.12989/SCS.2018.26.2.125