Computers and Concrete

  • 제26권1호
  • /
  • Pages.63-74
  • /
  • 2020
  • /
  • 1598-8198(pISSN)
  • /
  • 1598-818X(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Bending analysis of functionally graded porous plates via a refined shear deformation theory

  • Zine, Abdallah (Faculty of Technology, Civil Engineering Department, Material and Hydrology Laboratory, University of Sidi Bel Abbes) ;
  • Bousahla, Abdelmoumen Anis (Laboratoire de Modelisation et Simulation Multi-echelle, Universite de Sidi Bel Abbes) ;
  • Bourada, Fouad (Faculty of Technology, Civil Engineering Department, Material and Hydrology Laboratory, University of Sidi Bel Abbes) ;
  • Benrahou, Kouider Halim (Faculty of Technology, Civil Engineering Department, Material and Hydrology Laboratory, University of Sidi Bel Abbes) ;
  • Tounsi, Abdeldjebbar (Faculty of Technology, Civil Engineering Department, Material and Hydrology Laboratory, University of Sidi Bel Abbes) ;
  • Adda Bedia, E.A. (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals) ;
  • Mahmoud, S.R. (GRC Department, Jeddah Community College, King Abdulaziz University) ;
  • Tounsi, Abdelouahed (Faculty of Technology, Civil Engineering Department, Material and Hydrology Laboratory, University of Sidi Bel Abbes)
  • 투고 : 2020.02.03
  • 심사 : 2020.06.10
  • 발행 : 2020.07.25
⟨ 이전 논문 다음 논문 ⟩

초록

In this investigation, study of the bending response of functionally graded (FG) porous plates is presented using a cubic shear deformation theory. The properties of the FG-plate vary according to a power-law distribution which is modified to approximate material characteristics for considering the effect of porosities. The equilibrium equations are derived by using the principle of virtual work and solved by using Navier's procedure. Various numerical results are discussed to demonstrate the influence of the variation of the power index, the porosity parameter and the geometric ratios on the bending response of FG porous plates.

키워드

참고문헌

  1. Abdelmalek, A., Bouazza, M., Zidour, M. and Benseddiq, N. (2019), "Hygrothermal effects on the free vibration behavior of composite plate using nth-order shear deformation theory: a micromechanical approach", Iran J. Sci. Technol. Tran. Mech. Eng., 43, 61-73. https://doi.org/10.1007/s40997-017-0140-y.
  2. Abedini, M., Raman, S.N., Mutalib, A.A. and Akhlaghi, E. (2019), "Strengthening of the panel zone in steel moment-resisting frames", Adv. Comput. Des., 4(4), 327-342. https://doi.org/10.12989/acd.2019.4.4.327.
  3. Abrate, S. (2006), "Free vibration, buckling, and static deflections of functionally graded plates", Compos. Sci. Technol., 66(14), 2383-2394. https://doi.org/10.1016/j.compscitech.2006.02.032.
  4. Akbas, S.D. (2018), "Forced vibration analysis of functionally graded porous deep beams", Compos. Struct., 186, 293-302. https://doi.org/10.1016/j.compstruct.2017.12.013.
  5. Akbas, S.D. (2019a), "Hygrothermal post-buckling analysis of laminated composite beams", Int. J. Appl. Mech., 11(1), 1950009. https://doi.org/10.1142/S1758825119500091.
  6. Akbas, S.D. (2019b), "Forced vibration analysis of functionally graded sandwich deep beams", Coupl. Syst. Mech., 8(3), 259-271. https://doi.org/10.12989/csm.2019.8.3.259.
  7. Al-Maliki, A.F., Faleh, N.M. and Alasadi, A.A. (2019), "Finite element formulation and vibration of nonlocal refined metal foam beams with symmetric and non-symmetric porosities", Struct. Monit. Maint., 6(2), 147-159. https://doi.org/10.12989/smm.2019.6.2.147.
  8. Alizadeh, M. and Fattahi, A.M. (2019), "Non-classical plate model for FGMs", Eng. Comput., 35, 215-228. https://doi.org/10.1007/s00366-018-0594-6.
  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. Arshid, E. and Khorshidvand, A.R. (2018), "Free vibration analysis of saturated porous FG circular plates integrated with piezoelectric actuators via differential quadrature method", Thin Wall. Struct., 125, 220-233. https://doi.org/10.1016/j.tws.2018.01.007.
  11. Avcar, M. (2014), "Free vibration analysis of beams considering different geometric characteristics and boundary conditions", Int. J. Mech. Appl., 4(3), 94-100. https://doi.org/10.5923/j.mechanics.20140403.03.
  12. Avcar, M. (2019), "Free vibration of imperfect sigmoid and power law functionally graded beams", Steel Compos. Struct., 30(6), 603-615. https://doi.org/10.12989/scs.2019.30.6.603.
  13. Ayat, H., Kellouche, Y., Ghrici, M. and Boukhatem, B. (2018), "Compressive strength prediction of limestone filler concrete using artificial neural networks", Adv. Comput. Des., 3(3), 289-302. https://doi.org/10.12989/acd.2018.3.3.289.
  14. Babaei, M., Hajmohammad, M.H. and Asemi, K. (2019), "Natural frequency and dynamic analyses of functionally graded saturated porous annular sector plate and cylindrical panel based on 3D elasticity", Aerosp. Sci. Technol., 105524. https://doi.org/10.1016/j.ast.2019.105524.
  15. Barati, M.R. (2017a), "Dynamic response of porous functionally graded material nanobeams subjected to moving nanoparticle based on nonlocal strain gradient theory", Mater. Res. Express, 4(11), 115017. https://doi.org/10.1088/2053-1591/aa9765.
  16. Barati, M.R. (2017b), "Nonlocal-strain gradient forced vibration analysis of metal foam nanoplates with uniform and graded porosities", Adv Nano Res., 5(4), 393-414. https://doi.org/10.12989/anr.2017.5.4.393.
  17. Barati, M.R. and Shahverdi, H. (2020), "Finite element forced vibration analysis of refined shear deformable nanocomposite graphene platelet-reinforced beams", J. Brazil. Soc. Mech. Sci. Eng., 42, 33. https://doi.org/10.1007/s40430-019-2118-8.
  18. Beena, K.P. and Parvathy, U. (2014), "Linear static analysis of functionally graded plate using spline finite strip method", Compos. Struct., 117, 309-315. https://doi.org/10.1016/j.compstruct.2014.07.002.
  19. Castellazzi, G., Gentilini, C., Krysl, P. and Elishakoff, I. (2013), "Static analysis of functionally graded plates using a nodal integrated finite element approach", Compos. Struct., 103, 197-200. https://doi.org/10.1016/j.compstruct.2013.04.013.
  20. Chen, D., Kitipornchai, S. and Yang, J. (2018), "Dynamic response and energy absorption of functionally graded porous structures", Mater. Des., 140, 473-487. https://doi.org/10.1016/j.matdes.2017.12.019.
  21. Chen, D., Yang, J. and Kitipornchai, S. (2019), "Buckling and bending analyses of a novel functionally graded porous plate using Chebyshev-Ritz method", Arch. Civil Mech. Eng., 19(1), 157-170. https://doi.org/10.1016/j.acme.2018.09.004.
  22. Cheng, Z.Q. and Batra, R.C. (2000), "Deflection relationships between the homogeneous Kirchhoff plate theory and different functionally graded plate theories", Arch. Mech., 52(1), 143-158.
  23. Dihaj, A., Zidour, M., Meradjah, M., Rakrak, K., Heireche, H. and Chemi, A. (2018), "Free vibration analysis of chiral double-walled carbon nanotube embedded in an elastic medium using non-local elasticity theory and Euler Bernoulli beam model", Struct. Eng. Mech., 65(3), 335-342. https://doi.org/10.12989/sem.2018.65.3.335.
  24. Dong, Y.H. and Li, Y.H. (2017), "A unified nonlinear analytical solution of bending, buckling and vibration for the temperature-dependent FG rectangular plates subjected to thermal load", Compos. Struct., 159, 689-701. https://doi.org/10.1016/j.compstruct.2016.10.001.
  25. Ebrahimi, F. and Barati, M.R. (2018), "Stability analysis of functionally graded heterogeneous piezoelectric nanobeams based on nonlocal elasticity theory", Adv. Nano Res., 6(2), 93-112. https://doi.org/10.12989/anr.2018.6.2.093.
  26. Ebrahimi, F. and Rastgo, A. (2008), "An analytical study on the free vibration of smart circular thin FGM plate based on classical plate theory", Thin Wall. Struct., 46(12), 1402-1408. https://doi.org/10.1016/j.tws.2008.03.008.
  27. Eltaher, M.A., Almalki, T.A., Almitani, K.H., Ahmed, K.I.E. and Abdraboh, A.M. (2019), "Modal participation of fixed-fixed single-walled carbon nanotube with vacancies", Int. J. Adv. Struct. Eng., 11, 151-163. https://doi.org/10.1007/s40091-019-0222-8.
  28. Eltaher, M.A., Fouda, N., El-midany, T. and Sadoun, A.M. (2018), "Modified porosity model in analysis of functionally graded porous nanobeams", J. Brazil. Soc. Mech. Sci. Eng., 40. https://doi.org/10.1007/s40430-018-1065-0.
  29. Eltaher, M.A., Mohamed, S.A. and Melaibari, A. (2020), "Static stability of a unified composite beams under varying axial loads", Thin Wall. Struct., 147, 106488. https://doi.org/10.1016/j.tws.2019.106488.
  30. Faleh, N.M., Ahmed, R.A. and Fenjan, R.M. (2018), "On vibrations of porous FG nanoshells", Int. J. Eng. Sci., 133, 1-14. https://doi.org/10.1016/j.ijengsci.2018.08.007.
  31. Faleh, N.M., Fenjan, R.M. and Ahmed, R.A. (2020), "Forced vibrations of multi-phase crystalline porous shells based on strain gradient elasticity and pulse load effects", J. Vib. Eng. Technol., 1-9. https://doi.org/10.1007/s42417-020-00203-8.
  32. Fattahi, A.M. and Sahmani, S. (2017), "Size dependency in the axial Postbuckling behavior of nanopanels made of functionally graded material considering surface elasticity", Arab. J. Sci. Eng., 42, 4617-4633. https://doi.org/10.1007/s13369-017-2600-5.
  33. Fattahi, A.M., Safaei, B. and Ahmed, N.A. (2019b), "A comparison for the non-classical plate model based on axial buckling of single-layered graphene sheets", Eur. Phys. J. Plus, 134, 555. https://doi.org/10.1140/epjp/i2019-12912-7.
  34. Fattahi, A.M., Sahmani, S. and Ahmed, N.A. (2019a), "Nonlocal strain gradient beam model for nonlinear secondary resonance analysis of functionally graded porous micro/nano-beams under periodic hard excitations", Mech. Bas. Des. Struct. Mach., 48(4), 403-432. https://doi.org/10.1080/15397734.2019.1624176.
  35. Fenjan, R.M., Ahmed, R.A., Alasadi, A.A. and Faleh, N.M. (2019a), "Nonlocal strain gradient thermal vibration analysis of double-coupled metal foam plate system with uniform and non-uniform porosities", Coupl. Syst. Mech., 8(3), 247-257. https://doi.org/10.12989/csm.2019.8.3.247.
  36. Ferreira, A.J.M., Batra, R.C., Roque, C.M.C., Qian, L.F. and Martins, P.A.L.S. (2005), "Static analysis of functionally graded plates using third-order shear deformation theory and a meshless method", Compos. Struct., 69(4), 449-457. https://doi.org/10.1016/j.compstruct.2004.08.003.
  37. Fladr, J., Bily, P. and Broukalova, I. (2019), "Evaluation of steel fiber distribution in concrete by computer aided image analysis", Compos. Mater. Eng., 1(1), 49-70. https://doi.org/10.12989/cme.2019.1.1.049.
  38. Foroutan, K., Shaterzadeh, A. and Ahmadi, H. (2019), "Nonlinear static and dynamic hygrothermal buckling analysis of imperfect functionally graded porous cylindrical shells", Appl. Math. Model., 77, 539-553. https://doi.org/10.1016/j.apm.2019.07.062.
  39. Forsat, M., Badnava, S., Mirjavadi, S.S., Barati, M.R. and Hamouda, A.M.S. (2020), "Small scale effects on transient vibrations of porous FG cylindrical nanoshells based on nonlocal strain gradient theory", Eur. Phys. J. Plus, 135(1), 81. https://doi.org/10.1140/epjp/s13360-019-00042-x.
  40. Ghannadpour, S.A.M. and Mehrparvar, M. (2020), "Modeling and evaluation of rectangular hole effect on nonlinear behavior of imperfect composite plates by an effective simulation technique", Compos. Mater. Eng., 2(1), 25-41. https://doi.org/10.12989/cme.2020.2.1.025.
  41. Ghodrati, B., Yaghootian, A., Zadeh, A.G. and Sedighi, H.M. (2018), "Lamb wave extraction of dispersion curves in micro/nano-plates using couple stress theories", Wave. Rand. Complex Media, 28(1), 15-34. https://doi.org/10.1080/17455030.2017.1308582.
  42. Gupta, A. and Talha, M. (2018), "Influence of porosity on the flexural and vibration response of gradient plate using nonpolynomial higher-order shear and normal deformation theory", Int. J. Mech. Mater. Des., 14, 277-296. https://doi.org/10.1007/s10999-017-9369-2.
  43. Hadji, L., Zouatnia, N. and Bernard, F. (2019), "An analytical solution for bending and free vibration responses of functionally graded beams with porosities: Effect of the micromechanical models", Struct. Eng. Mech., 69(2), 231-241. https://doi.org/10.12989/sem.2019.69.2.231.
  44. Hajmohammad, M.H., Kolahchi, R., Zarei, M.S. and Nouri, A.H. (2019), "Dynamic response of auxetic honeycomb plates integrated with agglomerated CNT-reinforced face sheets subjected to blast load based on visco-sinusoidal theory", Int. J. Mech. Sci., 153, 391-401. https://doi.org/10.1016/j.ijmecsci.2019.02.008.
  45. Hamed, M.A., Mohamed, S.A. and Eltaher, M.A. (2020), "Buckling analysis of sandwich beam rested on elastic foundation and subjected to varying axial in-plane loads", Steel Compos. Struct., 34(1), 75. https://doi.org/10.12989/scs.2020.34.1.075.
  46. Hamed, M.A., Sadoun, A.M. and Eltaher, M.A. (2019), "Effects of porosity models on static behavior of size dependent functionally graded beam", Struct. Eng. Mech., 71(1), 89-98. https://doi.org/10.12989/sem.2019.71.1.089.
  47. Hamidi, A., Zidour, M., Bouakkaz, K. and Bensattalah, T. (2018), "Thermal and small-scale effects on vibration of embedded armchair single-walled carbon nanotubes", J. Nano Res., 51, 24-38. https://doi.org/10.4028/www.scientific.net/JNanoR.51.24.
  48. Hosseini-Hashemi, S., Fadaee, M. and Atashipour, S.R. (2011), "A new exact analytical approach for free vibration of Reissner-Mindlin functionally graded rectangular plates", Int. J. Mech. Sci., 53(1), 11-22. https://doi.org/10.1016/j.ijmecsci.2010.10.002.
  49. Jabbari, M., Mojahedin, A. and Haghi, M. (2014), "Buckling analysis of thin circular FG plates made of saturated porous-soft ferromagnetic materials in transverse magnetic field", Thin Wall. Struct., 85, 50-56. https://doi.org/10.1016/j.tws.2014.07.018.
  50. Jamali, M., Shojaee, T., Mohammadi, B. and Kolahchi, R. (2019), "Cut out effect on nonlinear post-buckling behavior of FG-CNTRC micro plate subjected to magnetic field via FSDT", Adv. Nano Res., 7(6), 405-417. https://doi.org/10.12989/anr.2019.7.6.405.
  51. Jouneghani, F.Z., Dimitri, R. and Tornabene, F. (2018), "Structural response of porous FG nanobeams under hygro-thermo-mechanical loadings", Compos. Part B: Eng., 152, 71-78. https://doi.org/10.1016/j.compositesb.2018.06.023.
  52. Karami, B. and Janghorban, M. (2019), "On the dynamics of porous nanotubes with variable material properties and variable thickness", Int. J. Eng. Sci., 136, 53-66. https://doi.org/10.1016/j.ijengsci.2019.01.002.
  53. Karami, B., Shahsavari, D. and Janghorban, M. (2019), "On the dynamics of porous doubly-curved nanoshells", Int. J. Eng. Sci., 143, 39-55. https://doi.org/10.1016/j.ijengsci.2019.06.014.
  54. Kolahchi, R. and Cheraghbak, A. (2017), "Agglomeration effects on the dynamic buckling of viscoelastic microplates reinforced with SWCNTs using Bolotin method", Nonlin. Dyn., 90(1), 479-492. https://doi.org/10.1007/s11071-017-3676-x.
  55. Kolahchi, R., Zarei, M.S., Hajmohammad, M.H. and Nouri, A. (2017), "Wave propagation of embedded viscoelastic FG-CNT-reinforced sandwich plates integrated with sensor and actuator based on refined zigzag theory", Int. J. Eng. Sci., 130, 534-545. https://doi.org/10.1016/j.ijmecsci.2017.06.039.
  56. Koochi, A., Sedighi, H.M. and Abadyan, M. (2014), "Modeling the size dependent pull-in instability of beam-type NEMS using strain gradient theory", Lat. Am. J. Solid. Struct., 11(10), 1806-1829. http://dx.doi.org/10.1590/S1679-78252014001000007.
  57. Lal, A., Jagtap, K.R. and Singh, B.N. (2017), "Thermo-mechanically induced finite element based nonlinear static response of elastically supported functionally graded plate with random system properties", Adv. Comput. Des., 2(3), 165-194. https://doi.org/10.12989/acd.2017.2.3.165.
  58. Lee, N.J., Lai, G.S., Lau, W.J. and Ismail, A.F. (2020), "Effect of poly(ethylene glycol) on the properties of mixed matrix membranes for improved filtration of highly concentrated oily solution", Compos. Mater. Eng., 2(1), 43-51. https://doi.org/10.12989/cme.2020.2.1.043.
  59. Levinson, M. (1980), "An accurate, simple theory of the statics and dynamics of elastic plates", Mecha. Res. Commun., 7(6), 343-350. https://doi.org/10.1016/0093-6413(80)90049-x.
  60. Lopez-Chavarria, S., Luevanos-Rojas, A., Medina-Elizondo, M., Sandoval-Rivas, R. and Velazquez-Santillan, F. (2019), "Optimal design for the reinforced concrete circular isolated footings", Adv. Comput. Des., 4(3), 273-294. https://doi.org/10.12989/acd.2019.4.3.273.
  61. Malekzadeh, P. (2009), "Three-dimensional free vibration analysis of thick functionally graded plates on elastic foundations", Compos. Struct., 89(3), 367-373. https://doi.org/10.1016/j.compstruct.2008.08.007.
  62. Mantari, J.L., Ramos, I.A., Carrera, E. and Petrolo, M. (2016), "Static analysis of functionally graded plates using new non-polynomial displacement fields via Carrera Unified Formulation", Compos. Part B: Eng., 89, 127-142. https://doi.org/10.1016/j.compositesb.2015.11.025.
  63. Mirjavadi, S., Forsat, M., Barati, M.R., Abdella, G.M., Mohasel Afshari, B., Hamouda, A.M.S. and Rabby, S. (2019b), "Dynamic response of metal foam FG porous cylindrical micro-shells due to moving loads with strain gradient size-dependency", Eur. Phys. J. Plus, 134(5), 214. https://doi.org/10.1140/epjp/i2019-12540-3.
  64. Mirjavadi, S.S., Forsat, M., Hamouda, A. and Barati, M.R. (2019a), "Dynamic response of functionally graded graphene nanoplatelet reinforced shells with porosity distributions under transverse dynamic loads", Mater. Res. Express, 6(7), 075045. https://doi.org/10.1088/2053-1591/ab1552.
  65. Moayedi, H., Darabi, R., Ghabussi, A., Habibi, M. and Foong, L.K. (2020), "Weld orientation effects on the formability of tailor welded thin steel sheets", Thin Wall. Struct., 149, 106669. https://doi.org/10.1016/j.tws.2020.106669
  66. Mohamed, N., Mohamed, A., Eltaher, M.A., Mohamed, S.A. and Seddek, L.F. (2019), "Energy equivalent model in analysis of postbuckling of imperfect carbon nanotubes resting on nonlinear elastic foundation", Struct. Eng. Mech., 70(6), 737-750. https://doi.org/10.12989/sem.2019.70.6.737.
  67. Motezaker, M. and Kolahchi, R. (2017), "Seismic response of concrete columns with nanofiber reinforced polymer layer", Comput. Concrete, 20(3), 361-368. https://doi.org/10.12989/cac.2017.20.3.361
  68. Oyarhossein, M.A., Alizadeh, A.A., Habibi, M., Makkiabadi, M., Daman, M., Safarpour, H. and Jung, D.W. (2020), "Dynamic response of the nonlocal strain-stress gradient in laminated polymer composites microtubes", Sci. Rep., 10, 5616. https://doi.org/10.1038/s41598-020-61855-w.
  69. Pradhan, K.K. and Chakraverty, S. (2015), "Static analysis of functionally graded thin rectangular plates with various boundary supports", Arch. Civil Mech. Eng., 15(3), 721-734. https://doi.org/10.1016/j.acme.2014.09.008.
  70. Rajabi, J. and Mohammadimehr, M. (2019), "Bending analysis of a micro sandwich skew plate using extended Kantorovich method based on Eshelby-Mori-Tanaka approach", Comput. Concrete, 23(5), 361-376. https://doi.org/10.12989/cac.2019.23.5.361.
  71. Ramirez, F., Heyliger, P.R. and Pan, E. (2006), "Static analysis of functionally graded elastic anisotropic plates using a discrete layer approach", Compos. Part B: Eng., 37(1), 10-20. https://doi.org/10.1016/j.compositesb.2005.05.009.
  72. Reddy, J.N. (1984), "A simple higher-order theory for laminated composite plates", J. Appl. Mech., 51(4), 745. https://doi.org/10.1115/1.3167719.
  73. Rezaiee-Pajand, M., Masoodi, A.R. and Mokhtari, M. (2018), "Static analysis of functionally graded non-prismatic sandwich beams", Adv. Comput. Des., 3(2), 165-190. https://doi.org/10.12989/acd.2018.3.2.165.
  74. Rouzegar, J. and Abad, F. (2015), "Free vibration analysis of FG plate with piezoelectric layers using four-variable refined plate theory", Thin Wall. Struct., 89, 76-83. https://doi.org/10.1016/j.tws.2014.12.010.
  75. Safa, A., Hadji, L., Bourada, M. and Zouatnia, N. (2019), "Thermal vibration analysis of FGM beams using an efficient shear deformation beam theory", Earthq. Struct., 17(3), 329-336. https://doi.org/10.12989/eas.2019.17.3.329.
  76. Safaei, B., Ahmed, N.A. and Fattahi, A.M. (2019), "Free vibration analysis of polyethylene/CNT plates", Eur. Phys. J. Plus, 134, 271. https://doi.org/10.1140/epjp/i2019-12650-x
  77. Sahmani, S. and Fattahi, A.M. (2017), "Thermo-electro-mechanical size-dependent postbuckling response of axially loaded piezoelectric shear deformable nanoshells via nonlocal elasticity theory", Microsyst. Technol., 23, 5105-5119. https://doi.org/10.1007/s00542-017-3316-x.
  78. Sahmani, S. and Fattahi, A.M. (2018), "Small scale effects on buckling and postbuckling behaviors of axially loaded FGM nanoshells based on nonlocal strain gradient elasticity theory", Appl. Math. Mech., 39, 561-580. https://doi.org/10.1007/s10483-018-2321-8.
  79. Sahmani, S., Fattahi, A.M. and Ahmed, N.A. (2019a), "Analytical mathematical solution for vibrational response of postbuckled laminated FG-GPLRC nonlocal strain gradient micro-/nanobeams", Eng. Comput., 35, 1173-1189. https://doi.org/10.1007/s00366-018-0657-8.
  80. Sahmani, S., Fattahi, A.M. and Ahmed, N.A. (2019b), "Surface elastic shell model for nonlinear primary resonant dynamics of FG porous nanoshells incorporating modal interactions", Int. J. Mech. Sci., 165, 105203. https://doi.org/10.1016/j.ijmecsci.2019.105203.
  81. Sahmani, S., Fattahi, A.M. and Ahmed, N.A. (2019c), "Analytical treatment on the nonlocal strain gradient vibrational response of postbuckled functionally graded porous micro-/nanoplates reinforced with GPL", Eng. Comput., 1-20. https://doi.org/10.1007/s00366-019-00782-5.
  82. Sahouane, A., Hadji, L. and Bourada, M. (2019), "Numerical analysis for free vibration of functionally graded beams using an original HSDBT", Earthq. Struct., 17(1), 31-37. https://doi.org/10.12989/eas.2019.17.1.031.
  83. Sedighi, H.M. and Sheikhanzadeh, A. (2017), "Static and dynamic pull-in instability of nano-beams resting on elastic foundation based on the nonlocal elasticity theory", Chin. J. Mech. Eng., 30(2), 385-397. https://doi.org/10.1007/s10033-017-0079-3.
  84. Sedighi, H.M., Daneshmand, F. and Abadyan, M. (2016), "Modeling the effects of material properties on the pull-in instability of nonlocal functionally graded nano-actuators", ZAMM, 96(3), 385-400. https://doi.org/10.1002/zamm.201400160.
  85. Sedighi, H.M., Daneshmand, F. and Abadyan, M. (2017), "Modified model for instability analysis of symmetric FGM double-sided nano-bridge: Corrections due to surface layer, finite conductivity and size effect", Compos. Struct., 132, 545-557. https://doi.org/10.1016/j.compstruct.2015.05.076.
  86. Selmi, A. (2019), "Effectiveness of SWNT in reducing the crack effect on the dynamic behavior of aluminium alloy", Adv. Nano Res., 7(5), 365-377. https://doi.org/10.12989/anr.2019.7.5.365.
  87. Shokrieh, M.M. and Kondori, M.S. (2020), "Effects of adding graphene nanoparticles in decreasing of residual stresses of carbon/epoxy laminated composites", Compos. Mater. Eng., 2(1), 53-64. https://doi.org/10.12989/cme.2020.2.1.053.
  88. Soliman, A.E., Eltaher, M.A., Attia, M.A. and Alshorbagy, A.E. (2018a), "Analysis of crack occurs under unsteady pressure and temperature in a natural gas facility by applying FGM", Struct. Eng. Mech., 66(1), 97-111. https://doi.org/10.12989/sem.2018.66.1.097.
  89. Soliman, A.E., Eltaher, M.A., Attia, M.A. and Alshorbagy, A.E. (2018b), "Nonlinear transient analysis of FG pipe subjected to internal pressure and unsteady temperature in a natural gas facility", Struct. Eng. Mech., 66(1), 85-96. https://doi.org/10.12989/sem.2018.66.1.085.
  90. Thanh, C.L., Tran, L.V., Quoc Bui, T., Nguyen, H.X. and Abdel-Wahab, M. (2019), "Isogeometric analysis for size-dependent nonlinear thermal stability of porous FG microplates", Compos. Struct., 221, 110838. https://doi.org/10.1016/j.compstruct.2019.04.010.
  91. Vu, T.V., Khosravifard, A., Hematiyan, M.R. and Bui, T.Q. (2018), "A new refined simple TSDT-based effective meshfree method for analysis of through-thickness FG plates", Appl. Math. Model., 57, 514-534. https://doi.org/10.1016/j.apm.2018.01.004.
  92. Wu, D., Liu, A., Huang, Y., Huang, Y., Pi, Y. and Gao, W. (2018), "Dynamic analysis of functionally graded porous structures through finite element analysis", Eng. Struct., 165, 287-301. https://doi.org/10.1016/j.engstruct.2018.03.023.
  93. Xiang, S. and Kang, G. (2013), "Static analysis of functionally graded plates by the various shear deformation theory", Compos. Struct., 99, 224-230. https://doi.org/10.1016/j.compstruct.2012.11.021.
  94. Yaghoobi, H., Fereidoon, A., Nouri, M.K. and Mareishi, S. (2015), "Thermal buckling analysis of piezoelectric functionally graded plates with temperature-dependent properties", Mech. Adv. Mater. Struct., 22(10), 864-875. https://doi.org/10.1080/15376494.2013.864436.
  95. Yamanouchi, M., Koizumi, M., Hirai, T. and Shiota, I. (1990), "On the design of functionally gradient materials", Proceedings of the 1st International Symposium on Functionally Gradient Materials, Sendai, Japan.
  96. YaylacI, M., Terzi, C. and Avcar, M. (2019), "Numerical analysis of the receding contact problem of two bonded layers resting on an elastic half plane", Struct. Eng. Mech., 72(6), 775-783. https://doi.org/10.12989/sem.2019.72.6.775.
  97. 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.
  98. Zenkour, A.M. (2013), "Bending of FGM plates by a simplified four-unknown shear and normal deformations theory", Int. J. Appl. Mech., 5(2), 1350020. https://doi.org/10.1142/s1758825113500208.
  99. Zenkour, A.M. and Alghanmi, R.A. (2018). "Bending of functionally graded plates via a refined quasi-3D shear and normal deformation theory", Curv. Layer. Struct., 5(1), 190-190. https://doi.org/10.1515/cls-2018-0014.

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