Computers and Concrete

  • 제25권1호
  • /
  • Pages.37-57
  • /
  • 2020
  • /
  • 1598-8198(pISSN)
  • /
  • 1598-818X(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

A study on the structural behaviour of functionally graded porous plates on elastic foundation using a new quasi-3D model: Bending and free vibration analysis

  • Kaddari, Miloud (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Kaci, Abdelhakim (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Bousahla, Abdelmoumen Anis (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals) ;
  • Tounsi, Abdelouahed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Bourada, Fouad (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Tounsi, Abdeldjebbar (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Bedia, E.A. Adda (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals) ;
  • Al-Osta, Mohammed A. (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals)
  • 투고 : 2019.11.20
  • 심사 : 2019.12.24
  • 발행 : 2020.01.25
⟨ 이전 논문 다음 논문 ⟩

초록

This work investigates a new type of quasi-3D hyperbolic shear deformation theory is proposed in this study to discuss the statics and free vibration of functionally graded porous plates resting on elastic foundations. Material properties of porous FG plate are defined by rule of the mixture with an additional term of porosity in the through-thickness direction. By including indeterminate integral variables, the number of unknowns and governing equations of the present theory is reduced, and therefore, it is easy to use. The present approach to plate theory takes into account both transverse shear and normal deformations and satisfies the boundary conditions of zero tensile stress on the plate surfaces. The equations of motion are derived from the Hamilton principle. Analytical solutions are obtained for a simply supported plate. Contrary to any other theory, the number of unknown functions involved in the displacement field is only five, as compared to six or more in the case of other shear and normal deformation theories. A comparison with the corresponding results is made to verify the accuracy and efficiency of the present theory. The influences of the porosity parameter, power-law index, aspect ratio, thickness ratio and the foundation parameters on bending and vibration of porous FG plate.

키워드

참고문헌

  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. Adim, B. and Daouadji, T.H. (2016), "Effects of thickness stretching in FGM plates using a quasi-3D higher order shear deformation theory", Adv. Mater. Res., 5(4), 223-244. https://doi.org/10.12989/amr.2016.5.4.223.
  3. Akavci, S. and Tanrikulu, A. (2015), "Static and free vibration analysis of functionally graded plates based on a new quasi-3D and 2D shear deformation theories", Compos. Part B: Eng., 83, 203-215. https://doi.org/10.1016/j.compositesb.2015.08.043.
  4. Akbas, S.D. (2015), "Wave propagation of a functionally graded beam in thermal environments", Steel Compos. Struct., 19(6), 1421-1447. http://dx.doi.org/10.12989/scs.2015.19.6.1421.
  5. Al-Osta, M.A. (2019), "Shear behaviour of RC beams retrofitted using UHPFRC panels epoxied to the sides", Comput. Concrete, 24(1), 37-49. https://doi.org/10.12989/cac.2019.24.1.037.
  6. Amar, L.H.H., Kaci, A. and Tounsi, A. (2017), "On the size-dependent behavior of functionally graded micro-beams with porosities", Struct. Eng. Mech., 64(5), 527-541. https://doi.org/10.12989/sem.2017.64.5.527.
  7. Amar, L.H.H., Kaci, A., Yeghnem, R. and Tounsi, A. (2018), "A new four-unknown refined theory based on modified couple stress theory for size-dependent bending and vibration analysis of functionally graded micro-plate", Steel Compos. Struct., 26(1), 89-102. https://doi.org/10.12989/scs.2018.26.1.089.
  8. Arefi M. (2015), "Elastic solution of a curved beam made of functionally graded materials with different cross sections", Steel Compos. Struct., 18(3), 659-672. http://dx.doi.org/10.12989/scs.2015.18.3.659.
  9. 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. http://dx.doi.org/10.12989/sss.2015.15.5.1345.
  10. 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.
  11. Baferani, A.H., Saidi, A. and Ehteshami, H. (2011), "Accurate solution for free vibration analysis of functionally graded thick rectangular plates resting on elastic foundation", Compos. Struct., 93(7), 1842-1853. https://doi.org/10.1016/j.compstruct.2011.01.020.
  12. Belkacem, A., Tahar, H.D., Abderrezak, R., Amine, B. M., Mohamed, Z. and Boussad, A. (2018), "Mechanical buckling analysis of hybrid laminated composite plates under different boundary conditions", Struct. Eng. Mech., 66(6), 761-769. https://doi.org/10.12989/sem.2018.66.6.761.
  13. Bensaid, I. (2017), "A refined nonlocal hyperbolic shear deformation beam model for bending and dynamic analysis of nanoscale beams", Adv. Nano Res., 5(2), 113-126. https://doi.org/10.12989/anr.2017.5.2.113.
  14. Bisen, H.B., Hirwani, C.K., Satankar, R.K., Panda, S.K., Mehar, K. and Patel, B. (2018), "Numerical study of frequency and deflection responses of natural fiber (Luffa) reinforced polymer composite and experimental validation", J. Nat. Fib., 1-15. https://doi.org/10.1080/15440478.2018.1503129.
  15. Bouguenina, O., Belakhdar, K., Tounsi, A. and Adda Bedia, E.A. (2015), "Numerical analysis of FGM plates with variable thickness subjected to thermal buckling". Steel Compos. Struct., 19(3), 679-695. http://dx.doi.org/10.12989/scs.2015.19.3.679.
  16. Carrera, E., Brischetto, S., Cinefra, M. and Soave, M. (2011). "Effects of thickness stretching in functionally graded plates and shells", Compos.: Part B., 42, 123-133. https://doi.org/10.1016/j.compositesb.2010.10.005.
  17. Carrera, E., Brishetto, S. and RRobaldo, A. (2008), "Variable kinematic model for the analysis of functionally graded material plates", AIAA J., 46, 194-203. https://doi.org/10.2514/1.32490.
  18. Chandra Mouli, B., Ramji, K., Kar, V.R., Panda, S.K., Lalepalli, A.K. and Pandey, H.K. (2018), "Numerical study of temperature dependent eigenfrequency responses of tilted functionally graded shallow shell structures", Struct. Eng. Mech., 68(5), 527-536. https://doi.org/10.12989/sem.2018.68.5.527.
  19. Cukanovic, D., Radakovic, A., Bogdanovic, G., Milanovic, M., Redzovic, H. and Dragovic, D. (2018), "New shape function for the bending analysis of functionally graded plate", Mater., 11(12), 2381. https://doi.org/10.3390/ma11122381.
  20. 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.
  21. 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.
  22. 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. http://dx.doi.org/10.12989/scs.2016.20.1.205.
  23. Ehyaei, J., Akbarshahi, A. and Shafiei, N. (2017), "Influence of porosity and axial preload on vibration behavior of rotating FG nanobeam", Adv. Nano Res., 5(2), 141-169. https://doi.org/10.12989/anr.2017.5.2.141.
  24. Fadoun, O.O. (2019), "Analysis of axisymmetric fractional vibration of an isotropic thin disc in finite deformation", Comput. Concrete, 23(5), 303-309. https://doi.org/10.12989/cac.2019.23.5.303.
  25. 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.
  26. Farzam-Rad, S.A., Hassani, B. and Karamodin, A. (2017), "Isogeometric analysis of functionally graded plates using a new quasi-3D shear deformation theory based on physical neutral surface", Compos.: Part B Eng., 108, 174-189. https://doi.org/10.1016/j.compositesb.2016.09.029.
  27. 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.
  28. Hadji, L., Meziane, M.A.A. and Safa, A. (2018), "Mechanical behaviour of FGM sandwich plates using a quasi-3D higher order shear and normal deformation theory", Struct. Eng. Mech., 66(6), 771-781. https://doi.org/10.12989/sem.2017.61.1.049.
  29. Hebali, H., Tounsi, A., Houari, M.S.A., Bessaim, A. and Bedia, E.A.A. (2014), "New quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", J. Eng. Mech., 140(2), 374-383. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000665.
  30. 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. https://doi.org/10.1016/j.oceaneng.2018.04.035.
  31. Hirwani, C.K., Panda, S.K. and Patel, B.K. (2018c), "Theoretical and experimental validation of nonlinear deflection and stress responses of an internally debonded layer structure using different higher-order theories", Acta Mechanica, 229(8), 3453-3473. https://doi.org/10.1007/s00707-018-2173-8.
  32. Hirwani, C.K., Panda, S.K., Mahapatra, S.S., Mandal, S.K., Srivastava, L. and Buragohain, M.K. (2018a), "Flexural strength of delaminated composite plate-An experimental validation", Int. J. Damage Mech., 27(2), 296-329. https://doi.org/10.1177/1056789516676515.
  33. Hirwani, C.K., Panda, S.K., Mahapatra, T.R., Mandal, S.K., Mahapatra, S.S. and De, A.K. (2018b), "Delamination effect on flexuralresponses of layered curved shallow shell panel-experimental and numerical analysis", Int. J. Comput. Meth., 15(4), 1850027. https://doi.org/10.1142/S0219876218500275.
  34. Hirwani, C.K., Patil, R.K., Panda, S.K., Mahapatra, S.S., Mandal, S.K., Srivastava, L. and Buragohain, M.K. (2016a), "Experimental and numerical analysis of free vibration of delaminated curved panel", Aerosp. Sci. Technol., 54, 353-370. https://doi.org/10.1016/j.ast.2016.05.009.
  35. Hirwani, C.K., Sahoo, S.S. and Panda, S.K. (2016b), "Effect of delamination on vibration behaviour of woven Glass/Epoxy composite plate-An experimental study", IOP Conf. Ser.: Mater. Sci. Eng., 115(1), 012010. https://doi.org/10.1088/1757-899X/115/1/012010.
  36. Jha, D., Kant, T. and Singh, R. (2013), "Free vibration response of functionally graded thick plates with shear and normal deformations effects", Compos. Struct., 96, 799-823. https://doi.org/10.1016/j.compstruct.2012.09.034.
  37. Jin, G., Su, Z., Shi, S., Ye, T. and Gao, S. (2014), "Three-dimensional exact solution for the free vibration of arbitrarily thick functionally graded rectangular plates with general boundary conditions", Compos. Struct., 108, 565-577. https://doi.org/10.1016/j.compstruct.2013.09.051.
  38. Kar, V.R. and Panda, S.K. (2015), "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.
  39. Kar, V.R. and Panda, S.K. (2016), "Nonlinear thermomechanical behavior of functionally graded material cylindrical/hyperbolic/elliptical shell panel with temperature-dependent and temperature-independent properties", J. Press. Ves. Technol., 138(6), 061202. https://doi.org/10.1115/1.4033701.
  40. Karami, B. and Janghorban, M. (2019), "A new size-dependent shear deformation theory for free vibration analysis of functionally graded/anisotropic nanobeams", Thin Wall. Struct., 143, 106-227. https://doi.org/10.1016/j.tws.2019.106227
  41. Keikha, R., Heidari, A., Hosseinabadi, H. and Haghighi, M.S. (2018), "Classical shell theory for instability analysis of concrete pipes conveying nanofluid", Comput. Concrete, 22(2), 161-166. https://doi.org/10.12989/cac.2018.22.2.161.
  42. Kerr, A.D. (1964), "Elastic and viscoelastic foundation models", J. Appl. Mech., 31(3), 491-498. https://doi.org/10.1115/1.3629667.
  43. Kunche, M.C., Mishra, P.K., Nallala, H.B., Hirwani, C.K., Katariya, P.V., Panda, S. and Panda, S.K. (2019), "Theoretical and experimental modal responses of adhesive bonded T-joints", Wind Struct., 29(5), 361-369. https://doi.org/10.12989/was.2019.29.5.361.
  44. Laoufi, I., Ameur, A., Zidi, M., Adda Bedia, E.A. and Bousahla, A.A. (2016), "Mechanical and hygro-thermal behaviour of functionally graded plates using a hyperbolic shear deformation theory", Steel Compos. Struct., 20(4), 889-912. https://doi.org/10.12989/scs.2016.20.4.889.
  45. Liu, Y. (2011), "A refined shear deformation plate theory", Int. J. Comput. Meth. Eng. Sci. Mech., 12(3), 141-149. https://doi.org/10.1080/15502287.2011.564267
  46. Mantari, J., Granados, E., Hinostroza, M. and Soares, C.G. (2014), "Modelling advanced composite plates resting on elastic foundation by using a quasi-3D hybrid type HSDT", Compos. Struct., 118, 455-471. https://doi.org/10.1016/j.compstruct.2014.07.039.
  47. Mantari, J.L, Oktem, A.S. and Soares, O.G. (2012), "Bending response of functionally graded plates by using a new higher order shear deformation theory", Compos. Struct., 94, 714-723. https://doi.org/10.1016/j.compstruct.2011.09.007.
  48. Mehar, K. and Panda, S.K. (2018), "Elastic bending and stress analysis of carbon nanotube-reinforced composite plate: Experimental, numerical, and simulation", Adv. Polym. Technol., 37(6), 1643-1657. https://doi.org/10.1002/adv.21821.
  49. Mehar, K. and Panda, S.K. (2019), "Theoretical deflection analysis of multi-walled carbon nanotube reinforced sandwich panel and experimental verification", Compos. Part B: Eng., 167, 317-328. https://doi.org/10.1016/j.compositesb.2018.12.058.
  50. Mehar, K., Panda, S.K. and Mahapatra, T.R. (2017), "Theoretical and experimental investigation of vibration characteristic of carbon nanotube reinforced polymer composite structure", Int. J. Mech. Sci., 133, 319-329. https://doi.org/10.1016/j.ijmecsci.2017.08.057.
  51. Mehar, K., Panda, S.K. and Mahapatra, T.R. (2019), "Large deformation bending responses of nanotube-reinforced polymer composite panel structure: Numerical and experimental analyses", Proc. Inst. Mech. Eng., Part G: J. Aerosp. Eng., 233(5), 1695-1704. https://doi.org/10.1177/0954410018761192.
  52. Mindlin, R.D. (1951), "Thickness-shear and flexural vibrations of crystal plates", J. Appl. Phys., 22(3), 316-323. https://doi.org/10.1063/1.1699948.
  53. Moradi-Dastjerdi, R. (2016), "Wave propagation in functionally graded composite cylinders reinforced by aggregated carbon nanotube". Struct. Eng. Mech., 57(3), 441-456. https://doi.org/10.12989/sem.2016.57.3.441.
  54. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Cinefra, M., Roque, C.M.C., Jorge, R.M.N. and Soares, C.M. (2013), "Static, free vibration and buckling analysis of isotropic and sandwich functionally graded plates using a quasi-3D higher-order shear deformation theory and a meshless technique", Compos. Part B: Eng., 44(1), 657-674. https://doi.org/10.1016/j.compositesb.2012.01.089.
  55. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Roque, C.M.C., Cinefra, M., Jorge, R.M.N. and Soares, C.M.M. (2012), "A quasi-3D sinusoidal shear deformation theory for the static and free vibration analysis of functionally graded plates", Compos. Part B: Eng., 43(2), 711-725. https://doi.org/10.1016/j.compositesb.2011.08.009.
  56. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Roque, C.M.C., Cinefra, M., Jorge, R.M.N. Soares, C.M.M. (2012). "A quasi-3D sinusoidal shear deformation theory for the static and free vibration analysis of functionally graded plates", Compos. Part B., 43, 711-725. https://doi.org/10.1016/j.compositesb.2011.08.009.
  57. Nguyen, V.H., Nguyen, T.K., Tai, H.T. and Vo, T.P. (2014), "A new inverse trigonometric shear deformation theory for isotropic and functionally graded sandwich plates", Compos. B, 66, 233-246. https://doi.org/10.1016/j.compositesb.2014.05.012.
  58. Pandey, H.K., Hirwani, C.K., Sharma, N., Katariya, P.V. and Panda, S.K. (2019), "Effect of nano glass cenosphere filler on hybrid composite eigenfrequency responses - An FEM approach and experimental verification", Adv. Nano Res., 7(6), 419-429. https://doi.org/10.12989/anr.2019.7.6.419.
  59. Pasternak, P. (1954), "On a new method of analysis of an elastic foundation by means of two foundation constants", Gosudarstvennoe Izdatelstvo Literaturipo Stroitelstvu i Arkhitekture, Moscow.
  60. Pradhan, K.K. and Chakraverty, S. (2015), "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.
  61. Qian, L.F. and Batra, R.C. (2005), "Three-dimensional transient heat conduction in a functionally graded thick plate with a higher-order plate theory and a meshless local Petrov-Galerkin Method", Comput. Mech., 35(3), 214-226. https://doi.org/10.1007/s00466-004-0617-6.
  62. 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.
  63. Reissner, E. (1945), "The effect of transverse shear deformation on the bending of elastic plates", J. Appl. Mech., A69-A77.
  64. Sahoo, S.S., Hirwani, C.K., Panda, S.K. and Sen, D. (2018), "Numerical analysis of vibration and transient behaviour of laminated composite curved shallow shell structure: An experimental validation", Scientia Iranica, 25(4), 2218-2232.
  65. Sahoo, S.S., Panda, S.K. and Singh, V.K. (2017a), "Experimental and numerical investigation of static and free vibration responses of woven glass/epoxy laminated composite plate", Proc. Inst. Mech. Eng. Part L: J. Mater.: Des. Appl., 231(5), 463-478. https://doi.org/10.1177/1464420715600191.
  66. Sahoo, S.S., Panda, S.K., Mahapatra T.R. and Hirwani, C.K. (2019), "Numerical analysis of transient responses of delaminated layered structure using different mid-plane theories and experimental validation", Iran. J. Sci. Technol. Tran. Mech. Eng., 43(1), 41-56. https://doi.org/10.1007/s40997-017-0111-3.
  67. Sahoo, S.S., Panda, S.K., Singh, V.K. and Mahapatra T.R. (2017b), "Numerical investigation on the nonlinear flexural behaviour of wrapped glass/epoxy laminated composite panel and experimental validation", Arch. Appl. Mech., 87, 315-333. https://doi.org/10.1007/s00419-016-1195-8.
  68. Sahoo, S.S., Singh, V.K. and Panda, S.K. (2016), "Nonlinear flexural analysis of shallow carbon/epoxy laminated composite curved panels: experimental and numerical investigation", J. Eng. Mech., 142(4), 04016008. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001040.
  69. Salari, E., Ashoori, A. and Vanini, S.A.S. (2019), "Porosity-dependent asymmetric thermal buckling of inhomogeneous annular nanoplates resting on elastic substrate", Adv. Nano Res., 7(1), 25-38. https://doi.org/10.12989/anr.2019.7.1.025.
  70. Shahsavari, D., Shahsavari, M., Li, L. and Karami, B. (2018), "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.
  71. Shimpi, R.P., Arya, H. and Naik, N.K. (2003), "A higher order displacement model for the plate analysis", J. Reinf. Plast. Compos., 22(22), 1667-1688. https://doi.org/10.1177/073168403027618.
  72. Srinivas, S., Joga, C.V. and Rao, A.K. (1970), "Bending, vibration and buckling of simply supported thick orthotropic rectangular plate and laminates", Int. J. Solid. Struct., 6, 1463-1481. https://doi.org/10.1016/0020-7683(70)90076-4.
  73. Thai, H.T. and Choi, D.H. (2011), "A refined plate theory for functionally graded plates resting on elastic foundation", Compos. Sci. Technol., 71(16), 1850-1858. https://doi.org/10.1016/j.compscitech.2011.08.016.
  74. Thai, H.T. and Kim, S.E. (2013), "A simple higher order shear deformation theory for bending and free vibration of functionally graded plates", Compos. Struct., 96, 165-173. https://doi.org/10.1016/j.compstruct.2012.08.025.
  75. Thai, H.T. and Kim, S.E. (2013), "A simple quasi-3D sinusoidal shear deformation theory for functionally graded plates", Compos. Struct., 99, 172-180. https://doi.org/10.1016/j.compstruct.2012.11.030.
  76. Thai, H.T., Vo, T.P., Bui, T.Q. and Nguyen, T.K. (2014), "A quasi-3D hyperbolic shear deformation theory for functionally graded plates", Acta Mechanica, 225(3), 951-964. https://doi.org/10.1007/s00707-013-0994-z.
  77. Wu, C.P. and Chiu, K.H. (2011), "RMVT-based meshless collocation and element- free Galerkin methods for the quasi-3D free analysis of multilayed composite and FGM plates", Compos. Struct., 93(5), 1433-1448. https://doi.org/10.1016/j.compstruct.2010.07.001.
  78. Zenkour, A.M. (2006), "Generalized shear deformation theory for bending analysis of functionally graded material", Appl. Math. Model., 30, 67-84. https://doi.org/10.1016/j.apm.2005.03.009.
  79. Zenkour, A.M. (2018), "A quasi-3D refined theory for functionally graded single-layered and sandwich plates with porosities", Compos. Struct., 201, 38-48. https://doi.org/10.1016/j.compstruct.2018.05.147.
  80. Zenkour, A.M. (2019), "Quasi-3D refined theory functionally graded porous plates: Displacements and stresses", Appl. Math. Model. 22(1), 22-35. https://doi.org/10.24411/1683-805X-2019-11003.
  81. Zenkour, A.M. and Sobhy, M. (2013), "Dynamic bending response of thermoelastic functionally graded plates resting on elastic foundations", Aerosp. Sci. Technol., 29(1), 7-17. https://doi.org/10.1016/j.ast.2013.01.003.
  82. Zhou, D., Cheung, Y., Au, F. and Lo, S. (2002), "Three-dimensional vibration analysis of thick rectangular plates using Chebyshev polynomial and Ritz method", Int. J. Solid. Struct., 39, 6339-6353. https://doi.org/10.1016/S0020-7683(02)00460-2.

피인용 문헌

  1. Analysis of Rotary Vibration of Rigid Friction Pipe Pile in Unsaturated Soil vol.2020, 2020, https://doi.org/10.1155/2020/2807574
  2. A Spline Finite Point Method for Nonlinear Bending Analysis of FG Plates in Thermal Environments Based on a Locking-free Thin/Thick Plate Theory vol.2020, 2020, https://doi.org/10.1155/2020/2943705
  3. Effect of the rotation on the thermal stress wave propagation in non-homogeneous viscoelastic body vol.21, pp.1, 2020, https://doi.org/10.12989/gae.2020.21.1.001
  4. Analysis of post-buckling of higher-order graphene oxide reinforced concrete plates with geometrical imperfection vol.9, pp.4, 2020, https://doi.org/10.12989/acc.2020.9.4.397
  5. Finite element based post-buckling analysis of refined graphene oxide reinforced concrete beams with geometrical imperfection vol.25, pp.4, 2020, https://doi.org/10.12989/cac.2020.25.4.283
  6. Multiphysical theoretical prediction and experimental verification of vibroacoustic responses of fruit fiber‐reinforced polymeric composite vol.41, pp.11, 2020, https://doi.org/10.1002/pc.25724
  7. Analysis of orthotropic plates by the two-dimensional generalized FIT method vol.26, pp.5, 2020, https://doi.org/10.12989/cac.2020.26.5.421
  8. A mechanical model to investigate Aedesaegypti mosquito bite using new techniques and its applications vol.11, pp.6, 2020, https://doi.org/10.12989/mwt.2020.11.6.399
  9. Predictions of the maximum plate end stresses of imperfect FRP strengthened RC beams: study and analysis vol.9, pp.4, 2020, https://doi.org/10.12989/amr.2020.9.4.265
  10. Effect of porosity distribution rate for bending analysis of imperfect FGM plates resting on Winkler-Pasternak foundations under various boundary conditions vol.9, pp.6, 2020, https://doi.org/10.12989/csm.2020.9.6.575
  11. New Finite Modeling of Free and Forced Vibration Responses of Piezoelectric FG Plates Resting on Elastic Foundations in Thermal Environments vol.2021, 2020, https://doi.org/10.1155/2021/6672370
  12. In-Line and Cross-Flow Coupling Vibration Response Characteristics of a Marine Viscoelastic Riser Subjected to Two-Phase Internal Flow vol.2021, 2020, https://doi.org/10.1155/2021/7866802
  13. On the Finite Element Model of Rotating Functionally Graded Graphene Beams Resting on Elastic Foundation vol.2021, 2021, https://doi.org/10.1155/2021/1586388
  14. Free Vibration Exploration of Rotating FGM Porosity Beams under Axial Load considering the Initial Geometrical Imperfection vol.2021, 2020, https://doi.org/10.1155/2021/5519946
  15. Free Vibration Investigations of Rotating FG Beams Resting on Elastic Foundation with Initial Geometrical Imperfection in Thermal Environments vol.2021, 2020, https://doi.org/10.1155/2021/5533920
  16. A Refined Model for Analysis of Beams on Two-Parameter Foundations by Iterative Method vol.2021, 2021, https://doi.org/10.1155/2021/5562212
  17. Thermal frequency analysis of FG sandwich structure under variable temperature loading vol.77, pp.1, 2020, https://doi.org/10.12989/sem.2021.77.1.057
  18. Size dependent vibration of embedded functionally graded nanoplate in hygrothermal environment by Rayleigh-Ritz method vol.10, pp.1, 2020, https://doi.org/10.12989/anr.2021.10.1.025
  19. On thermally induced instability of FG-CNTRC cylindrical panels vol.10, pp.1, 2021, https://doi.org/10.12989/anr.2021.10.1.043
  20. Numerical and experimental investigation for monitoring and prediction of performance in the soft actuator vol.77, pp.2, 2021, https://doi.org/10.12989/sem.2021.77.2.167
  21. Study and analysis of the free vibration for FGM microbeam containing various distribution shape of porosity vol.77, pp.2, 2020, https://doi.org/10.12989/sem.2021.77.2.217
  22. Orthotropic magneto-thermoelastic solid with higher order dual-phase-lag model in frequency domain vol.77, pp.3, 2020, https://doi.org/10.12989/sem.2021.77.3.315
  23. Geometrically nonlinear thermo-mechanical analysis of graphene-reinforced moving polymer nanoplates vol.10, pp.2, 2020, https://doi.org/10.12989/anr.2021.10.2.151
  24. Frequency characteristics and sensitivity analysis of a size-dependent laminated nanoshell vol.10, pp.2, 2020, https://doi.org/10.12989/anr.2021.10.2.175
  25. Vibration analysis of porous FGM plate resting on elastic foundations: Effect of the distribution shape of porosity vol.10, pp.1, 2020, https://doi.org/10.12989/csm.2021.10.1.061
  26. Elastic wave phenomenon of nanobeams including thickness stretching effect vol.10, pp.3, 2020, https://doi.org/10.12989/anr.2021.10.3.271
  27. Nonlocal free vibration analysis of porous FG nanobeams using hyperbolic shear deformation beam theory vol.10, pp.3, 2020, https://doi.org/10.12989/anr.2021.10.3.281
  28. Dynamic response of functionally graded plates with a porous middle layer under time-dependent load vol.27, pp.3, 2021, https://doi.org/10.12989/cac.2021.27.3.269
  29. Exact third-order static and free vibration analyses of functionally graded porous curved beam vol.39, pp.1, 2021, https://doi.org/10.12989/scs.2021.39.1.001
  30. Electromagnetic field and initial stress on a porothermoelastic medium vol.78, pp.1, 2021, https://doi.org/10.12989/sem.2021.78.1.001
  31. Computer simulation for stability analysis of the viscoelastic annular plate with reinforced concrete face sheets vol.27, pp.4, 2020, https://doi.org/10.12989/cac.2021.27.4.369
  32. Stress analysis of a pre-stretched orthotropic plate with finite dimensions vol.45, pp.2, 2021, https://doi.org/10.1139/tcsme-2019-0241
  33. Temperature jump and concentration slip effects on bioconvection past a vertical porous plate in the existence of nanoparticles and gyrotactic microorganism with inclined MHD vol.11, pp.1, 2020, https://doi.org/10.12989/anr.2021.11.1.0127
  34. The effects of ring and fraction laws: Vibration of rotating isotropic cylindrical shell vol.11, pp.1, 2021, https://doi.org/10.12989/anr.2021.11.1.019
  35. Surface wave scattering analysis in an initially stressed stratified media vol.38, pp.8, 2020, https://doi.org/10.1108/ec-03-2020-0133
  36. Free vibration of multi-cracked beams vol.79, pp.4, 2020, https://doi.org/10.12989/sem.2021.79.4.441
  37. Compressive mechanical behavior and model of composite elastic-porous metal materials vol.8, pp.12, 2020, https://doi.org/10.1088/2053-1591/ac40b5
  38. Influence of porosity distribution on free vibration and buckling analysis of multi-directional functionally graded sandwich plates vol.279, 2020, https://doi.org/10.1016/j.compstruct.2021.114795