Geomechanics and Engineering

  • 제34권3호
  • /
  • Pages.233-250
  • /
  • 2023
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  • 2005-307X(pISSN)
  • /
  • 2092-6219(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

A novel hyperbolic integral-Quasi-3D theory for flexural response of laminated composite plates

  • Ahmed Frih (Laboratoire des Structures et Materiaux Avances dans le Genie Civil et Travaux Publics, Faculte de Technologie, Departement de Genie Civil, Universite de Sidi Bel Abbes) ;
  • Fouad Bourada (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Abdelhakim Kaci (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Mohammed Bouremana (Laboratoire des Structures et Materiaux Avances dans le Genie Civil et Travaux Publics, Faculte de Technologie, Departement de Genie Civil, Universite de Sidi Bel Abbes) ;
  • Abdelouahed Tounsi (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Mohammed A. Al-Osta (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals) ;
  • Khaled Mohamed Khedher (Department of Civil Engineering, College of Engineering, King Khalid University) ;
  • Mohamed Abdelaziz Salem (Department of Industrial Engineering, College of Engineering, King Khalid University)
  • 투고 : 2023.04.10
  • 심사 : 2023.06.19
  • 발행 : 2023.08.10
⟨ 이전 논문 다음 논문 ⟩

초록

This paper investigates the flexural analysis of isotropic, transversely isotropic, and laminated composite plates using a new higher-order normal and shear deformation theory. In the present theory, only five unknown functions are involved compared to six or more unknowns used in the other similar theories. The developed theory does not need a shear correction factor. It can satisfy the zero traction boundary conditions on the top and the bottom surfaces of the plate as well as account for sufficient distribution of the transverse shear strains. The thickness stretching effect is considered in the computation. A simply supported was considered on all edges of the plate. The plate is subjected to uniform and sinusoidal distributed load in the static analysis. Laminated composite, isotropic, and transversely isotropic plates are considered. The governing equations are obtained utilizing the virtual work principle. The differential equations are solved via Navier's procedure. The results obtained from the developed theory are compared with other higher-order theories considered in the previous studies and 3D elasticity solutions. The results showed that the proposed theory accurately and effectively predicts the bidirectional bending responses of laminated composite plates. Several parametric studies are presented to illustrate the various parameters influencing the static response of the laminated composite plates.

키워드

과제정보

The Authors extend their appreciation to the Deanship Scientific Research at King Khalid University for funding this work through large group Research Project under grant number: RGP2/422/44.

참고문헌

  1. Adhikari, B. andSingh, B.N. (2018), "An efficient higher order non-polynomial Quasi 3-D theory for dynamic responses of laminated composite plates", Compos. Struct., 189, 386-397. https://doi.org/10.1016/j.compstruct.2017.10.044.
  2. Adhikari, B. and Singh, B.N. (2019), "Dynamic response of functionally graded plates resting on two-parameter-based elastic foundation model using a quasi-3D theory", Mech. Based Des. Struct. Machines. 47(4), 399-429. https://doi.org/10.1080/15397734.2018.1555965.
  3. Aguiar, R.M., Moleiro, F. and Soares, C.M. (2012), "Assessment of mixed and displacement-based models for static analysis of composite beams of different cross-sections", Compos. Struct., 94(2), 601-616. https://doi.org/10.1016/j.compstruct.2011.08.028.
  4. Ahmed, R.A., Fenjan, R.M. and Faleh, N.M. (2019), "Analyzing post-buckling behavior of continuously graded FG nanobeams with geometrical imperfections", Geomech. Eng., 17(2), 175-180. https://doi.org/10.12989/gae.2019.17.2.175.
  5. Akavci, S.S. and Tanrikulu, A.H. (2008), "Buckling and free vibration analyses of laminated composite plates by using two new hyperbolic shear-deformation theories", Mech. Compos. Mater., 44, 145-154. https://doi.org/10.1007/s11029-008-9004-2.
  6. Akbas, S.D. (2015), "Wave propagation of a functionally graded beam in thermal environments", Steel Compos. Struct., 19(6), 1421-1447. https://doi.org/10.12989/scs.2015.19.6.1421.
  7. Akbas, S.D. (2022), "Moving-load dynamic analysis of AFG beams under thermal effect", Steel Compos. Struct., 42(5), 649-655. https://doi.org/10.12989/scs.2022.42.5.649.
  8. Aldousari, S.M. (2017), "Bending analysis of different material distributions of functionally graded beam", Appl. Phys. A, 123(4), 1-9. https://doi.org/10.1007/s00339-017-0854-0.
  9. Alimoradzadeh, M. and Akbas, S.D. (2022), "Nonlinear dynamic behavior of functionally graded beams resting on nonlinear viscoelastic foundation under moving mass in thermal environment", Struct. Eng. Mech., 81(6), 705-714. https://doi.org/10.12989/sem.2022.81.6.705.
  10. Alnujaie, A., Akbas, S.D., Eltaher, M.A. and Assie, A. (2021), "Forced vibration of a functionally graded porous beam resting on viscoelastic foundation", Geomech. Eng., 24(1), 91-103. https://doi.org/10.12989/gae.2021.24.1.091.
  11. Al-Toki, M.H.Z., Ali, H. A.K., Faleh, N.M. and Fenjan, R.M. (2022), "Numerical assessment of nonlocal dynamic stability of graded porous beams in thermal environment rested on elastic foundation", Geomech. Eng., 28(5), 455-461. https://doi.org/10.12989/gae.2022.28.5.455.
  12. Arefi, M. and Zur, K.K. (2020), "Free vibration analysis of functionally graded cylindrical nanoshells resting on Pasternak foundation based on two-dimensional analysis", Steel Compos. Struct., 34(4), 615-623. https://doi.org/10.12989/scs.2020.34.4.615.
  13. 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.
  14. Azandariani, M.G., Gholami, M. and Nikzad, A. (2022), "Eringen's nonlocal theory for non-linear bending analysis of BGF Timoshenko nanobeams", Adv. Nano Res., 12(1), 37-47. https://doi.org/10.12989/anr.2022.12.1.037.
  15. Bashiri, A.H., Akbas, S.D., Abdelrahman, A.A., Assie, A., Eltaher, M.A. and Mohamed, E.F. (2021), "Vibration of multilayered functionally graded deep beams under thermal load", Geomech. Eng., 24(6), 545-557. https://doi.org/10.12989/gae.2021.24.6.545.
  16. Bochkareva, S.A. and Lekomtsev, S.V. (2022), "Natural vibrations and hydroelastic stability of laminated composite circular cylindrical shells", Struct. Eng. Mech., 81(6), 769-780. https://doi.org/10.12989/sem.2022.81.6.769.
  17. Carrera, E., Brischetto, S., Cinefra, M. and Soave, M. (2011), "Effects of thickness stretching in functionally graded plates and shells", Compos. Part B: Eng., 42(2), 123-133. https://doi.org/10.1016/j.compositesb.2010.10.005.
  18. Chen, C.S., Hsu, C.Y. and Tzou, G.J. (2009), "Vibration and stability of functionally graded plates based on a higher-order deformation theory", J. Reinforced Plast. Compos., 28(10), 1215-1234. https://doi.org/10.1177/0731684408088884.
  19. Chen, X., Zhao, J.L., She, G.L., Jing, Y., Pu, H.Y. and Luo, J. (2022), "Nonlinear free vibration analysis of functionally graded carbon nanotube reinforced fluid-conveying pipe in thermal environment", Steel Compos. Struct., 45(5), 641-652. https://doi.org/10.12989/scs.2022.45.5.641.
  20. Chinnapandi, L.B.M., Pitchaimani, J. and Eltaher, M.A. (2022), "Vibro-acoustics of functionally graded porous beams subjected to thermo-mechanical loads", Steel Compos. Struct., 44(6), 829-843. https://doi.org/10.12989/scs.2022.44.6.829.
  21. Cho, J.R. (2022b), "Thermal buckling analysis of metal-ceramic functionally graded plates by natural element method", Struct. Eng. Mech., 84(6), 723-731. https://doi.org/10.12989/sem.2022.84.6.723.
  22. Cho, J.R. (2022a), "Nonlinear bending analysis of functionally graded CNT-reinforced composite plates", Steel Compos. Struct., 42(1), 23-32. https://doi.org/10.12989/scs.2022.42.1.023.
  23. Choi, S.H., Heo, I., Kim, J.H., Jeong, H., Lee, J.Y. and Kim, K.S. (2022), "Flexural behavior of post-tensioned precast concrete girder at negative moment region", Comput. Concrete, 30(1), 75-84. https://doi.org/10.12989/cac.2022.30.1.075.
  24. Cuong-Le, T., Ferreira, A.J.M. and Abdel Wahab, M. (2019b), "A refined size-dependent couple stress theory for laminated composite micro-plates using isogeometric analysis", Thin Wall. Struct., 145, 106427. https://doi.org/10.1016/j.tws.2019.106427.
  25. Cuong-Le, T., Nguyen, K.D., Nguyen-Trong, N., Khatir, S., Nguyen-Xuan, H. and Abdel-Wahab, M. (2020a), "A three-dimensional solution for free vibration and buckling of annular plate, conical, cylinder and cylindrical shell of FG porous-cellular materials using IGA", Compos. Struct., 259, 113216. https://doi.org/10.1016/j.compstruct.2020.113216.
  26. Cuong-Le, T., Nguyen, K.D., Hoang-Le, M., Sang-To, T., Phan-Vu, P. and Abdel Wahab, M. (2022a), "Nonlocal strain gradient IGA numerical solution for static bending, free vibration and buckling of sigmoid FG sandwich nanoplate", Physica B: Condensed Matter., 631, 413726. https://doi.org/10.1016/j.physb.2022.413726.
  27. Cuong-Le, T., Nguyen, K.D., Lee, J., Rabczuk, T. and Nguyen-Xuan, H. (2022b), "A 3D nano scale IGA for free vibration and buckling analyses of multi-directional FGM nanoshells", Nanotechnology, 33(6), 065703. https://doi.org/10.1088/1361-6528/ac32f9.
  28. Cuong-Le, T., Nguyen, T.N., Vu, T.H., Khatir, S. and Abdel Wahab, M. (2020b), "A geometrically nonlinear size-dependent hypothesis for porous functionally graded micro-plate", Eng. with Comput., 38(2022), 449-460. https://doi.org/10.1007/s00366-020-01154-0.
  29. Cuong-Le, T., Tran, L.V., Vu-Huu, T. and Abdel-Wahab, M. (2019a), "The size-dependent thermal bending and buckling analyses of composite laminate microplate based on new modified couple stress theory and isogeometric analysis", Comput. Method. Appl. M., 350, 337-361. https://doi.org/10.1016/j.cma.2019.02.028.
  30. Ding, F., Ding, H., He, C., Wang, L. and Lyu, F. (2022), "Method for flexural stiffness of steel-concrete composite beams based on stiffness combination coefficients", Comput. Concrete, 29(3), 127-144. https://doi.org/10.12989/cac.2022.29.3.127.
  31. Ding, H.X. and She, G.L. (2021), "A higher-order beam model for the snap-buckling analysis of FG pipes conveying fluid", Struct. Eng. Mech., 80(1), 63-72. https://doi.org/10.12989/sem.2021.80.1.063.
  32. Ding, HX. and She, G.L. (2023), "Nonlinear resonance of axially moving graphene platelet-reinforced metal foam cylindrical shells with geometric imperfection", Archiv. Civ. Mech. Eng., 23, 97 (2023). https://doi.org/10.1007/s43452-023-00634-6.
  33. Ding, H.X., Zhang, Y.W. and She, G.L. (2022), "On the resonance problems in FG-GPLRC beams with different boundary conditions resting on elastic foundations", Comput. Concrete., 30(6), 433-443. https://doi.org/10.12989/cac.2022.30.6.433.
  34. Doan, T.N., Thanh, N.T., Van Chuong, P., Tho, N.C., Ta, N.T. and Nguyen, H.N. (2020), "Analysis of stress concentration phenomenon of cylinder laminated shells using higher-order shear deformation Quasi-3D theory", Compos. Struct., 232, 111526. https://doi.org/10.1016/j.compstruct.2019.111526.
  35. Dogruoglu, A.N. and Omurtag, M.H. (2000), "Stability analysis of composite-plate foundation interaction by mixed FEM", J. Eng. Mech., 126(9), 928-936. https://doi.org/10.1061/(ASCE)0733-9399(2000)126:9(928).
  36. Du, M., Liu, J., Ye, W., Yang, F. and Lin, G. (2022), "A new semi-analytical approach for bending, buckling and free vibration analyses of power law functionally graded beams", Struct. Eng. Mech., 81(2), 179-194. https://doi.org/10.12989/sem.2022.81.2.179.
  37. Faleh, N.M., Abboud, I.K. and Nori, A.F. (2020), "Nonlinear stability of smart nonlocal magneto-electro-thermo-elastic beams with geometric imperfection and piezoelectric phase effects", Smart Struct. Syst., 25(6), 707-717. https://doi.org/10.12989/sss.2020.25.6.707.
  38. Fan, L., Kong, D., Song, J., Moradi, Z., Safa, M. and Khadimallah, M.A. (2022), "Optimization dynamic responses of laminated multiphase shell in thermo-electro-mechanical conditions", Adv. Nano Res., 13(1), 29-45. https://doi.org/10.12989/anr.2022.13.1.029.
  39. Fang, W., Yu, T. and Bui, T.Q. (2019), "Analysis of thick porous beams by a quasi-3D theory and isogeometric analysis", Compos. Struct., 221, 110890. https://doi.org/10.1016/j.compstruct.2019.04.062.
  40. Fenjan, R.M., Ahmed, R.A., Faleh, N.M. and Hani, F.M. (2020), "Static stability analysis of smart nonlocal thermo-piezo-magnetic plates via a quasi-3D formulation", Smart Struct. Syst., 26(1), 77-87. https://doi.org/10.12989/sss.2020.26.1.077.
  41. Gan, L.L. and She, G.L. (2023), "Nonlinear snap-buckling and resonance of FG-GPLRC curved beams with different boundary conditions", Geomech. Eng., 32(5), 541-551. https://doi.org/10.12989/gae.2023.32.5.541.
  42. Gan, L.L., Xu, J.Q. and She, G.L. (2023), "Wave propagation of graphene platelets reinforced metal foams circular plates", Struct. Eng. Mech., 85(5), 645-654. https://doi.org/10.12989/sem.2023.85.5.645.
  43. Ghandourah, E., Hussain, M., Khadimallah, M.A., Alazwari, M., Ali, M.R. and Hefni, M.A. (2023), "Validity assessment of aspect ratios based on Timoshenko-beam model: Structural design", Comput. Concrete., 31(1), 1-7. https://doi.org/10.12989/cac.2023.31.1.001.
  44. Ghasemabadian, M.A. and Kadkhodayan, M. (2016), "Investigation of buckling behavior of functionally graded piezoelectric (FGP) rectangular plates under open and closed circuit conditions", Struct. Eng. Mech., 60(2), 271-299. https://doi.org/10.12989/sem.2016.60.2.271.
  45. Ghugal, Y.M. and Shimpi, R.P. (2001), "A review of refined shear deformation theories for isotropic and anisotropic laminated beams", J. Reinf. Plast. Comp., 20(3), 255-272. https://doi.org/10.1177/073168401772678283.
  46. Gibson, R.F. (2016), "Principles of composite material mechanics", CRC Press. 20(3). https://doi.org/10.1177/073168401772678283.
  47. Hadji, L. (2020), "Influence of the distribution shape of porosity on the bending of FGM beam using a new higher order shear deformation model", Smart Struct. Syst., 26(2), 253-262. https://doi.org/10.12989/sss.2020.26.2.253.
  48. Hagos, R.W., Choi, G., Sung, H. and Chang, S. (2022), "Substructuring-based dynamic reduction method for vibration analysis of periodic composite structures", Compos. Mater. Eng., 4(1), 43-62. https://doi.org/10.12989/cme.2022.4.1.043.
  49. Han, B., Hui, W.W., Zhang, Q.C., Zhao, Z.Y., Jin, F., Zhang, Q., Lu, T.J. and Lu, B.H. (2018), "A refined quasi-3D zigzag beam theory for free vibration and stability analysis of multilayered composite beams subjected to thermomechanical loading", Compos. Struct., 204, 620-633. https://doi.org/10.1016/j.compstruct.2018.08.005.
  50. Huang, M.H. and Thambiratnam, D.P. (2001), "Analysis of plate resting on elastic supports and elastic foundation by finite strip method", Comput. Struct., 79(29-30), 2547-2557. https://doi.org/10.1016/S0045-7949(01)00134-1.
  51. Huang, X., Shan, H., Chu, W. and Chen, Y. (2022), "Computational and mathematical simulation for the size-dependent dynamic behavior of the high-order FG nanotubes, including the porosity under the thermal effects", Adv. Nano Res.h, 12(1), 101-115. https://doi.org/10.12989/anr.2022.12.1.101.
  52. Hussain, M., Asghar, S., Khadimallah, M.A., Ayed, H., Alghamdi, S., Bhutto, J.K., Mahmoud, S.R. and Tounsi, A. (2022), "Effect of dimensionless nonlocal parameter: Vibration of double-walled CNTs", Comput. Concrete, 30(4), 269-276. https://doi.org/10.12989/cac.2022.30.4.269.
  53. Jha, D.K., Kant, T. and Singh, R.K. (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.
  54. 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.
  55. Kar,V.R., Mahapatra, T.R. and Panda, S.K. (2015), "Nonlinear flexural analysis of laminated composite flat panel under hygro-thermo-mechanical loading", Steel Compos. Struct., 19(4), 1011-1033. https://doi.org/10.12989/scs.2015.19.4.1011.
  56. Kharghani, N. and Soares, C.G. (2020), "Experimental, numerical and analytical study of buckling of rectangular composite laminates", Eur. J. Mech.-A/Solids, 79, 103869. https://doi.org/10.1016/j.euromechsol.2019.103869.
  57. Khatir, S., Tiachacht, S., Cuong-Le, T, Quoc Bui, T. and Abdel Wahab, M. (2019), "Damage assessment in composite laminates using ANN-PSO-IGA and Cornwell indicator.", Compos. Struct., 230, 111509. https://doi.org/10.1016/j.compstruct.2019.111509.
  58. Khatir, S., Tiachacht, S., Cuong-Le, T., Ghandourah, E., Mirjalili, S. and Abdel Wahab, M. (2021), "An improved artificial neural network using arithmetic optimization algorithm for damage assessment in FGM composite plates", Compos. Struct., 273, 114287. https://doi.org/10.1016/j.compstruct.2021.114.
  59. Kolahchi, R., Safari, M. and Esmailpour, M. (2016), "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.
  60. Kumar, H.S.N. and Kattimani, S. (2022), "Nonlinear analysis of two-directional functionally graded doubly curved panels with porosities", Struct. Eng. Mech., 82(4), 477-490. https://doi.org/10.12989/sem.2022.82.4.477.
  61. Li, Y.P., She, G.L., Gan, L.L. and Liu, H.B. (2023), "Nonlinear thermal post-buckling analysis of graphene platelets reinforced metal foams plates with initial geometrical imperfection", Steel Compos. Struct., 46(5), 649-658. https://doi.org/10.12989/scs.2023.46.5.649.
  62. Liu, Y., Wang, X., Liu, L., Wu, B. and Yang, Q. (2022), "On the forced vibration of high-order functionally graded nanotubes under the rotation via intelligent modelling", Adv. Nano Res., 13(1), 47-61. https://doi.org/10.12989/anr.2022.13.1.047.
  63. Madenci, E. (2019), "A refined functional and mixed formulation to static analyses of fgm beams", Struct. Eng. Mech., 69(4), 427-437. https://doi.org/10.12989/sem.2019.69.4.427.
  64. Madenci, E. (2021), "Free vibration and static analyses of metal-ceramic FG beams via high-order variational MFEM", Steel Compos. Struct., 39(5), 493-509. https://doi.org/10.12989/scs.2021.39.5.493.
  65. Madenci, E. and Ozutok, A. (2020), "Variational approximate for high order bending analysis of laminated composite plates", Struct. Eng. Mech., 73(1), 97-108. https://doi.org/10.12989/sem.2020.73.1.097.
  66. Madenci, E. and Ozkilic, Y.O. (2021), "Cyclic response of self-centering SRC walls with frame beams as boundary", Steel Compos. Struct., 40(2), 157-173. https://doi.org/10.12989/scs.2021.40.2.157.
  67. Madenci, E., Ozkilic, Y.O., Aksoylu, C., Asyraf, M.R.M., Syamsir, A., Supian, A.B.M. and Elizaveta, B. (2023), "Experimental and Analytical investigation of flexural behavior of carbon nanotube reinforced textile based composites", Materials., 16, 2222. https://doi.org/10.3390/ma16062222.
  68. Madenci, E., Ozkilic, Y.O., Aksoylu, C., Asyraf, M.R.M., Syamsir, A., Supian, A.B.M. and Mamaev, N. (2023), "Buckling analysis of CNT-reinforced polymer composite beam using experimental and analytical methods", Materials., 16, 614. https://doi.org/10.3390/ma16020614.
  69. Man, Y. (2022), "On the dynamic stability of a composite beam via modified high-order theory", Comput. Concrete, 30(2), 151-164. https://doi.org/10.12989/cac.2022.30.2.151.
  70. Mansouri, M.R., Beter, J., Fuchs, P.F., Schrittesser, B. and Pinter, G. (2021), "Quantifying matrix-fiber mechanical interactions in hyperelastic materials", Int. J. Mech. Sci., 195, 106268. https://doi.org/10.1016/j.ijmecsci.2021.106268.
  71. Mantari, J.L. and Canales, F.G. (2016), "A unified quasi-3D HSDT for the bending analysis of laminated beams", Aerosp. Sci. Technol., 54, 267-275. https://doi.org/10.1016/j.ast.2016.04.026.
  72. Mantari, J.L. and Soares, C.G. (2012), "Generalized hybrid quasi-3D shear deformation theory for the static analysis of advanced composite plates", Compos. Struct., 94(8), 2561-2575. https://doi.org/10.1016/j.compstruct.2012.02.019.
  73. Mantari, J.L. and Soares, C.G. (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.
  74. Matsunaga, H. (2009), "Stress analysis of functionally graded plates subjected to thermal and mechanical loadings", Compos. Struct.s, 87(4), 344-357. https://doi.org/10.1016/j.compstruct.2008.02.002.
  75. Mindlin, R.D. (1951), "Influence of rotatory inertia and shear on flexural motions of isotropic elastic plates", J. Appl. Mech., 31-38. https://doi.org/10.1115/1.4010217.
  76. Mouritz, A.P., Gellert, E., Burchill, P. and Challis, K. (2001), "Review of advanced composite structures for naval ships and submarines", Compos. Struct., 53(1), 21-42. https://doi.org/10.1016/S0263-8223(00)00175-6.
  77. Mula, S.N., Leite, A.M.S. and Loja, M.A.R. (2022), "Analytical and numerical study of failure in composite plates", Compos. Mater. Eng., 4(1), 23-41. https://doi.org/10.12989/cme.2022.4.1.023.
  78. Navale, K.U. and Pise, C.P. (2021)., "A review on high order shear deformation theory for orthotropic composite laminates", Int. J. Eng. Res. Technol., 10(1), 477-481. https://doi.org/10.17577/IJERTV10IS010156.
  79. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Cinefra, M., Roque, C.M.C., Jorge, R.M.N. and Soares, C.M.M. (2012b), "A quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", Compos. Struct., 94(5), 1814-1825. https://doi.org/10.1016/j.compstruct.2011.12.005.
  80. 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.g, 44(1), 657-674. https://doi.org/10.1016/j.compositesb.2012.01.089.
  81. 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. (2012a), "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.
  82. Nikbakt, S., Kamarian, S. and Shakeri, M. (2018), "A review on optimization of composite structures Part I: Laminated composites", Compos. Struct., 195, 158-185. https://doi.org/10.1016/j.compstruct.2018.03.063.
  83. Noor, A.K. (1973), "Free vibrations of multilayered composite plates", AIAA J., 11(7), 1038-1039. https://doi.org/10.2514/3.6868.
  84. Onyeka, F.C. and Edozie, O.T. (2021), "Analytical solution of thick rectangular plate with clamped and free support boundary condition using polynomial shear deformation theory", Adv. Sci. Tech. Eng. Syst. J., 6(1), 1427-1439. https://doi.org/10.25046/aj0601162.
  85. Ozutok, A., Madenci, E. and Kadioglu, F. (2014), "Free vibration analysis of angle-ply laminate composite beams by mixed finite element formulation using the Gateaux differential", Sci. Eng. Compos. Mater., 21(2), 257-266. https://doi.org/10.1515/secm2013-0043.
  86. Pagano, N.J. (1970), "Exact solutions for rectangular bidirectional composites and sandwich plates", J. Compos. Mater., 4(1), 20-34. https://doi.org/10.1177/002199837000400102.
  87. Polat, A. and Kaya, Y. (2022), "Analysis of discontinuous contact problem in two functionally graded layers resting on a rigid plane by using finite element method", Comput. Concrete, 29(4), 247-253. https://doi.org/10.12989/cac.2022.29.4.247.
  88. Rachedi, M.A., Benyoucef, S., Bouhadra, A., BachirBouiadjra, R., Sekkal, M. and Benachour, A. (2020), "Impact of the homogenization models on the thermoelastic response of FG plates on variable elastic foundation", Geomech. Eng., 22(1), 65-80. https://doi.org/10.12989/gae.2020.22.1.065.
  89. Ramady, A., Dakhel, B., Balubaid, M. and Mahmoud, S.R. (2020), "A mathematical approach for the effect of the rotation on thermal stresses in the piezo-electric homogeneous material", Comput. Concrete., 25(5), 471-478. https://doi.org/10.12989/cac.2020.25.5.471.
  90. Ramteke, P.M., Panda, S.K. and Sharma, N. (2019), "Effect of grading pattern and porosity on the eigen characteristics of porous functionally graded structure", Steel Compos. Struct., 33(6), 865-875. https://doi.org/10.12989/scs.2019.33.6.865.
  91. Reddy, J.N. (2011), "A general nonlinear third-order theory of functionally graded plates", Int. J. Aerosp. Lightweight Struct.(IJALS), 1(1). https://doi.org/10.3850/S201042861100002X.
  92. Reissner, E. (1944), "On the theory of bending of elastic plates", J. Math. Phys., 23, 184-191. https://doi.org/10.1002/sapm1944231184.
  93. Reissner, E. (1945), "The effect of transverse shear deformation on the bending of elastic plates", J. Appl. Mech., 12(2), 69-77. https://doi.org/10.1115/1.4009435.
  94. Rezaiee-Pajand, M., Sobhani, E. and Masoodi, A.R. (2022), "Vibrational behavior of exponentially graded joined conical-conical shells", Steel Compos. Struct., 43(5), 603-623. https://doi.org/10.12989/scs.2022.43.5.603.
  95. Sayyad, A.S. and Ghugal, Y.M. (2014), "A new shear and normal deformation theory for isotropic, transversely isotropic, laminated composite and sandwich plates", Int. J. Mech. Mater. Design, 10(3), 247-267. https://doi.org/10.1007/s10999-014-9244-3.
  96. Selmi, A. (2020), "Exact solution for nonlinear vibration of clamped-clamped functionally graded buckled beam", Smart Struct. Syst., 26(3), 361-371. https://doi.org/10.12989/sss.2020.26.3.361.
  97. Selmi, A. (2022), "Dynamic behavior of cracked ceramic reinforced aluminum composite beam", Smart Struct. Syst., 29(3), 387-393. https://doi.org/10.12989/sss.2022.29.3.387.
  98. Selmi, A. and Bisharat, A. (2018), "Free vibration of functionally graded SWNT reinforced aluminum alloy beam", J. Vibroeng., 20(5), 2151-2164. https://doi.org/10.21595/jve.2018.19445.
  99. Setoodeh, A.R. and Karami, G. (2004), "Static, free vibration and buckling analysis of anisotropic thick laminated composite plates on distributed and point elastic supports using a 3-D layer-wise FEM", Eng. Struct., 26(2), 211-220. https://doi.org/10.1016/j.engstruct.2003.09.009.
  100. Shahsavari, D., Karami, B., Fahham, H.R. and Li, L. (2018), "On the shear buckling of porous nanoplates using a new size-dependent quasi-3D shear deformation theory", Acta Mechanica, 229(11), 4549-4573. https://doi.org/10.1007/s00707-018-2247-7.
  101. Shao, D., Wang, Q., Tao, Y., Shao, W. and Wu, W. (2021), "A unified thermal vibration and transient analysis for quasi-3D shear deformation composite laminated beams with general boundary conditions", Int. J. Mech. Sci., 198, 106357. https://doi.org/10.1016/j.ijmecsci.2021.106357.
  102. She, G.L., Ding, H.X. and Zhang, Y.W. (2022), "Wave propagation in a FG circular plate via the physical neutral surface concept", Struct. Eng. Mech., 82(2), 225-232. https://doi.org/10.12989/sem.2022.82.2.225.
  103. Sobhy, M. and Zenkour, A.M. (2018), "Nonlocal thermal and mechanical buckling of nonlinear orthotropic viscoelastic nanoplates embedded in a visco-pasternak medium", Int. J. Appl. Mech., 10(8), 1850086. https://doi.org/10.1142/S1758825118500862.
  104. Soliman A.E., Eltaher M.A., Attia M.A. and Alshorbagy A.E. (2018), "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.
  105. Talha, M. and Singh, B. (2010), "Static response and free vibration analysis of FGM plates using higher order shear deformation theory", Appl. Math. Model., 34(12), 3991-4011. https://doi.org/10.1016/j.apm.2010.03.034.
  106. 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.
  107. Tran, T.M. and Cuong-Le, T. (2022), "A nonlocal IGA numerical solution for free vibration and buckling analysis of porous sigmoid functionally graded (P-SFGM) nanoplate", Int. J. Struct. Stab. Dyn., 22(16), 2250193. https://doi.org/10.1142/S0219455422501930.
  108. Vinyas, M. (2020), "On frequency response of porous functionally graded magneto-electro-elastic circular and annular plates with different electro-magnetic conditions using HSDT", Compos. Struct., 240, 112044. https://doi.org/10.1016/j.compstruct.2020.112044.
  109. Wang, Y.Q. and Zu, J.W. (2017), " Vibration behaviors of functionally graded rectangular plates with porosities and moving in thermal environment", Aerosp. Sci. Technol., 69, 550-562. https://doi.org/10.1016/j.ast.2017.07.023.
  110. Wang, Y.Q., Huang, X.B. and Li, J. (2016), "Hydroelastic dynamic analysis of axially moving plates in continuous hot-dip galvanizing process", Int. J. Mech. Sci., 110, 201-216. https://doi.org/10.1016/j.ijmecsci.2016.03.010.
  111. Wu, X. and Fang, T. (2022), "Intelligent computer modeling of large amplitude behavior of FG inhomogeneous nanotubes", Adv. Nano Res., 12(6), 617-627. https://doi.org/10.12989/anr.2022.12.6.617.
  112. Xiao, H., Yan, K. and She, G. (2021), "Study on the characteristics of wave propagation in functionally graded porous square plates", Geomech. Eng., 26(6), 607-615. https://doi.org/10.12989/gae.2021.26.6.607.
  113. Xu, J.Q. and She, G.L. (2022), "Thermal post-buckling analysis of porous functionally graded pipes with initial geometric imperfection", Geomech. Eng., 31(3), 329-337. https://doi.org/10.12989/gae.2022.31.3.329.
  114. Yaylaci, M. and Avcar, M. (2020), "Finite element modeling of contact between an elastic layer and two elastic quarter planes", Comput. Concrete., 26(2), 107-114. https://doi.org/10.12989/cac.2020.26.2.107.
  115. Yaylaci, M., Abanoz, M., Yaylaci, E.U., Olmez, H., Sekban, D.M., and Birinci, A. (2022), "The contact problem of the functionally graded layer resting on rigid foundation pressed via rigid punch", Steel Compos. Struct., 43(5), 661-672. https://doi.org/10.12989/scs.2022.43.5.661.
  116. Yaylaci, M., Adiyaman, G., Oner, E. and Birinci, A. (2021a), "Investigation of continuous and discontinuous contact cases in the contact mechanics of graded materials using analytical method and FEM", Comput. Concrete., 27(3), 199-210. https://doi.org/10.12989/cac.2021.27.3.199.
  117. Yaylaci, M., Yayli, M., Yaylaci, E.U., Olmez, H. and Birinci, A. (2021), "Analyzing the contact problem of a functionally graded layer resting on an elastic half plane with theory of elasticity, finite element method and multilayer perceptron", Struct. Eng. Mech., 78(5), 585-597. https://doi.org/10.12989/sem.2021.78.5.585.
  118. Ye, L., Lu, Y., Su, Z. and Meng, G. (2005), "Functionalized composite structures for new generation airframes: A review", Compos. Sci. Technol., 65(9), 1436-1446. https://doi.org/10.1016/j.compscitech.2004.12.015.
  119. Zenkour, A.M. (2007), "Benchmark trigonometric and 3-D elasticity solutions for an exponentially graded thick rectangular plate", Arch. Appl. Mech., 77(4), 197-214. https://doi.org/10.1007/s00419-006-0084-y.
  120. 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.
  121. Zenkour, A.M. and El-Shahrany, H.D. (2021), "Quasi-3D theory for the vibration and deflection of a magnetostrictive composite plate resting on a viscoelastic medium", Compos. Struct., 269, 114028. https://doi.org/10.1016/j.compstruct.2021.114028.
  122. Zenzen, R., Khatir, S., Belaidi, I., Cuong-Le, T. and Abdel Wahab, M. (2020), "A modified transmissibility indicator and Artificial Neural Network for damage identification and quantification in laminated composite structures", Compos. Struct., 248, 112497. https://doi.org/10.1016/j.compstruct.2020.112497.
  123. Zhang W. (2001), "Global and chaotic dynamics for a parametrically excited thin plate", J Sound Vib., 239, 1013-1036. https://doi.org/10.1006/jsvi.2000.3182.
  124. Zhang, Y.Y., Wang, Y.X., Zhang, X., Shen, H.M. and She, G.L. (2021), "On snap-buckling of FG-CNTR curved nanobeams considering surface effects", Steel Compos. Struct., 38(3), 293-304. https://doi.org/10.12989/scs.2021.38.3.293.
  125. Zhang, Y.W. and She, G.L. (2022), "Wave propagation and vibration of FG pipes conveying hot fluid", Steel Compos. Struct., 42(3), 397-405. https://doi.org/10.12989/scs.2022.42.3.397.
  126. Zhang, Y.W., She, G.L. and Ding, H.X. (2023c), "Nonlinear resonance of graphene platelets reinforced metal foams plates under axial motion with geometric imperfections", Eur. J. Mech. -A/Solids, 98, 104887. https://doi.org/10.1016/j.euromechsol.2022.104887.
  127. Zhang, Y.W., Ding, H.X. and She, G.L. (2023a), "Wave propagation in spherical and cylindrical panels reinforced with carbon nanotubes", Steel Compos. Struct., 46(1), 133-141. https://doi.org/10.12989/scs.2023.46.1.133.
  128. Zhang, Y.W., She, G.L., Gan, L.L. and Li, Y.P. (2023b), "Thermal post-buckling behavior of GPLRMF cylindrical shells with initial geometrical imperfection", Geomech. Eng., 32(6), 615-625. https://doi.org/10.12989/gae.2023.32.6.615.
  129. Zhang, Y.W. and She, G.L. (2023), "Nonlinear low-velocity impact response of graphene platelet-reinforced metal foam cylindrical shells under axial motion with geometrical imperfection", Nonlinear. Dyn., 111, 6317-6334. https://doi.org/10.1007/s11071-022-08186-9.
  130. Zhou, J., Moradi, Z., Safa, M. and Khadimallah, M.A. (2022), "Intelligent modeling to investigate the stability of a two-dimensional functionally graded porosity-dependent nanobeam", Comput. Concrete., 30(2), 85-97. https://doi.org/10.12989/cac.2022.30.2.085.
  131. Zhu, F.Y., Lim, H.J., Choi, H. and Yun, G.J. (2022), "A hierarchical micromechanics model for nonlinear behavior with damage of SMC composites with wavy fiber", Compos. Mater. Eng., 4(1), 1-21. https://doi.org/10.12989/cme.2022.4.1.001.