Acknowledgement
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.
References
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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).
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Gibson, R.F. (2016), "Principles of composite material mechanics", CRC Press. 20(3). https://doi.org/10.1177/073168401772678283.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Noor, A.K. (1973), "Free vibrations of multilayered composite plates", AIAA J., 11(7), 1038-1039. https://doi.org/10.2514/3.6868.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Reissner, E. (1944), "On the theory of bending of elastic plates", J. Math. Phys., 23, 184-191. https://doi.org/10.1002/sapm1944231184.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.