This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Sahmani S, Aghdam MM. Nonlocal strain gradient shell model for axial buckling and postbuckling analysis of magneto-electro-elastic composite nanoshells. Composites Part B: Engineering. 2018;132:258-74. Available from: https://www.sciencedirect.com/science/article/pii/S1359836817312209.SahmaniSAghdamMM.Nonlocal strain gradient shell model for axial buckling and postbuckling analysis of magneto-electro-elastic composite nanoshells. Composites Part B: Engineering. 2018;132:258-74. Available from: https://www.sciencedirect.com/science/article/pii/S1359836817312209.Search in Google Scholar
Farajpour MR, Shahidi AR, Hadi A, Farajpour A. Influence of initial edge displacement on the nonlinear vibration, electrical and magnetic instabilities of magneto-electro-elastic nanofilms. Mechanics of Advanced Materials and Structures. 2019;26(17):1469-81. Available from: https://doi.org/10.1080/15376494.2018.1432820FarajpourMRShahidiARHadiAFarajpourA.Influence of initial edge displacement on the nonlinear vibration, electrical and magnetic instabilities of magneto-electro-elastic nanofilms. Mechanics of Advanced Materials and Structures. 2019;26(17):1469-81. Available from: https://doi.org/10.1080/15376494.2018.1432820Search in Google Scholar
Yakhno VG. An explicit formula for modeling wave propagation in magneto-electro-elastic materials. Journal of Electromagnetic Waves and Applications. 2018;32(7):899-912. Available from: https://doi.org/10.1080/09205071.2017.1410076YakhnoVG.An explicit formula for modeling wave propagation in magneto-electro-elastic materials. Journal of Electromagnetic Waves and Applications. 2018;32(7):899-912. Available from: https://doi.org/10.1080/09205071.2017.1410076Search in Google Scholar
Haghgoo M, Hassanzadeh-Aghdam M-K, Ansari R. Effect of piezoelectric interphase on the effective magneto-electro-elastic properties of three-phase smart composites: A micromechanical study. Mechanics of Advanced Materials and Structures. 2019;26(23):1935-50. Available from: https://doi.org/10.1080/15376494.2018.1455932HaghgooMHassanzadeh-AghdamM-KAnsariR.Effect of piezoelectric interphase on the effective magneto-electro-elastic properties of three-phase smart composites: A micromechanical study. Mechanics of Advanced Materials and Structures. 2019;26(23):1935-50. Available from: https://doi.org/10.1080/15376494.2018.1455932Search in Google Scholar
Chen W, Yan Z, Wang L. On mechanics of functionally graded hard-magnetic soft beams. International Journal of Engineering Science. 2020;157:103391. Available from: https://www.sciencedirect.com/science/article/pii/S0020722520301786ChenWYanZWangL.On mechanics of functionally graded hard-magnetic soft beams. International Journal of Engineering Science. 2020;157:103391. Available from: https://www.sciencedirect.com/science/article/pii/S0020722520301786Search in Google Scholar
Taati E. On buckling and post-buckling behavior of functionally graded micro-beams in thermal environment. International Journal of Engineering Science. 2018;128:63-78. Available from: https://www.sciencedirect.com/science/article/pii/S0020722518302489TaatiE.On buckling and post-buckling behavior of functionally graded micro-beams in thermal environment. International Journal of Engineering Science. 2018;128:63-78. Available from: https://www.sciencedirect.com/science/article/pii/S0020722518302489Search in Google Scholar
Dahmane M, Benadouda M, Fellah A, Saimi A, Hassen AA, Bensaid I. Porosities-dependent wave propagation in bi-directional functionally graded cantilever beam with higher-order shear model. Mechanics of Advanced Materials and Structures. Available from: https://doi.org/10.1080/15376494.2023.2253546DahmaneMBenadoudaMFellahASaimiAHassenAABensaidI.Porosities-dependent wave propagation in bi-directional functionally graded cantilever beam with higher-order shear model. Mechanics of Advanced Materials and Structures. Available from: https://doi.org/10.1080/15376494.2023.2253546Search in Google Scholar
Khaje Khabaz M, Eftekhari SA, Hashemian M, Toghraie D. Optimal vibration control of multi-layer micro-beams actuated by piezoelectric layer based on modified couple stress and surface stress elasticity theories. Physica A: Statistical Mechanics and its Applications. 2020;546:123998. Available from: https://www.sciencedirect.com/science/article/pii/S0378437119322137Khaje KhabazMEftekhariSAHashemianMToghraieD.Optimal vibration control of multi-layer micro-beams actuated by piezoelectric layer based on modified couple stress and surface stress elasticity theories. Physica A: Statistical Mechanics and its Applications. 2020;546:123998. Available from: https://www.sciencedirect.com/science/article/pii/S0378437119322137Search in Google Scholar
Bhangale RK, Ganesan N. Free vibration of simply supported functionally graded and layered magneto-electro-elastic plates by finite element method. Journal of Sound and Vibration. 2006;294(4):1016-38. Available from: https://www.sciencedirect.com/science/article/pii/S0022460X06000320BhangaleRKGanesanN.Free vibration of simply supported functionally graded and layered magneto-electro-elastic plates by finite element method. Journal of Sound and Vibration. 2006;294(4):1016-38. Available from: https://www.sciencedirect.com/science/article/pii/S0022460X06000320Search in Google Scholar
Sladek J, Sladek V, Krahulec S, Chen CS, Young DL. Analyses of Circular Magnetoelectroelastic Plates with Functionally Graded Material Properties. Mechanics of Advanced Materials and Structures. 2015;22(6):479-89. Available from: https://doi.org/10.1080/15376494.2013.807448SladekJSladekVKrahulecSChenCSYoungDL.Analyses of Circular Magnetoelectroelastic Plates with Functionally Graded Material Properties. Mechanics of Advanced Materials and Structures. 2015;22(6):479-89. Available from: https://doi.org/10.1080/15376494.2013.807448Search in Google Scholar
Mahesh V. Porosity effect on the nonlinear deflection of functionally graded magneto-electro-elastic smart shells under combined loading. Mechanics of Advanced Materials and Structures. 2022;29(19):270725. Available from: https://doi.org/10.1080/15376494.2021.1875086MaheshV.Porosity effect on the nonlinear deflection of functionally graded magneto-electro-elastic smart shells under combined loading. Mechanics of Advanced Materials and Structures. 2022;29(19):2707-25. Available from: https://doi.org/10.1080/15376494.2021.1875086Search in Google Scholar
Zhang GY, Qu YL, Gao XL, Jin F. A transversely isotropic magneto-electro-elastic Timoshenko beam model incorporating microstructure and foundation effects. Mechanics of Materials. 2020;149:103412. Available from: https://www.sciencedirect.com/science/article/pii/S0167663620301137ZhangGYQuYLGaoXLJinF.A transversely isotropic magneto-electro-elastic Timoshenko beam model incorporating microstructure and foundation effects. Mechanics of Materials. 2020;149:103412. Available from: https://www.sciencedirect.com/science/article/pii/S0167663620301137Search in Google Scholar
Hong J, Wang S, Zhang G, Mi C. On the Bending and Vibration Analysis of Functionally Graded Magneto-Electro-Elastic Timoshenko Microbeams. Crystals. 2021;11(10):1206. Available from: https://www.mdpi.com/2073-4352/11/10/1206HongJWangSZhangGMiC.On the Bending and Vibration Analysis of Functionally Graded Magneto-Electro-Elastic Timoshenko Microbeams. Crystals. 2021;11(10):1206. Available from: https://www.mdpi.com/2073-4352/11/10/1206Search in Google Scholar
Hong J, Wang S, Qiu X, Zhang G. Bending and Wave Propagation Analysis of Magneto-Electro-Elastic Functionally Graded Porous Microbeams. Crystals. 2022;12(5):732. Available from: https://doi.org/10.3390/cryst12050732HongJWangSQiuXZhangG.Bending and Wave Propagation Analysis of Magneto-Electro-Elastic Functionally Graded Porous Microbeams. Crystals. 2022;12(5):732. Available from: https://doi.org/10.3390/cryst12050732Search in Google Scholar
Qu YL, Li P, Zhang GY, Jin F, Gao XL. A microstructure-dependent anisotropic magneto-electro-elastic Mindlin plate model based on an extended modified couple stress theory. Acta Mechanica. 2020;231(10):4323-50. Available from: https://doi.org/10.1007/s00707-020-02745-0QuYLLiPZhangGYJinFGaoXL.A microstructure-dependent anisotropic magneto-electro-elastic Mindlin plate model based on an extended modified couple stress theory. Acta Mechanica. 2020;231(10):4323-50. Available from: https://doi.org/10.1007/s00707-020-02745-0Search in Google Scholar
Wang S, Hong J, Gu S, Xiao Z, Zhang G. A size-dependent isogeometric model for magneto-electro-elastic graded curved beams in advanced structures. Composite Structures. 2025;358:118877. Available from: https://doi.org/10.1016/j.compstruct.2025.118877WangSHongJGuSXiaoZZhangG.A size-dependent isogeometric model for magneto-electro-elastic graded curved beams in advanced structures. Composite Structures. 2025;358:118877. Available from: https://doi.org/10.1016/j.compstruct.2025.118877Search in Google Scholar
Zheng Y-f, Qu D-y, Liu L-c, Chen C-p. Size-dependent nonlinear bending analysis of nonlocal magneto-electro-elastic laminated nanobeams resting on elastic foundation. International Journal of Non-Linear Mechanics. 2023;148:104255. Available from: https://www.sciencedirect.com/science/article/pii/S0020746222002256.ZhengY-fQuD-yLiuL-cChenC-p.Size-dependent nonlinear bending analysis of nonlocal magneto-electro-elastic laminated nanobeams resting on elastic foundation. International Journal of Non-Linear Mechanics. 2023;148:104255. Available from: https://www.sciencedi-rect.com/science/article/pii/S0020746222002256.Search in Google Scholar
Alibeigi B, Tadi Beni Y, Mehralian F. On the thermal buckling of magneto-electro-elastic piezoelectric nanobeams. The European Physical Journal Plus. 2018;133(3):133. Available from: https://doi.org/10.1140/epjp/i2018-11954-7AlibeigiBTadi BeniYMehralianF.On the thermal buckling of magneto-electro-elastic piezoelectric nanobeams. The European Physical Journal Plus. 2018;133(3):133. Available from: https://doi.org/10.1140/epjp/i2018-11954-7Search in Google Scholar
Ghobadi A, Beni YT, Golestanian H. Nonlinear thermo-electromechanical vibration analysis of size-dependent functionally graded flexoelectric nano-plate exposed magnetic field. Archive of Applied Mechanics. 2020;90(9):2025-70. Available from: https://doi.org/10.1007/s00419-020-01708-0GhobadiABeniYTGolestanianH.Nonlinear thermo-electromechanical vibration analysis of size-dependent functionally graded flexoelectric nano-plate exposed magnetic field. Archive of Applied Mechanics. 2020;90(9):2025-70. Available from: https://doi.org/10.1007/s00419-020-01708-0Search in Google Scholar
Zheng Y-f, Zhou Y, Wang F, Chen C-p. Nonlinear deformation analysis of magneto-electro-elastic nanobeams resting on elastic foundation by using nonlocal modified couple stress theory. European Journal of Mechanics - A/Solids. 2024;103:105158. Available from: https://www.sciencedirect.com/science/article/pii/S0997753823002504ZhengY-fZhouYWangFChenC-p.Nonlinear deformation analysis of magneto-electro-elastic nanobeams resting on elastic foundation by using nonlocal modified couple stress theory. European Journal of Mechanics - A/Solids. 2024;103:105158. Available from: https://www.sciencedirect.com/science/article/pii/S0997753823002504Search in Google Scholar
Habibi B, Beni YT, Mehralian F. Free vibration of magneto-electroelastic nanobeams based on modified couple stress theory in thermal environment. Mechanics of Advanced Materials and Structures. 2019;26(7):601-13. Available from: https://doi.org/10.1080/15376494.2017.1410902HabibiBBeniYTMehralianF.Free vibration of magneto-electroelastic nanobeams based on modified couple stress theory in thermal environment. Mechanics of Advanced Materials and Structures. 2019;26(7):601-13. Available from: https://doi.org/10.1080/15376494.2017.1410902Search in Google Scholar
Alibeigi B, Tadi Beni Y. On the size-dependent magneto/electromechanical buckling of nanobeams. The European Physical Journal Plus. 2018;133(10):398. Available from: https://doi.org/10.1140/epjp/i2018-12208-6AlibeigiBTadi BeniY.On the size-dependent magneto/electromechanical buckling of nanobeams. The European Physical Journal Plus. 2018;133(10):398. Available from: https://doi.org/10.1140/epjp/i2018-12208-6Search in Google Scholar
Zheng Y-f, Liu L-C, Qu D-y, Chen C-p. Nonlinear postbuckling analysis of magneto-electro-thermo-elastic laminated microbeams based on modified couple stress theory. Applied Mathematical Modelling. 2023;118:89-106. Available from: https://www.sciencedirect.com/science/article/pii/S0307904X23000227ZhengY-fLiuL-CQuD-yChenC-p.Nonlinear postbuckling analysis of magneto-electro-thermo-elastic laminated microbeams based on modified couple stress theory. Applied Mathematical Modelling. 2023;118:89-106. Available from: https://www.sciencedirect.com/science/article/pii/S0307904X23000227Search in Google Scholar
Fattaheian Dehkordi S, Tadi Beni Y. Size-dependent continuum-based model of a truncated flexoelectric/flexomagnetic functionally graded conical nano/microshells. Applied Physics A. 2022;128(4):320. Available from: https://doi.org/10.1007/s00339-022-05386-3Fattaheian DehkordiSTadi BeniY.Size-dependent continuum-based model of a truncated flexoelectric/flexomagnetic functionally graded conical nano/microshells. Applied Physics A. 2022;128(4):320. Available from: https://doi.org/10.1007/s00339-022-05386-3Search in Google Scholar
Lyu Z, Ma M. Nonlinear dynamic modeling of geometrically imperfect magneto-electro-elastic nanobeam made of functionally graded material. Thin-Walled Structures. 2023;191:111004. Available from: https://www.sciencedirect.com/science/article/pii/S0263823123004822LyuZMaM.Nonlinear dynamic modeling of geometrically imperfect magneto-electro-elastic nanobeam made of functionally graded material. Thin-Walled Structures. 2023;191:111004. Available from: https://www.sciencedirect.com/science/article/pii/S0263823123004822Search in Google Scholar
Wang S, Hong J, Wei D, Zhang G. Bending and wave propagation analysis of axially functionally graded beams based on a reformulated strain gradient elasticity theory. Applied Mathematics and Mechanics. 2023;44(10):1803-20. Available from: https://doi.org/10.1007/s10483-023-3042-6.WangSHongJWeiDZhangG.Bending and wave propagation analysis of axially functionally graded beams based on a reformulated strain gradient elasticity theory. Applied Mathematics and Mechanics. 2023;44(10):1803-20. Available from: https://doi.org/10.1007/s10483-023-3042-6.Search in Google Scholar
Wang S, Hong J, Yin S, Zhang G. Isogeometric analysis of magneto-electro-elastic functionally graded Mindlin microplates. Thin-Walled Structures. 2024;198:111740. Available from: https://www.sciencedirect.com/science/article/pii/S0263823124001836WangSHongJYinSZhangG.Isogeometric analysis of magneto-electro-elastic functionally graded Mindlin microplates. Thin-Walled Structures. 2024;198:111740. Available from: https://www.sciencedi-rect.com/science/article/pii/S0263823124001836Search in Google Scholar
Lam DCC, Yang F, Chong ACM, Wang J, Tong P. Experiments and theory in strain gradient elasticity. Journal of the Mechanics and Physics of Solids. 2003;51(8):1477-508. Available from: https://www.sciencedirect.com/science/article/pii/S002250960300053XLamDCCYangFChongACMWangJTongP.Experiments and theory in strain gradient elasticity. Journal of the Mechanics and Physics of Solids. 2003;51(8):1477-508. Available from: https://www.sciencedirect.com/science/article/pii/S002250960300053XSearch in Google Scholar
McFarland AW, Colton JS. Role of material microstructure in plate stiffness with relevance to microcantilever sensors. Journal of Micromechanics and Microengineering. 2005;15(5):1060. Available from: https://dx.doi.org/10.1088/0960-1317/15/5/024McFarlandAWColtonJS.Role of material microstructure in plate stiffness with relevance to microcantilever sensors. Journal of Micromechanics and Microengineering. 2005;15(5):1060. Available from: https://dx.doi.org/10.1088/0960-1317/15/5/024Search in Google Scholar
Toupin RA. Elastic materials with couple-stresses. Archive for Rational Mechanics and Analysis. 1962;11(1):385-414. Available from: https://doi.org/10.1007/BF00253945ToupinRA.Elastic materials with couple-stresses. Archive for Rational Mechanics and Analysis. 1962;11(1):385-414. Available from: https://doi.org/10.1007/BF00253945Search in Google Scholar
Mindlin RD. Influence of couple-stresses on stress concentrations. Experimental Mechanics. 1963;3(1):1-7. Available from: https://doi.org/10.1007/BF02327219MindlinRD.Influence of couple-stresses on stress concentrations. Experimental Mechanics. 1963;3(1):1-7. Available from: https://doi.org/10.1007/BF02327219Search in Google Scholar
Mindlin RD. Micro-structure in linear elasticity. Archive for Rational Mechanics and Analysis. 1964;16(1):51-78. Available from: https://doi.org/10.1007/BF00248490MindlinRD.Micro-structure in linear elasticity. Archive for Rational Mechanics and Analysis. 1964;16(1):51-78. Available from: https://doi.org/10.1007/BF00248490Search in Google Scholar
Mindlin RD, Eshel NN. On first strain-gradient theories in linear elasticity. International Journal of Solids and Structures. 1968;4(1):109-24. Available from: https://www.sciencedirect.com/science/article/pii/002076836890036XMindlinRDEshelNN.On first strain-gradient theories in linear elasticity. International Journal of Solids and Structures. 1968;4(1):109-24. Available from: https://www.sciencedirect.com/science/article/pii/002076836890036XSearch in Google Scholar
Polizzotto C. A hierarchy of simplified constitutive models within isotropic strain gradient elasticity. European Journal of Mechanics - A/Solids. 2017;61:92-109. Available from: https://www.sciencedirect.com/science/article/pii/S0997753816302145PolizzottoC.A hierarchy of simplified constitutive models within isotropic strain gradient elasticity. European Journal of Mechanics - A/Solids. 2017;61:92-109. Available from: https://www.sciencedi-rect.com/science/article/pii/S0997753816302145Search in Google Scholar
B.S. Altan, E.C. Aifantis. On Some Aspects in the Special Theory of Gradient Elasticity. Journal of the Mechanical Behavior of Materials. 1997;8(3):231-82. Available from: https://doi.org/10.1515/JMBM.1997.8.3.231AltanB.S.AifantisE.C.On Some Aspects in the Special Theory of Gradient Elasticity. Journal of the Mechanical Behavior of Materials. 1997;8(3):231-82. Available from: https://doi.org/10.1515/JMBM.1997.8.3.231Search in Google Scholar
Ebrahimi F, Barati MR. Vibration analysis of embedded biaxially loaded magneto-electrically actuated inhomogeneous nanoscale plates. Journal of Vibration and Control. 2018;24(16):3587-607. Available from: https://journals.sagepub.com/doi/abs/10.1177/1077546317708105EbrahimiFBaratiMR.Vibration analysis of embedded biaxially loaded magneto-electrically actuated inhomogeneous nanoscale plates. Journal of Vibration and Control. 2018;24(16):3587-607. Available from: https://journals.sagepub.com/doi/abs/10.1177/1077546317708105Search in Google Scholar
Kiani A, Sheikhkhoshkar M, Jamalpoor A, Khanzadi M. Free vibration problem of embedded magneto-electro-thermo-elastic nanoplate made of functionally graded materials via nonlocal third-order shear deformation theory. Journal of Intelligent Material Systems and Structures. 2018;29(5):741-63. Available from: https://journals.sagepub.com/doi/abs/10.1177/1045389X17721034KianiASheikhkhoshkarMJamalpoorAKhanzadiM.Free vibration problem of embedded magneto-electro-thermo-elastic nanoplate made of functionally graded materials via nonlocal third-order shear deformation theory. Journal of Intelligent Material Systems and Structures. 2018;29(5):741-63. Available from: https://journals.sagepub.com/doi/abs/10.1177/1045389X17721034Search in Google Scholar
Liu H, Lv Z. Vibration performance evaluation of smart magneto-electro-elastic nanobeam with consideration of nanomaterial uncertainties. Journal of Intelligent Material Systems and Structures. 2019;30(18-19):2932-52. Available from: https://journals.sagepub.com/doi/abs/10.1177/1045389X19873418LiuHLvZ.Vibration performance evaluation of smart magneto-electro-elastic nanobeam with consideration of nanomaterial uncertainties. Journal of Intelligent Material Systems and Structures. 2019;30(18-19):2932-52. Available from: https://journals.sagepub.com/doi/abs/10.1177/1045389X19873418Search in Google Scholar
Xiao W-s, Gao Y, Zhu H. Buckling and post-buckling of magneto-electro-thermo-elastic functionally graded porous nanobeams. Microsystem Technologies. 2019;25(6):2451-70. Available from: https://doi.org/10.1007/s00542-018-4145-2XiaoW-sGaoYZhuH.Buckling and post-buckling of magneto-electro-thermo-elastic functionally graded porous nanobeams. Microsystem Technologies. 2019;25(6):2451-70. Available from: https://doi.org/10.1007/s00542-018-4145-2Search in Google Scholar
Lim CW, Zhang G, Reddy JN. A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation. Journal of the Mechanics and Physics of Solids. 2015;78:298-313. Available from: https://www.sciencedirect.com/science/article/pii/S0022509615000320LimCWZhangGReddyJN.A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation. Journal of the Mechanics and Physics of Solids. 2015;78:298-313. Available from: https://www.sciencedirect.com/science/article/pii/S0022509615000320Search in Google Scholar
Şimşek M. Nonlinear free vibration of a functionally graded nanobeam using nonlocal strain gradient theory and a novel Hamiltonian approach. International Journal of Engineering Science. 2016;105:12-27. Available from: https://www.sciencedirect.com/science/article/pii/S0020722516300520ŞimşekM.Nonlinear free vibration of a functionally graded nanobeam using nonlocal strain gradient theory and a novel Hamiltonian approach. International Journal of Engineering Science. 2016;105:12-27. Available from: https://www.sciencedirect.com/science/article/pii/S0020722516300520Search in Google Scholar
Li X, Li L, Hu Y, Ding Z, Deng W. Bending, buckling and vibration of axially functionally graded beams based on nonlocal strain gradient theory. Composite Structures. 2017;165:250-65. Available from: https://www.sciencedirect.com/science/article/pii/S0263822316304974LiXLiLHuYDingZDengW.Bending, buckling and vibration of axially functionally graded beams based on nonlocal strain gradient theory. Composite Structures. 2017;165:250-65. Available from: https://www.sciencedirect.com/science/article/pii/S0263822316304974Search in Google Scholar
Nguyen T-K, Vo TP, Thai H-T. Static and free vibration of axially loaded functionally graded beams based on the first-order shear deformation theory. Composites Part B: Engineering. 2013;55:147-57. Available from: https://www.sciencedirect.com/science/article/pii/S1359836813003223NguyenT-KVoTPThaiH-T.Static and free vibration of axially loaded functionally graded beams based on the first-order shear deformation theory. Composites Part B: Engineering. 2013;55:147-57. Available from: https://www.sciencedirect.com/science/article/pii/S1359836813003223Search in Google Scholar
Li S-R, Batra RC. Relations between buckling loads of functionally graded Timoshenko and homogeneous Euler–Bernoulli beams. Composite Structures. 2013;95:5-9. Available from: https://www.sciencedirect.com/science/article/pii/S0263822312003558LiS-RBatraRC.Relations between buckling loads of functionally graded Timoshenko and homogeneous Euler–Bernoulli beams. Composite Structures. 2013;95:5-9. Available from: https://www.sciencedirect.com/science/article/pii/S0263822312003558Search in Google Scholar
Nguyen T-K, Nguyen B-D. A new higher-order shear deformation theory for static, buckling and free vibration analysis of functionally graded sandwich beams. Journal of Sandwich Structures & Materials. 2015;17(6):613-31. Available from: https://journals.sagepub.com/doi/abs/10.1177/1099636215589237NguyenT-KNguyenB-D.A new higher-order shear deformation theory for static, buckling and free vibration analysis of functionally graded sandwich beams. Journal of Sandwich Structures & Materials. 2015;17(6):613-31. Available from: https://journals.sagepub.com/doi/abs/10.1177/1099636215589237Search in Google Scholar
Van Vinh P. Deflections, stresses and free vibration analysis of bi-functionally graded sandwich plates resting on Pasternak’s elastic foundations via a hybrid quasi-3D theory. Mechanics Based Design of Structures and Machines. 2021:1-32. Available from: https://doi.org/10.1080/15397734.2021.1894948Van VinhP.Deflections, stresses and free vibration analysis of bi-functionally graded sandwich plates resting on Pasternak’s elastic foundations via a hybrid quasi-3D theory. Mechanics Based Design of Structures and Machines. 2021:1-32. Available from: https://doi.org/10.1080/15397734.2021.1894948Search in Google Scholar
Adhikari B, Singh BN. Dynamic response of functionally graded plates resting on two-parameter-based elastic foundation model using a quasi-3D theory. Mechanics Based Design of Structures and Machines. 2019;47(4):399-429. Available from: https://doi.org/10.1080/15397734.2018.1555965AdhikariBSinghBN.Dynamic response of functionally graded plates resting on two-parameter-based elastic foundation model using a quasi-3D theory. Mechanics Based Design of Structures and Machines. 2019;47(4):399-429. Available from: https://doi.org/10.1080/15397734.2018.1555965Search in Google Scholar
Bensaid I, Saimi A. Dynamic investigation of functionally graded porous beams resting on viscoelastic foundation using generalised differential quadrature method. Australian Journal of Mechanical Engineering. 2022:1-20. Available from: https://doi.org/10.1080/14484846.2021.2017115BensaidISaimiA.Dynamic investigation of functionally graded porous beams resting on viscoelastic foundation using generalised differential quadrature method. Australian Journal of Mechanical Engineering. 2022:1-20. Available from: https://doi.org/10.1080/14484846.2021.2017115Search in Google Scholar
Ahmed S, Abdelhamid H, Ismail B, Ahmed F. An Differential Quadrature Finite Element and the Differential Quadrature Hierarchical Finite Element Methods for the Dynamics Analysis of on Board Shaft. European Journal of Computational Mechanics. 2021;29(4-6):303–44. Available from: https://journals.riverpublishers.com/index.php/EJCM/article/view/5999AhmedSAbdelhamidHIsmailBAhmedF.An Differential Quadrature Finite Element and the Differential Quadrature Hierarchical Finite Element Methods for the Dynamics Analysis of on Board Shaft. European Journal of Computational Mechanics. 2021;29(4-6):303–44. Available from: https://journals.riverpublishers.com/index.php/EJCM/article/view/5999Search in Google Scholar
Houalef IE, Bensaid I, Saimi A, Cheikh A. An analysis of vibration and buckling behaviors of nano-composite beams reinforced with agglomerated carbon nanotubes via differential quadrature finite element method. Mechanics of Advanced Materials and Structures. 2023:1-19. Available from: https://doi.org/10.1080/15376494.2023.2185706HoualefIEBensaidISaimiACheikhA.An analysis of vibration and buckling behaviors of nano-composite beams reinforced with agglomerated carbon nanotubes via differential quadrature finite element method. Mechanics of Advanced Materials and Structures. 2023:1-19. Available from: https://doi.org/10.1080/15376494.2023.2185706Search in Google Scholar
Saimi A, Bensaid I, Houalef IE. Dynamic analysis of a porous microbeam model based on refined beam strain gradient theory via differential quadrature hierarchical finite element method. Advances in Materials Research. 2023;12(2):133-59.SaimiABensaidIHoualefIE.Dynamic analysis of a porous microbeam model based on refined beam strain gradient theory via differential quadrature hierarchical finite element method. Advances in Materials Research. 2023;12(2):133-59.Search in Google Scholar
Saimi A, Bensaid I, Civalek Ö. A study on the crack presence effect on dynamical behaviour of bi-directional compositionally imperfect material graded micro beams. Composite Structures. 2023;316:117032. Available from: https://www.sciencedirect.com/science/article/pii/S0263822323003768SaimiABensaidICivalekÖ.A study on the crack presence effect on dynamical behaviour of bi-directional compositionally imperfect material graded micro beams. Composite Structures. 2023;316:117032. Available from: https://www.sciencedirect.com/science/article/pii/S0263822323003768Search in Google Scholar
Saimi A, Bensaid I, Khouani B, Mazari MY, Houalef IE, Cheikh A. A Novel Differential Quadrature Galerkin Method for Dynamic and Stability Behaviour of Bi-directional Functionally Graded Porous Micro Beams. European Journal of Computational Mechanics. 2023;32(04):393-440. Available from: https://journals.riverpublish-ers.com/index.php/EJCM/article/view/23191SaimiABensaidIKhouaniBMazariMYHoualefIECheikhA.A Novel Differential Quadrature Galerkin Method for Dynamic and Stability Behaviour of Bi-directional Functionally Graded Porous Micro Beams. European Journal of Computational Mechanics. 2023;32(04):393-440. Available from: https://journals.riverpublish-ers.com/index.php/EJCM/article/view/23191Search in Google Scholar
Tadi Beni Y. Size-dependent electromechanical bending, buckling, and free vibration analysis of functionally graded piezoelectric nanobeams. Journal of Intelligent Material Systems and Structures. 2016;27(16):2199-215. Available from: https://journals.sagepub.com/doi/abs/10.1177/1045389X15624798Tadi BeniY.Size-dependent electromechanical bending, buckling, and free vibration analysis of functionally graded piezoelectric nanobeams. Journal of Intelligent Material Systems and Structures. 2016;27(16):2199-215. Available from: https://journals.sagepub.com/doi/abs/10.1177/1045389X15624798Search in Google Scholar
Tadi Beni Y. Size-dependent analysis of piezoelectric nanobeams including electro-mechanical coupling. Mechanics Research Communications. 2016;75:67-80. Available from: https://www.sciencedirect.com/science/article/pii/S0093641316300477Tadi BeniY.Size-dependent analysis of piezoelectric nanobeams including electro-mechanical coupling. Mechanics Research Communications. 2016;75:67-80. Available from: https://www.sciencedirect.com/science/article/pii/S0093641316300477Search in Google Scholar
Senthil VG, Vasundara VV, Vijay KV. A review and critique of theories for piezoelectric laminates. Smart Materials and Structures. 2000;9(1):24. Available from: https://dx.doi.org/10.1088/0964-1726/9/1/304SenthilVGVasundaraVVVijayKV.A review and critique of theories for piezoelectric laminates. Smart Materials and Structures. 2000;9(1):24. Available from: https://dx.doi.org/10.1088/0964-1726/9/1/304Search in Google Scholar
Wang Q, Quek ST, Sun CT, Liu X. Analysis of piezoelectric coupled circular plate. Smart Materials and Structures. 2001;10(2):229. Available from: https://dx.doi.org/10.1088/0964-1726/10/2/308WangQQuekSTSunCTLiuX.Analysis of piezoelectric coupled circular plate. Smart Materials and Structures. 2001;10(2):229. Available from: https://dx.doi.org/10.1088/0964-1726/10/2/308Search in Google Scholar
Liu C, Liu B, Zhao L, Xing Y, Ma C, Li H. A differential quadrature hierarchical finite element method and its applications to vibration and bending of Mindlin plates with curvilinear domains. International Journal for Numerical Methods in Engineering. 2017;109(2):174-97. Available from: https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.5277LiuCLiuBZhaoLXingYMaCLiH.A differential quadrature hierarchical finite element method and its applications to vibration and bending of Mindlin plates with curvilinear domains. International Journal for Numerical Methods in Engineering. 2017;109(2):174-97. Available from: https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.5277Search in Google Scholar
Li JY. Magnetoelectroelastic multi-inclusion and inhomogeneity problems and their applications in composite materials. International Journal of Engineering Science. 2000;38(18):1993-2011. Available from: https://www.sciencedirect.com/science/article/pii/S0020722500000148LiJY.Magneto-Electroelastic multi-inclusion and inhomogeneity problems and their applications in composite materials. International Journal of Engineering Science. 2000;38(18):1993-2011. Available from: https://www.sciencedirect.com/science/article/pii/S0020722500000148Search in Google Scholar
Zhang GY, Gao XL. Elastic wave propagation in 3-D periodic composites: Band gaps incorporating microstructure effects. Composite Structures. 2018;204:920-32. Available from: https://www.sciencedirect.com/science/article/pii/S0263822318318270ZhangGYGaoXL.Elastic wave propagation in 3-D periodic composites: Band gaps incorporating microstructure effects. Composite Structures. 2018;204:920-32. Available from: https://www.sciencedirect.com/science/article/pii/S0263822318318270Search in Google Scholar