Skip to main content

Advertisement

SpringerLink
Log in

Computational Analysis of Smart Magneto-Electro-Elastic Materials and Structures: Review and Classification

  • Original Paper
  • Published:
Archives of Computational Methods in Engineering Aims and scope Submit manuscript

Abstract

Magneto-electro-elastic (MEE) materials have been receiving a special attention from the research community owing to their specialized performance and coupled behavior under thermal, electric, magnetic and mechanical loads. The possibility of prospective energy conversion means, have additionally been added to the cause of researching about these materials. Therefore, the review presented here may be considered as a topical discussion on MEE materials and structures. Through this paper, all critical concepts revolving around MEE materials are discussed in separate sections ranging from the very definition of MEE materials, their material phenomenon, types and properties, to certain fundamental theories and micromechanical models, structural analyses of MEE structures and their nano-sized counterparts, effects of various external and internal parameters and prospective applications of these materials. The present study is in no ways exhaustive to the methods and results observed, but it may be considered as a guide to researchers and scholars about the behavior of MEE materials, wherein critical observations and analyses’ techniques are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Nan CW, Bichurin MI, Dong S, Viehland D, Srinivasan G (2008) Multiferroic magnetoelectric composites: historical perspective, status, and future directions. J Appl Phys 103:031101–1–031101–35

    Google Scholar 

  2. Hadjiloizi DA, Kalamkarov AL, Metti C, Georgiades AV (2014) Analysis of smart piezo-magneto-thermo-elastic composite and reinforced plates: part II—applications. Curved Layer Struct 1(1):32–58

    Google Scholar 

  3. Yousefi-Koma A, Zimcik DG (2003) Applications of smart structures to aircraft for performance enhancement. Can Aeronaut Sp J 49(4):163–172

    Google Scholar 

  4. Zheludev NI, Plum E, Valente J, Youngs IJ, Ou J-Y (2015) A magneto-electro-optical effect in a plasmonic nanowire material. Nat Commun 6:1–6

    Google Scholar 

  5. Franciosi P (2013) Transversally isotropic magneto-electro-elastic composites with co-(dis) continuous phases. Int J Solids Struct 50:1013–1031

    Google Scholar 

  6. Pakam N, Arockiarajan A (2012) An analytical model for predicting the effective properties of magneto-electro-elastic (MEE) composites. Comput Mater Sci 65:19–28

    Google Scholar 

  7. Sladek J, Sladek V, Repka M, Kasala J, Bishay P (2017) Evaluation of effective material properties in magneto-electro-elastic composite materials. Compos Struct 174:176–186

    Google Scholar 

  8. Zhang Z, Wang X (2015) Effective multi-field properties of electro-magneto-thermoelastic composites estimated by finite element method approach. Acta Mech Solida Sin 28:145–155

    Google Scholar 

  9. Bravo-Castillero J, Sixto-Camacho LM, Brenner R, Guinovart-Díaz R, Pérez-Fernández LD, Rodríguez-Ramos R, Sabina FJ (2015) Temperature-related effective properties and exact relations for thermo-magneto-electro-elastic fibrous composites. Comput Math Appl 69:980–996

    MathSciNet  MATH  Google Scholar 

  10. Lee J, Boyd JG IV, Lagoudas DC (2005) Effective properties of three-phase electro-magneto-elastic composites. Int J Eng Sci 43:790–825

    MathSciNet  MATH  Google Scholar 

  11. Starkov IA, Starkov AS (2016) Effective parameters of multilayered thermo-electro-magneto-elastic solids. Solid State Commun 226:5–7. https://doi.org/10.1016/j.ssc.2015.11.002

    Article  Google Scholar 

  12. Kuo HY (2013) Effective property of multiferroic fibrous composites with imperfect interfaces. Smart Mater Struct 22(10):105005

    Google Scholar 

  13. Aboudi J (2001) Micromechanical analysis of fully coupled multiphase composites. Smart Mater Struct 10:867–877

    Google Scholar 

  14. Ye J, Cai H, Wang Y, Jing Z, Shi B, Qiu Y, Chen X (2018) Effective mechanical properties of piezoelectric–piezomagnetic hybrid smart composites. J Intell Mater Syst Struct 29:1711–1723

    Google Scholar 

  15. Keller SM, Sepulveda AE, Carman GP (2016) Effective magnetoelectric properties of magnetoelectroelastic (multiferroic) materials and effects on plane wave dynamics. Prog Electromagn Res 154:115–126

    Google Scholar 

  16. Espinosa-Almeyda Y, Camacho-Montes H, Rodriguez-Ramos R, Guinovart-Díaz R, López-Realpozo JC, Bravo-Castillero J, Sabina FJ (2017) Influence of imperfect interface and fiber distribution on the antiplaneeffective magneto-electro-elastic properties for fiber reinforcedcomposite. Int J Solids Struct 112:155–168

    MATH  Google Scholar 

  17. Chen W, Pan E, Wang H, Zhang C (2010) Theory of indentation on multiferroic composite materials. J Mech Phys Solids 58:1524–1551

    MathSciNet  MATH  Google Scholar 

  18. Hashemi R (2016) Magneto-electro-elastic properties of multiferroic composites containing periodic distribution of general multi-coated inhomogeneities. Int J Eng Sci 103:59–76

    MathSciNet  MATH  Google Scholar 

  19. Weichen S, Kuang ZB (2003) Conservation laws in non-homogeneous electro-magneto-elastic materials. Eur J Mech A Solids 22:217–230

    MathSciNet  MATH  Google Scholar 

  20. Preobrazhensky V, Pernod P, Giordano S, Goueygou M, Tiercelin N, Talbi A (2014) Magneto-electro-elastic effective properties of multilayered artificial multiferroics with arbitrary lamination direction. Int J Eng Sci 78:134–153

    MathSciNet  MATH  Google Scholar 

  21. Yang ZX, Dang PF, Han QK, Jin ZH (2018) Natural characteristics analysis of magneto-electro-elastic multilayered plate using analytical and finite element method. Compos Struct 185:411–420

    Google Scholar 

  22. Koutsawa Y (2015) Overall thermo-magneto-electro-elastic properties of multiferroics composite materials with arbitrary heterogeneities spatial distributions. Compos Struct 133:764–773

    Google Scholar 

  23. Pakam N, Arockiarajan A (2014) Study on effective properties of 1-3-2 type magneto-electro-elastic composites. Sens Actuators A Phys 209:87–99

    Google Scholar 

  24. Srinivas S, Li JY (2005) The effective magnetoelectric coefficients of polycrystalline multiferroic composites. Acta Mater 53:4135–4142

    Google Scholar 

  25. Haghgoo M, Ansari R, Hassanzadeh-Aghdam MK, Darvizeh A (2018) Fully coupled thermo-magneto-electro-elastic properties of unidirectional smart composites with a piezoelectric interphase. Proc Inst Mech Eng Part C J Mech Eng Sci 233:2813–2829

    Google Scholar 

  26. Bakkali A, Azrar L, Aljinaidi AA (2016) Viscomagnetoelectroelastic effective properties’ modeling for multi-phase and multi-coated magnetoelectroelastic composites. J Intell Mater Syst Struct 27:2261–2286

    Google Scholar 

  27. Wang B (2012) Fracture and effective properties of finite magnetoelectroelastic media. J Intell Mater Syst Struct 23:1699–1712

    Google Scholar 

  28. El-Karamany AS (2009) Uniqueness theorem and Hamilton’s principle in linear micropolar thermopiezoelectric/piezomagnetic continuum with two relaxation times. Meccanica 44:47–59

    MathSciNet  MATH  Google Scholar 

  29. Soh AK, Liu JX (2005) On the constitutive equations of magnetoelectroelastic solids. J Intell Mater Syst Struct 16:597–602

    Google Scholar 

  30. Green G (1889) An essay on the application of mathematical analysis to the theories of electricity and magnetism, vol i. Mayer and Muller, Baden, pp 1–5

    Google Scholar 

  31. Delkhosh M, Delkhosh M, Jamali M (2012) Green’s function and its applications. J Basic Appl Sci Res 2012:8865–8876

    MATH  Google Scholar 

  32. Liu J, Liu X, Zhao Y (2001) Green’s functions for anisotropic magnetoelectroelastic solids with an elliptical cavity or a crack. Int J Eng Sci 39:1405–1418

    MATH  Google Scholar 

  33. Piessens R (2000) The hankel transform. In: Poularikas AD (ed) The transforms and applications handbook, 2nd edn. CRC Press, Boca Raton, pp 1–29

    Google Scholar 

  34. Debanath L, Bhatta D (2015) Integral transforms and their applications. CRC Press, Boca Raton

    Google Scholar 

  35. Dold A, Eckmann B, Takens E (1991) Lecture notes in mathematics Rudolf Gorenflo Sergio Vessella. Springer, Berlin

    Google Scholar 

  36. Abel NH (2012) Solution de quelques problèmes à l'aide d'intégrales définies. In: Sylow L, Lie S (eds) Oeuvres complètes de Niels Henrik Abel: nouvelle édition (Cambridge Library Collection - Mathematics). Cambridge University Press, Cambridge, pp 11–27. https://doi.org/10.1017/CBO9781139245807.003

    Chapter  Google Scholar 

  37. Hackbusch W (1995) Abel’s integral equations. In: Integral equations: theory and numerical treatment. Birkhäuser, Basel, pp 201–215. https://doi.org/10.1007/978-3-0348-9215-5

    Chapter  MATH  Google Scholar 

  38. Griffiths DF, Lorenz J (1978) An analysis of the Petrov–Galerkin finite element method. Comput Methods Appl Mech Eng 14:39–64

    MathSciNet  MATH  Google Scholar 

  39. Mori T, Tanaka K (1973) Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metall 21(5):571–574

    Google Scholar 

  40. Benveniste Y (1987) A new approach to the application of Mori–Tanaka’s theory in composite materials. Mech Mater 6:147–157

    Google Scholar 

  41. Hill R (1964) Theory of mechanical properties of fibre strengthened material. J Mech Phys Solids 12:199–212

    MathSciNet  Google Scholar 

  42. Eshelby JD (1957) The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc R Soc Lond Ser A Math Phys Sci 241:376–396

    MathSciNet  MATH  Google Scholar 

  43. Hill R (1965) A self-consistent mechanics of composite materials. J Mech Phys Solids 13:213–222

    Google Scholar 

  44. Atluri SN, Shen S (2001) The meshless local Petrov–Galerkin (MLPG) method: a simple and less-costly alternative to the finite element and boundary element methods. Comput Model Eng Sci 3:11–51

    MathSciNet  MATH  Google Scholar 

  45. Liu GR, Gu YT (2000) Meshless local Petrov–Galerkin (MLPG) method in combination with finite element and boundary element approaches. Comput Mech 26:536–546

    MATH  Google Scholar 

  46. Born M, Wolf E (1999) Principles of optics. Cambridge University Press, Cambridge, pp 75–110

    Google Scholar 

  47. Pfeiffer F, Wriggers P (2007) Lecture notes in applied and computational mechanics, vol 52. Springer, Berlin

    Google Scholar 

  48. Bhattacharya B (2017) Smart materials and intelligent system design. Smart Mater Struct 26:095015

    Google Scholar 

  49. Li XY, Wu F, Jin X, Chen WQ (2015) 3D coupled field in a transversely isotropic magneto-electro-elastic half space punched by an elliptic indenter. J Mech Phys Solids 75:1–44

    MathSciNet  MATH  Google Scholar 

  50. Wang R, Han Q, Pan E (2010) An analytical solution for a multilayered magneto-electro-elastic circular plate under simply supported lateral boundary conditions. Smart Mater Struct 19:1–8

    Google Scholar 

  51. Huang DJ, Ding HJ, Chen WQ (2007) Analytical solution for functionally graded magneto-electro-elastic plane beams. Int J Eng Sci 45:467–485

    Google Scholar 

  52. Serpilli M (2017) Asymptotic interface models in magneto-electro-thermo-elastic composites. Meccanica 52:1407–1424

    MathSciNet  MATH  Google Scholar 

  53. Milazzo A, Benedetti I, Orlando C (2006) Boundary element method for magneto electro elastic laminates. Comput Model Eng Sci 15:17–30

    MathSciNet  MATH  Google Scholar 

  54. Liu M-F, Chang T-P (2009) Closed form expression for the vibration problem of a transversely isotropic magneto-electro-elastic plate. J Appl Mech 77:024502-1–024502-8

    Google Scholar 

  55. Zhou YT, Kim TW (2015) Dynamic contact modeling of anisotropic magneto-electro-elastic materials with volume fraction changes. Compos Struct 131:1099–1110

    Google Scholar 

  56. Zhou YT, Kim TW (2014) An exact analysis of sliding frictional contact of a rigid punch over the surface of magneto-electro-elastic materials. Acta Mech 225:625–645

    MathSciNet  MATH  Google Scholar 

  57. Othman MIA, Song Y (2008) Effect of rotation on plane waves of generalized electro-magneto-thermoviscoelasticity with two relaxation times. Appl Math Model 32:811–825

    MathSciNet  MATH  Google Scholar 

  58. Challagulla KS, Georgiades AV (2011) Micromechanical analysis of magneto-electro-thermo-elastic composite materials with applications to multilayered structures. Int J Eng Sci 49:85–104

    Google Scholar 

  59. Pan E, Han F (2005) Exact solution for functionally graded and layered magneto-electro-elastic plates. Int J Eng Sci 43:321–339

    Google Scholar 

  60. Giordano S (2014) Explicit nonlinear homogenization for magneto-electro-elastic laminated materials. Mech Res Commun 55:18–29

    Google Scholar 

  61. Li Y, Dang H, Xu G, Fan C, Zhao M (2016) Extended displacement discontinuity boundary integral equation and boundary element method for cracks in thermo-magneto-electro-elastic media. Smart Mater Struct 25:1–17

    Google Scholar 

  62. Chen WQ, Lee KY, Ding HJ (2004) General solution for transversely isotropic magneto-electro-thermo- elasticity and the potential theory method. Int J Eng Sci 42:1361–1379

    MATH  Google Scholar 

  63. Corcolle R, Daniel L, Bouillault F (2008) Generic formalism for homogenization of coupled behavior: application to magnetoelectroelastic behavior. Phys Rev B Condens Matter Mater Phys 78:1–12

    Google Scholar 

  64. Zhu BJ, Qin TY (2007) Hypersingular integral equation method for a three-dimensional crack in anisotropic electro-magneto-elastic bimaterials. Theor Appl Fract Mech 47:219–232

    Google Scholar 

  65. Huang JH, Chiu YH, Liu HK (1998) Magneto-electro-elastic Eshelby tensors for a piezoelectric-piezomagnetic composite reinforced by ellipsoidal inclusions. J Appl Phys 83:5364–5370

    Google Scholar 

  66. Tan P, Tong L (2002) Modeling for the electro-magneto-thermo-elastic properties of piezoelectric-magnetic fiber reinforced composites. Compos Part A Appl Sci Manuf 33:631–645

    Google Scholar 

  67. Seadawy AR, Manafian J (2018) New soliton solution to the longitudinal wave equation in a magneto-electro-elastic circular rod. Results Phys 8:1158–1167

    Google Scholar 

  68. Pérez-Fernández LD, Bravo-Castillero J, Rodríguez-Ramos R, Sabina FJ (2009) On the constitutive relations and energy potentials of linear thermo-magneto-electro-elasticity. Mech Res Commun 36:343–350

    MathSciNet  MATH  Google Scholar 

  69. Wang J, Chen L, Fang S (2003) State vector approach to analysis of multilayered magneto-electro-elastic plates. Int J Solids Struct 40:1669–1680

    MATH  Google Scholar 

  70. Wang X-M, Shen Y-P (1996) The conservation laws and path-independent integrals with an application for linear electro-magnetic-elastic media. Int J Solids Struct 33:865–878

    MATH  Google Scholar 

  71. Yakhno V (2018) The well-posedness of dynamical equations of magneto-electro-elasticity. Mediterr J Math 15:1–12

    MathSciNet  MATH  Google Scholar 

  72. Pan E (2002) Three-dimensional Green’s functions in aniotropic magneto-electro-elastic bimaterials. Z fAngew Math Phys 53:815–838

    MATH  Google Scholar 

  73. Kuang ZB (2013) Two theoretical problems in electro-magneto-elastic analysis. Acta Mech 224:1201–1212

    MathSciNet  MATH  Google Scholar 

  74. Li JYU (2003) Uniqueness and reciprocity theorems for linear thermo-electro-magneto-elasticity. Q J Mech Appl Math 56:35–43

    MathSciNet  MATH  Google Scholar 

  75. Bravo-Castillero J, Rodríguez-Ramos R, Guinovart-Díaz R, Mechkour H, Brenner R, Camacho-Montes H, Sabina FJ (2012) Universal relations and effective coefficients of magneto-electro-elastic perforated structures. Q J Mech Appl Math 65:61–85

    MathSciNet  MATH  Google Scholar 

  76. Wang X, Pan E, Albrecht JD, Feng WJ (2009) Effective properties of multilayered functionally graded multiferroic composites. Compos Struct 87:206–214

    Google Scholar 

  77. Jiang X, Pan E (2004) Exact solution for 2D polygonal inclusion problem in anisotropic magnetoelectroelastic full-, half-, and bimaterial-planes. Int J Solids Struct 41:4361–4382

    MATH  Google Scholar 

  78. Pan E (2002) Exact solution for simply supported and multilayered magneto-electro-elastic plates. J Appl Mech 68:608

    MATH  Google Scholar 

  79. Zhu X, Huang Z, Jiang A, Chen WQ, Nishimura N (2010) Fast multipole boundary element analysis for 2D problems of magneto-electro-elastic media. Eng Anal Bound Elem 34:927–933

    MathSciNet  MATH  Google Scholar 

  80. Kuo HY, Bhattacharya K (2013) Fibrous composites of piezoelectric and piezomagnetic phases. Mech Mater 60:159–170

    Google Scholar 

  81. Miehe C, Vallicotti D, Teichtmeister S (2015) Homogenization and multiscale stability analysis in finite magneto-electro-elasticity. Application to soft matter EE, ME and MEE composites. Comput Methods Appl Mech Eng 300:294–346

    MathSciNet  MATH  Google Scholar 

  82. Bravo-Castillero J, Rodríguez-Ramos R, Mechkour H, Otero JA, Sabina FJ (2008) Homogenization of magneto-electro-elastic multilaminated materials. Q J Mech Appl Math 61:311–332

    MathSciNet  MATH  Google Scholar 

  83. Phoenix SS, Satsangi SK, Singh BN (2009) Layer-wise modelling of magneto-electro-elastic plates. J Sound Vib 324:798–815

    Google Scholar 

  84. Sun KH, Kim YY (2010) Layout design optimization for magneto-electro-elastic laminate composites for maximized energy conversion under mechanical loading. Smart Mater Struct 19:1–4

    Google Scholar 

  85. Li JY, Dunn ML (2009) Micromechanics of magnetoelectroelastic composite materials: average fields and effective behavior. J Intell Mater Syst Struct 9:404–416

    Google Scholar 

  86. Kim JY (2011) Micromechanical analysis of effective properties of magneto-electro-thermo- elastic multilayer composites. Int J Eng Sci 49:1001–1018

    MATH  Google Scholar 

  87. Bakkali A, Azrar L, Ali Aljinaidi A (2013) Micromechanical modeling of magnetoelectroelastic composite materials with multicoated inclusions and functionally graded interphases. J Intell Mater Syst Struct 24:1754–1769

    Google Scholar 

  88. Wang BL, Hoffman M (2010) Closed form solution for a line inclusion in magnetoelectroelastic media. Int J Appl Electromagn Mech 34:119–129

    Google Scholar 

  89. Sladek J, Sladek V, Krahulec S, Wünsche M, Zhang C (2012) MLPG analysis of layered composites with piezoelectric and piezomagnetic phases. Comput Mater Contin 29:75–101

    Google Scholar 

  90. Aboudi J (2004) The generalized method of cells and high-fidelity generalized method of cells micromechanical models—a review. Mech Adv Mater Struct 11:329–366

    Google Scholar 

  91. Koutsawa Y, Biscani F, Belouettar S, Nasser H, Carrera E (2011) Toward micromechanics of coupled fields materials containing functionally graded inhomogeneities: multi-coating approach. Mech Adv Mater Struct 18:524–530

    Google Scholar 

  92. Zhong Y, Qin W, Yu W, Zhou X, Jiao L (2015) Variational asymptotic homogenization of magneto-electro-elastic materials with coated fibers. Compos Struct 133:300–311

    Google Scholar 

  93. Tang T (2008) Variational asymptotic micromechanics modeling of composite materials. All Graduate Theses and Dissertations. 72. https://digitalcommons.usu.edu/etd/72

  94. Wu B, Zhang C, Chen W, Zhang C (2015) Surface effects on anti-plane shear waves propagating in magneto-electro-elastic nanoplates Smart Mater. Struct. 24:95017

    Google Scholar 

  95. Zenkour AM, Abouelregal AE (2016) Non-simple magnetothermoelastic solid cylinder with variable thermal conductivity due to harmonically varying heat Earthquakes Struct. 10:681–697

    Google Scholar 

  96. Ebrahimi F F 2018 Vibration analysis of carbon nanotubes with multiple cracks in thermal environment Adv. nano Res.6 57–80

  97. Ebrahimi F A 2017 Investigating vibration behavior of smart imperfect functionally graded beam subjected to magnetic-electric fields based on refined shear deformation theory Adv. nano Res.5 281–301

  98. Ebrahimi FP (2018) Elastic wave dispersion modelling within rotating functionally graded nanobeams in thermal environment. Adv Nano Res 6:201–217

    Google Scholar 

  99. Draiche K, Tounsi A, Mahmoud SR (2016) A refined theory with stretching effect for the flexure analysis of laminated composite plates. Geomech Eng 11:671–690

    Google Scholar 

  100. Draiche K, Tounsi A, Khalfi Y (2014) A trigonometric four variable plate theory for free vibration of rectangular composite plates with patch mass. Steel Compos Struct 17:69–81

    Google Scholar 

  101. Bourada M, Kaci A, Houari MSA, Tounsi A (2015) A new simple shear and normal deformations theory for functionally graded beams. Steel Compos Struct 18:409–423

    Google Scholar 

  102. Bouafia K, Kaci A, Houari MSA, Benzair A, Tounsi A (2017) A nonlocal quasi-3D theory for bending and free flexural vibration behaviors of functionally graded nanobeams. Smart Struct Syst 19:115–126

    Google Scholar 

  103. Abdelbari S, Fekrar A, Heireche H, Said H, Tounsi A, Adda Bedia EA (2016) An efficient and simple shear deformation theory for free vibration of functionally graded rectangular plates on Winkler–Pasternak elastic foundations. Wind Struct 22:329–348

    Google Scholar 

  104. Zenkour AM, Abouelregal AE (2014) The effect of two temperatures on a FG nanobeam induced by a sinusoidal pulse heating. Struct Eng Mech 51:199–214

    Google Scholar 

  105. Zemri A, Houari MSA, Bousahla AA, Tounsi A (2015) A mechanical response of functionally graded nanoscale beam: an assessment of a refined nonlocal shear deformation theory beam theory. Struct Eng Mech 54:693–710

    Google Scholar 

  106. Tounsi A, Houari MSA, Bessaim A (2016) A new 3-unknowns non-polynomial plate theory for buckling and vibration of functionally graded sandwich plate. Struct Eng Mech 60:547–565

    Google Scholar 

  107. Tounsi A, Benguediab S, Adda Bedia EA, Semmah A, Zidour M (2013) Nonlocal effects on thermal buckling properties of double-walled carbon nanotubes. Adv Nano Res 1:1–11

    Google Scholar 

  108. Shahsavari DBL (2018) A high-order gradient model for wave propagation analysis of porous FG nanoplates. Steel Compos Struct 29:53–66

    Google Scholar 

  109. Ma LH, Ke LL, Wang YZ, Wang YS (2017) Wave propagation in magneto-electro-elastic nanobeams via two nonlocal beam models. Phys E Low-Dimens Syst Nanostruct 86:253–261

    Google Scholar 

  110. Karami BDSMRLA (2018) Thermal buckling of smart porous functionally graded nanobeam rested on Kerr foundation. Steel Compos Struct 29:349–362

    Google Scholar 

  111. Karami BMA (2017) Effects of triaxial magnetic field on the anisotropic nanoplates. Steel Compos Struct 25:361–374

    Google Scholar 

  112. Dav G, Milazzo A (2011) A regular variational boundary model for free vibrations of magneto-electro-elastic structures. Eng Anal Bound Elem 35:303–312

    MathSciNet  MATH  Google Scholar 

  113. Simões Moita JM, Mota Soares CM, Mota Soares CA (2009) Analyses of magneto-electro-elastic plates using a higher order finite element model. Compos Struct 91:421–426

    Google Scholar 

  114. Soni S, Jain NK, Joshi PV (2017) Analytical modeling for nonlinear vibration analysis of partially cracked thin magneto-electro-elastic plate coupled with fluid. Nonlinear Dyn 90:137–170

    MathSciNet  Google Scholar 

  115. Chang TP (2013) Deterministic and random vibration analysis of fluid-contacting transversely isotropic magneto-electro-elastic plates. Comput Fluids 84:247–254

    MathSciNet  MATH  Google Scholar 

  116. Lorenzi A, Priimenko VI (1996) Identification problems related to electro-magneto-elastic interactions. J Inverse Ill-Posed Probl 4:115–144

    MathSciNet  MATH  Google Scholar 

  117. Chang TP (2013) On the natural frequency of transversely isotropic magneto-electro-elastic plates in contact with fluid. Appl Math Model 37:2503–2515

    MathSciNet  MATH  Google Scholar 

  118. Ramirez F, Heyliger PR, Pan E (2006) Free vibration response of two-dimensional magneto-electro-elastic laminated plates. J Sound Vib 292:626–644

    Google Scholar 

  119. Kumaravel A, Ganesan N, Sethuraman R (2010) Buckling and vibration analysis of layered and multiphase magneto-electro-elastic cylinders subjected to uniform thermal loading. Multidiscip Model Mater Struct 6:475–492

    Google Scholar 

  120. Cai Y, Meng G, Zhou L (2018) An inhomogeneous cell-based smoothed finite element method for free vibration calculation of functionally graded magnetoelectroelastic structures. Shock Vib 2018:1–17

    Google Scholar 

  121. Lang Z, Xuewu L (2013) Buckling and vibration analysis of functionally graded magneto-electro-thermo-elastic circular cylindrical shells. Appl Math Model 37:2279–2292

    MathSciNet  MATH  Google Scholar 

  122. Mahesh V, Sagar PJ, Kattimani S (2018) Influence of coupled fields on free vibration and static behavior of functionally graded magneto-electro-thermo-elastic plate. J Intell Mater Syst Struct 29:1430–1455

    Google Scholar 

  123. Vinyas M, Sandeep AS, Ebrahimi F (2019) A finite element—based assessment of free vibration behaviour of circular and annular magneto-electro-elastic plates using higher order shear deformation theory. J Intell Mater Syst Struct 30:2478–2501

    Google Scholar 

  124. Vinyas M (2019) Vibration control of skew magneto-electro-elastic plates using active constrained layer damping. Compos Struct 208:600–617

    Google Scholar 

  125. Kattimani SC, Ray MC (2015) Control of geometrically nonlinear vibrations of functionally graded magneto-electro-elastic plates. Int J Mech Sci 99:154–167

    Google Scholar 

  126. Vinyas M, Harursampath D, Nguyen-Thoi T (2019) Influence of active constrained layer damping on the coupled vibration response of functionally graded magneto-electro-elastic plates with skewed edges. Def Technol. https://doi.org/10.1016/j.dt.2019.11.016

    Article  Google Scholar 

  127. Vinyas M (2019) Interphase effect on the controlled frequency response of three-phase smart magneto-electro-elastic plates embedded with active constrained layer damping: FE study. Mater Res Express 6:125707

    Google Scholar 

  128. Razavi S, Shooshtari A (2014) Free vibration analysis of a magneto-electro-elastic doubly-curved shell resting on a Pasternak-type elastic foundation. Smart Mater Struct 23:105003

    Google Scholar 

  129. Li Y, Zhang J (2014) Free vibration analysis of magnetoelectroelastic plate resting on a Pasternak foundation. Smart Mater Struct 23:25002

    Google Scholar 

  130. Shooshtari A, Razavi S (2015) Large amplitude free vibration of symmetrically laminated magneto-electro-elastic rectangular plates on Pasternak type foundation. Mech Res Commun 69:103–113

    Google Scholar 

  131. Vaezi M, Shirbani MM, Hajnayeb A (2016) Free vibration analysis of magneto-electro-elastic microbeams subjected to magneto-electric loads. Phys E Low-Dimens Syst Nanostruct 75:280–286

    Google Scholar 

  132. Annigeri AR, Ganesan N, Swarnamani S (2007) Free vibration behaviour of multiphase and layered magneto-electro-elastic beam. J Sound Vib 299:44–63

    Google Scholar 

  133. Bhangale RK, Ganesan N (2006) Free vibration of functionally graded non-homogeneous magneto-electro- elastic cylindrical shell. Int J Comput Methods Eng Sci Mech 7:191–200

    MATH  Google Scholar 

  134. Jiangyi C, Hualing C, Ernian P (2006) Free vibration of functionally graded, magneto-electro-elastic, and multilayered plates. Acta Mech Solida Sin 19:160–166

    Google Scholar 

  135. Xin L, Hu Z (2015) Free vibration of layered magneto-electro-elastic beams by SS-DSC approach. Compos Struct 125:96–103

    Google Scholar 

  136. Xin L, Hu Z (2015) Free vibration of simply supported and multilayered magneto-electro-elastic plates. Compos Struct 121:344–350

    Google Scholar 

  137. Bhangale RK, Ganesan N (2006) Free vibration of simply supported functionally graded and layered magneto-electro-elastic plates by finite element method. J Sound Vib 294:1016–1038

    MATH  Google Scholar 

  138. Annigeri AR, Ganesan N, Swarnamani S (2006) Free vibrations of simply supported layered and multiphase magneto-electro-elastic cylindrical shells. Smart Mater Struct 15:459–467

    Google Scholar 

  139. Bhangale RK, Ganesan N (2005) Free vibration studies of simply supported non-homogeneous functionally graded magneto-electro-elastic finite cylindrical shells. J Sound Vib 288:412–422

    Google Scholar 

  140. Chen JY, Heyliger PR, Pan E (2014) Free vibration of three-dimensional multilayered magneto-electro-elastic plates under combined clamped/free boundary conditions. J Sound Vib 333:4017–4029

    Google Scholar 

  141. Buchanan GR (2004) Layered versus multiphase magneto-electro-elastic composites. Compos Part B Eng 35:413–420

    Google Scholar 

  142. Ramirez F, Heyliger PR, Pan E (2006) Discrete layer solution to free vibrations of functionally graded magneto-electro-elastic plates. Mech Adv Mater Struct 13:249–266

    Google Scholar 

  143. Vinyas M, Kattimani SC (2019) Finite element simulation of controlled frequency response of skew multiphase magneto-electro-elastic plates. J Intell Mater Syst Struct 30:1757–1771

    Google Scholar 

  144. Shooshtari A, Razavi S (2015) Linear and nonlinear free vibration of a multilayered magneto-electro-elastic doubly-curved shell on elastic foundation. Compos Part B Eng 78:95–108

    Google Scholar 

  145. Chen J, Chen H, Pan E, Heyliger PR (2007) Modal analysis of magneto-electro-elastic plates using the state-vector approach. J Sound Vib 304:722–734

    Google Scholar 

  146. Razavi S, Shooshtari A (2014) Nonlinear free vibration of magneto-electro-elastic rectangular plates. Compos Struct 119:377–384

    Google Scholar 

  147. Shooshtari A, Razavi S (2014) Nonlinear vibration analysis of rectangular magneto-electro-elastic thin plates. Int J Eng 28:139–147

    Google Scholar 

  148. Biju B, Ganesan N, Shankar K (2011) Response of multiphase magneto-electro-elastic sensors under harmonic mechanical loading. Int J Eng Sci Technol 1:216–227

    Google Scholar 

  149. Chen WQ, Lee KY, Ding HJ (2005) On free vibration of non-homogeneous transversely isotropic magneto-electro-elastic plates. J Sound Vib 279:237–251

    Google Scholar 

  150. Wang J, Qu L, Qian F (2010) State vector approach of free-vibration analysis of magneto-electro-elastic hybrid laminated plates. Compos Struct 92:1318–1324

    Google Scholar 

  151. Xu XJ, Deng ZC, Zhang K, Meng JM (2016) Surface effects on the bending, buckling and free vibration analysis of magneto-electro-elastic beams. Acta Mech 227:1557–1573

    MathSciNet  MATH  Google Scholar 

  152. Wang Y, Xu R, Ding H, Chen J (2010) Three-dimensional exact solutions for free vibrations of simply supported magneto-electro-elastic cylindrical panels. Int J Eng Sci 48:1778–1796

    MATH  Google Scholar 

  153. Ebrahimi F, Jafari A, Barati MR (2017) Vibration analysis of magneto-electro-elastic heterogeneous porous material plates resting on elastic foundations. Thin-Walled Struct 119:33–46

    Google Scholar 

  154. Shooshtari A, Razavi S (2017) Vibration of a multiphase magneto-electro-elastic simply supported rectangular plate subjected to harmonic forces. J Intell Mater Syst Struct 28:451–467

    Google Scholar 

  155. Annigeri AR, Ganesan N, Swarnamani S (2006) Free vibrations of clamped-clamped magneto-electro-elastic cylindrical shells. J Sound Vib 292:300–314

    Google Scholar 

  156. Piovan MT, Olmedo Salazar JF (2015) A 1D model for the dynamic analysis of magneto-electro-elastic beams with curved configuration. Mech Res Commun 67:34–38

    Google Scholar 

  157. Zhao MH, Wang H, Yang F, Liu T (2006) A magnetoelectroelastic medium with an elliptical cavity under combined mechanical-electric-magnetic loading. Theor Appl Fract Mech 45:227–237

    Google Scholar 

  158. Wu CP, Lu YC (2009) A modified Pagano method for the 3D dynamic responses of functionally graded magneto-electro-elastic plates. Compos Struct 90:363–372

    Google Scholar 

  159. Liu JX, Soh AK, Fang DN (2005) A moving dislocation in a magneto-electro-elastic solid. Mech Res Commun 32:504–513

    MathSciNet  MATH  Google Scholar 

  160. Sladek J, Sladek V, Krahulec S, Chen CS, Young DL (2015) Analyses of circular magnetoelectroelastic plates with functionally graded material properties. Mech Adv Mater Struct 22:479–489

    Google Scholar 

  161. Li XF (2005) Dynamic analysis of a cracked magnetoelectroelastic medium under antiplane mechanical and inplane electric and magnetic impacts. Int J Solids Struct 42:3185–3205

    MATH  Google Scholar 

  162. Feng WJ, Pan E (2008) Dynamic fracture behavior of an internal interfacial crack between two dissimilar magneto-electro-elastic plates. Eng Fract Mech 75:1468–1487

    Google Scholar 

  163. Albarody TMB, Al-Kayiem HH (2014) Dynamic analysis of laminated composite thermo-magneto-electro-elastic shells. J Mech Sci Technol 28:4877–4891

    Google Scholar 

  164. Hu K, Chen Z, Fu J (2014) Dynamic analysis of an interface crack between magnetoelectroelastic and functionally graded elastic layers under anti-plane mechanical and in-plane electro-magnetic loadings. Compos Struct 107:142–148

    Google Scholar 

  165. Ewolo Ngak FP, Ntamack GE, Azrar L (2019) Dynamic analysis of multilayered magnetoelectroelastic plates based on a pseudo-Stroh formalism and Lagrange polynomials. J Intell Mater Syst Struct 30:939–962

    Google Scholar 

  166. Rojas-Díaz R, García-Sánchez F, Sáez A, Zhang C (2009) Dynamic crack interactions in magnetoelectroelastic composite materials. Int J Fract 157:119–130

    MATH  Google Scholar 

  167. Feng WJ, Pan E, Wang X (2007) Dynamic fracture analysis of a penny-shaped crack in a magnetoelectroelastic layer. Int J Solids Struct 44:7955–7974

    MATH  Google Scholar 

  168. Feng WJ, Su RKL (2007) Dynamic fracture behaviors of cracks in a functionally graded magneto-electro-elastic plate. Eur J Mech A Solids 26:363–379

    MATH  Google Scholar 

  169. Feng WJ, Su RKL (2006) Dynamic internal crack problem of a functionally graded magneto-electro-elastic strip. Int J Solids Struct 43:5196–5216

    MATH  Google Scholar 

  170. Akbarzadeh A, Chen Z (2014) Thermo-magneto-electro-elastic responses of rotating hollow cylinders. Mech Adv Mater Struct 21:67–80

    Google Scholar 

  171. Biju B, Ganesan N, Shankar K (2011) Dynamic response of multiphase magnetoelectroelastic sensors using 3D magnetic vector potential approach. IEEE Sens J 11:2169–2176

    Google Scholar 

  172. Tsai YH, Wu CP (2008) Dynamic responses of functionally graded magneto-electro-elastic shells with open-circuit surface conditions. Int J Eng Sci 46:843–857

    MATH  Google Scholar 

  173. Hu K, Chen Z (2013) Dynamic response of a cracked magnetoelectroelastic layer sandwiched between two elastic layers. ZAMM Z Angew Math Mech 93:676–687

    MathSciNet  MATH  Google Scholar 

  174. Biju B, Ganesan N, Shankar K (2013) Effect of displacement current in magneto-electro-elastic 3D beam subjected to dynamic loading. Mech Adv Mater Struct 20:189–198

    Google Scholar 

  175. Vinyas M, Kattimani SC (2017) Multiphysics response of magneto-electro-elastic beams in thermo-mechanical environment. Coupled Syst Mech 6:351–368

    Google Scholar 

  176. Vinyas M, Kattimani SC (2018) Finite element evaluation of free vibration characteristics of magneto-electro-elastic rectangular plates in hygrothermal environment using higher-order shear deformation theory. Compos Struct 202:1339–1352

    Google Scholar 

  177. Kondaiah P, Shankar K, Ganesan N (2013) Pyroelectric and pyromagnetic effects on behavior of magneto-electro-elastic plate. Coupled Syst Mech 2:1–22

    Google Scholar 

  178. Bagheri R, Ayatollahi M, Mousavi SM (2017) Stress analysis of a functionally graded magneto-electro-elastic strip with multiple moving cracks. Math Mech Solids 22:304–323

    MathSciNet  MATH  Google Scholar 

  179. Bui TQ, Zhang C (2013) Analysis of generalized dynamic intensity factors of cracked magnetoelectroelastic solids by X-FEM. Finite Elem Anal Des 69:19–36

    Google Scholar 

  180. Milazzo A, Orlando C, Alaimo A (2009) An analytical solution for the magneto-electro-elastic bimorph beam forced vibrations problem. Smart Mater Struct 18:085012

    Google Scholar 

  181. Zhou L, Li M, Meng G, Zhao H (2018) An effective cell-based smoothed finite element model for the transient responses of magneto-electro-elastic structures. J Intell Mater Syst Struct 29:3006–3022

    Google Scholar 

  182. Zhou L, Ren S, Liu C, Ma Z (2019) A valid inhomogeneous cell-based smoothed finite element model for the transient characteristics of functionally graded magneto-electro-elastic structures. Compos Struct 208:298–313

    Google Scholar 

  183. Daga A, Ganesan N, Shankar K (2009) Behaviour of magneto-electro-elastic sensors under transient mechanical loading. Sens Actuators A Phys 150:46–55

    Google Scholar 

  184. Daga A, Ganesan N, Shankar K (2007) Comparative studies of the transient response for PECP, MSCP, barium titanate, magneto-electro-elastic finite cylindrical shell under constant internal pressure using finite element method. Finite Elem Anal Des 44:89–104

    Google Scholar 

  185. Biju B, Ganesan N, Shankar K (2010) The transient dynamic response of multiphase magneto-electroelastic sensors bonded to a shell structure. Proc Inst Mech Eng Part L J Mater Des Appl 224:123–132

    Google Scholar 

  186. Biju B, Ganesan N, Shankar K (2012) Transient dynamic behavior of two phase magneto-electro-elastic sensors bonded to elastic rectangular plates. Int J Smart Sens Intell Syst 5:645–672

    Google Scholar 

  187. Dai HL, Wang X (2006) Magneto-thermo-electro-elastic transient response in a piezoelectric hollow cylinder subjected to complex loadings. Int J Solids Struct 43:5628–5646

    MATH  Google Scholar 

  188. Hou PF, Leung AYT (2004) The transient responses of magneto-electro-elastic hollow cylinders. Smart Mater Struct 13:762–776

    Google Scholar 

  189. Daga A, Ganesan N, Shankar K (2009) Transient response of a magneto-electro-elastic simply supported cylinder using finite element. J Mech Mater Struct 4:1341–1364

    MATH  Google Scholar 

  190. Daga A, Ganesan N, Shankar K (2009) Transient dynamic response of cantilever magneto-electro-elastic beam using finite elements. Int J Comput Methods Eng Sci Mech 10:173–185

    MATH  Google Scholar 

  191. Wang HM, Ding HJ (2006) Transient responses of a magneto-electro-elastic hollow sphere for fully coupled spherically symmetric problem. Eur J Mech A Solids 25:965–980

    MATH  Google Scholar 

  192. Rojas-Díaz R, García-Sánchez F, Sáez A, Rodríguez-Mayorga E, Zhang C (2011) Fracture analysis of plane piezoelectric/piezomagnetic multiphase composites under transient loading. Comput Methods Appl Mech Eng 200:2931–2942

    MathSciNet  MATH  Google Scholar 

  193. Wang BL, Han JC, Du SY (2010) Transient fracture of a layered magnetoelectroelastic medium. Mech Mater 42:354–364

    Google Scholar 

  194. Wünsche M, Sáez A, García-Sánchez F, Zhang C (2012) Transient dynamic crack analysis in linear magnetoelectroelastic solids by a hypersingular time-domain BEM. Eur J Mech A Solids 32:118–130

    MathSciNet  MATH  Google Scholar 

  195. Wang BL, Niraula OP (2007) Transient thermal fracture analysis of transversely isotropic magneto-electro-elastic materials. J Therm Stress 30:297–317

    Google Scholar 

  196. Ootao Y, Tanigawa Y (2005) Transient analysis of multilayered magneto-electro-thermoelastic strip due to nonuniform heat supply. Compos Struct 68:471–480

    Google Scholar 

  197. Chen X (2009) Dynamic crack propagation in a magneto-electro-elastic solid subjected to mixed loads: transient mode-III problem. Int J Solids Struct 46:4025–4037

    MATH  Google Scholar 

  198. Lei J, Zhang C, Bui TQ (2015) Transient dynamic interface crack analysis in magnetoelectroelastic bi-materials by a time-domain BEM. Eur J Mech A Solids 49:146–157

    MathSciNet  MATH  Google Scholar 

  199. Yong HD, Zhou YH (2007) Transient response of a cracked magnetoelectroelastic strip under anti-plane impact. Int J Solids Struct 44:705–717

    MATH  Google Scholar 

  200. Zhong XC, Liu F, Li XF (2009) Transient response of a magnetoelectroelastic solid with two collinear dielectric cracks under impacts. Int J Solids Struct 46:2950–2958

    MATH  Google Scholar 

  201. Zhou ZG, Wang B, Sun YG (2004) Two collinear interface cracks in magneto-electro-elastic composites. Int J Eng Sci 42:1155–1167

    MATH  Google Scholar 

  202. Su RKL, Feng WJ, Liu J (2007) Transient response of interface cracks between dissimilar magneto-electro-elastic strips under out-of-plane mechanical and in-plane magneto-electrical impact loads. Compos Struct 78:119–128

    Google Scholar 

  203. Rojas-Díaz R, García-Sánchez F, Sáez A (2010) Analysis of cracked magnetoelectroelastic composites under time-harmonic loading. Int J Solids Struct 47:71–80

    MATH  Google Scholar 

  204. Bouderba B, Houari MSA, Tounsi A, Mahmoud SR (2016) Thermal stability of functionally graded sandwich plates using a simple shear deformation theory. Struct Eng Mech 58:397–422

    Google Scholar 

  205. Bouderba B, Houari MSA, Tounsi A (2013) Thermomechanical bending response of FGM thick plates resting on Winkler–Pasternak elastic foundations. Steel Compos Struct 14:85–104

    Google Scholar 

  206. Wang X, Zhong Z (2003) A circular tube or bar of cylindrically anisotropic magnetoelectroelastic material under pressuring loading. Int J Eng Sci 41:2143–2159

    Google Scholar 

  207. Vinyas M, Kattimani SC (2017) A Finite element based assessment of static behavior of multiphase magneto-electro-elastic beams under different thermal loading. Struct Eng Mech 62:519–535

    Google Scholar 

  208. Vinyas M, Kattimani SC, Joladarashi S (2018) Hygrothermal coupling analysis of magneto-electroelastic beams using finite element methods. J Therm Stress 41:1063–1079

    Google Scholar 

  209. Milazzo A (2014) Large deflection of magneto-electro-elastic laminated plates. Appl Math Model 38:1737–1752

    MathSciNet  MATH  Google Scholar 

  210. Alaimo A, Benedetti I, Milazzo A (2014) A finite element formulation for large deflection of multilayered magneto-electro-elastic plates. Compos Struct 107:643–653

    Google Scholar 

  211. Xue CX, Pan E, Zhang SY, Chu HJ (2011) Large deflection of a rectangular magnetoelectroelastic thin plate. Mech Res Commun 38:518–523

    MATH  Google Scholar 

  212. Liu M (2011) An exact deformation analysis for the magneto-electro-elastic fiber-reinforced thin plate. Appl Math Model 35:2443–2461

    MathSciNet  MATH  Google Scholar 

  213. Kuo H, Pan E (2011) Effective magnetoelectric effect in multicoated circular fibrous multiferroic composites. J Appl Phys 109:1–6

    Google Scholar 

  214. Mousavi SM, Paavola J (2013) Analysis of functionally graded magneto-electro-elastic layer with multiple cracks. Theor Appl Fract Mech 66:1–8

    Google Scholar 

  215. Bishay PL, Sladek J, Sladek V, Atluri SN (2012) Analysis of functionally graded magneto-electro-elastic composites using hybrid/mixed finite elements and node-wise material properties. Comput Mater Contin 29:213–261

    Google Scholar 

  216. Ma C, Lee J (2009) Theoretical analysis of in-plane problem in functionally graded nonhomogeneous magnetoelectroelastic bimaterials. Int J Solids Struct 46:4208–4220

    MATH  Google Scholar 

  217. Carrera E, Fagiano C, Nali P, Brischetto S (2009) Refined multilayered plate elements for coupled magneto-electro-elastic analysis. Multidiscip Model Mat Struct 5:119–138

    Google Scholar 

  218. Badri TM, Al-Kayiem HH (2013) Analytical Solution for simply supported and multilayered magneto-thermo-electro-elastic plates. Asian J Sci Res 6:236–244

    Google Scholar 

  219. Zhou ZH, Xu XS, Leung AYT (2013) Hamiltonian analysis of a magnetoelectroelastic notch in a mode III singularity. Smart Mater Struct 22:1–12

    Google Scholar 

  220. Akbarzadeh AH, Chen ZT (2012) Magnetoelectroelastic behavior of rotating cylinders resting on an elastic foundation under hygrothermal loading. Smart Mater Struct 21:1–17

    Google Scholar 

  221. Vinyas M, Kattimani SC (2017) Hygrothermal analysis of magneto-electro-elastic plate using 3D finite element analysis. Compos Struct 180:617–637. https://doi.org/10.1016/j.compstruct.2017.08.015

    Article  Google Scholar 

  222. Vinyas M, Kattimani S, Harursampath D, Trung N (2019) Coupled evaluation of the free vibration characteristics of magneto-electro-elastic skew plates in hygrothermal environment. Smart Struct Syst 24:267–292

    Google Scholar 

  223. Vinyas M, Nischith G, Loja MAR, Ebrahimi F, Duc ND (2019) Numerical analysis of the vibration response of skew magneto-electro-elastic plates based on the higher-order shear deformation theory. Compos Struct 214:132–142

    Google Scholar 

  224. Vinyas M, Kattimani S (2017) Investigation of the effect of BaTiO3/CoFe2O4 particle arrangement on the static response of magneto-electro-thermo-elastic plates. Compos Struct 85:51–64. https://doi.org/10.1016/j.compstruct.2017.10.073

    Article  Google Scholar 

  225. Sladek J, Sladek V, Krahulec S, Pan E (2013) The MLPG analyses of large deflections of magnetoelectroelastic plates. Eng Anal Bound Elem 37:673–682

    MathSciNet  MATH  Google Scholar 

  226. Lage RG, Soares CMM (2004) Layerwise partial mixed finite element analysis of magneto-electro-elastic plates. Comput Struct 82:1293–1301

    Google Scholar 

  227. Zenkour AM, Abbas IA (2014) Magneto-thermoelastic response of an infinite functionally graded cylinder using the finite element method. J Vib Control 20:1907–1919

    MathSciNet  MATH  Google Scholar 

  228. Niraula OP, Wang BL (2006) A magneto-electro-elastic material with a penny-shaped crack subjected to temperature loading. Acta Mech 187:151–168

    MATH  Google Scholar 

  229. Guinovart-díaz R, Rodríguez-ramos R, Bravo-castillero J, Federico J, Galindo GM, Wang Y (2013) Plane magneto-electro-elastic moduli of fiber composites with interphase plane magneto-electro-elastic moduli of fiber composites with interphase. Mech Adv Mater Struct 20:552–563

    Google Scholar 

  230. Ma C, Lee J (2009) Theoretical analysis of generalized loadings and image forces in a planar magnetoelectroelastic layered half-plane. J Mech Phys Solids 57:598–620

    MATH  Google Scholar 

  231. Bhangale RK, Ganesan N (2006) Static analysis of simply supported functionally graded and layered magneto-electro-elastic plates. Int J Solids Struct 43:3230–3253

    MATH  Google Scholar 

  232. Vinyas M, Kattimani SC (2017) Static studies of stepped functionally graded magneto-electro-elastic beam subjected to different thermal loads. Compos Struct 163:216–237

    Google Scholar 

  233. Vinyas M, Kattimani SC (2017) Static analysis of stepped functionally graded magneto-electro-elastic plates in thermal environment: a finite element study. Compos Struct 178:63–86

    Google Scholar 

  234. Vinyas M, Kattimani SC (2017) Static behavior of thermally loaded multilayered magneto-electro-elastic beam. Struct Eng Mech 63:481–495

    Google Scholar 

  235. Guo J, Chen J, Pan E (2016) Static deformation of anisotropic layered magnetoelectroelastic plates based on modified couple-stress theory. Compos Part B 107:84–96

    Google Scholar 

  236. Huang DJ, Ding HJ, Chen WQ (2010) Static analysis of anisotropic functionally graded magneto-electro-elastic beams subjected to arbitrary loading. Eur J Mech A Solids 29:356–369

    Google Scholar 

  237. Chen JY, Pan E, Heyliger PR (2015) Static deformation of a spherically anisotropic and multilayered magneto-electro-elastic hollow sphere. Int J Solids Struct 60–61:66–74. https://doi.org/10.1016/j.ijsolstr.2015.02.004

    Article  Google Scholar 

  238. Kumaravel A, Ganesan N, Sethuraman R (2007) Steady-state analysis of a three-layered electro-magneto-elastic strip in a thermal environment. Smart Mater Struct 16:282–295

    Google Scholar 

  239. Daga A, Ganesan N, Shankar K (2009) Studies on magnetoelectric effect for magneto-electro-elastic cylinder using finite element method. Multidiscip Model Mater Struct 5:307–310

    Google Scholar 

  240. Aboudi J (2017) The electric, magnetic, and elastic fields in damaged composites created by heat flow. J Intell Mater Syst Struct 29:1670–1684

    Google Scholar 

  241. Wu C, Chen S, Chiu K (2010) Three-dimensional static behavior of functionally graded magneto-electro-elastic plates using the modified Pagano method. Mech Res Commun 37:54–60

    MATH  Google Scholar 

  242. Li X, Li L, Hu Y (2018) Instability of functionally graded micro-beams via micro-structure-dependent beam theory. Appl Math Mech Engl Ed 39:923–952

    MathSciNet  MATH  Google Scholar 

  243. Akgöz B, Civalek Ö (2011) Application of strain gradient elasticity theory for buckling analysis of protein microtubules. Curr Appl Phys 11:1133–1138

    MATH  Google Scholar 

  244. Akgöz B, Civalek Ö (2011) Strain gradient elasticity and modified couple stress models for buckling analysis of axially loaded micro-scaled beams. Int J Eng Sci 49:1268–1280

    MathSciNet  MATH  Google Scholar 

  245. Jamalpoor A, Ahmadi-Savadkoohi A, Hosseini-Hashemi S (2016) Free vibration and biaxial buckling analysis of magneto-electro-elastic microplate resting on visco-Pasternak substrate via modified strain gradient theory. Smart Mater Struct 25:1–18

    Google Scholar 

  246. Li YS (2014) Buckling analysis of magnetoelectroelastic plate resting on Pasternak elastic foundation. Mech Res Commun 56:104–114

    Google Scholar 

  247. Kiran MC, Kattimani S (2018) Buckling analysis of skew magneto-electro-elastic plates under in-plane loading. J Intell Mater Syst Struct 29:2206–2222

    Google Scholar 

  248. Zhou YH, Gao Y, Zheng XJ (2003) Buckling and post-buckling analysis for magneto-elastic-plastic ferromagnetic beam-plates with unmovable simple supports. Int J Solids Struct 40:2875–2887

    MATH  Google Scholar 

  249. Mahmoud SR, Abd-Alla AM, Tounsi A, Marin M (2015) The problem of wave propagation in magneto-rotating orthotropic non-homogeneous medium. JVC J Vib Control 21:3281–3291

    MathSciNet  MATH  Google Scholar 

  250. Boukhari A, Atmane HA, Tounsi A, Adda Bedia EA, Mahmoud SR (2016) An efficient shear deformation theory for wave propagation of functionally graded material plates. Struct Eng Mech 57:837–859

    Google Scholar 

  251. Wang BL, Mai YW, Niraula OP (2007) A horizontal shear surface wave in magnetoelectroelastic materials. Philos Mag Lett 87:53–58

    Google Scholar 

  252. Calas H, Otero JA, Rodríguez-Ramos R, Monsivais G, Stern C (2008) Dispersion relations for SH wave in magneto-electro-elastic heterostructures. Int J Solids Struct 45:5356–5367

    MATH  Google Scholar 

  253. Nie G, Liu J, Fang X, An Z (2012) Shear horizontal (SH) waves propagating in piezoelectric–piezomagnetic bilayer system with an imperfect interface. Acta Mech 223:1999–2009

    MathSciNet  MATH  Google Scholar 

  254. Parkus H, Sedov LI (1966) Irreversible aspects of continuum mechanics and transfer of physical characteristics in moving fluids. Springer, Berlin

    MATH  Google Scholar 

  255. Chen J, Pan E, Chen H (2007) Wave propagation in magneto-electro-elastic multilayered plates. Int J Solids Struct 44:1073–1085

    MATH  Google Scholar 

  256. Zhou YY, Lü CF, Chen WQ (2012) Bulk wave propagation in layered piezomagnetic/piezoelectric plates with initial stresses or interface imperfections. Compos Struct 94:2736–2745

    Google Scholar 

  257. Hashemi MS, Kilic B, Akgül A (2016) On solitons and invariant solutions of the magneto-electro-elastic circular rod. Waves Random Complex Media 26:259–271

    MathSciNet  MATH  Google Scholar 

  258. Wu XH, Shen YP, Sun Q (2007) Lamb wave propagation in magnetoelectroelastic plates. Appl Acoust 68:1224–1240

    Google Scholar 

  259. Du J, Jin X, Wang J (2007) Love wave propagation in layered magneto-electro-elastic structures with initial stress. Acta Mech 192:169–189

    MATH  Google Scholar 

  260. Wei J, Su X (2008) Transient-state response of wave propagation in magneto-electro-elastic square column. Acta Mech Solida Sin 21:491–499

    Google Scholar 

  261. Xue CX, Pan E (2013) On the longitudinal wave along a functionally graded magneto-electro- elastic rod. Int J Eng Sci 62:48–55

    Google Scholar 

  262. Feng WJ, Pan E, Wang X, Jin J (2009) Rayleigh waves in magneto-electro-elastic half planes. Acta Mech 202:127–134

    MATH  Google Scholar 

  263. Xue CX, Pan E, Zhang SY (2011) Solitary waves in a magneto-electro-elastic circular rod. Smart Mater Struct 20:105010

    Google Scholar 

  264. Abd-Alla AM, Othman MIA, Abo-Dahab SM (2016) Reflection of plane waves from electro-magneto-thermoelastic half-space with a dual-phase-lag model. Comput Mater Contin 51:63–79

    Google Scholar 

  265. Du JK, Shen YP, Ye DY, Yue FR (2004) Scattering of anti-plane shear waves by a partially debonded magneto-electro-elastic circular cylindrical inhomogeneity. Int J Eng Sci 42:887–913

    Google Scholar 

  266. Feng WJ, Jin J, Pan E (2008) Stoneley (interfacial) waves between two magneto-electro-elastic half planes. Philos Mag 88:1801–1810

    Google Scholar 

  267. Xiao D, Han Q, Liu Y, Li C (2016) Guided wave propagation in an infinite functionally graded magneto-electro-elastic plate by the Chebyshev spectral element method. Compos Struct 153:704–711

    Google Scholar 

  268. Piliposyan D (2012) Shear surface waves at the interface of two magneto-electro-elastic media. Multidiscip Model Mater Struct 8:417–426

    Google Scholar 

  269. Li L, Wei P (2015) The direction dependence of surface wave speed at the surface of magneto-electro-elastic half-space. Acta Mech Solida Sin 28:102–110

    Google Scholar 

  270. Li L, Wei PJ (2014) The piezoelectric and piezomagnetic effect on the surface wave velocity of magneto-electro-elastic solids. J Sound Vib 333:2312–2326

    Google Scholar 

  271. Jiangong Y, Qiujuan M (2010) Wave characteristics in magneto-electro-elastic functionally graded spherical curved plates. Mech Adv Mater Struct 17:287–301

    Google Scholar 

  272. Arefi M, Zenkour AM (2017) Wave propagation analysis of a functionally graded magneto-electro-elastic nanobeam rest on visco-Pasternak foundation. Mech Res Commun 79:51–62

    Google Scholar 

  273. Wei JP, Su XY (2008) Wave propagation in a magneto-electroelastic plate. Sci China Ser G Phys Mech Astron 51:651–666

    Google Scholar 

  274. Chen J, Guo J, Pan E (2017) Wave propagation in magneto-electro-elastic multilayered plates with nonlocal effect. J Sound Vib 400:550–563

    Google Scholar 

  275. Narendar S (2016) Wave dispersion in functionally graded magneto-electro-elastic nonlocal rod. Aerosp Sci Technol 51:42–51

    Google Scholar 

  276. Danoyan Z, Ghazaryan K, Piliposian G (2009) Surface gap wave propagation in layered electro-magneto-elastic structures. Waves Random Complex Media 19:521–534

    MathSciNet  MATH  Google Scholar 

  277. Piliposyan DG, Ghazaryan KB, Piliposian GT (2014) Internal resonances in a periodic magneto-electro-elastic structure. J Appl Phys 116:044107

    Google Scholar 

  278. Eltaher MA, Alshorbagy AE, Mahmoud FF (2013) Determination of neutral axis position and its effect on natural frequencies of functionally graded macro/nanobeams. Compos Struct 99:193–201

    Google Scholar 

  279. Eltaher MA, Abdelrahman AA, Al-Nabawy A, Khater M, Mansour A (2014) Vibration of nonlinear graduation of nano-Timoshenko beam considering the neutral axis position. Appl Math Comput 235:512–529

    MathSciNet  MATH  Google Scholar 

  280. Civalek Ö (2017) Free vibration of carbon nanotubes reinforced (CNTR) and functionally graded shells and plates based on FSDT via discrete singular convolution method, vol 111. Elsevier, Amsterdam

    Google Scholar 

  281. Ansari R, Gholami R, Darabi MA (2012) A nonlinear Timoshenko beam formulation based on strain gradient theory. J Mech Mater Struct 7:195–211

    Google Scholar 

  282. Akgöz B, Civalek Ö (2014) Longitudinal vibration analysis for microbars based on strain gradient elasticity theory. JVC J Vib Control 20:606–616

    MathSciNet  Google Scholar 

  283. Chatrou LW, Escribano MP, Viruel MA, Maas JW, James E, Hormaza JI (2018) accepted manuscript. Mech Adv Mater Struct 25:611–621

    Google Scholar 

  284. Akgöz B, Civalek Ö (2013) Free vibration analysis of axially functionally graded tapered Bernoulli–Euler microbeams based on the modified couple stress theory. Compos Struct 98:314–322

    Google Scholar 

  285. El Meiche N, Tounsi A, Ziane N, Mechab I, El EA (2011) A new hyperbolic shear deformation theory for buckling and vibration of functionally graded sandwich plate. Int J Mech Sci 53:237–247

    Google Scholar 

  286. Ebrahimi F, Jafari A, Barati MR (2017) Free vibration analysis of smart porous plates subjected to various physical fields considering neutral surface position. Arab J Sci Eng 42:1865–1881

    MathSciNet  MATH  Google Scholar 

  287. Ebrahimi F, Daman M (2017) Analytical investigation of the surface effects on nonlocal vibration behavior of nanosize curved beams. Adv Nano Res 5:35–47

    Google Scholar 

  288. Ebrahimi F, Daman M (2017) Nonlocal thermo-electro-mechanical vibration analysis of smart curved FG piezoelectric Timoshenko nanobeam. Smart Struct Syst 20:351–368

    Google Scholar 

  289. Ebrahimi F, Barati MR (2018) Free vibration analysis of couple stress rotating nanobeams with surface effect under in-plane axial magnetic field. JVC J Vib Control 24:5097–5107

    MathSciNet  Google Scholar 

  290. Ebrahimi F, Barati MR (2017) Porosity-dependent vibration analysis of piezo-magnetically actuated heterogeneous nanobeams. Mech Syst Signal Process 93:445–459

    Google Scholar 

  291. Demir Ç, Civalek Ö (2017) A new nonlocal FEM via Hermitian cubic shape functions for thermal vibration of nano beams surrounded by an elastic matrix. Compos Struct 168:872–884

    Google Scholar 

  292. Ebrahimi F, Barati MR (2018) Vibration analysis of embedded biaxially loaded magneto-electrically actuated inhomogeneous nanoscale plates. JVC J Vib Control 24:3587–3607

    MathSciNet  Google Scholar 

  293. Li YS, Ma P, Wang W (2015) Bending, buckling, and free vibration of magnetoelectroelastic nanobeam based on nonlocal theory. J Intell Mater Syst Struct 27:1139–1149

    Google Scholar 

  294. Jandaghian AA, Rahmani O (2016) Free vibration analysis of magneto-electro- thermo-elastic nanobeams resting on a Pasternak foundation. Smart Mater Struct 25:1–16

    Google Scholar 

  295. Kiani A, Sheikhkhoshkar M (2017) Free vibration problem of embedded nanoplate made of functionally graded materials via nonlocal third-order shear deformation theory. Intell Mater Syst Struct 29:741–763

    Google Scholar 

  296. Ansari R, Hasrati E, Gholami R, Sadeghi F (2015) Nonlinear analysis of forced vibration of nonlocal third-order shear deformable beam model of magneto-electro-thermo elastic nanobeams. Compos Part B 83:226–241

    Google Scholar 

  297. Ke L, Wang Y (2014) Free vibration of size-dependent magneto-electro-elastic nanobeams based on the nonlocal theory. Phys E Low-Dimens Syst Nanostruct 63:52–61

    Google Scholar 

  298. Mohammadimehr M, Okhravi SV, Alavi SMA (2016) Free vibration analysis of magneto-electro-elastic cylindrical composite panel reinforced by various distributions of CNTs with considering open and closed circuits boundary conditions based on FSDT. J Vib Control 24:1551–1569

    MathSciNet  Google Scholar 

  299. Vinyas M (2019) A higher-order free vibration analysis of carbon nanotube-reinforced magneto-electro-elastic plates using finite element methods 158:286–301

    Google Scholar 

  300. Farajpour MR, Shahidi AR, Hadi A, Farajpour A (2019) Influence of initial edge displacement on the nonlinear vibration, electrical and magnetic instabilities of magneto-electro-elastic nanofilms. Mech Adv Mater Struct 26:1469–1481

    Google Scholar 

  301. Ansari R, Gholami R (2016) Nonlocal free vibration in the pre- and post- buckled states of magneto-electro-thermo elastic rectangular nanoplates with various edge conditions. Smart Mater Struct 25:1–17

    Google Scholar 

  302. Ke L, Wang Y, Yang J, Kitipornchai S (2014) Free vibration of size-dependent magneto-electro-elastic nanoplates based on the nonlocal theory. Acta Mech Sin 30:516–525

    MathSciNet  MATH  Google Scholar 

  303. Farajpour A, Yazdi MRH, Rastgoo A, Loghmani M, Mohammadi M (2015) Nonlocal nonlinear plate model for large amplitude vibration of magneto-electro-elastic nanoplates. Compos Struct 140:323–336

    Google Scholar 

  304. Ebrahimi F, Barati MR (2016) A nonlocal higher-order refined magneto-electro-viscoelastic beam model for dynamic analysis of smart nanostructures. Int J Eng Sci 107:183–196

    Google Scholar 

  305. Ansari R, Gholami R (2016) Size-dependent nonlinear vibrations of first-order shear deformable magneto-electro-thermo elastic nanoplates based on the nonlocal. Int J Appl Mech 8:1650053

    Google Scholar 

  306. Zamani M, Hadi A (2016) Non-local analysis of free vibration of bi-directional functionally graded Euler–Bernoulli nano-beams. Int J Eng Sci 105:1–11

    MathSciNet  MATH  Google Scholar 

  307. Karimi M, Reza A (2017) Nonlocal, refined plate, and surface effects theories used to analyze free vibration of magnetoelectroelastic nanoplates under thermo-mechanical and shear loadings. Appl Phys A 123:1–17

    Google Scholar 

  308. Amiri A, Fakhari SM, Pournaki IJ, Rezazadeh G, Shabani R (2015) Vibration analysis of circular magneto-electro-elastic nano-plates based on eringen’s nonlocal theory. Int J Eng Trans C: Asp 28:1808–1817

    Google Scholar 

  309. Ghadiri M, Safarpour H (2016) Free vibration analysis of embedded magneto-electro-thermo- elastic cylindrical nanoshell based on the modified couple stress theory. Appl Phys A 122:833

    Google Scholar 

  310. Ke L, Wang Y, Yang J, Kitipornchai S (2014) The size-dependent vibration of embedded magneto-electro-elastic cylindrical nanoshells. Smart Mater Struct 23:125036

    Google Scholar 

  311. Ebrahimi F, Barati MR (2016) A unified formulation for dynamic analysis of nonlocal heterogeneous nanobeams in hygro-thermal environment. Appl Phys A Mater Sci Process 122:1–14

    Google Scholar 

  312. Numanoğlu HM, Akgöz B, Civalek Ö (2018) On dynamic analysis of nanorods. Int J Eng Sci 130:33–50

    Google Scholar 

  313. Ebrahimi F, Barati MR (2017) Electro-magnetic effects on nonlocal dynamic behavior of embedded piezoelectric nanoscale beams. J Intell Mater Syst Struct 28:2007–2022

    Google Scholar 

  314. Ebrahimi F, Barati MR (2017) Size-dependent dynamic modeling of inhomogeneous curved nanobeams embedded in elastic medium based on nonlocal strain gradient theory. Proc Inst Mech Eng Part C J Mech Eng Sci 231:4457–4469

    Google Scholar 

  315. Gholami R, Ansari R, Darvizeh A, Sahmani S (2014) Axial buckling and dynamic stability of functionally graded microshells based on the modified couple stress theory. Int J Struct Stab Dyn 15:1450070

    MathSciNet  MATH  Google Scholar 

  316. Ansari R, Gholami R (2017) Dynamic stability analysis of multi-walled carbon nanotubes with arbitrary boundary conditions based on the nonlocal elasticity theory. Mech Adv Mater Struct 24:1180–1188

    Google Scholar 

  317. Ansari R, Gholami R, Sahmani S (2012) On the dynamic stability of embedded single-walled carbon nanotubes including thermal environment effects. Sci Iran 19:919–925

    Google Scholar 

  318. Karami B, Shahsavari D, Karami M, Li L (2019) Hygrothermal wave characteristic of nanobeam-type inhomogeneous materials with porosity under magnetic field. Proc Inst Mech Eng Part C J Mech Eng Sci 233:2149–2169

    Google Scholar 

  319. Ding Z, Li L, Hu Y (2018) A modified precise integration method for transient dynamic analysis in structural systems with multiple damping models. Mech Syst Signal Process 98:613–633

    Google Scholar 

  320. Zenkour AM, Arefi M (2017) Nonlocal transient electrothermomechanical vibration and bending analysis of a functionally graded piezoelectric single-layered nanosheet rest on visco-Pasternak foundation. J Therm Stress 40:167–184

    Google Scholar 

  321. Akgöz B, Civalek Ö (2012) Comment on “static and dynamic analysis of micro beams based on strain gradient elasticity theory” by S. Kong, S. Zhou, Z. Nie, and K. Wang (Int J Eng Sci 47:487–498, 2009). Int J Eng Sci 50(1):279–281

  322. Akgoz B, Civalek O (2016) Static and dynamic response of sector-shaped graphene sheets. Mech Adv Mater Struct 23:432–442

    Google Scholar 

  323. Civalek Ö (2013) Nonlinear dynamic response of laminated plates resting on nonlinear elastic foundations by the discrete singular convolution-differential quadrature coupled approaches. Compos Part B Eng 50:171–179

    Google Scholar 

  324. Civalek Ö (2014) Geometrically nonlinear dynamic and static analysis of shallow spherical shell resting on two-parameters elastic foundations. Int J PressVessel Pip 113:1–9

    Google Scholar 

  325. Civalek Ö (2005) Geometrically nonlinear dynamic analysis of doubly curved isotropic shells resting on elastic foundation by a combination of harmonic differential quadrature-finite difference methods. Int J Press Vessel Pip 82:470–479

    Google Scholar 

  326. Civalek Ö (2006) Harmonic differential quadrature-finite differences coupled approaches for geometrically nonlinear static and dynamic analysis of rectangular plates on elastic foundation. J Sound Vib 294:966–980

    Google Scholar 

  327. Ebrahimi F, Barati MR (2018) Influence of neutral surface position on dynamic characteristics of in-homogeneous piezo-magnetically actuated nanoscale plates. Proc Inst Mech Eng Part C J Mech Eng Sci 232:3125–3143

    Google Scholar 

  328. Ebrahimi F, Daman M (2017) Dynamic modeling of embedded curved nanobeams incorporating surface effects. Coupled Syst Mech 5:255–267

    Google Scholar 

  329. Ebrahimi F, Barati MR (2017) Damping vibration analysis of smart piezoelectric polymeric nanoplates on viscoelastic substrate based on nonlocal strain gradient theory. Smart Mater Struct 26:065018

    Google Scholar 

  330. Zenkour AM, Arefi M, Alshehri NA (2017) Size-dependent analysis of a sandwich curved nanobeam integrated with piezomagnetic face-sheets. Results Phys 7:2172–2182

    Google Scholar 

  331. Arefi M, Zenkour AM (2017) Transient sinusoidal shear deformation formulation of a size-dependent three-layer piezo-magnetic curved nanobeam. Acta Mech 228:3657–3674

    MathSciNet  MATH  Google Scholar 

  332. Ebrahimi F, Barati MR (2016) Dynamic modeling of a thermo-piezo-electrically actuated nanosize beam subjected to a magnetic field. Appl Phys A Mater Sci Process 122:1–18

    Google Scholar 

  333. Arefi M, Zenkour AM (2017) Size-dependent free vibration and dynamic analyses of piezo-electro-magnetic sandwich nanoplates resting on viscoelastic foundation. Phys B Condens Matter 521:188–197

    Google Scholar 

  334. Gholami R, Ansari R (2018) Nonlinear bending of third-order shear deformable carbon nanotube/fiber/polymer multiscale laminated composite rectangular plates with different edge supports. Eur Phys J Plus 133:282

    Google Scholar 

  335. Eltaher MA, Omar FA, Abdalla WS, Gad EH (2019) Bending and vibrational behaviors of piezoelectric nonlocal nanobeam including surface elasticity. Waves Random Complex Media 29:264–280

    MathSciNet  Google Scholar 

  336. Eltaher MA, Hamed MA, Sadoun AM, Mansour A (2014) Mechanical analysis of higher order gradient nanobeams. Appl Math Comput 229:260–272

    MathSciNet  MATH  Google Scholar 

  337. Alshorbagy AE, Eltaher MA, Mahmoud FF (2013) Static analysis of nanobeams using nonlocal FEM. J Mech Sci Technol 27:2035–2041

    Google Scholar 

  338. Eltaher MA, Emam SA, Mahmoud FF (2013) Static and stability analysis of nonlocal functionally graded nanobeams. Compos Struct 96:82–88

    Google Scholar 

  339. Ebrahimi F, Barati MR (2016) Size-dependent thermal stability analysis of graded piezomagnetic nanoplates on elastic medium subjected to various thermal environments. Appl Phys A Mater Sci Process 122:1–17

    Google Scholar 

  340. Mahmoud FF, Eltaher MA, Alshorbagy AE, Meletis EI (2012) Static analysis of nanobeams including surface effects by nonlocal finite element. J Mech Sci Technol 26:3555–3563

    Google Scholar 

  341. Tang H, Li L, Hu Y (2019) Coupling effect of thickness and shear deformation on size-dependent bending of micro/nano-scale porous beams. Appl Math Model 66:527–547

    MathSciNet  MATH  Google Scholar 

  342. Arefi M, Zenkour AM (2016) A simplified shear and normal deformations nonlocal theory for bending of functionally graded piezomagnetic sandwich nanobeams in magneto-thermo-electric environment. J Sandw Struct Mater 18:624–651

    Google Scholar 

  343. Zenkour AM, Abouelregal AE (2014) Effect of harmonically varying heat on FG nanobeams in the context of a nonlocal two-temperature thermoelasticity theory. Eur J Comput Mech 23:1–14

    MATH  Google Scholar 

  344. Arefi M, Soltan Arani AH (2018) Higher order shear deformation bending results of a magnetoelectrothermoelastic functionally graded nanobeam in thermal, mechanical, electrical, and magnetic environments. Mech Based Des Struct Mach 46:669–692

    Google Scholar 

  345. Wang W, Li P, Jin F (2016) Two-dimensional linear elasticity theory of magneto-electro-elastic plates considering surface and nonlocal effects for nanoscale device applications. Smart Mater Struct 25:1–15

    Google Scholar 

  346. Lezgy-Nazargah M, Cheraghi N (2017) An exact Peano series solution for bending analysis of imperfect layered functionally graded neutral magneto-electro-elastic plates resting on elastic foundations. Mech Adv Mater Struct 24:183–199

    Google Scholar 

  347. Arefi M, Zenkour AM (2019) Effect of thermo-magneto-electro-mechanical fields on the bending behaviors of a three-layered nanoplate based on sinusoidal shear-deformation plate theory. J Sandw Struct Mater 21:639–669

    Google Scholar 

  348. Shahsavari D, Karami B, Fahham HR, Li L (2018) On the shear buckling of porous nanoplates using a new size-dependent quasi-3D shear deformation theory. Acta Mech 229:4549–4573

    MathSciNet  Google Scholar 

  349. Mercan K, Civalek Ö (2017) Buckling analysis of silicon carbide nanotubes (SiCNTs) with surface effect and nonlocal elasticity using the method of HDQ. Compos Part B Eng 114:34–45

    Google Scholar 

  350. Ebrahimi F, Karimiasl M (2018) Nonlocal and surface effects on the buckling behavior of flexoelectric sandwich nanobeams. Mech Adv Mater Struct 25:943–952

    Google Scholar 

  351. Ebrahimi F, Barati MR (2016) Temperature distribution effects on buckling behavior of smart heterogeneous nanosize plates based on nonlocal four-variable refined plate theory. Int J Smart Nano Mater 7:119–143

    Google Scholar 

  352. Ebrahimi F, Barati MR (2017) Modeling of smart magnetically affected flexoelectric/piezoelectric nanostructures incorporating surface effects. Nanomater Nanotechnol 7:1–11

    Google Scholar 

  353. Ebrahimi F, Barati MR (2017) Buckling analysis of nonlocal third-order shear deformable functionally graded piezoelectric nanobeams embedded in elastic medium. J Braz Soc Mech Sci Eng 39:937–952

    Google Scholar 

  354. Ebrahimi F, Barati MR (2016) Nonlocal thermal buckling analysis of embedded magneto-electro-thermo-elastic nonhomogeneous nanoplates. Iran J Sci Technol Trans Mech Eng 40:243–264

    Google Scholar 

  355. Barati MR, Zenkour AM, Shahverdi H (2016) Thermo-mechanical buckling analysis of embedded nanosize FG plates in thermal environments via an inverse cotangential theory. Compos Struct 141:203–212

    Google Scholar 

  356. Akbarzadeh Khorshidi M, Shariati M, Emam SA (2016) Postbuckling of functionally graded nanobeams based on modified couple stress theory under general beam theory, vol 110. Elsevier, Amsterdam

    MATH  Google Scholar 

  357. Mercan K, Emsen E, Civalek Ö (2019) Effect of silicon dioxide substrate on buckling behavior of zinc oxide nanotubes via size-dependent continuum theories. Compos Struct 218:130–141

    Google Scholar 

  358. Mercan K, Civalek Ö (2017) Buckling analysis of silicon carbide nanotubes (SiCNTs). Int J Eng Appl Sci 8:101–108

    Google Scholar 

  359. Khater ME, Eltaher MA, Abdel-Rahman E, Yavuz M (2014) Surface and thermal load effects on the buckling of curved nanowires. Eng Sci Technol Int J 17:279–283

    Google Scholar 

  360. Karami B, Shahsavari D, Li L, Karami M, Janghorban M (2019) Thermal buckling of embedded sandwich piezoelectric nanoplates with functionally graded core by a nonlocal second-order shear deformation theory. Proc Inst Mech Eng Part C J Mech Eng Sci 233:287–301

    Google Scholar 

  361. Gholami R, Ansari R (2017) A unified nonlocal nonlinear higher-order shear deformable plate model for postbuckling analysis of piezoelectric–piezomagnetic rectangular nanoplates with various edge supports. Compos Struct 166:202–218

    Google Scholar 

  362. Eltaher MA, Khairy A, Sadoun AM, Omar FA (2014) Static and buckling analysis of functionally graded Timoshenko nanobeams. Appl Math Comput 229:283–295

    MathSciNet  MATH  Google Scholar 

  363. Eltaher MA, Kabeel AM, Almitani KH, Abdraboh AM (2018) Static bending and buckling of perforated nonlocal size-dependent nanobeams. Microsyst Technol 24:4881–4893

    Google Scholar 

  364. Ebrahimi F, Shaghaghi GR, Boreiry M (2015) A semi-analytical evaluation of surface and nonlocal effects on buckling and vibrational characteristics of nanotubes with various boundary conditions. Int J Struct Stab Dyn 16:1550023

    MathSciNet  MATH  Google Scholar 

  365. Ebrahimi F, Jafari A (2016) Buckling behavior of smart MEE-FG porous plate with various boundary conditions based on refined theory. Adv Mater Res 5:279–298

    Google Scholar 

  366. Ebrahimi F, Barati MR (2016) Static stability analysis of smart magneto-electro-elastic heterogeneous nanoplates embedded in an elastic medium based on a four-variable refined plate theory. Smart Mater Struct 25:1–21

    Google Scholar 

  367. Ebrahimi F, Barati MR (2016) An exact solution for buckling analysis of embedded piezo-electro-magnetically actuated nanoscale beams. Adv Nano Res 4:65–84

    Google Scholar 

  368. Alibeigi B, Tadi Beni Y, Mehralian F (2018) On the thermal buckling of magneto-electro-elastic piezoelectric nanobeams. Eur Phys J Plus 133:1–18

    Google Scholar 

  369. Ebrahimi F, Reza Barati M (2016) Magnetic field effects on buckling behavior of smart size-dependent graded nanoscale beams. Eur Phys J Plus. 131:282

    Google Scholar 

  370. Ebrahimi F, Barati MR (2017) Buckling analysis of piezoelectrically actuated smart nanoscale plates subjected to magnetic field. J Intell Mater Syst Struct 28:1472–1490

    Google Scholar 

  371. Li YS, Cai ZY, Shi SY (2014) Buckling and free vibration of magnetoelectroelastic nanoplate based on nonlocal theory. Compos Struct 111:522–529

    Google Scholar 

  372. Gholami R, Ansari R, Gholami Y (2017) Size-dependent bending, buckling and vibration of higher-order shear deformable magneto- electro-thermo-elastic rectangular nanoplates. Mater Res Express 4–065702:1–45

    Google Scholar 

  373. Park WT, Han SC (2018) Buckling analysis of nano-scale magneto-electro-elastic plates using the nonlocal elasticity theory. Adv Mech Eng 10:1–16

    Google Scholar 

  374. Ebrahimi F, Barati MR (2017) Buckling analysis of smart size-dependent higher order magneto-electro-thermo-elastic functionally graded nanosize beams. J Mech 33:23–33

    Google Scholar 

  375. Ebrahimi F, Barati MR (2016) Magneto-electro-elastic buckling analysis of nonlocal curved nanobeams. Eur Phys J Plus 131:1–13

    Google Scholar 

  376. Jamalpoor A, Ahmadi-Savadkoohi A, Hosseini M, Hosseini-Hashemi S (2017) Free vibration and biaxial buckling analysis of double magneto-electro-elastic nanoplate-systems coupled by a visco-Pasternak medium via nonlocal elasticity theory. Eur J Mech A Solids 63:84–98

    MathSciNet  MATH  Google Scholar 

  377. Ansari R, Gholami R (2017) Nonlocal nonlinear first-order shear deformable beam model for postbuckling analysis of magneto-electro-thermo elastic nanobeams. Sci Iran 23:3099–3114

    Google Scholar 

  378. Sahmani S, Aghdam MM (2018) Nonlocal strain gradient shell model for axial buckling and postbuckling analysis of magneto-electro-elastic composite nanoshells. Compos Part B Eng 132:258–274

    Google Scholar 

  379. Ansari R, Gholami R (2016) Size-dependent buckling and postbuckling analyses of first-order shear deformable magneto-electro-thermo elastic nanoplates based on the nonlocal elasticity theory. Int J Struct Stab Dyn 17:1750014

    MathSciNet  Google Scholar 

  380. Arefi M (2016) Analysis of wave in a functionally graded magneto-electro-elastic nano-rod using nonlocal elasticity model subjected to electric and magnetic potentials. Acta Mech 227:2529–2542

    MathSciNet  MATH  Google Scholar 

  381. Ebrahimi F, Dabbagh A (2017) On flexural wave propagation responses of smart FG magneto-electro-elastic nanoplates via nonlocal strain gradient theory. Compos Struct 162:281–293

    Google Scholar 

  382. Ebrahimi F, Dabbagh A (2017) Nonlocal strain gradient based wave dispersion behavior of smart rotating magneto-electro-elastic nanoplates. Mater Res Express 4:1–19

    Google Scholar 

  383. Ebrahimi F, Dabbagh A (2017) Wave propagation analysis of embedded nanoplates based on a nonlocal strain gradient-based surface piezoelectricity theory. Eur Phys J Plus 132:1–14

    Google Scholar 

  384. Ebrahimi F, Barati MR (2018) Size-dependent thermally affected wave propagation analysis in nonlocal strain gradient functionally graded nanoplates via a quasi-3D plate theory. Proc Inst Mech Eng Part C J Mech Eng Sci 232:162–173

    Google Scholar 

  385. Arefi M, Zenkour AM (2017) Employing the coupled stress components and surface elasticity for nonlocal solution of wave propagation of a functionally graded piezoelectric love nanorod model. J Intell Mater Syst Struct 28:2403–2413

    Google Scholar 

  386. Amiri A, Talebitooti R, Li L (2018) Wave propagation in viscous-fluid-conveying piezoelectric nanotubes considering surface stress effects and Knudsen number based on nonlocal strain gradient theory. Eur Phys J Plus 133:1–17

    Google Scholar 

  387. Ebrahimi F, Dabbagh A (2019) Wave dispersion characteristics of heterogeneous nanoscale beams via a novel porosity-based homogenization scheme. Eur Phys J Plus 134:1–8

    Google Scholar 

  388. Karami B, Shahsavari D, Janghorban M, Li L (2019) Wave dispersion of nanobeams incorporating stretching effect. Waves Random Complex Media 2:1–21

    Google Scholar 

  389. Ebrahimi F, Dabbagh A (2018) Wave dispersion characteristics of nonlocal strain gradient double-layered graphene sheets in hygro-thermal environments. Struct Eng Mech 65:645–656

    Google Scholar 

  390. Ebrahimi F, Barati MR, Dabbagh A (2016) A nonlocal strain gradient theory for wave propagation analysis in temperature-dependent inhomogeneous nanoplates. Int J Eng Sci 107:169–182

    Google Scholar 

  391. Ebrahimi F, Barati MR (2016) Wave propagation analysis of quasi-3D FG nanobeams in thermal environment based on nonlocal strain gradient theory. Appl Phys A Mater Sci Process 122:1–15

    Google Scholar 

  392. Ebrahimi F, Barati MR (2017) Flexural wave propagation analysis of embedded S-FGM nanobeams under longitudinal magnetic field based on nonlocal strain gradient theory. Arab J Sci Eng 42:1715–1726

    MathSciNet  MATH  Google Scholar 

  393. Barati MR (2017) On wave propagation in nanoporous materials. Int J Eng Sci 116:1–11

    MathSciNet  MATH  Google Scholar 

  394. Ebrahimi F, Barati MR, Dabbagh A (2018) Wave propagation in embedded inhomogeneous nanoscale plates incorporating thermal effects. Waves Random Complex Media 28:215–235

    MathSciNet  Google Scholar 

  395. Ebrahimi F, Barati MR, Haghi P (2018) Wave propagation analysis of size-dependent rotating inhomogeneous nanobeams based on nonlocal elasticity theory. JVC J Vib Control 24:3809–3818

    MathSciNet  Google Scholar 

  396. Ebrahimi F, Barati MR, Dabbagh A (2016) Wave dispersion characteristics of axially loaded magneto-electro-elastic nanobeams. Appl Phys A Mater Sci Process 122:1–12

    Google Scholar 

  397. Ebrahimi F, Dabbagh A (2018) Wave dispersion characteristics of rotating heterogeneous magneto-electro-elastic nanobeams based on nonlocal strain gradient elasticity theory. J Electromagn Waves Appl 32:138–169

    Google Scholar 

  398. Hu KQ, Kang YL, Qin QH (2007) A moving crack in a rectangular magnetoelectroelastic body. Eng Fract Mech 74:751–770

    Google Scholar 

  399. Hu K, Li G (2005) Constant moving crack in a magnetoelectroelastic material under anti-plane shear loading. Int J Solids Struct 42:2823–2835

    MATH  Google Scholar 

  400. Li YD, Lee KY (2008) Anti-plane crack intersecting the interface in a bonded smart structure with graded magnetoelectroelastic properties. Theor Appl Fract Mech 50:235–242

    Google Scholar 

  401. Hu K, Chen Z, Wang X (2018) Boundary effect on crack kinking in a magnetoelectroelastic strip with a central crack. Eng Fract Mech 201:336–352

    Google Scholar 

  402. Hu KQ, Kang YL, Li GQ (2006) Moving crack at the interface between two dissimilar magnetoelectroelastic materials. Acta Mech 182:1–16

    MATH  Google Scholar 

  403. Sih GC, Yu HY (2005) Volume fraction effect of magnetoelectroelastic composite on enhancement and impediment of crack growth. Compos Struct 68:1–11

    Google Scholar 

  404. Zhou ZH, Xu XS, Leung AYT (2011) Analytical mode III electromagnetic permeable cracks in magnetoelectroelastic materials. Comput Struct 89:631–645

    Google Scholar 

  405. Zhong XC, Li XF (2006) A finite length crack propagating along the interface of two dissimilar magnetoelectroelastic materials. Int J Eng Sci 44:1394–1407

    Google Scholar 

  406. Guo JH, Lu ZX (2010) Anti-plane analysis of multiple cracks originating from a circular hole in a magnetoelectroelastic solid. Int J Solids Struct 47:1847–1856

    MATH  Google Scholar 

  407. Fu J, Hu K, Chen Z, Chen L, Qian L (2013) A moving crack propagating in a functionally graded magnetoelectroelastic strip under different crack face conditions. Theor Appl Fract Mech 66:16–25

    Google Scholar 

  408. Wang BL, Mai YW (2007) Applicability of the crack-face electromagnetic boundary conditions for fracture of magnetoelectroelastic materials. Int J Solids Struct 44:387–398

    MATH  Google Scholar 

  409. Wang B, Han J (2006) Discussion on electromagnetic crack face boundary conditions for the fracture mechanics of magneto-electro-elastic materials. Acta Mech Sin Xuebao 22:233–242

    MATH  Google Scholar 

  410. Hu K, Chen Z (2012) Pre-curving analysis of an opening crack in a magnetoelectroelastic strip under in-plane impact loadings. J Appl Phys 112:124911

    Google Scholar 

  411. Hu K, Chen Z (2013) Pre-kinking of a moving crack in a magnetoelectroelastic material under in-plane loading, vol 50. Elsevier, Amsterdam

    Google Scholar 

  412. Sih GC, Chen EP (2003) Dilatational and distortional behavior of cracks in magnetoelectroelastic materials. Theor Appl Fract Mech 40:1–21

    Google Scholar 

  413. Wang BL, Han JC (2010) Effect of finite cracking on the magneto-electric coupling properties of magneto-electro-elastic composite laminates. J Intell Mater Syst Struct 21:1669–1679

    Google Scholar 

  414. Zhou ZG, Wu LZ, Wang B (2005) The dynamic behavior of two collinear interface cracks in magneto-electro-elastic materials. Eur J Mech A Solids 24:253–262

    MATH  Google Scholar 

  415. Wang B-L, Mai Y-W (2006) Closed-form solution for an antiplane interface crack between two dissimilar magnetoelectroelastic layers. J Appl Mech 73:281

    MATH  Google Scholar 

  416. Zhao M, Guo Z, Fan C, Zhang R, Pan E (2013) Three-dimensional vertical cracks in magnetoelectroelastic media via the extended displacement discontinuity boundary integral equation method. J Intell Mater Syst Struct 24:1969–1984

    Google Scholar 

  417. Sih GC, Jones R, Song ZF (2003) Piezomagnetic and piezoelectric poling effects on mode I and II crack initiation behavior of magnetoelectroelastic materials. Theor Appl Fract Mech 40:161–186

    Google Scholar 

  418. Li YD, Lee KY, Pan JW (2011) Collinear unequal crack series in magnetoelectroelastic materials: anti-plane case. ZAMM Z Angew Math Mech 91:743–752

    MathSciNet  MATH  Google Scholar 

  419. Li YD, Lee KY (2010) Collinear unequal crack series in magnetoelectroelastic materials: mode I case solved via new real fundamental solutions. Eng Fract Mech 77:2772–2790

    Google Scholar 

  420. Wang BL, Mai YW (2003) Crack tip field in piezoelectric/piezomagnetic media. Eur J Mech A Solids 22:591–602

    MATH  Google Scholar 

  421. Zhou ZH, Xu XS, Leung AYT (2010) Mode III edge-crack in magneto-electro-elastic media by symplectic expansion. Eng Fract Mech 77:3157–3173

    Google Scholar 

  422. Li YD, Lee KY (2009) Dynamic responses of a crack in a layered graded magnetoelectroelastic sensor subjected to harmonic waves. Acta Mech 204:217–234

    MATH  Google Scholar 

  423. Song ZF, Sih GC (2003) Crack initiation behavior in magnetoelectroelastic composite under in-plane deformation. Theor Appl Fract Mech 39:189–207

    Google Scholar 

  424. Soh AK, Liu JX (2009) Mode III interfacial edge crack in a magnetoelectroelastic bimaterial. Key Eng Mater 261–263:393–398

    Google Scholar 

  425. Zhao Y, Zhao M, Pan E (2015) Displacement discontinuity analysis of a nonlinear interfacial crack in three-dimensional transversely isotropic magneto-electro-elastic bi-materials. Eng Anal Bound Elem 61:254–264

    MathSciNet  MATH  Google Scholar 

  426. Gao CF, Noda N (2004) Thermal-induced interfacial cracking of magnetoelectroelastic materials. Int J Eng Sci 42:1347–1360

    Google Scholar 

  427. Fei-Xiang F, Lee KY, Li YD (2011) Multiple cracks on the arc-shaped interface in a semi-cylindrical magneto-electro-elastic composite with an orthotropic substrate. Eng Fract Mech 78:2029–2041

    Google Scholar 

  428. Hu KQ, Li GQ (2005) Electro-magneto-elastic analysis of a piezoelectromagnetic strip with a finite crack under longitudinal shear. Mech Mater 37:925–934

    Google Scholar 

  429. Zhong XC (2009) Analysis of a dielectric crack in a magnetoelectroelastic layer. Int J Solids Struct 46:4221–4230

    MATH  Google Scholar 

  430. Tian WY, Gabbert U (2004) Multiple crack interaction problem in magnetoelectroelastic solids. Eur J Mech A Solids 23:599–614

    MATH  Google Scholar 

  431. Hu K, Chen Z, Fu J (2015) Moving Dugdale crack along the interface of two dissimilar magnetoelectroelastic materials. Acta Mech 226:2065–2076

    MathSciNet  MATH  Google Scholar 

  432. Li R, Kardomateas GA (2006) The mode III interface crack in piezo-electro-magneto-elastic dissimilar bimaterials. J Appl Mech 73:220

    MATH  Google Scholar 

  433. Hu K, Chen Z (2014) An interface crack moving between magnetoelectroelastic and functionally graded elastic layers. Appl Math Model 38:910–925

    MathSciNet  MATH  Google Scholar 

  434. Gao C-F, Kessler H, Balke H (2003) Crack problems in magnetoelectroelastic solids. Part I: exact solution of a crack. Int J Eng Sci 41:969–981

    MATH  Google Scholar 

  435. Feng WJ, Pan E, Wang X (2008) Stress analysis of a penny-shaped crack in a magneto-electro-thermo-elastic layer under uniform heat flow and shear loads. J Therm Stress 31:497–514

    Google Scholar 

  436. Zhao M, Yang F, Liu T (2006) Analysis of a penny-shaped crack in a magneto-electro-elastic medium. Philos Mag 86:4397–4416

    Google Scholar 

  437. Wang BL, Sun YG, Zhang HY (2008) Analysis of a penny-shaped crack in magnetoelectroelastic materials. J Appl Phys 103:083530

    Google Scholar 

  438. Hu KQ, Qin QH, Kang YL (2007) Anti-plane shear crack in a magnetoelectroelastic layer sandwiched between dissimilar half spaces. Eng Fract Mech 74:1139–1147

    Google Scholar 

  439. Wang BL, Han JC (2007) Multiple cracking of magnetoelectroelastic materials in coupling thermo-electro-magneto-mechanical loading environments. Comput Mater Sci 39:291–304

    Google Scholar 

  440. Niraula OP, Wang BL (2006) Thermal stress analysis in magneto-electro-thermo-elasticity with a penny-shaped crack under uniform heat flow. J Therm Stress 29:423–437

    Google Scholar 

  441. Wang BL, Han JC, Mai YW (2006) Mode III fracture of a magnetoelectroelastic layer: exact solution and discussion of the crack face electromagnetic boundary conditions. Int J Fract 139:27–38

    MATH  Google Scholar 

  442. Spyropoulos CP, Sih GC, Song ZF (2003) Magnetoelectroelastic composite with poling parallel to plane of line crack under out-of-plane deformation. Theor Appl Fract Mech 39:281–289

    Google Scholar 

  443. Tian WY, Gabbert U (2005) Parallel crack near the interface of magnetoelectroelastic bimaterials. Comput Mater Sci 32:562–567

    Google Scholar 

  444. Zhou ZG, Chen Y, Wang B (2007) The behavior of two parallel interface cracks in magneto-electro-elastic materials under an anti-plane shear stress loading. Compos Struct 77:97–103

    Google Scholar 

  445. Huang GY, Wang BL, Mai YW (2009) Effect of interfacial cracks on the effective properties of magnetoelectroelastic composites. J Intell Mater Syst Struct 20:963–968

    Google Scholar 

  446. Zhou ZG, Wang B (2004) Two parallel symmetry permeable cracks in functionally graded piezoelectric/piezomagnetic materials under anti-plane shear loading. Int J Solids Struct 41:4407–4422

    MATH  Google Scholar 

  447. Li C, Tong L (2015) 2D fracture analysis of magnetoelectroelastic composites by the SBFEM. Compos Struct 132:984–994

    Google Scholar 

  448. Li YD, Lee KY (2008) Fracture analysis and improved design for a symmetrically bonded smart structure with linearly non-homogeneous magnetoelectroelastic properties. Eng Fract Mech 75:3161–3172

    Google Scholar 

  449. Zhong XC, Li XF (2008) Fracture analysis of a magnetoelectroelastic solid with a penny-shaped crack by considering the effects of the opening crack interior. Int J Eng Sci 46:374–390

    MATH  Google Scholar 

  450. Feng WJ, Su RKL, Pan E (2007) Fracture analysis of a penny-shaped magnetically dielectric crack in a magnetoelectroelastic material. Int J Fract 146:125–138

    MATH  Google Scholar 

  451. Su RKL, Feng WJ (2008) Fracture behavior of a bonded magneto-electro-elastic rectangular plate with an interface crack. Arch Appl Mech 78:343–362

    MATH  Google Scholar 

  452. Sladek J, Sladek V, Solek P, Zhang C (2010) Fracture analysis in continuously nonhomogeneous magneto-electro-elastic solids under a thermal load by the MLPG. Int J Solids Struct 47:1381–1391

    MATH  Google Scholar 

  453. Tian WY, Rajapakse RKND (2005) Fracture analysis of magnetoelectroelastic solids by using path independent integrals. Int J Fract 131:311–335

    MATH  Google Scholar 

  454. Li Y, Feng W, Xu Z (2009) Fracture analysis of cracked 2D planar and axisymmetric problems of magneto-electro-elastic materials by the MLPG coupled with FEM. Comput Methods Appl Mech Eng 198:2347–2359

    MATH  Google Scholar 

  455. Sladek J, Sladek V, Solek P, Pan E (2008) Fracture analysis of cracks in magneto-electro-elastic solids by the MLPG. Comput Mech 42:697–714

    MATH  Google Scholar 

  456. Rojas-Díaz R, Sukumar N, Saez A, García-Sánchez F (2011) A quasi continuum methodology for multiscale analyses of discrete microstructural. Int J Numer Methods Eng 88:1238–1259

    Google Scholar 

  457. Gao CF, Tong P, Zhang TY (2004) Fracture mechanics for a mode III crack in a magnetoelectroelastic solid. Int J Solids Struct 41:6613–6629

    MATH  Google Scholar 

  458. García-Sánchez F, Rojas-Díaz R, Sáez A, Zhang C (2007) Fracture of magnetoelectroelastic composite materials using boundary element method (BEM). Theor Appl Fract Mech 47:192–204

    Google Scholar 

  459. Rangelov T, Stoynov Y, Dineva P (2011) Dynamic fracture behavior of functionally graded magnetoelectroelastic solids by BIEM. Int J Solids Struct 48:2987–2999

    Google Scholar 

  460. Espinosa-Almeyda Y, López-Realpozo JC, Rodríguez-Ramos R, Bravo-Castillero J, Guinovart-Díaz R, Camacho-Montes H, Sabina FJ (2011) Effects of interface contacts on the magneto electro-elastic coupling for fiber reinforced composites. Int J Solids Struct 48:1525–1533

    MATH  Google Scholar 

  461. Wang YZ (2015) Influences of imperfect interface on effective magnetoelectric properties in multiferroic composites with elliptical fibers. Smart Mater Struct 24:045021

    Google Scholar 

  462. Feng WJ, Xue Y, Zou ZZ (2005) Crack growth of an interface crack between two dissimilar magneto-electro-elastic materials under anti-plane mechanical and in-plane electric magnetic impact. Theor Appl Fract Mech 43:376–394

    Google Scholar 

  463. Gao CF, Tong P, Zhang TY (2003) Interfacial crack problems in magneto-electroelastic solids. Int J Eng Sci 41:2105–2121

    Google Scholar 

  464. Vinyas M, Sunny KK, Harursampath D, Nguyen-Thoi T, Loja MAR (2019) Influence of interphase on the multi-physics coupled frequency of three-phase smart magneto-electro-elastic composite plates. Compos Struct 226:111254

    Google Scholar 

  465. Avetisyan A (2015) On the formulation of the electro-elasticity theory boundary value problems for electro-magneto-elastic composites with interface roughness. Proc NAS RA Mech 68:29–42

    MathSciNet  Google Scholar 

  466. Lee YG, Zou WN, Pan E (2015) Eshelby’s problem of polygonal inclusions with polynomial eigenstrains in an anisotropic magneto-electro-elastic full plane. Proc R Soc A Math Phys Eng Sci 471:1–20

    MathSciNet  MATH  Google Scholar 

  467. Dinzart F, Sabar H (2011) Magneto-electro-elastic coated inclusion problem and its application to magnetic-piezoelectric composite materials. Int J Solids Struct 48:2393–2401

    Google Scholar 

  468. Wang X, Shen YP (2003) Inclusions of arbitrary shape in magnetoelectroelastic composite materials. Int J Eng Sci 41:85–102

    MathSciNet  MATH  Google Scholar 

  469. Li JY (2003) Magnetoelectroelastic multi-inclusion and inhomogeneity problems and their applications in composite materials. Int J Eng Sci 38:1993–2011

    Google Scholar 

  470. Li G, Wang B, Han J, Du S (2009) Anti-plane analysis for elliptical inclusion in magnetoelectroelastic materials. Acta Mech Solida Sin 22:137–142

    Google Scholar 

  471. Sharma P, Ganti S (2004) Size-dependent Eshelby’s tensor for embedded nano-inclusions incorporating surface/interface energies. J Appl Mech 71:663–671

    MATH  Google Scholar 

  472. Sangghaleh A (2014) Surface loading on and internal defects in layered magneto-electro-elastic materials and structures. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

  473. Vinyas M, Kattimani S, Loja MAR, Vishwas M (2018) Effect of BaTiO3/CoFe2O4 micro-topological textures on the coupled static behaviour of magneto-electro-thermo-elastic beams in different thermal environment. Mater Res Express 5:1–29

    Google Scholar 

  474. Pan E, Wang R (2009) Effects of geometric size and mechanical boundary conditions on magnetoelectric coupling in multiferroic composites. J Phys D Appl Phys 42:245503

    Google Scholar 

  475. Zhou K, Li YD, Liu SL (2017) Effects of the volume fraction of piezoelectric particles in the magneto-electro-elastic interfacial region on the fracture behavior of a laminate multiferroic plate. Acta Mech 228:1229–1248

    MathSciNet  MATH  Google Scholar 

  476. Han X, Pan E (2012) Fields produced by three-dimensional dislocation loops in anisotropic magneto-electro-elastic materials. Mech Mater 59:110–125

    Google Scholar 

  477. Rao BN, Kuna M (2008) Interaction integrals for fracture analysis of functionally graded magnetoelectroelastic materials. Int J Fract 153:15–37

    MATH  Google Scholar 

  478. Loja MAR, Mota Soares CM, Barbosa JI (2014) Optimization of magneto-electro-elastic composite structures using differential evolution. Compos Struct 107:276–287

    Google Scholar 

  479. Kiran MC, Kattimani SC, Vinyas M (2018) Porosity influence on structural behaviour of skew functionally graded magneto-electro-elastic plate. Compos Struct 191:36–77

    Google Scholar 

  480. Ebrahimi F, Jafari A, Vinyas M (2019) Assessment of porosity influence on dynamic characteristics of smart heterogeneous magneto-electro-elastic plates. Struct Eng Mech 72:113–129

    Google Scholar 

  481. Ma J, Ke LL, Wang YS, Aizikovich SM (2015) Thermal contact of magneto-electro-elastic materials subjected to a conducting flat punch. J Strain Anal Eng Des 50:513–527

    Google Scholar 

  482. Miehe C, Vallicotti D, Teichtmeister S (2016) Homogenization and multiscale stability analysis in finite magneto-electro-elasticity. Application to soft matter EE, ME and MEE composites, vol 300. Elsevier, Amsterdam

    MATH  Google Scholar 

  483. Ajdour M, Bakkali A, Azrar L, El Omri A (2016) Modeling and analysis of loaded multilayered magnetoelectroelastic structures composite materials: applications. Adv Electromagn 5:91

    Google Scholar 

  484. Liu L (2014) An energy formulation of continuum magneto-electro-elasticity with applications. J Mech Phys Solids 63:451–480

    MathSciNet  MATH  Google Scholar 

  485. Khanmirza E, Jamalpoor A, Kiani A (2017) Nano-scale mass sensor based on the vibration analysis of a magneto-electro-elastic nanoplate resting on a visco-Pasternak substrate. Eur Phys J Plus 132:1–16

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Aerospace Engineering, Indian Institute of Science, Bangalore, 560012, India

    M. Vinyas

Authors
  1. M. Vinyas
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Vinyas.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Vinyas, M. Computational Analysis of Smart Magneto-Electro-Elastic Materials and Structures: Review and Classification. Arch Computat Methods Eng 28, 1205–1248 (2021). https://doi.org/10.1007/s11831-020-09406-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11831-020-09406-4

Search

Navigation