A refined sin hyperbolic shear deformation theory for sandwich FG plates by enhanced meshfree with new correlation function

  • Tan-Van VuEmail author
  • Jose L. Curiel-Sosa
  • Tinh Quoc BuiEmail author


The moving Kriging interpolation-based (MKI) meshfree method is extended to mechanical behavior analysis of isotropic and sandwich functionally graded material plates. The MKI meshfree method, which is free of shear correction factors effect in plate analysis, is further enhanced by introducing a new multi-quadric correlation function, eliminating drawbacks of its conventional form, gaining accurate solution. In this paper, a new refined sin hyperbolic shear deformation plate theory (N-RSHSDT) is introduced for plate kinematics. The present theory gives rise to four governing equations only, and achieves the sin hyperbolic distribution of the transverse shear strains through the plate thickness. To show the accuracy and effectiveness of the developed method, numerical experiments are performed for both isotropic and sandwich composite plates.


Sandwich plates Functionally graded materials Meshfree Hyperbolic shear deformation theory Moving Kriging interpolation 



Tan-Van Vu would like to acknowledge the financial support of the University of Architecture Ho Chi Minh City, Vietnam under Grant No.152/HD-NCKH.

Compliance with ethical standards

Conflict of interest

The authors declare that there are no conflict of interest.


  1. Baferani, A.H., Saidi, A.R., Jomehzadeh, E.: An exact solution for free vibration of thin functionally graded rectangular plates. Proc. Inst. Mech. E Part C J. Mech. Eng. Sci. 225(C3), 526–536 (2011)CrossRefzbMATHGoogle Scholar
  2. Bessaim, A., Houari, M.S.A., Tounsi, A., Mahmoud, S.R., Adda Bedia, E.A.: A new higher-order shear and normal deformation theory for the static and free vibration analysis of sandwich plates with functionally graded isotropic face sheets. J. Sand. Struct. Mater. 15, 671–703 (2013)CrossRefGoogle Scholar
  3. Bui, Q.T., Nguyen, N.M.: A moving Kriging interpolation-based meshfree method for free vibration analysis of Kirchhoff plates. Comput. Struct. 89, 380–394 (2011)CrossRefGoogle Scholar
  4. Bui, Q.T., Nguyen, N.T., Nguyen, D.H.: A moving Kriging interpolation-based meshless method for numerical simulation of Kirchhoff plate problems. Int. J. Numer. Meth. Eng. 77, 1371–1395 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  5. Bui, Q.T., Nguyen, N.M., Zhang, Ch.: An efficient meshfree method for vibration analysis of laminated composite plates. Comput. Mech. 48, 175–193 (2011)CrossRefzbMATHGoogle Scholar
  6. Bui, Q.T., Doan, H.D., Do, V.T., Hirose, S., Nguyen, D.D.: High frequency modes meshfree analysis of Reissner-Mindlin plates. J. Sci. Adv. Mater. Dev. 1, 400–412 (2016)Google Scholar
  7. Carrera, E., Brischetto, S.: Analysis of thickness locking in classical, refined and mixed multilayered plate theories. Compos. Struct. 82, 549–562 (2008a)CrossRefGoogle Scholar
  8. Carrera, E., Brischetto, S.: Analysis of thickness locking in classical, refined and mixed theories for layered shells. Compos. Struct. 85, 83–90 (2008b)CrossRefGoogle Scholar
  9. Carrera, E., Brischetto, S., Cinefra, M., Soave, M.: Effects of thickness stretching in functionally graded plates and shells. Compos. Part B Eng. 42(2), 123–133 (2011)CrossRefGoogle Scholar
  10. Chen, J.S., Hillman, M., Chi, S.W.: Meshfree methods: progress made after 20 years. J. Eng. Mech 143, 04017001 (2017)CrossRefGoogle Scholar
  11. Do, V.T., Bui, Q.T., Yu, T.T., Pham, T.D., Nguyen, T.C.: Role of material combination and new results of mechanical behavior for FG sandwich plates in thermal environment. J. Comput. Sci. 21, 164–181 (2017)MathSciNetCrossRefGoogle Scholar
  12. Ha, H.K.: Finite element analysis of sandwich plates: an overview. Comput. Struct. 37, 397–403 (1990)CrossRefGoogle Scholar
  13. Lee, Y.Y., Zhao, X., Liew, K.M.: Thermoelastic analysis of functionally graded plates using the element-free kp-Ritz method. Smart Mater. Struct. 18(3), 35007 (2009)CrossRefGoogle Scholar
  14. Li, Q., Iu, V.P., Kou, K.P.: Three-dimensional vibration analysis of functionally graded material sandwich plates. J. Sound Vib. 311, 498–515 (2008)CrossRefGoogle Scholar
  15. Mohammadi, M., Saidi, A., Jomehzadeh, E.: Levy solution for buckling analysis of functionally graded rectangular plates. Appl. Compos. Mater. 17, 81–93 (2010)CrossRefGoogle Scholar
  16. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Cinefra, M., Jorge, R.M.N., Soares, C.M.M.: Static analysis of functionally graded sandwich plates according to a hyperbolic theory considering Zig-Zag and warping effects. Adv. Eng. Softw. 52, 30–43 (2012)CrossRefGoogle Scholar
  17. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Cinefra, M., Roque, C.M.C., Jorge, R.M.N.: Static free vibration and buckling analysis of isotropic and sandwich functionally graded plates using a quasi-3D higher-order shear deformation theory and a meshless technique. Compos. Part B Eng. 44, 657–674 (2013)CrossRefGoogle Scholar
  18. Reddy, J.N.: Analysis of functionally graded plates. Int. J. Numer. Methods Eng. 47, 663–684 (2000)CrossRefzbMATHGoogle Scholar
  19. Sadamoto, S., Tanaka, S., Taniguchi, K., Ozdemir, M., Bui, Q.T., Murakami, C., Yanagihara, D.: Buckling analysis of stiffened plate structures by an improved meshfree flat shell formulation. Thin Walled Struct. 117, 303–313 (2017)CrossRefGoogle Scholar
  20. Vu, T.V., Phan, V.S.: A modified moving Kriging interpolation-based meshfree method with refined sinusoidal shear deformation theory for analysis of functionally graded plates. In: Proceedings of the International Conference on Advances in Computational Mechanics, pp. 485–501 (2017)Google Scholar
  21. Vu, T.V., Nguyen, N.H., Khosravifard, A., Hematiyan, M.R., Tanakad, S., Bui, T.Q.: A simple FSDT-based meshfree method for analysis of functionally graded plates. Eng. Anal. Bound. Elem. 79, 1–12 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  22. Vu, T.V., Khosravifard, A., Hematiyan, M.R., Bui, T.Q.: A new refined simple TSDT-based effective meshfree method for analysis of through-thickness FG plates. Appl. Math. Model. 57, 514–534 (2018)MathSciNetCrossRefGoogle Scholar
  23. Yaghoobi, H., Yaghoobi, P.: Buckling analysis of sandwich plates with FGM face sheets resting on elastic foundation with various boundary conditions: an analytical approach. Meccanica 48, 2019–2035 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  24. Yin, S.H., Yu, T.T., Liu, P.: Free vibration analyses of FGM thin plates by isogeometric analysis based on classical plate theory and physical neutral surface. Adv. Mech. Eng. ArticleID 634584 (2013)Google Scholar
  25. Yin, S.H., Jack, S.H., Yu, T.T., Bui, Q.T., Boras, P.A.S.: Isogeometric locking-free plate element: a simple first order shear deformation theory for functionally graded plates. Compos. Struct. 118, 121–138 (2014)CrossRefGoogle Scholar
  26. Zenkour, A.M.A.: Comprehensive analysis of functionally graded sandwich plates: part 2 buckling and free vibration. Int. J. Solids Struct. 42, 5243–5258 (2005)CrossRefzbMATHGoogle Scholar

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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of Civil EngineeringUniversity of Architecture Ho Chi Minh CityHo Chi Minh CityVietnam
  2. 2.Department of Mechanical EngineeringUniversity of SheffieldSheffieldUK
  3. 3.Institute for Research and DevelopmentDuy Tan UniversityDa Nang CityVietnam
  4. 4.Department of Civil and Environmental EngineeringTokyo Institute of TechnologyTokyoJapan

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