Skip to main content
SpringerLink
Log in

Effects of elastically restrained edges on FG sandwich annular plates by using a novel solution procedure based on layerwise formulation

  • Original Research Article
  • Published:
Archives of Civil and Mechanical Engineering Aims and scope Submit manuscript

Abstract

In practical applications, sandwich plates are often connected to other members, supported by damaged clamped/simply supported boundary conditions or supported by elastic restraints. Therefore, the mentioned structures may not always be simulated bythe classical boundary conditions, i.e., ideal simply supported, clamped and free edges. Also, these structures may be subjected to various loads. In this study, for the first time, a novel economical analytical solution procedure is presented for axisymmetric static analysis of sandwich annular plates, by using the layerwise and 3D elasticity theories. Based on the proposed approach, functionally graded sandwich annular plates with various elastically restrained edges under arbitrary distributed loads may be analyzed and all of the displacements and stresses components may be exactly achieved. Also, imposed loads at the boundaries may be evaluated. Transverse shear and normal stresses boundary conditions on the top and bottom of the sandwich plate and the interlaminar continuity conditions of the in-plane displacement, transverse shear and normal stresses are exactly satisfied. Accuracyand efficiency ofthe presented solution procedure are demonstratedbycomparing the obtained results for sandwich plates with the classical edge conditions as some special cases of the elastic supports with results of the three-dimensional theory of elasticity.

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

Similar content being viewed by others

References

  1. P.C. Dumir, M.L. Gandhi, YogendraNath, Nonlinear static and transient analysis of orthotropic thin circular plates with elastically restrained edge under central load, Journal of Composite Materials 17 (1983) 478–491.

    Article  Google Scholar 

  2. G.D. Galletly, Optimum design of thin circular plates on an elastic foundation, Proceedings of the Institution of Mechanical Engineers 173 (1) (1959) 678–696.

    Article  MathSciNet  Google Scholar 

  3. L.W. Zhang, W.C. Cui, K.M. Liew, Vibration analysis of functionally graded carbon nanotube reinforced composite thick plates with elastically restrained edges, International Journal of Mechanical Sciences 103 (2015) 9–21.

    Article  Google Scholar 

  4. J.N. Reddy, A review of refined theories of laminated composite plates, Shock & Vibration Digest 22 (1991) 3–17.

    Article  Google Scholar 

  5. Mallikarjuna, T. Kant, A critical review and some results of recently developed refined theories of fiber-reinforced laminated composites and sandwiches, Composite Structures 23 (1993) 293–312.

    Article  Google Scholar 

  6. E. Carrera, Theories and finite elements for multilayered, anisotropic, composite plates and shells, Archives of Computational Methods in Engineering 9 (2) (2002) 87–140.

    Article  MathSciNet  Google Scholar 

  7. E. Carrera, S. Brischetto, A survey with numerical assessment of classical and refined theories for the analysis of sandwich plates, Applied Mechanics Reviews 62 (1) (2008) 010803.

    Article  Google Scholar 

  8. S.D. Poisson, Memoire surl’equilibre et le mouvement des corpselastique, Memoires de l’Académie Royale des Sciences de l’Institut 8 (1829) 357–570.

    Google Scholar 

  9. G. Kirchhoff, Uber das Gleichgewicht und die Bewegung einer elastischen Scheibe, Journal für die reine und angewandte Mathematik 40 (1850) 51–88.

    Google Scholar 

  10. A.E.H. Love, The Mathematical Theory of Elasticity, 4th ed., Cambridge University Press, Cambridge, 1927.

    MATH  Google Scholar 

  11. E. Reissner, The effect of transverse shear deformation on the bending of elastic plates, ASME Journal of Applied Mechanics 12 (1945) 69–76.

    MathSciNet  MATH  Google Scholar 

  12. R.D. Mindlin, Influence of rotatory inertia and shear in flexural motions of isotropic elastic plates, ASME Journal of Applied Mechanics 18 (1951) 1031–1036.

    MATH  Google Scholar 

  13. J.N. Reddy, Mechanics of Laminated Composite Plates: Theory and Analysis, CRC Press, 1997.

    MATH  Google Scholar 

  14. J.N. Reddy, A simple higher order theories for laminated composites plates, Journal of Applied Mechanics 52 (1984) 742–745.

    Google Scholar 

  15. K.K. Pradhan, S. Chakraverty, Static analysis of functionally graded thin rectangular plates with various boundary supports, Archives of Civil and Mechanical Engineering 15 (3) (2015) 721–734.

    Article  Google Scholar 

  16. A.M. Zenkour, Effects of hygrothermal conditions on cross-ply laminated plates resting on elastic foundations, Archives of Civil and Mechanical Engineering 14 (2014) 144–159.

    Article  MathSciNet  Google Scholar 

  17. A. Sabik, I. Kreja, Linear analysis of laminated multilayered plates with the application of zig-zag function, Archives of Civil and Mechanical Engineering 8 (2008) 61–72.

    Article  Google Scholar 

  18. K.H. Lee, N.R. Senthilnathan, S.P. Lim, S.T. Chow, An improved zig-zag model for the bending of laminated composite plates, Composite Structures 15 (2) (1990) 137–148.

    Article  Google Scholar 

  19. M. Ćetković, D.J. Vuksanović, Bending, free vibrations and buckling of laminated composite and sandwich plates using a layerwise displacement model, Composite Structures 88 (2) (2009) 219–227.

    Article  Google Scholar 

  20. K.H. Lee, L. Cao, A predictor-corrector zig-zag model for the bending of laminated composite plates, International Journal of Solids and Structures 33 (6) (1996) 879–897.

    Article  Google Scholar 

  21. S.M.R. Khalili, M. Shariyat, I. Rajabi, A finite element based global-local theory for static analysis of rectangular sandwich and laminated composite plates, Composite Structures 107 (2014) 177–189.

    Article  Google Scholar 

  22. M.M. Alipour, M. Shariyat, Analytical stress analysis of annular FGM sandwich plates with non-uniform shear and normal tractions, employing a zigzag-elasticity plate theory, Aerospace Science and Technology 32 (2014) 235–259.

    Article  Google Scholar 

  23. M.M. Alipour, M. Shariyat, Analytical zigzag formulation with 3D elasticity corrections for bending and stress analysis of circular/annular composite sandwich plates with auxetic cores, Composite Structures 132 (2015) 175–197.

    Article  Google Scholar 

  24. M.K. Pandit, A.H. Sheikh, B.N. Singh, An improved higher order zigzag theory for the static analysis of laminated sandwich plate with soft core, Finite Elements in Analysis and Design 44 (2008) 602–610.

    Article  Google Scholar 

  25. R. Sahoo, B.N. Singh, A new shear deformation theory for the static analysis of laminated composite and sandwich plates, International Journal of Mechanical Sciences 75 (2013) 324–336.

    Article  Google Scholar 

  26. B. Liu, A.J.M. Ferreira, Y.F. Xing, A.M.A. Neves, Analysis of composite plates using a layerwise theory and a differential quadrature finite element method, Composite Structures (2015), https://doi.org/10.1016/j.compstruct.2015.07.101.

    Google Scholar 

  27. E.S. Ventsel, A boundary element method applied to sandwich plates of arbitrary plan form, Engineering Analysis with Boundary Elements 27 (2003) 597–601.

    Article  Google Scholar 

  28. N. Grover, B.N. Singh, D.K. Maiti, Analytical and finite element modeling of laminated composite and sandwich plates: an assessment of a new shear deformation theory for free vibration response, International Journal of Mechanical Sciences 67 (2013) 89–99.

    Article  Google Scholar 

  29. E. Altunsaray, I. Bayer, Deflection and free vibration of symmetrically laminated quasi-isotropic thin rectangular plates for different boundary conditions, Ocean Engineering 57 (2013) 197–222.

    Article  Google Scholar 

  30. S. Xiang, K. Wang, Y. Ai, Y. Sha, H. Shi, Analysis of isotropic, sandwich and laminated plates by a meshless method and various shear deformation theories, Composite Structures 91 (2009) 31–37.

    Article  Google Scholar 

  31. M.M. Alipour, M. Shariyat, An elasticity-equilibrium-based zigzag theory for axisymmetric bending and stress analysis of the functionally graded circular sandwich plates, using a Maclaurin-type series solution, European Journal of Mechanics A: Solids 34 (2012) 78–101.

    Article  MathSciNet  Google Scholar 

  32. M.M. Alipour, M. Shariyat, An analytical global-local Taylor transformation-based vibration solution for annular FGM sandwich plates supported by nonuniform elastic foundations, Archives of Civil and Mechanical Engineering 14 (2014) 6–24.

    Article  Google Scholar 

  33. M.M. Alipour, M. Shariyat, Analytical zigzag-elasticity transient and forced dynamic stress and displacement response prediction of the annular FGM sandwich plates, Composite Structures 106 (2013) 426–445.

    Article  Google Scholar 

  34. M.M. Alipour, An analytical approach for bending and stress analysis of cross/angle-ply laminated composite plates under arbitrary non-uniform loads and elastic foundations, Archives of Civil and Mechanical Engineering 16 (2) (2016) 193–210.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, University of Mazandaran, Babolsar, 47416-13534, Iran

    M. M. Alipour

Authors
  1. M. M. Alipour
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. M. Alipour.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Alipour, M.M. Effects of elastically restrained edges on FG sandwich annular plates by using a novel solution procedure based on layerwise formulation. Archiv.Civ.Mech.Eng 16, 678–694 (2016). https://doi.org/10.1016/j.acme.2016.04.015

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1016/j.acme.2016.04.015

Keywords

Search

Navigation