Structural Engineering and Mechanics

  • 제49권5호
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  • Pages.661-672
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  • 2014
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Exact solution for transverse bending analysis of embedded laminated Mindlin plate

  • Heydari, Mohammad Mehdi (Young Researchers and Elite Club, Kashan Branch, Islamic Azad University) ;
  • Kolahchi, Reza (Young Researchers and Elite Club, Kashan Branch, Islamic Azad University) ;
  • Heydari, Morteza (Young Researchers and Elite Club, Kashan Branch, Islamic Azad University) ;
  • Abbasi, Ali (Young Researchers and Elite Club, Kashan Branch, Islamic Azad University)
  • 투고 : 2013.08.05
  • 심사 : 2014.02.01
  • 발행 : 2014.03.10
⟨ 이전 논문 다음 논문 ⟩

초록

Laminated Rectangular plates embedded in elastic foundations are used in many mechanical structures. This study presents an analytical approach for transverse bending analysis of an embedded symmetric laminated rectangular plate using Mindlin plate theory. The surrounding elastic medium is simulated using Pasternak foundation. Adopting the Mindlin plate theory, the governing equations are derived based on strain-displacement relation, energy method and Hamilton's principle. The exact analysis is performed for this case when all four ends are simply supported. The effects of the plate length, elastic medium and applied force on the plate transverse bending are shown. Results indicate that the maximum deflection of the laminated plate decreases when considering an elastic medium. In addition, the deflection of the laminated plate increases with increasing the plate width and length.

키워드

참고문헌

  1. Akavci, S.S., Yerli, H.R. and Dogan, A. (2007), "The first order shear deformation theory for symmetrically laminated composite plates on elastic foundation", Arab. J. Sci. Eng., 32(2), 341-348.
  2. Akhavan, H., Hosseini Hashemi, Sh., Rokni Damavandi, T.H., Alibeigloo, A. and Vahabi, Sh. (2009a), "Exact solutions for rectangular Mindlin plates under in-plane loads resting on Pasternak elastic foundation. Part I: buckling analysis", Comput. Mat. Sci., 44, 968-978. https://doi.org/10.1016/j.commatsci.2008.07.004
  3. Akhavan, H., Hosseini Hashemi, Sh., Rokni Damavandi, T.H., Alibeigloo, A. and Vahabi, Sh. (2009a), "Exact solutions for rectangular Mindlin plates under in-plane loads resting on Pasternak elastic foundation. Part II: frequency analysis", Comput. Mat. Sci., 44, 951-961. https://doi.org/10.1016/j.commatsci.2008.07.001
  4. Baltacioglu, A.K., Civalek, O ., Akgoz, B. and Demir, F. (2011), "Large deflection analysis of laminated composite plates resting on nonlinear elastic foundations by the method of discrete singular convolution", Int. J. Pres. Ves. Pip., 88, 290-300. https://doi.org/10.1016/j.ijpvp.2011.06.004
  5. Bezine, G. (1988), "A new boundary element method for bending of plates on elastic foundations", Int. J. Sol. Struct., 24(6), 557-565. https://doi.org/10.1016/0020-7683(88)90057-1
  6. Buczkowski, R. and Torbacki, W. (2001), "Finite element modelling of thick plates on two-parameter elastic foundation", Int. J. Num. Anal. Meth. Geo., 25, 1409-1427. https://doi.org/10.1002/nag.187
  7. Choudhary, S.S. and Tungikar, V.B. (2011), "A simple finite element for nonlinear analysis of composite plates", Int. J. Eng. Sci. Tech., 3, 4897-4907.
  8. Chucheepsakul, S. and Chinnaboon, B. (2003), "Plates on two-parameter elastic foundations with nonlinear boundary conditions by the boundary element method", Comp. Struct., 81, 2739-2748. https://doi.org/10.1016/S0045-7949(03)00340-7
  9. Dash, P. and Singh, B.N. (2010), "Geometrically nonlinear bending analysis of laminated composite plate", Commun. Non. Sci. Num. Simul., 15, 3170-3181. https://doi.org/10.1016/j.cnsns.2009.11.017
  10. El-Zafrany, A., Fadhil, S. and Al-Hosani, K. (1995), "A new fundamental solution for boundary element analysis of this plates on winkler foundation", Int. J. Numer. Meth. Eng., 38, 887-903. https://doi.org/10.1002/nme.1620380602
  11. Fares, M.E. (1999), "Non-linear bending analysis of composite laminated plates using a refined first-order theory", Comp. Struct., 46,257-266. https://doi.org/10.1016/S0263-8223(99)00062-8
  12. Ferreira, A.J.M., Roque, C.M.C. and Martins P.A.L.S. (2003), "Analysis of composite plates using higherorder shear deformation theory and a finite point formulation based on the multiquadric radial basis function method", Comp. Part B, 34, 627-636. https://doi.org/10.1016/S1359-8368(03)00083-0
  13. Khajeansari, A., Baradaran, G.H. and Yvonnet, J. (2012), "An explicit solution for bending of nanowires lying on Winkler-Pasternak elastic substrate medium based on the Euler-Bernoulli beam theory", Int. J. Eng. Sci., 52, 115-128. https://doi.org/10.1016/j.ijengsci.2011.11.004
  14. Mindlin, R.D. (1951), "Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates", J. Appl. Mech., 18, 31-38.
  15. Norman, F., Knight, Jr. and Qi, Y.Q. (1997), "On a consistent first-order shear-deformation theory for laminated plates", Comp. Part B, 28B, 397-405.
  16. Pasternak, P.L. (1954), "New method calculation for flexible substructures on two parameter elastic foundation", Gosudarstvennogo Izdatelstoo, Literatury po Stroitelstvu i Architekture, Moskau, 1-56.
  17. Pietrzakowski, M. (2008), "Piezoelectric control of composite plate vibration: effect of electric potential distribution", Comp. Struct., 86(9), 948-954. https://doi.org/10.1016/j.compstruc.2007.04.023
  18. Ponnusamy, P. and Selvamani, R. (2012), "Wave propagation in a generalized thermo elastic plate embedded in elastic medium", Interact. Multis. Mech., 5(1), 13-26. https://doi.org/10.12989/imm.2012.5.1.013
  19. Reddy, J.N. (1984), "A simple higher order theory for laminated composite plates", J. Appl. Mech., 51, 745-752. https://doi.org/10.1115/1.3167719
  20. Reddy, B.S., Reddy, A.R., Kumar, J.S. and Reddy, K.V.K. (2012), "Bending analysis of laminated composite plates using finite element method", Int. J. Eng. Sci. Tech., 4, 177-190. https://doi.org/10.7763/IJET.2012.V4.344
  21. Reissner, E. (1945), "The effect of transverse shear deformation on the bending of elastic plates", J. Appl. Mech., 12, 69-77.
  22. Samaei, A.T., Abbasion, S. and Mirsayar, M.M. (2011), "Buckling analysis of a single-layer graphene sheet embedded in an elastic medium based on nonlocal Mindlin plate theory", Mech. Res. Comm., 38, 481-485. https://doi.org/10.1016/j.mechrescom.2011.06.003
  23. Sladek, J., Sladek, V. and Mang, H.A. (2002), "Meshless local boundary integral equation method for simply supported and clamped plates resting on elastic foundation", Comp. Meth. Appl. Mech. Eng., 191, 5943-5959. https://doi.org/10.1016/S0045-7825(02)00505-4
  24. Swaminathan, K. and Ragounadin, D. (2004), "Analytical solutions using a higher-order refined theory for the static analysis of antisymmetric angle-ply composite and sandwich plates", Comp. Struct., 64, 405-417. https://doi.org/10.1016/j.compstruct.2003.09.042
  25. Yas, M.H. and Sobhani, B. (2010), "Free vibration analysis of continuous grading fiber reinforced plates on elastic foundation", Int. J. Eng. Sci., 48, 1881-1895. https://doi.org/10.1016/j.ijengsci.2010.06.015
  26. Zenkour, A.M. (2003), "Exact mixed-classical solutions for the bending analysis of shear deformable rectangular plates", Appl. Math. Mod., 27, 515-534. https://doi.org/10.1016/S0307-904X(03)00046-5

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