Smart Structures and Systems

  • 제15권6호
  • /
  • Pages.1569-1582
  • /
  • 2015
  • /
  • 1738-1584(pISSN)
  • /
  • 1738-1991(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

A comparative study for bending of cross-ply laminated plates resting on elastic foundations

  • Zenkour, Ashraf M. (Department of Mathematics, Faculty of Science, King Abdulaziz University)
  • 투고 : 2014.03.29
  • 심사 : 2014.06.29
  • 발행 : 2015.06.25
⟨ 이전 논문 다음 논문 ⟩

초록

Two hyperbolic displacement models are used for the bending response of simply-supported orthotropic laminated composite plates resting on two-parameter elastic foundations under mechanical loading. The models contain hyperbolic expressions to account for the parabolic distributions of transverse shear stresses and to satisfy the zero shear-stress conditions at the top and bottom surfaces of the plates. The present theory takes into account not only the transverse shear strains, but also their parabolic variation across the plate thickness and requires no shear correction coefficients in computing the shear stresses. The governing equations are derived and their closed-form solutions are obtained. The accuracy of the models presented is demonstrated by comparing the results obtained with solutions of other theories models given in the literature. It is found that the theories proposed can predict the bending analysis of cross-ply laminated composite plates resting on elastic foundations rather accurately. The effects of Winkler and Pasternak foundation parameters, transverse shear deformations, plate aspect ratio, and side-to-thickness ratio on deflections and stresses are investigated.

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, 341-348.
  2. Akgoz, B. and Civalek, O. (2011), "Nonlinear vibration analysis of laminated plates restingon nonlinear twoparameters elastic foundations", Steel Compos. Struct., 11(5), 403-421. https://doi.org/10.12989/scs.2011.11.5.403
  3. Al Khateeb, S.A. and Zenkour, A.M. (2014), "A refined four-unknown plate theory for advanced plates resting on elastic foundations in hygrothermal environment", Compos. Struct., 111, 240-248. https://doi.org/10.1016/j.compstruct.2013.12.033
  4. Brischetto, S. (2012), "Hygrothermal loading effects in bending analysis of multilayered composite plates", Comput. Model. Eng. Sci., 88, 367-418.
  5. Carrera, E. (2002), "Theories and finite elements for multilayered, anisotropic, composite plates and shells", Arch. Comput. Meth. Eng., 9(2), 87-140. https://doi.org/10.1007/BF02736649
  6. Carrera, E. and Ciuffreda, A. (2005), "A unified formulation to assess theories of multilayered plates for various bending problems", Compos. Struct., 69, 271-293. https://doi.org/10.1016/j.compstruct.2004.07.003
  7. Cheng, Z.Q. and Batra, R.C. (2000a), "Deflection relationships between the homogeneous Kirchhoff's plate theory and different functionally graded plate theories", Arch. Mech., 52, 143-158.
  8. Cheng, Z.Q. and Batra, R.C. (2000b), "Exact correspondence between eigenvalues of membranes and functionally graded simply supported polygonal plates", J. Sound Vib., 229, 879-895. https://doi.org/10.1006/jsvi.1999.2525
  9. Chien, R.D. and Chen, C.S. (2006), "Nonlinear vibration of laminated plates on an elastic foundation", Thin Wall. Struct., 44, 852-860. https://doi.org/10.1016/j.tws.2006.08.016
  10. Chudinovich, I. and Constanda, C. (2000), "Integral representations of the solutions for a bending plate on an elastic foundation", Acta Mech., 139(1-4), 33-42. https://doi.org/10.1007/BF01170180
  11. Dumir, P.C. (2003), "Nonlinear dynamic response of isotropic thin rectangular plates on elastic foundations", Acta Mech., 71(1-4), 233-244. https://doi.org/10.1007/BF01173950
  12. Eratll, N. and Akoz, A.Y. (1997), "The mixed finite element formulation for the thick plates on elastic foundations", Comput. Struct., 65, 515-529. https://doi.org/10.1016/S0045-7949(96)00403-8
  13. Han, J.B. and Liew, K.M. (1997), "Numerical differential quadrature method for Reissner/Mindlin plates on two-parameter foundations", Int. J. Mech. Sci., 39, 977-989. https://doi.org/10.1016/S0020-7403(97)00001-5
  14. Jaiswal, O.R. and Iyengar, R.N. (1993), "Dynamic response of a beam on elastic foundation of finite depth under a moving force", Acta Mech., 96, 67-83. https://doi.org/10.1007/BF01340701
  15. Lanhe, W. (2004), "Thermal buckling of a simply-supported moderately thick rectangular FGM plate", Compos. Struct., 64, 211-218. https://doi.org/10.1016/j.compstruct.2003.08.004
  16. Liew, K.M., Han, J.B., Xiao, Z.M. and Du, H. (1996), "Differential quadrature method for Mindlin plates on Winkler foundations", Int. J. Mech. Sci., 38, 405-421. https://doi.org/10.1016/0020-7403(95)00062-3
  17. Omurtag, M.H. and Kadioglu, F. (1998), "Free vibration analysis of orthotropic plates resting on Pastrnak foundation by mixed finite element formulation", Comput. Struct., 67, 253-265. https://doi.org/10.1016/S0045-7949(97)00128-4
  18. Pagano, N.J. (1970), "Exact solutions for rectangular bidirectional composites and sandwich plates", J. Compos. Mater., 4, 20-34. https://doi.org/10.1177/002199837000400102
  19. Rao, J.S. (1999), Dynamics of Plates, Narosa Publishing House, New York, NY, USA.
  20. Reddy, J.N. (2000)"Analysis of functionally graded plates", Int. J. Numer. Meth. Eng., 47, 663-684. https://doi.org/10.1002/(SICI)1097-0207(20000110/30)47:1/3<663::AID-NME787>3.0.CO;2-8
  21. Reddy, J.N. and Hsu, Y.S. (1980), "Effects of shear deformation and anisotropy on the thermal bending of layered composite plates", J. Therm. Stresses, 3, 475-493. https://doi.org/10.1080/01495738008926984
  22. Sahin, O.S. (2005), "Thermal buckling of hybrid angle-ply laminated composite plates with a hole", Compos. Sci. Tech., 65, 1780-1790. https://doi.org/10.1016/j.compscitech.2005.03.007
  23. Shen, H.S. and Zhu, Z.H. (2012), "Postbuckling of sandwich plates with nanotube-reinforced composite face sheets resting on elastic foundations", Eur. J. Mech. A/Solids, 35, 10-21. https://doi.org/10.1016/j.euromechsol.2012.01.005
  24. Singh, B.N., Lal, A. and Kumar, R. (2007), "Post buckling response of laminated composite plate on elastic foundation with random system properties", Commun. Nonlin. Sci. Numer. Simul., 14, 284-300.
  25. Tsiatas, G.C. (2010), "Nonlinear analysis of non-uniform beams on nonlinear elastic foundation", Acta Mech., 209, 141-152. https://doi.org/10.1007/s00707-009-0174-3
  26. Zenkour, A.M., Allam, M.N.M. and Radwan, A.F. (2013), "Bending of cross-ply laminated plates resting on elastic foundations under thermo-mechanical loading", Int. J. Mech. Mater. Des., 9, 239-251. https://doi.org/10.1007/s10999-012-9212-8
  27. Zenkour, A.M., Allam, M.N.M. and Radwan, A.F. (2014), "Effects of hygrothermal conditions on cross-ply laminated plates resting on elastic foundations", Arch. Civil Mech. Eng., 14, 144-159. https://doi.org/10.1016/j.acme.2013.07.008
  28. Zenkour, A.M., Allam, M.N.M. and Sobhy, M. (2010), "Bending analysis of FG viscoelastic sandwich beams with elastic cores resting on Pasternak's elastic foundations", Acta Mech., 212, 233-252. https://doi.org/10.1007/s00707-009-0252-6
  29. Zenkour, A.M., Allam, M.N.M. and Sobhy, M. (2011), "Bending of a fiber-reinforced viscoelastic composite plate resting on elastic foundations", Arch. Appl. Mech., 81, 77-96. https://doi.org/10.1007/s00419-009-0396-9
  30. Zenkour, A.M. (2004a), "Buckling of fiber-reinforced viscoelastic composite plates using various plate theories", J. Eng. Math., 50, 75-93. https://doi.org/10.1023/B:ENGI.0000042123.94111.35
  31. Zenkour, A.M. (2004b), "Thermal effects on the bending response of fber-reinforced viscoelastic composite plates using a sinusoidal shear deformation theory", Acta Mech., 171, 171-187. https://doi.org/10.1007/s00707-004-0145-7
  32. Zenkour, A.M. (2006), "Generalized shear deformation theory for bending analysis of functionally graded plates", Appl. Math. Model., 30, 67-84. https://doi.org/10.1016/j.apm.2005.03.009
  33. Zenkour, A.M. (2009), "The refined sinusoidal theory for FGM plates on elastic foundations", Int. J. Mech. Sci., 51, 869-880. https://doi.org/10.1016/j.ijmecsci.2009.09.026

피인용 문헌

  1. Stochastic hygro-thermo-mechanically induced nonlinear static analysis of piezoelectric elastically support sandwich plate using secant function based shear deformation theory (SFSDT) vol.05, pp.04, 2016, https://doi.org/10.1142/S2047684116500202
  2. Electro-mechanical vibration of smart piezoelectric FG plates with porosities according to a refined four-variable theory vol.24, pp.12, 2017, https://doi.org/10.1080/15376494.2016.1196799
  3. Buckling analysis of higher order graded smart piezoelectric plates with porosities resting on elastic foundation vol.117, 2016, https://doi.org/10.1016/j.ijmecsci.2016.09.012
  4. Analysis of multilayered composite plates resting on elastic foundations in thermal environment using a hyperbolic model vol.39, pp.7, 2017, https://doi.org/10.1007/s40430-017-0773-1
  5. Electro-thermoelastic vibration of plates made of porous functionally graded piezoelectric materials under various boundary conditions vol.24, pp.10, 2018, https://doi.org/10.1177/1077546316672788
  6. Hygrothermo-mechanical buckling of FGM plates resting on elastic foundations using a quasi-3D model pp.1550-2295, 2019, https://doi.org/10.1080/15502287.2019.1568618
  7. Vibration analysis of generalized thermoelastic microbeams resting on visco-Pasternak's foundations vol.4, pp.3, 2017, https://doi.org/10.12989/aas.2017.4.3.269
  8. Quasi-3D Refined Theory for Functionally Graded Porous Plates: Displacements and Stresses vol.23, pp.1, 2015, https://doi.org/10.1134/s1029959920010051
  9. Thermal flexural analysis of anti-symmetric cross-ply laminated plates using a four variable refined theory vol.25, pp.4, 2015, https://doi.org/10.12989/sss.2020.25.4.409
  10. Buckling of carbon nanotube (CNT)-reinforced composite skew plates by the discrete singular convolution method vol.231, pp.6, 2015, https://doi.org/10.1007/s00707-020-02653-3