Structural Engineering and Mechanics

  • 제44권1호
  • /
  • Pages.15-34
  • /
  • 2012
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Analytical solution for bending analysis of soft-core composite sandwich plates using improved high-order theory

  • Kheirikhah, M.M. (Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University) ;
  • Khalili, S.M.R. (Centre of Excellence for Research in Advanced Materials & Structures, Faculty of Mechanical Engineering, K.N. Toosi University of Technology) ;
  • Fard, K. Malekzadeh (Department of Structural Engineering and Simulation, Space Research Institute)
  • 투고 : 2011.09.15
  • 심사 : 2012.08.09
  • 발행 : 2012.10.10
⟨ 이전 논문 다음 논문 ⟩

초록

In the present paper, an improved high-order theory is used for bending analysis of soft-core sandwich plates. Third-order plate assumptions are used for face sheets and quadratic and cubic functions are assumed for transverse and in-plane displacements of the orthotropic soft core. Continuity conditions for transverse shear stresses at the interfaces as well as the conditions of zero transverse shear stresses on the upper and lower surfaces of the plate are satisfied. Also, transverse flexibility and transverse normal strain and stress of the orthotropic core are considered. The equations of motion and boundary conditions are derived by principle of minimum potential energy. Analytical solution for bending analysis of simply supported sandwich plates under various transverse loads are presented using Navier's solution. Comparison of the present results with those of the three-dimensional theory of elasticity and some plate theories in the literature confirms the accuracy of the proposed theory.

키워드

참고문헌

  1. Ahn, N. and Lee, K. (2011), "A study on transverse vibration characteristics of a sandwich plate with asymmetrical faces", Struct. Eng. Mech., 40(4), 501-515. https://doi.org/10.12989/sem.2011.40.4.501
  2. Bhaskar, K. and Varadan, T.K. (1989), "Refinement of higher order laminated plate theories", AIAA J., 27, 1830-1831. https://doi.org/10.2514/3.10345
  3. Brischetto, S., Carrera, E. and Demasi, L. (2009), "Improved bending analysis of sandwich plates using a zig-zag function", Compos. Struct., 89(3), 408-415. https://doi.org/10.1016/j.compstruct.2008.09.001
  4. Carrera, E. (1998), "Mixed layer-wise models for multilayered plates analysis", Compos. Struct., 43, 57-70. https://doi.org/10.1016/S0263-8223(98)00097-X
  5. Carrera, E. and Demasi, L. (2003), "Two benchmarks to assess two-dimensional theories of sandwich composite plates", AIAA J., 41, 1356-1362. https://doi.org/10.2514/2.2081
  6. Carrera, E. and Brischetto, S.A. (2009), "Survey with numerical assessment of classical and refined theories for the analysis of sandwich plates", Appl. Mech. Rev., 62, 1-17.
  7. Cetkovic, M. and Vuksanovic, D.J. (2008), "Bending, free vibrations and buckling of laminated composite and sandwich plates using a layerwise displacement model", Compos. Struct., 88, 219-227.
  8. Cho, M. and Parmerter, R.R. (1992), "An efficient higher order plate theory for laminated composites", Compos. Struct., 20, 113-123. https://doi.org/10.1016/0263-8223(92)90067-M
  9. Cho, M. and Parmerter, R.R. (1993), "Efficient higher order composite plate theory for general lamination configurations", AIAA J., 31(7), 1299-1306. https://doi.org/10.2514/3.11767
  10. Dafedar, J.B., Desai, Y.M. and Mufti, A.A. (2003), "Stability of sandwich plates by mixed, higherorder analytical formulation", Int. J. Solids Struct., 40, 4501-4517. https://doi.org/10.1016/S0020-7683(03)00283-X
  11. Dawe, D.J. and Yuan, W.X. (2001), "Overall and local buckling of sandwich plates with laminated faceplates. Part I: analysis", Comput. Meth. Appl. Mech. Eng., 190, 5197-5213. https://doi.org/10.1016/S0045-7825(01)00169-4
  12. Demasi, L. (2009), "${\infty}^6$ Mixed plate theories based on the generalized unified formulation. PartIII, advanced mixed high order shear deformation theories", Compos. Struct., 87(3), 183-194. https://doi.org/10.1016/j.compstruct.2008.07.011
  13. Di Sciuva, M. (1986), "Bending, vibration and bucking of simply-supported thick multilayered orthotropic plates, an evaluation of a new displacement model", J. Sound Vib., 105(3), 425-442. https://doi.org/10.1016/0022-460X(86)90169-0
  14. Di Sciuva, M. (1992), "Multilayered anisotropic plate models with continuous interlaminar stress", Comput. Struct., 22(3), 149-167. https://doi.org/10.1016/0263-8223(92)90003-U
  15. Frostig, Y. (1998), "Buckling of sandwich panels with a transversely flexible core, high-order theory", Int. J. Solids Struct., 35, 183-204. https://doi.org/10.1016/S0020-7683(97)00078-4
  16. Frostig, Y. and Thomsen, O.T. (2004), "High-order free vibration of sandwich panels with a flexible core", Int. J. Solids Struct., 41, 1697-724. https://doi.org/10.1016/j.ijsolstr.2003.09.051
  17. Frostig, Y. and Thomsen, O.T. (2009), "On the free vibration of sandwich panels with a transversely flexible and temperature-dependent core material - Part I: Mathematical formulation", Compos. Sci. Technol., 69, 856-862. https://doi.org/10.1016/j.compscitech.2008.03.003
  18. Ganapathi, M., Patel, B.P. and Makhecha, D.P. (2004), "Nonlinear dynamic analysis of thick composite/sandwich laminates using an accurate higher-order theory", Compos. Part B, 35, 345-355. https://doi.org/10.1016/S1359-8368(02)00075-6
  19. Hohe, J. and Librescu, L. (2004), "Advances in the modeling of deformation and buckling of structural sandwich panels", Mech. Adv. Mater. Struct., 11, 395-424. https://doi.org/10.1080/15376490490451561
  20. Hohe, J., Librescu, L. and Oh, S.Y. (2006), "Dynamic buckling of flat and curved sandwich panels with transversely compressible core", Compos. Struct., 74, 10-24. https://doi.org/10.1016/j.compstruct.2005.03.003
  21. Kant, T. and Swaminathan, K. (2000), "Analytical solutions using a higher order refined theory for the stability analysis of laminated composite and sandwich plates", Struct. Eng. Mech., 10, 337-357. https://doi.org/10.12989/sem.2000.10.4.337
  22. Kant, T. and Swaminathan, K. (2002), "Analytical solutions for the static analysis of laminated composite and sandwich plates based on a higher order refined theory", Compos. Struct., 56, 329-344. https://doi.org/10.1016/S0263-8223(02)00017-X
  23. Kapuria, S. and Achary, G.G.S. (2004), "An efficient higher-order zigzag theory for laminated plates subjected to thermal loading", Int. J. Solids Struct., 41, 4661-4684. https://doi.org/10.1016/j.ijsolstr.2004.02.020
  24. Kheirikhah, M.M., Khalili, S.M.R. and Malekzadeh Fard, K. (2011), "Biaxial buckling analysis of soft-core composite sandwich plates using improved high-order theory", Eur. Jo. Mech. A/Solids, 31, 54-66.
  25. Kim, J.S. (2007), "Free vibration of laminated and sandwich plates using enhanced plate theories", J. Sound Vib., 308, 268-286. https://doi.org/10.1016/j.jsv.2007.07.040
  26. Kulkarni, S.D. and Kapuria, S. (2008), "Free vibration analysis of composite and sandwich plates using an improved discrete Kirchhoff quadrilateral element based on third-order zigzag theory", Computat. Mech., 42, 803-824. https://doi.org/10.1007/s00466-008-0285-z
  27. Li, X. and Liu, D. (1995), "Zigzag theory for composite laminates", AIAA J., 33(6), 1163-1165. https://doi.org/10.2514/3.12671
  28. Li, X. and Liu, D. (1995), "A laminate theory based on global-local superposition", Commun. Numer. Meth. Eng., 11, 633-641. https://doi.org/10.1002/cnm.1640110802
  29. Li, X. and Liu, D. (1997), "Generalized laminate theories based on double superposition hypothesis", Int. J. Numer. Meth. Eng., 40, 1197-1212. https://doi.org/10.1002/(SICI)1097-0207(19970415)40:7<1197::AID-NME109>3.0.CO;2-B
  30. Malekzadeh, K., Khalili, M.R. and Mittal, R.K. (2004), "Damped vibrations of sandwich plates with a viscoelastic soft flexible core, an improved high-order approach", Proceeding of 12th Int Conf of Mech Eng, Tehran, Iran.
  31. Malekzadeh, K., Khalili, M.R. and Mittal, R.K. (2005), "Prediction of low velocity impact response of composite sandwich panels using new three degrees-of-freedom model", Proceeding of 13th Int Conf of Mech Eng, Esfahan, Iran.
  32. Matsunaga, H. (2002), "Assessment of a global higher-order deformation theory for laminated composite and sandwich plates", Compos. Struct., 56(3), 279-291. https://doi.org/10.1016/S0263-8223(02)00013-2
  33. 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
  34. Pagano, N.J. (1969), "Exact solution of composite laminates in cylindrical bending", J. Compos. Mater., 3, 398-411. https://doi.org/10.1177/002199836900300304
  35. Pai, P.F. and Palazotto, A.N. (2001), "A high-order sandwich plate theory accounting for 3D stresses", Int. J. Solids Struct., 38, 5054-5062.
  36. Pandit, M.K., Sheikh, A.H. and Singh, B.N. (2008), "An improved higher order zigzag theory for the static analysis of laminated sandwich plate with soft core", Finite Elem. Analy. Des., 44, 602-610. https://doi.org/10.1016/j.finel.2008.02.001
  37. Plagianakos, T.S. and Saravanos, D.A. (2009), "Higher-order layerwise laminate theory for the prediction of interlaminar shear stresses in thick composite and sandwich composite plates", Compos. Struct., 87(1), 23-35. https://doi.org/10.1016/j.compstruct.2007.12.002
  38. Rao, M.K. and Desai, Y.M. (2004), "Analytical solutions for vibrations of laminated and sandwich plates using mixed theory", Compos. Struct., 63, 361-373. https://doi.org/10.1016/S0263-8223(03)00185-5
  39. Reddy, J.N. (1987), "A refined nonlinear theory of plates with transverse shear deformation", Int. J. Solids Struct., 20, 881-896.
  40. Reddy, J.N. (2004), Mechanics of Laminated Composite Plates and Shells, Theory and Analysis, 2nd Edition, CRC Press, New York.
  41. Rezaiee-Pajand, M., Shahabian, F. and Tavakoli, F.H. (2012), "A new higher-order triangular plate bending element for the analysis of laminated composite and sandwich plates", Struct. Eng. Mech., 43(2), 253-271. https://doi.org/10.12989/sem.2012.43.2.253
  42. Robbins, D.H. and Reddy, J.N. (1993), "Modelling of thick composites using a layerwise laminate theory", Int. J. Numer. Meth. Eng., 36, 665-677.
  43. Shariyat, M. (2010), "A generalized global-local high-order theory for bending and vibration analyses of sandwich plates subjected to thermo-mechanical loads", Int. J. Mech. Sci., 52, 495-514. https://doi.org/10.1016/j.ijmecsci.2009.11.010
  44. Shariyat, M. (2010), "A generalized high-order global-local plate theory for nonlinear bending and buckling analyses of imperfect sandwich plates subjected to thermo-mechanical loads", Compos. Struct., 92, 130-143. https://doi.org/10.1016/j.compstruct.2009.07.007
  45. Shariyat, M. (2010), "Non-linear dynamic thermo-mechanical buckling analysis of the imperfect sandwich plates based on a generalized three-dimensional high-order global-local plate theory", Compos. Struct., 92, 72-85. https://doi.org/10.1016/j.compstruct.2009.06.013
  46. 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", Compos. Struct., 64, 405-417. https://doi.org/10.1016/j.compstruct.2003.09.042
  47. Toledano, A. and Murakami, H. (1987), "A composite plate theory for arbitrary laminated configurations", J. Appl. Mech., 54, 181-189. https://doi.org/10.1115/1.3172955
  48. Zhen, W., Ronggeng, C. and Wanji, C. (2005), "Refined laminated composite plate element based on global-local higher-order shear deformation theory", Compos. Struct., 70, 135-152. https://doi.org/10.1016/j.compstruct.2004.08.019
  49. Zhen, W. and Wanji, C. (2006), "Free vibration of laminated composite and sandwich plates using global-local higher-order theory", J. Sound Vib., 298, 333-349. https://doi.org/10.1016/j.jsv.2006.05.022
  50. Zhen, W. and Wanji, C. (2007), "Thermomechanical buckling of laminated composite and sandwich plates using global-local higher order theory", Int. J. Mech. Sci., 49, 712-721. https://doi.org/10.1016/j.ijmecsci.2006.10.006
  51. Zhen, W. and Wanji, C. (2010), "A $C^0$-type higher-order theory for bending analysis of laminated composite and sandwich plates", Compos. Struct., 92, 653-661. https://doi.org/10.1016/j.compstruct.2009.09.032
  52. Zhen, W., Wanji, C. and Xiaohui, R. (2010), "An accurate higher-order theory and $C^0$ finite element for free vibration analysis of laminated composite and sandwich plates", Compos. Struct., 92, 1299-1307. https://doi.org/10.1016/j.compstruct.2009.11.011

피인용 문헌

  1. Higher order flutter analysis of doubly curved sandwich panels with variable thickness under aerothermoelastic loading vol.60, pp.1, 2016, https://doi.org/10.12989/sem.2016.60.1.001
  2. Analysis and prediction of ultimate strength of high-strength SFRC plates under in-plane and transverse loads vol.52, pp.6, 2014, https://doi.org/10.12989/sem.2014.52.6.1273
  3. Free vibration analysis of corrugated-face sheet composite sandwich plates vol.38, pp.7, 2016, https://doi.org/10.1007/s40430-015-0306-8
  4. Vibration Analysis of a Cylindrical Sandwich Panel with Flexible Core Using an Improved Higher-Order Theory vol.14, pp.4, 2017, https://doi.org/10.1590/1679-78253410
  5. New enhanced higher order free vibration analysis of thick truncated conical sandwich shells with flexible cores vol.55, pp.4, 2015, https://doi.org/10.12989/sem.2015.55.4.719
  6. Bending and buckling analysis of corrugated composite sandwich plates vol.38, pp.8, 2016, https://doi.org/10.1007/s40430-016-0498-6
  7. Buckling Analysis of Soft-Core Composite Sandwich Plates Using 3D Finite Element Method vol.105-107, pp.1662-7482, 2011, https://doi.org/10.4028/www.scientific.net/AMM.105-107.1768
  8. Static analysis of sandwich plates embedded with shape memory alloy wires using active strain energy tuning method vol.41, pp.3, 2019, https://doi.org/10.1007/s40430-019-1666-2
  9. Free Vibration Analysis of Composite-Faced Soft-Core Sandwich Plates Using a High-Order Theory vol.32, pp.6, 2012, https://doi.org/10.1061/(asce)as.1943-5525.0001091
  10. Multi-objective genetic algorithm optimization of composite sandwich plates using a higher-order theory vol.42, pp.10, 2012, https://doi.org/10.1007/s40430-020-02596-9
  11. Vibration analysis of sandwich beam with honeycomb core and piezoelectric facesheets affected by PD controller vol.28, pp.2, 2012, https://doi.org/10.12989/sss.2021.28.2.195