Steel and Composite Structures

  • 제21권4호
  • /
  • Pages.849-862
  • /
  • 2016
  • /
  • 1229-9367(pISSN)
  • /
  • 1598-6233(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Buckling behaviours of functionally graded polymeric thin-walled hemispherical shells

  • Uysal, Mine U. (Department of Mechanical Engineering, Yildiz Technical University)
  • 투고 : 2016.01.28
  • 심사 : 2016.06.18
  • 발행 : 2016.07.20
⟨ 이전 논문 다음 논문 ⟩

초록

This paper investigates the static buckling behaviours of Functionally Gradient Polymeric Material (FGPM) shells in the form of hemispherical segment. A new FGPM model based on experimental was considered to investigate the buckling problem of thin-walled spherical shells loaded by the external pressure. The spherical shells were formed by FGPM which was produced adding the two types of graphite powders into epoxy resin. The graphite powders were added to the epoxy resin as volume of 3, 6, 9, and 12%. Halpin-Tsai and Paul models were used to determine the elastic moduli of the parts of FGPM. The detailed static buckling analyses were performed by using finite element method. The influences of the types and volume of graphite powders on the buckling behaviour of the FGPM structures were investigated. The buckling loads of hemispherical FGPM shells based on Halpin-Tsai and Paul models were compared with those determined from the analytical solution of non-graphite condition existing for homogeneous material model. The comparisons between these material models showed that Paul model was overestimated. Besides, the critical buckling loads were predicted. The higher critical buckling loads were estimated for the PV60/65 graphite powder due to the compatible of the PV60/65 graphite powder with resin.

키워드

참고문헌

  1. $ANSYS^{(R)}$ (2010), Ansys Inc., Canonsburg, PA, USA.
  2. Arefi, M. (2014), "Generalized shear deformation theory for thermo elastic analyses of the functionally graded cylindrical shells", Struct. Eng. Mech., Int. J., 50(3), 403-417. https://doi.org/10.12989/sem.2014.50.3.403
  3. Bouguenina, O., Belakhdar, K., Tounsi, A. and Bedia, E.A.A. (2015), "Numerical analysis of FGM plates with variable thickness subjected to thermal buckling", Steel Compos. Struct., Int. J., 19(3), 679-695. https://doi.org/10.12989/scs.2015.19.3.679
  4. Carrera, E. and Brischetto, S. (2009), "A survey with numerical assessment of classical and refined theories for the analysis of sandwich plates", Appl. Mech. Rev., 62(1), 1-17.
  5. Chao, C.C. and Lin, I.S. (1990), "Static and dynamic snap-through of orthotropic spherical caps", Compos. Struct., 14(4), 281-301. https://doi.org/10.1016/0263-8223(90)90011-3
  6. Chattopadhyay, A. and Ferreira J. (1993), "Design sensitivity and optimization of composite cylinders", J. Compos. Eng., 3(2), 169-179. https://doi.org/10.1016/0961-9526(93)90040-Q
  7. Chen, C., Zhu, X., Hou, H., Zhang, L., Shen, X. and Tang, T. (2014), "A survey with numerical assessment of classical and refined theories for the analysis of sandwich plates", Steel Compos. Struct., Int. J., 16(3), 269-288. https://doi.org/10.12989/scs.2014.16.3.269
  8. Chien, C.M., Huang, T. and Schachar, R.A. (2006), "Analysis of human crystalline lens accommodation", J. Biomech., 39(4), 672-680. https://doi.org/10.1016/j.jbiomech.2005.01.017
  9. Davies, P. and Chauchot, P. (1999), Composites for Marine Applications - Part 2: Underwater Structures, Kluwer Academic Publishers, Dordrecht, Netherlands.
  10. Fekrar, A., Meiche, N.E., Bessaim, A., Tounsi, A. and Bedia, E.A.A. (2012), "Buckling analysis of functionally graded hybrid composite plates using a new four variable refined plate theory", Steel Compos. Struct., Int. J., 13(1), 91-107. https://doi.org/10.12989/scs.2012.13.1.091
  11. Fornes, T.D. and Paul, D.R. (2003), "Modeling properties of nylon 6/clay nanocomposites using composite theories", Polymer, 44(17), 4993-5013. https://doi.org/10.1016/S0032-3861(03)00471-3
  12. Foroutan, M., Dastjerdi, R.M. and Bahreini, R.S. (2011), "Static analysis of FGM cylinders by a mesh-free method", Steel Compos. Struct., Int. J., 12(1), 1-11.
  13. Ganapathi, M. and Varadan, T.K. (1982), "Dynamic buckling of orthotropic shallow spherical shells", Comput. Struct., 15(5), 517-520. https://doi.org/10.1016/0045-7949(82)90003-7
  14. Ganapathi, M. and Varadan, T.K. (1995), "Dynamic buckling of laminated anisotropic spherical caps", J. Appl. Mech., 62(1), 13-19. https://doi.org/10.1115/1.2895879
  15. Ganapathi, M. (2007), "Dynamic stability characteristics of functionally graded materials shallow spherical shells", Compos. Struct., 79(3), 338-343. https://doi.org/10.1016/j.compstruct.2006.01.012
  16. Grigolyuk, E.I. and Lopanitsyn, Y.A. (2002), "The axisymmetric postbuckling behaviour of shallow spherical domes", J. Appl. Math. Mech., 66(4), 605-616. https://doi.org/10.1016/S0021-8928(02)00079-5
  17. Hadji, L., Daouadji, T.H., Tounsi, A. and Bedia, E.A. (2014), "A higher order shear deformation theory for static and free vibration of FGM beam", Steel Compos. Struct., Int. J., 16(5), 507-519. https://doi.org/10.12989/scs.2014.16.5.507
  18. Halpin, J.C. and Kardos, J.L. (1976), "The Halpin-Tsai equations: A review", Polym. Eng. Sci., 16(5), 344-352. https://doi.org/10.1002/pen.760160512
  19. Hamed, E., Bradford, M.A. and Gilbert, R.I. (2010), "Nonlinear long-term behaviour of spherical shallow thin-walled concrete shells of revolution", Int. J. Solid. Struct., 47(2), 204-215. https://doi.org/10.1016/j.ijsolstr.2009.09.027
  20. Hou, C., Yin, Y. and Wang, C. (2006), "Axisymmetric nonlinear stability of a shallow conical shell with a spherical cap of arbitrary variable shell thickness", J. Eng. Mech.-ASCE, 132(10), 1146-1149. https://doi.org/10.1061/(ASCE)0733-9399(2006)132:10(1146)
  21. Huang, N.C. (1964), "Unsymmetrical buckling of thin shallow spherical shells", J. Appl. Mech.-T. ASME, 31(3), 447-457. https://doi.org/10.1115/1.3629662
  22. Huang, T. (2002), "A concept of deep water axisymmetric shell storage container equatorially anchored", Proceedings of the 12th International Offshore and Polar Engineering Conference, Kitakyushu, Japan, May.
  23. Jiammeepreecha, W., Chucheepsakul, S. and Huang, T. (2012), "Nonlinear static analysis of deep water axisymmetric half drop shell storage container with constrained volume", Proceedings of the 22nd International Offshore and Polar Engineering Conference, Rhodes, Greece, June.
  24. Jianping, P. and Harik, I.E. (1992), "Axisymmetric general shells and jointed shells of revolution", J. Struct. Eng.-ASCE, 118(11), 3186-3202. https://doi.org/10.1061/(ASCE)0733-9445(1992)118:11(3186)
  25. Jordan, J., Jacop, K.I., Tannenbaum, R., Sharaf, M.A. and Jasiuk, I. (2005), "Experimental trends in polymer nanocomposites-A review", Mater. Sci. Eng. A-Struct., 393(1-2), 1-11. https://doi.org/10.1016/j.msea.2004.09.044
  26. Kaci, A., Tounsi, A., Bakhti, K. and Bedia, E.A.A. (2012), "Nonlinear cylindrical bending of functionally graded carbon nanotube-reinforced composite plates", Steel Compos. Struct., Int. J., 12(6), 491-504. https://doi.org/10.12989/scs.2012.12.6.491
  27. Kar, V.R. and Panda, S.K. (2015), "Nonlinear flexural vibration of shear deformable functionally graded spherical shell panel", Steel Compos. Struct., Int. J., 18(3), 693-709. https://doi.org/10.12989/scs.2015.18.3.693
  28. Koh-I-Noor (2010), Safety data sheets of graphite, Czech Republic.
  29. Lay, K.S. (1993), "Seismic coupled modeling of axisymmetric tanks containing liquid", J. Eng. Mech.-ASCE, 119(9), 1747-1761. https://doi.org/10.1061/(ASCE)0733-9399(1993)119:9(1747)
  30. Li, R.K.Y., Liang, J.Z. and Tjong, S.C. (1998), "Morphology and dynamic mechanical properties of glass beads filled low density polyethylene composite", J. Mater. Process. Tech., 79(1-3), 59-65. https://doi.org/10.1016/S0924-0136(97)00319-1
  31. Li, S., Wang, Z., Wu, G., Zhao, L. and Li, X. (2014), "Dynamic response of sandwich spherical shell with graded metallic foam cores subjected to blast loading", Compos. Part A-Appl. S., 56, 262-271. https://doi.org/10.1016/j.compositesa.2013.10.019
  32. Liang, J.Z., Li, R.K.Y. and Tjong, S.C. (1998), "Morphology and tensile properties of glass bead filled low density polyethylene composites: material properties", Polym. Test., 16(6), 529-548. https://doi.org/10.1016/S0142-9418(97)00017-2
  33. Librescu, L. and Maalawi, K.Y. (2007), "Material grading for improved aeroelastic stability in composite wings", J. Mech. Mater. Struct., 2(7), 101-114.
  34. Maalawi, K.Y. (2011), "Use of material grading for enhanced buckling design of thin-walled composite rings/long cylinders under external pressure", Compos. Struct., 93(2), 351-359. https://doi.org/10.1016/j.compstruct.2010.09.007
  35. Marcinowski, J. (2007), "Stability of relatively deep segments of spherical shells loaded by external pressure", Thin. Wall. Struct., 45(10-11), 906-910. https://doi.org/10.1016/j.tws.2007.08.034
  36. McGarry, F.J. (1994), "Polymer composites", Annu. Rev. Mater. Sci., 24, 63-82. https://doi.org/10.1146/annurev.ms.24.080194.000431
  37. Muc, A. (1992), "Buckling and postbuckling behaviour of laminated shallow spherical shells subjected to external pressure", Int. J. Nonlinear Mech., 27(3), 465-476. https://doi.org/10.1016/0020-7462(92)90013-W
  38. Najafov, A.M., Sofiyev, A.H., Hui, D., Karaca, Z., Kalpakci, V. and Ozcelik, M. (2014), "Stability of EG cylindrical shells with shear stresses on a Pasternak foundation", Steel Compos. Struct., Int. J., 17(4), 453-470. https://doi.org/10.12989/scs.2014.17.4.453
  39. Nielsen, L.E. and Landel, R.F. (1994), Mechanical Properties of Polymers and Composites, Marcel Dekker, New York, NY, USA.
  40. Niezgodzinski, T. and Swiniarski, J. (2010), "Numerical calculations of stability of spherical shells", Mech. Mech. Eng., 12(2), 325-337.
  41. Ochelski, S. and Gotowicki, P. (2009), "Experimental assessment of energy absorption capability or carbonepoxy and glass-epoxy composite", Compos. Struct., 87(3), 215-224. https://doi.org/10.1016/j.compstruct.2008.01.010
  42. Ohga, M., Wijenayaka, A.S. and Croll, J.G.A. (2005), "Buckling of sandwich cylindrical shells under axial loading", Steel Compos. Struct., Int. J., 5(1), 1-15. https://doi.org/10.12989/scs.2005.5.1.001
  43. Paul, B. (1960), "Prediction of elastic constants of multiphase materials", T. Metall. Soc. AIME, 218, 36-41.
  44. Prakash, T., Sundararajan, N. and Ganapathi, M. (2007), "On the nonlinear axisymmetric dynamic buckling behaviour of clamped functionally graded spherical caps", J. Sound. Vib., 299(1-2), 36-43. https://doi.org/10.1016/j.jsv.2006.06.060
  45. Shen, H.S. (2009), "Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments", Compos. Struct., 91(1), 9-19. https://doi.org/10.1016/j.compstruct.2009.04.026
  46. Simitses, G.J. (1996), "Buckling of moderately thick laminated cylindrical shells: A review", Compos. Part B-Eng, 27(6), 581-587. https://doi.org/10.1016/1359-8368(95)00013-5
  47. Sridharan, S. and Kasagi, A. (1997), "On the buckling and collapse of moderately thick composite cylinders under hydrostatic pressure", Compos. Part B-Eng, 28(5-6), 583-596. https://doi.org/10.1016/S1359-8368(96)00072-8
  48. Stabik, J., Suchon, L., Rojek, M. and Szczepanik, M. (2009), "Investigation of processing properties of polyamide filled with hard coal", J. Achieve. Mater. Manuf. Eng., 33(2), 142-149.
  49. Stabik, J., Dybowska, A. and Chomiak, M. (2010a), "Polymer composites filled with powders as polymer graded materials", J. Achieve. Mater. Manuf. Eng., 43(1), 153-161.
  50. Stabik, J., Szczepanik, M., Dybowska, A. and Suchon, L. (2010b), "Electrical properties of polymeric gradient materials based on epoxy resin filled with hard coal", J. Achieve. Mater Manuf. Eng., 38(1), 56-53.
  51. Stabik, J., Dybowska, A., Pluszynski, J., Szczepanik, M. and Suchon, L. (2010c), "Magnetic induction of polymer composites filled with ferrite powders", Arch. Mater. Sci. Eng., 41(1), 13-20.
  52. Stabik, J., Chomiak, M., Dybowska, A., Suchon, L. and Mrowiec, K. (2012), "Chosen manufacture methods of polymeric graded materials with electrical and magnetic properties gradation", J. Achieve. Mater Manuf. Eng., 54(2), 218-226.
  53. Stabik, J. and Chomiak, M. (2013), "Wear resistance of epoxy-hard coal composites", Arch. Mater. Sci. Eng., 64(2), 168-174.
  54. Szczepanik, M., Stabik, J., Łazarczyk, M. and Dybowska, A. (2009), "Influence of graphite on electrical properties of polymeric composites", Arch. Mater. Sci. Eng., 37(1), 37-44.
  55. Tillman, S.C. (1970), "On the buckling behaviour of shallow spherical caps under a uniform pressure load", Int. J. Solid. Struct., 6(1), 37-52. https://doi.org/10.1016/0020-7683(70)90080-6
  56. Tucher III, C.L. and Liang, E. (1999), "Stiffness predictions for unidirectional short-fiber composites: review and evaluation", Compos. Sci. Technol., 59(5), 655-671. https://doi.org/10.1016/S0266-3538(98)00120-1
  57. Uslu, M. (2010), "Polymeric matrix composite materials reinforced by graphite", M.Sc. Thesis (Erasmus Student); Silesian University of Technology, Poland.
  58. Uslu, M. and Kremzer, M. (2011), "Characteristics of graphite distributions in polymeric functionally gradient materials FGMs manufactured by the centrifugal casting method", Int. J. Art. Sci., 4(2), 1-9.
  59. Vo, K.K., Wang, C.M. and Chai, Y.H. (2006), "Membrane analysis and optimization of submerged domes with allowance for selfweight and skin cover load", Arch. Appl. Mech., 75(4), 235-247. https://doi.org/10.1007/s00419-005-0404-7
  60. Wang, C.M., Vo, K.K. and Chai, Y.H. (2006), "Membrane analysis and minimum weight design of submerged spherical domes", J. Struct. Eng.-ASCE, 132(2), 253-259. https://doi.org/10.1061/(ASCE)0733-9445(2006)132:2(253)
  61. Wu, C.P., Chen, Y.C. and Peng, S.T. (2013), "Buckling analysis of functionally graded material circular hollow cylinders under combined axial compression and external pressure", Thin-Wall. Struct., 69, 54-56. https://doi.org/10.1016/j.tws.2013.04.002
  62. Xu, C.S. (1991), "Buckling and post-buckling of symmetrically laminated moderately thick spherical caps", Int. J. Solid. Struct., 28(9), 1171-1184. https://doi.org/10.1016/0020-7683(91)90110-2
  63. Yas, M.H. and Garmsiri, K. (2010), "Three-dimensional free vibration analysis of cylindrical shells with continuous grading reinforcement", Steel Compos. Struct., Int. J., 10(4), 349-360.
  64. Yeh, H.L., Huang, T. and Schachar, R.A. (2000), "A closed shell structured eyeball model with application to radial keratotomy", J. Biomech. Eng.-T. ASME, 122(5), 504-510. https://doi.org/10.1115/1.1289626
  65. Zoelly, R. (1915), "Uber ein Knickungsproblem an der Kugelschalle", Ph.D. Dissertation; Zurich, Switzerland.

피인용 문헌

  1. Delamination of Multilayered Functionally Graded Beams with Material Nonlinearity 2017, https://doi.org/10.1142/S0219455418500517
  2. Non-linear delamination in two-dimensional functionally graded multilayered beam vol.9, pp.5, 2018, https://doi.org/10.1108/IJSI-12-2017-0079
  3. Nonlinear Delamination Analysis of Mulyilayered Functionally Graded Circular Shafts in Torsion vol.59, pp.6, 2018, https://doi.org/10.1134/S0021894418060160
  4. Lengthwise Cracks in Functionally Graded Beams Exhibiting Non-Linear Mechanical Behaviour of the Material vol.473, pp.1757-899X, 2019, https://doi.org/10.1088/1757-899X/473/1/012001
  5. Non-linear study of mode II delamination fracture in functionally graded beams vol.23, pp.3, 2016, https://doi.org/10.12989/scs.2017.23.3.263
  6. Elastic-plastic delamination of multilayered graded four-point bending beam vol.15, pp.1, 2016, https://doi.org/10.1108/wje-01-2017-0015
  7. Three dimensional dynamic response of functionally graded nanoplates under a moving load vol.66, pp.2, 2016, https://doi.org/10.12989/sem.2018.66.2.249
  8. Geometrically nonlinear analysis of FG doubly-curved and hyperbolical shells via laminated by new element vol.28, pp.3, 2016, https://doi.org/10.12989/scs.2018.28.3.389
  9. Deflection of axially functionally graded rectangular plates by Green's function method vol.30, pp.1, 2019, https://doi.org/10.12989/scs.2019.30.1.057
  10. Geometrically nonlinear meshfree analysis of 3D-shell structures based on the double directors shell theory with finite rotations vol.31, pp.4, 2016, https://doi.org/10.12989/scs.2019.31.4.397
  11. Inhomogeneous Beams with Different Behaviour in Tension and Compression: A Longitudinal Crack Study vol.60, pp.5, 2019, https://doi.org/10.1134/s0021894419050146
  12. Investigation of two parallel lengthwise cracks in an inhomogeneous beam of varying thickness vol.9, pp.4, 2016, https://doi.org/10.12989/csm.2020.9.4.381
  13. Delamination of multilayered non-linear elastic shafts in torsion vol.48, pp.3, 2020, https://doi.org/10.5937/fme2003681r
  14. Higher-order semi-layerwise models for doubly curved delaminated composite shells vol.91, pp.1, 2021, https://doi.org/10.1007/s00419-020-01755-7
  15. Viscoelastic inhomogeneous beam under time-dependent strains: A longitudinal crack analysis vol.6, pp.2, 2021, https://doi.org/10.12989/acd.2021.6.2.153
  16. Nonlinear buckling analysis of FGP shallow spherical shells under thermomechanical condition vol.40, pp.4, 2016, https://doi.org/10.12989/scs.2021.40.4.555
  17. Energy Dissipation in Viscoelastic Multilayered Inhomogeneous Beam Structures: An Analytical Study vol.1046, pp.None, 2016, https://doi.org/10.4028/www.scientific.net/msf.1046.39
  18. On the Analysis of Damping in Elastic-plastic Inhomogeneous Beams vol.1046, pp.None, 2021, https://doi.org/10.4028/www.scientific.net/msf.1046.59