Structural Engineering and Mechanics

  • 제63권2호
  • /
  • Pages.225-235
  • /
  • 2017
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Dynamic behaviour of orthotropic elliptic paraboloid shells with openings

  • Darilmaz, Kutlu (Department of Civil Engineering, Istanbul Technical University)
  • 투고 : 2016.08.11
  • 심사 : 2017.02.10
  • 발행 : 2017.07.25
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper a vibration study on orthotropic elliptic paraboloid shells with openings is carried out by using a hybrid stress finite element. The formulation of the element is based on Hellinger-Reissner variational principle. The element is developed by combining a hybrid plane stress element and a hybrid plate element. Natural frequencies of orthotropic elliptic paraboloid shells with and without openings are presented. The influence of aspect ratio, height ratio, opening ratio and material angle on the frequencies and mode shapes are investigated.

키워드

참고문헌

  1. Aass, A. (1963), "A contribution to the bending theory of elliptic paraboloid shells", IABSE, 23.
  2. Allman, D.J. (1984), "A compatible triangular element including vertex rotations for plane elasticity problems", Comput. Struct., 19, 1-8. https://doi.org/10.1016/0045-7949(84)90197-4
  3. Bergan, P.G. and Felippa, C.A. (1985), "A triangular membrane element with rotational degrees of freedom", Comput. Meth. Appl. Mech. Eng., 50, 25-69. https://doi.org/10.1016/0045-7825(85)90113-6
  4. Choi, C.K. and Lee, W.H. (1996), "Versatile variable-node flatshell element", J. Eng. Mech., 122(5), 432-441. https://doi.org/10.1061/(ASCE)0733-9399(1996)122:5(432)
  5. Chun, K.S., Kassegne, S.K. and Wondimu, B.K. (2009), "Hybrid/mixed assumed stress element for anisotropic laminated elliptical and parabolic shells", Finite Elem. Anal. Des., 45(11), 766-781. https://doi.org/10.1016/j.finel.2009.06.004
  6. Cook, R.D. (1986), "On the Allman triangle and a related quadrilateral element", Comput. Struct., 22, 1065-1067. https://doi.org/10.1016/0045-7949(86)90167-7
  7. Cook, R.D., Malkus D.S. and Plesha, M.E. (2001), Concepts and Applications of Finite Element Analysis, 4th Edition, Wiley.
  8. Chernobryvko, M.V., Avramov, K.V., Romanenko, V.N., Batutina, T.J. and Tonkonogenko, A.M. (2014), "Free linear vibrations of thin axisymmetric parabolic shells", Meccanica, 49(12), 2839-2845. https://doi.org/10.1007/s11012-014-0027-6
  9. Darilmaz, K. (2005), "An assumed-stress finite element for static and free vibration analysis of Reissner-Mindlin plates", Struct. Eng. Mech., 19(2), 199-215. https://doi.org/10.12989/sem.2005.19.2.199
  10. Darilmaz, K. and Kumbasar, N. (2006), "An 8-node assumed stress hybrid element for analysis of shells", Comput. Struct., 84, 1990-2000. https://doi.org/10.1016/j.compstruc.2006.08.003
  11. Darilmaz, K. (2007), "An assumed-stress hybrid element for static and free vibration analysis of folded plates", Struct. Eng. Mech., 25(4), 405-421. https://doi.org/10.12989/sem.2007.25.4.405
  12. Darilmaz, K. (2012), "Stiffened orthotropic corner supported hypar shells: Effect of stiffener location, rise/span ratio and fiber orientaton on vibration behavior", Steel Compos. Struct., 12(4), 275-289. https://doi.org/10.12989/scs.2012.12.4.275
  13. Darilmaz, K. (2017), "Static and free vibration behaviour of orthotropic elliptic paraboloid shells", Steel Compos. Struct., 23(6), 737-746. https://doi.org/10.12989/SCS.2017.23.6.737
  14. Feng, W., Hoa, S.V. and Huang, Q. (1997), "Classification of stress modes in assumed stress fields of hybrid finite elements", Int. J. Num. Meth. Eng., 40(23), 4313-4339. https://doi.org/10.1002/(SICI)1097-0207(19971215)40:23<4313::AID-NME259>3.0.CO;2-N
  15. Ghazijahani, T.G., Jiao, H. and Holloway, D. (2014), "Influence of a cutout on circular steel hollow sections under cyclic loading", J. Constr. Steel Res., 100, 12-20. https://doi.org/10.1016/j.jcsr.2014.04.015
  16. Ghazijahani, T.G., Jiao, H. and Holloway, D. (2015), "Structural behavior of shells with different cutouts under compression: An experimental study", J. Constr. Steel Res., 105, 129-137. https://doi.org/10.1016/j.jcsr.2014.10.020
  17. Ibrahimbegovic, A., Taylor, R.L. and Wilson, E.L. (1990), "A robust quadrilateral membrane finite element with drilling degrees of freedom", Int. J. Numer. Meth. Eng., 30(3), 445-457. https://doi.org/10.1002/nme.1620300305
  18. Javed, S., Viswanathan, K.K., Aziz, Z.A. and Lee, J.H. (2016), "Vibration analysis of a shear deformed anti-symmetric angleply conical shells with varying sinusoidal thickness", Struct. Eng. Mech., 58(6), 1001-1020. https://doi.org/10.12989/sem.2016.58.6.1001
  19. Jullien, J.F. and Limam, A. (1998), "Effects of openings of the buckling of cylindrical shells subjected to axial compression", Thin Wall. Struct., 31, 187-202 https://doi.org/10.1016/S0263-8231(98)00003-2
  20. Kang, J.H. (2014), "Free vibrations of combined hemisphericalcylindrical shells of revolution with a top opening", Int. J. Struct. Stab. Dyn., 14(1), 1350023. https://doi.org/10.1142/S0219455413500235
  21. Kang, J.H. (2015), "Vibration analysis of shallow or deep, complete parabolic shells with variable thickness", KSCE J. Civil Eng., 19(7), 2172-2178. https://doi.org/10.1007/s12205-015-1397-6
  22. MacNeal, R.H. and Harder, R.L. (1988), "A refined four-noded membrane element with rotational degrees of freedom", Comput. Struct., 28, 75-84. https://doi.org/10.1016/0045-7949(88)90094-6
  23. Mohraz, B. and Schnobrich, W.C. (1966), "The analysis of shallow shell structures by a discrete element system", Civil Engineering Studies, Structural Research Series No: 304.
  24. Nicholas, P.E., Padmanaban, K.P. and Vasudevan, D. (2014), "Buckling optimization of laminated composite plate with elliptical cutout using ANN and GA", Struct. Eng. Mech., 52(4), 815-827. https://doi.org/10.12989/sem.2014.52.4.815
  25. Pian, T.H.H. (1964), "Derivation of element stiffness matrices by assumed stress distributions", AIAA J., 12, 1333-1336.
  26. Pian, T.H.H. and Chen, D.P. (1983), "On the suppression of zero energy deformation modes", Int. J. Numer. Meth. Eng., 19, 1741-1752. https://doi.org/10.1002/nme.1620191202
  27. Punch, E.F. and Atluri, S.N. (1984), "Development and testing of stable, isoparametric curvilinear 2 and 3-D hybrid stress elements", Comput. Meth. Appl. Mech. Eng., 47, 331-356. https://doi.org/10.1016/0045-7825(84)90083-5
  28. Shariati, M. and Rokhi, MM, (2010), "Buckling of steel cylindrical shells with an elliptical cutout", Int. J. Steel Struct., 10(2), 193-205. https://doi.org/10.1007/BF03215830
  29. Rajanna, T., Banerjee, S., Desai, Y.M. and Prabhakara, D.L. (2016), "Vibration and buckling analyses of laminated panels with and without cutouts under compressive and tensile edge loads", Steel Compos. Struct., 21(1), 37-55. https://doi.org/10.12989/scs.2016.21.1.037
  30. Singh, S.B. and Kumar, D. (2010), "Cutout shape and size effects on response of quasi-isotropic composite laminate under uniaxial compression", Struct. Eng. Mech., 35(3), 335-348. https://doi.org/10.12989/sem.2010.35.3.335
  31. Torabi, H. and Shariati, M. (2014), "Buckling analysis of steel semi-spherical shells with square cutout under axial compression", Streng. Mater., 46(4), 531-542. https://doi.org/10.1007/s11223-014-9579-x
  32. Xie, X., Zheng, H. and Jin, G. (2015), "Free vibration of fourparameter functionally graded spherical and parabolic shells of revolution with arbitrary boundary conditions", Compos. Part B: Eng., 77, 59-73. https://doi.org/10.1016/j.compositesb.2015.03.016
  33. Yunus, S.M., Saigal, S. and Cook, R.D. (1989), "On improved hybrid finite elements with rotational degrees of freedom", Int. J. Numer. Meth. Eng., 28(4), 785-800. https://doi.org/10.1002/nme.1620280405