Structural Engineering and Mechanics

  • 제78권6호
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  • Pages.765-775
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  • 2021
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Doubly curved shell vibration using coupled finite element method

  • Chorfi, S.M. (Department of Mechanical Engineering, Faculty of Engineering, University of Tlemcen) ;
  • Houmat, A. (Department of Mechanical Engineering, Faculty of Engineering, University of Tlemcen)
  • 투고 : 2020.12.12
  • 심사 : 2021.04.28
  • 발행 : 2021.06.25
⟨ 이전 논문 다음 논문 ⟩

초록

In this study, we present an efficient coupled method for the doubly curved shell vibration modeling. The proposed model is based on the coupling of the hierarchical p-finite element method and the standard h-finite element method. The helements define the curved boundaries of the shell while the p-elements describe the interior domain. The connectivity between the two discretized domains is assured by the least square method. In comparison to conventional models, the coupled model captures accurately the shell curvilinear boundary with high computational efficiency and small number of elements. The proposed model is validated against both analytical solution and numerical simulation. Doubly curved shell structures with different cutouts are presented to show the robustness, applicability and computational convenience of the proposed coupled approach for complex shell geometries.

키워드

과제정보

The authors express their gratitude to the National Agency for Development of Research at Universities (ANDRU) of Algeria for the financial support received in the course of this study.

참고문헌

  1. Al-Furjan, M.S.H., Habibi, M., Jung, D.W., Sadeghi, S., Safarpour, H., Tounsi, A. and Chen, G. (2020a), "A computational framework for propagated waves in a sandwich doubly curved nanocomposite panel", Eng. Comput., 1-18. https://doi.org/10.1007/s00366-020-01130-8.
  2. Al-Furjan, M.S.H., Safarpour, H., Habibi, M., Safarpour, M. and Tounsi, A. (2020b), "A comprehensive computational approach for nonlinear thermal instability of the electrically FG-GPLRC disk based on GDQ method", Eng. Comput., 1-18. https://doi.org/10.1007/s00366-020-01088-7.
  3. Allam, O., Draiche, K., Bousahla, A.A., Bourada, F., Tounsi, A., Benrahou, K.H., Mahmoud, S.R., Adda Bedia, E.A. and Tounsi, A. (2020), "A generalized 4-unknown refined theory for bending and free vibration analysis of laminated composite and sandwich plates and shells", Comput. Concrete, 26(2), 185-201. http://doi.org/10.12989/cac.2020.26.2.185.
  4. Bicos, A.S. and Springer, G.S. (1989a), "Analysis of free damped vibration of laminated composite plates and shells", Int. J. Solid. Struct., 25, 129-149. https://doi.org/10.1016/0020-7683(89)90003-6.
  5. Bicos, A.S. and Springer, G.S. (1989b), "Vibrational characteristics of composite panels with cutouts", AIAA J., 27, 1116-1122. https://doi.org/10.2514/3.10230.
  6. Boyd, D.E. and Brugh, R.L. (1977), "Vibrations of stiffened cylinders with cutouts", J. Sound Vib., 52(1), 65-78. https://doi.org/10.1016/0022-460X(77)90389-3.
  7. Brogan, F., Forsberg, K. and Smith, S. (1969), "Dynamic behaviour of a cylinder with a cutout", Am. Inst. Aeronaut. Astronaut. J., 7, 903-911. https://doi.org/10.2514/3.5243.
  8. Chorfi, S.M. and Houmat, A. (2010), "Nonlinear free vibration of functionally graded doubly curved shallow shell of elliptical plan-form", Compos. Struct., 92, 2573-2581. https://doi.org/10.1016/j.compstruct.2010.02.001.
  9. Chorfi, S.M. and Houmat, A. (2009), "Nonlinear free vibration of moderately thick doubly curved shallow shell of elliptical planform", Int. J. Comput. Meth., 6(4), 615-632. https://doi.org/10.1142/S0219876209002030.
  10. Hota, S.S. and Chakravorty, D. (2007), "Free vibration of stiffened conoidal shell roofs with cutouts", J. Vib. Control, 13(3), 221-240. https://doi.org/10.1177%2F1077546307072353. https://doi.org/10.1177%2F1077546307072353
  11. Houmat, A. (2008), "Mapped infinite p-element for two-dimensional problems of unbounded domains", Comput. Geotech., 35(4), 608-615. https://doi.org/10.1016/j.compgeo.2007.09.007.
  12. Houmat, A. and Rashid, M.M. (2012), "Coupling of h and p finite elements: Application to free vibration analysis of plates with curvilinear plan-forms", Appl. Math. Model., 36(2), 505-520. https://doi.org/10.1016/j.apm.2011.07.048.
  13. Khadimallah, M.A., Hussain, M., Khedher, K.M., Naeem, M.N. and Tounsi, A. (2020), "Backward and forward rotating of FG ring support cylindrical shells", Steel Compos. Struct., 37(2), 137-150. http://doi.org/10.12989/scs.2020.37.2.137.
  14. Kurpa, L., Timchenko, G., Osetrov, A. and Shmatko, T. (2017), "Nonlinear vibration analysis of laminated shallow shells with clamped cutouts by the R-functions method", Nonlin. Dyn., 93, 133-147. https://doi.org/10.1007/s11071-017-3930-2.
  15. Lee, S.Y. and Chung, D.S. (2010), "Finite element delamination model for vibrating composite spherical shell panels with central cutouts", Finite Elem. Anal. Des., 46, 247-256. https://doi.org/10.1016/j.finel.2009.09.007.
  16. Liew, K.M. and Lim, C.W. (1994) "vibration of perforated doubly-curved shallow shells with rounded corners", Int. J. Solid. Struct., 31(11), 1519-1536. https://doi.org/10.1016/0020-7683(94)90012-4.
  17. Liew, K.M. and Lim, C.W. (1995), "A Ritz vibration analysis of doubly-curved rectangular shallow shells using a refined first-order theory", Comput. Meth. Appl. Mech. Eng., 127, 145-162. https://doi.org/10.1016/0045-7825(95)00837-1.
  18. Malinin, A.A. (1971), "Kolebaniia obolochek vrashcheniia Otverstiiami (Vibrations of shells of revolution with holes)", Mashinostroenie, 7, 22-27. (in Russian)
  19. Mallek, H., Jrad, H., Wali, M. and Dammak, F. (2021), "Nonlinear dynamic analysis of piezoelectric-bonded FG-CNTR composite structures using an improved FSDT theory", Eng. Comput., 37, 1389-1407. https://doi.org/10.1007/s00366-019-00891-1.
  20. Mallek, H., Jrad, H., Wali, M., Kessentini, A., Gamaoun, F. and Dammak, F. (2019), "Dynamic analysis of functionally graded carbon nanotube-reinforced shell structures with piezoelectric layers under dynamic loads", J. Vib. Control, 26(13-14), 1157-1172. https://doi.org/10.1177/1077546319892753.
  21. Mellouli, H., Jrad, H., Wali, M. and Dammak, F. (2020), "Free vibration analysis of FG-CNTRC shell structures using the meshfree radial point interpolation method", Comput. Math. Appl., 79(11), 3160-3178. https://doi.org/10.1016/j.camwa.2020.01.015.
  22. Nanda, N. and Bandyopadhyay, J.N. (2007), "Nonlinear free vibration analysis of laminated composite cylindrical shells with cutout", J. Reinf. Plast. Compos., 26(14), 1413-1427. https://doi.org/10.1177%2F0731684407079776. https://doi.org/10.1177%2F0731684407079776
  23. Nanda, N. and Bandyopadhyay, J.N. (2008), "Large amplitude free vibration of laminated composite shells with cutout", Aircraft Eng. Aerosp. Technol., 80(2), 165-174. https://doi.org/10.1108/00022660810859382.
  24. Patel, S.N., Datta, P.K. and Sheikh, A.H. (2009), "Dynamic stability analysis of stiffened shell panels with cutouts", J. Appl. Mech., 76(4), 041004-1. https://doi.org/10.1115/1.3086595.
  25. Poore, A.L., Barut, A. and Madenci, E. (2008), "Free vibration of laminated cylindrical shells with a circular cutout", J. Sound Vib., 312, 55-73. https://doi.org/10.1016/j.jsv.2007.10.025.
  26. Ravi Kumar, L., Datta P.K. and Prabhakara, D.L. (2004), "Tension buckling and parametric instability characteristics of doubly curved panels with circular cutout subjected to nonuniform tensile edge loading", Thin Wall. Struct., 42, 947-962. https://doi.org/10.1016/j.tws.2004.03.009.
  27. Reddy, J.N. (1984), "Exact solution of moderately thick laminated shells", Tran. ASME J. Appl. Mech., 110(5), 794. https://doi.org/10.1061/(ASCE)0733-9399(1984)110:5(794).
  28. Sahoo, S. (2014), "Laminated composite stiffened shallow spherical panels with cutouts under free vibration-A finite element approach", Eng. Sci. Technol., 17, 247-259. https://doi.org/10.1016/j.jestch.2014.07.002.
  29. Sahu, S.K. and Datta, P.K. (2002), "Dynamic stability of curved panels with cutouts", J. Sound Vib., 251(4), 683-696. https://doi.org/10.1006/jsvi.2001.3961.
  30. Sai Ram, K.S. and Sreedhar Babu, T. (2002), "Free vibration of composite spherical shell cap with and without a cutout", Comput. Struct., 80, 1749-1756. https://doi.org/10.1016/S0045- 7949(02)00210-9.
  31. Seregin, S.V. (2015), "Free vibrations of a thin circular cylindrical shell weakened by a hole", Russian Aeronautics (Iz.VUZ), 58(3), 258-262. https://doi.org/10.3103/S1068799815030022.
  32. Shopa, T.V. (2010), "Investigation of frequencies of natural vibrations of a transversally isotropic cylindrical panel with a circular hole", J. Math. Sci., 170(6), 721-733. https://doi.org/10.1007/s10958-010-0116-6.
  33. Sivasubramonian, B., Kulkarni A.M., Venkateswara Rao, G. and Krishnan, A. (1997), "Free vibration of curved panels with cutouts", J. Sound Vib., 200(2), 227-234. https://doi.org/10.1006/jsvi.1996.0637.
  34. Sivasubramonian, B., Venkateswara Rao, G. and Krishnan, A. (1999), "Free vibration of longitudinally stiffened curved panels with cutout", J. Sound Vib., 226(1), 41-55. https://doi.org/10.1006/jsvi.1999.2281.
  35. Sokolnikoff, I.S. (1956), Mathematical Theory of Elasticity, McGraw-Hill, New York.
  36. Srivastava, A.K.L., Datta, P.K. and Sheikh, A.H. (2003), "Dynamic instability of stiffened plates with cutout subjected to in-plane uniform edge loadings", Int. J. Struct. Stab. Dyn., 3(3), 391-403. https://doi.org/10.1142/S0219455403000963.
  37. Sun, F., Wang, P., Li, W., Fan, H. and Fang, D. (2017), "Effects of circular cutouts on mechanical behaviors of carbon fiber reinforced lattice-core sandwich cylinder", Compos. Part A: Appl. Sci. Manuf., 100, 313-323. http://doi.org/10.1016/j.compositesa.2017.05.029.
  38. Toda, S. and Komatsu, K. (1997), "Vibrations of circular cylindrical shells with cutouts", J. Sound Vib., 52(4), 497-510. https://doi.org/10.1016/0022-460X(77)90366-2.
  39. Wang, D.Y. and Foster, Jr. W.A. (1992), "Analysis of axisymmetric free vibration of isotropic shallow spherical shells with a circular hole", J. Sound Vib., 157(2), 331-343. https://doi.org/10.1016/0022-460X(92)90685-Q.
  40. Wang, D.Y. and Foster, Jr. W.A. (1993), "On axisymmetric vibration of shallow spherical shells with fixed circular cutout", Appl. Math. Comput., 57, 205-220. https://doi.org/10.1016/0096-3003(93)90147-7.
  41. Xu, C. and Chia, C.Y. (1995), "Non-linear vibration and buckling analysis of laminated shallow spherical shells with holes", Compos. Sci. Technol., 54, 67-74. https://doi.org/10.1016/0266-3538(95)00038-0.