Advertisement

Mechanics of Composite Materials

, Volume 55, Issue 4, pp 467–482 | Cite as

Nonlinear Buckling and Postbuckling of a FGM Toroidal Shell Segment Under a Torsional Load in a Thermal Environment Within Reddy’s Third-Order Shear Deformation Shell Theory

  • Pham Minh Vuong
  • Nguyen Dinh DucEmail author
Article
  • 14 Downloads

The nonlinear buckling and postbuckling of FGM toroidal shell segments surrounded by elastic foundations in a thermal environment and subjected to a torsional load are investigated by an analytical method. Based on Reddy’s third-order shear deformation shell theory (TSDT) with geometrical nonlinearity in the von Karman sense, the governing equations are derived. Using the Galerkin method and a stress function, closed-form expressions for determining the critical torsional load and postbuckling load–deflection curves are obtained. Effects of the geometrical shape, material properties, temperature field, and foundation parameters on the stability of the shells are examined in detail.

Keywords

nonlinear buckling and postbuckling FGM toroidal segment torsional load Reddy’s third-order shear deformation shell theory thermal environment 

Notes

Acknowledgements

This research was funded by the National University of Civil Engineering under Grant No. 216-2018 / KHXD. The authors are grateful for this support.

References

  1. 1.
    I. Sheinman and G. J. Simitses, “Buckling of imperfect stiffened cylinders under destabilizing loads including torsion,” AIAA J., 15, 1699-1703 (1977).CrossRefGoogle Scholar
  2. 2.
    G. J. Simitses, “Buckling of eccentrically stiffened cylinders under torsion,” AIAA J., 6, 1856-1860 (1967).CrossRefGoogle Scholar
  3. 3.
    N. Yamaki and K. Matsuda, “Post-buckling behavior of circular cylindrical shells under torsion,” Ingenieur-Archiv, 45, 79-89 (1975).CrossRefGoogle Scholar
  4. 4.
    D. Shaw and G.J. Simitses, “Instability of laminated cylinders in torsion,” J. Appl. Mech., 51, 188-191 (1984).CrossRefGoogle Scholar
  5. 5.
    A. H. Sofiyev and N. Kuruoglu, “Torsional vibration and buckling of the cylindrical shell with functionally graded coatings surrounded by an elastic medium,” Composites: Part B, 45, 1133-42 (2013).CrossRefGoogle Scholar
  6. 6.
    A. H. Sofiyev and E. Schnack, “The stability of functionally graded cylindrical shells under linearly increasing dynamic torsional loading,” Engineering Struct., 26, 1321-1331 (2004).CrossRefGoogle Scholar
  7. 7.
    H. S. Shen, “Boundary layer theory for the buckling and post-buckling of an anisotropic laminated cylindrical shell. Part III: Prediction under torsion,” Compos. Struct., 82, 371-381 (2008).CrossRefGoogle Scholar
  8. 8.
    X. Zhang and Q. Han, “Buckling and post-buckling behaviors of imperfect cylindrical shells subjected to torsion,” Thin-Walled Structures, 45, 1035-1043 (2007).CrossRefGoogle Scholar
  9. 9.
    D. S. Chehil and S. Cheng, “Elastic buckling of composite cylindrical shells under torsion,” J. Spacecraft and Rockets, 5, No. 8, 973-978 (1968).CrossRefGoogle Scholar
  10. 10.
    H. Huang and Q. Han, “Nonlinear buckling of torsion-loaded functionally graded cylindrical shells in thermal environment,” Europ. J. Mechanics-A/Solids, 29, 42-48 (2010).CrossRefGoogle Scholar
  11. 11.
    D. Tan, “Torsional buckling analysis of thin and thick shells of revolution,” Int. J. Solids and Struct., 37, 3055-3078 (2000).CrossRefGoogle Scholar
  12. 12.
    A. Tabiei and G. J. Simitses, “Buckling of moderately thick, laminated cylindrical shells under torsion,” AIAA J., 32, No. 3, 639-647 (1994).CrossRefGoogle Scholar
  13. 13.
    H. S. Shen, “Torsional post-buckling of nanotube-reinforced composite cylindrical shells in thermal environments,” Compos. Struct., 116, 477-488 (2014).CrossRefGoogle Scholar
  14. 14.
    N. D. Duc and H. V. Tung, “Mechanical and thermal postbuckling of shear-deformable FGM plates with temperature-dependent properties,” Mech. Compos. Mater., 46, No. 5, 461-476 (2010).CrossRefGoogle Scholar
  15. 15.
    Y. Kiani, “Thermal post-buckling of temperature dependent sandwich plates with FG-CNTRC face sheets,” J. Thermal Stresses, 41, No. 7, 866 - 882 (2018).CrossRefGoogle Scholar
  16. 16.
    S. S. Akavci, “Thermal buckling analysis of functionally graded plates on an elastic foundation according to a hyperbolic shear deformation theory,” Mech. Compos. Mater., 50, No. 22, 197-212 (2014).CrossRefGoogle Scholar
  17. 17.
    S. Benyoucef, I. Mechab, A. Tounsi, A. Fekrar, and H. Ait AtmaneEl Abbas Adda Bedia, “Bending of thick functionally graded plates resting on Winkler–Pasternak elastic foundations,” Mech. Compos. Mater., 46, No. 4, 425-434 (2010).CrossRefGoogle Scholar
  18. 18.
    S. Xiang, J. Wang, Y. T. Ai, and G.-Ch. Li, “Buckling analysis of laminated composite plates by using various higher-order shear deformation theories,” Mech. Compos. Mater., 51, No. 5, 645-654 (2015).CrossRefGoogle Scholar
  19. 19.
    N. D. Khoa, H. T. Thiem, and N. D. Duc, “Nonlinear buckling and postbuckling of imperfect piezoelectric S-FGM circular cylindrical shells with metal-ceramic-metal layers in thermal environment using Reddy’s third-order shear deformation shell theory,” J. Mech. Adv. Mater. Struct., (2017).  https://doi.org/10.1080/15376494.2017.1341583 CrossRefGoogle Scholar
  20. 20.
    T. Q. Quan, T. Phuong, D. N. Tuan, and N. D. Duc, “Nonlinear dynamic analysis and vibration of shear deformable eccentrically stiffened S-FGM cylindrical panels with metal-ceramic-metal layers resting on elastic foundations,” Compos. Struct., 126, 16-33 (2015).CrossRefGoogle Scholar
  21. 21.
    V. T. T. Anh and N. D. Duc, “Nonlinear response of shear deformable S-FGM shallow spherical shell with ceramicmetal-ceramic layers resting on elastic foundation in thermal environment,” J. Mech. Adv. Mater. Struct., 23, No. 8, 926-934 (2016).CrossRefGoogle Scholar
  22. 22.
    A. H. Sofiyev, Z. Zerin, B. P. Allahverdiev, D. Hui, F. Turan, and H. Erdem, “The dynamic instability of FG orthotropic conical shells within the SDT,” Steel and Compos. Struct., 25, No. 5, 581-591 (2017).Google Scholar
  23. 23.
    M. Stein and J.A. McElman, “Buckling of segments of toroidal shells,” AIAA J., 3, 1704-1709 (1965).CrossRefGoogle Scholar
  24. 24.
    J. W. Hutchinson, “Initial post-buckling behavior of toroidal shell segments,” Int. J. Solids Struct., 3, 97-115 (1967).CrossRefGoogle Scholar
  25. 25.
    D. G. Ninh, D. H. Bich, and B. H. Kien, “Torsional buckling and post-buckling behavior of eccentrically stiffened functionally graded toroidal shell segments surrounded by an elastic medium,” Acta Mechanica, 226, 3501-3519 (2015).CrossRefGoogle Scholar
  26. 26.
    D. V. Dung, and P. M. Vuong, “Nonlinear analysis on dynamic buckling of eccentrically stiffened functionally graded material toroidal shell segment surrounded by elastic foundations in thermal environment and under time-dependent torsional loads,” Appl. Mathematics and Mechanics (English Edition), 37, No. 7, 835-860 (2016).CrossRefGoogle Scholar
  27. 27.
    D. V. Dung and P. M. Vuong, “Analytical investigation on buckling and post-buckling of FGM toroidal shell segment surrounded by elastic foundation in thermal environment and under external pressure using TSDT,” Acta Mechanica, 228, No. 10, 3511-3531 (2017).CrossRefGoogle Scholar
  28. 28.
    J. N. Reddy and C. F. Liu, “A Higher-order shear deformation theory of laminated elastic shells,” Int. J. Eng. Sci., 23, 319-330 (1985).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Faculty of Civil and IndustrialNational University of Civil EngineeringHanoiVietnam
  2. 2.VNU Hanoi – University of ScienceHanoiVietnam
  3. 3.Advanced Materials and Structures LaboratoryVNU Hanoi -University of Engineering and TechnologyHanoiVietnam
  4. 4.Department of Civil and Environmental EngineeringSejong UniversitySeoulSouth Korea
  5. 5.Infrastructure Engineering Program -VNU-HanoiVietnam-Japan University (VJU)HanoiVietnam

Personalised recommendations