Skip to main content
SpringerLink
Log in

Static Stability Analysis and Design Aids of Curved Panels Subjected to Linearly Varying In-Plane Loading

  • Original Contribution
  • Published:
Journal of The Institution of Engineers (India): Series A Aims and scope Submit manuscript

Abstract

This paper presents an extensive numerical investigation on the buckling characteristics of curved panels, such as cylindrical, spherical and hyperbolic panels, under linearly varying in-plane load with respect to various types of loading, curvature, aspect ratio, Poisson's ratio and boundary condition using the finite element method. Three types of linearly varying in-plane loads, i.e. triangular, rectangular and trapezoidal in-plane loads are considered. The aspect ratio of the curved panels varies from 0.5 to 3.0. Six boundary conditions commonly used in the construction are considered. The above parametric study reveals that the critical buckling loads of curved panels are greatly influenced by the various parameters considered in the present investigation. In addition, a comparative study is made to find the influences of the various in-plane loads, such as triangular, parabolic, patch and concentrated in-plane loads, on the critical buckling load of cylindrical, spherical and hyperbolic panels. Finally, typical design charts in non-dimensional forms are also developed to obtain the critical buckling loads of various commonly used clamped spherical panels in construction. These design charts will be immensely helpful for the designers to find out the critical buckling load for clamped spherical panels of any dimension, any type of linearly varying in-plane load and any isotropic material directly from the chart at the time of preliminary design without the use of any commercially available finite element software, which is very complex and time taking. This novelty for the preparation of designed charts for clamped spherical curved panel can also be applied to other curved panels and boundary conditions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21

Similar content being viewed by others

References

  1. S.P. Timoshenko, J.M. Gere, Theory of Elastic Stability, 2nd edn. (Mc Graw Hill Education, New York City, 1961).

    Google Scholar 

  2. M.Z. Khan, A.C. Walker, The struct. Engineer 50, 225 (1972)

    Google Scholar 

  3. R.E. Kielb, L.S. Han, J. Sound Vib. 70, 543 (1980)

    Article  Google Scholar 

  4. M.M. Kaldas, S.M. Dickinson, J. Sound Vib. 75, 151 (1981)

    Article  Google Scholar 

  5. G. Baker, M.N. Pavlovic, J. Appl. Mech. 49, 177 (1982)

    Article  Google Scholar 

  6. A.W. Leissa, E.F. Ayoub, J. Sound Vib. 127, 155 (1988)

    Article  Google Scholar 

  7. C.J. Brown, Comput. Struct. 33, 1325 (1989)

    Article  Google Scholar 

  8. C.J. Brown, Comput. Struct. 41, 151 (1991)

    Article  Google Scholar 

  9. S. Kitipornchai, Y. Xiang, C.M. Wang, K.M. Liew, Int. J. Numer. Methods Eng. 36, 1299 (1993)

    Article  Google Scholar 

  10. C.M. Wang, K.M. Liew, Y. Xiang, S. Kitipornchai, Int. J. Solids Struct. 30, 1 (1993)

    Article  Google Scholar 

  11. K.M. Liew, Y. Xiang, S. Kitipornchai, Int. J. Mech. Sci. 38, 1127 (1996)

    Article  Google Scholar 

  12. K.M. Liew, X.L. Chen, Int. J. Solids Struct. 41, 1677 (2004)

    Article  Google Scholar 

  13. X. Wang, C.W. Bert, A.G. Striz, Comput. Struct. 48, 473 (1993)

    Article  Google Scholar 

  14. M.A. Bradford, M. Azhari, Comput. Struct. 56, 75 (1995)

    Article  Google Scholar 

  15. D.L. Prabhakara, P.K. Datta, Thin-Walled Struct. 27, 287 (1997)

    Article  Google Scholar 

  16. J.H. Kang, A.W. Leissa, Int. J. Struct. Stab. Dyn. 1, 527 (2001)

    Article  Google Scholar 

  17. A.W. Leissa, J.H. Kang, Int. J. Mech. Sci. 44, 1925 (2002)

    Article  Google Scholar 

  18. J.H. Kang, A.W. Leissa, Int. J. Solids Struct. 42, 4022 (2005)

    Article  Google Scholar 

  19. X. Wang, L. Gan, Y. Wang, J. Sound Vib. 298, 420 (2006)

    Article  Google Scholar 

  20. H. Zhong, C. Gu, J. Eng. Mech. 132, 578 (2006)

    Google Scholar 

  21. M. Eisenberger, A. Alexandrov, Thin-Walled Struct. 41, 871 (2003)

    Article  Google Scholar 

  22. C.W. Bert, K.K. Devarakonda, Int. J. Solids Struct. 40, 4097 (2003)

    Article  Google Scholar 

  23. X. Wang, X. Wang, X. Shi, Thin-Walled Struct. 44, 837 (2006)

    Article  Google Scholar 

  24. P. Jana, K. Bhaskar, Thin-Walled Struct. 44, 507 (2006)

    Article  Google Scholar 

  25. G. Ikhenazen, M. Saidani, A. Chelghoum, J. Constr. Steel Research. 66, 1112 (2010)

    Article  Google Scholar 

  26. X. Wang, Z. Yuan, Appl. Math. Model. 56, 83 (2018)

    Article  MathSciNet  Google Scholar 

  27. B. Baharlou, A.W. Leissa, Int. J. Mech. Sci. 29, 545 (1987)

    Article  Google Scholar 

  28. D.J. Dawe, S. Wang, Int. J. Mech. Sci. 37, 645 (1995)

    Article  Google Scholar 

  29. G.B. Chai, K.T. Ooi, P.W. Khong, Comput. Struct. 46, 77 (1993)

    Article  Google Scholar 

  30. G.B. Chai, P.W. Khong, Compos. Struct. 24, 99 (1993)

    Article  Google Scholar 

  31. H. Zhong, C. Gu, Compos. Struct. 80, 42 (2007)

    Article  Google Scholar 

  32. Z. Ni, J. Yuan, B. Chen, Compos. Struct. 107, 528 (2014)

    Article  Google Scholar 

  33. P. Sundaresan, G. Singh, G.V. Rao, Int. J. Mech. 40, 1105 (1998)

    Article  Google Scholar 

  34. A. Chakrabarti, A.H. Sheikh, Int. J. Mech. Sci. 47, 418 (2005)

    Article  Google Scholar 

  35. I. Shufrin, O. Rabinovitch, M. Eisenberger, Compos. Struct. 82, 521 (2008)

    Article  Google Scholar 

  36. R. Daripa, M.K. Singha, Thin-Walled Struct. 47, 601 (2009)

    Article  Google Scholar 

  37. A.V. Lopatin, E.V. Morozov, Compos. Struct. 92, 1423 (2010)

    Article  Google Scholar 

  38. A.V. Lopatin, E.V. Morozov, Compos. Struct. 93, 1900 (2011)

    Article  Google Scholar 

  39. A.V. Lopatin, E.V. Morozov, Eur. J. Mech. A/Solids. 81, 103960 (2020)

    Article  MathSciNet  Google Scholar 

  40. F. Bourada, K. Amara, A. Tounsi, Steel Compos. Struct. 21, 1287 (2016)

    Article  Google Scholar 

  41. S.K. Panda, L.S. Ramachandra, Int. J. Mech. Sci. 52, 819 (2010)

    Article  Google Scholar 

  42. S. Yamada, K. Uchiyama, M. Yamada, Int. J. Non-Linear. Mech. 18, 37 (1983)

    Article  Google Scholar 

  43. C.A. Featherston, C. Ruiz, J. Mech. Eng. 212, 183 (1998)

    Google Scholar 

  44. H. Matsunaga, J. Eng. Mech. 125, 613 (1999)

    Google Scholar 

  45. M.W. Hilburger, V.O. Britt, M.P. Nemeth, Am. Inst. Aeronaut. Astronaut. 99, 780 (1999)

    Google Scholar 

  46. M.W. Hilburger, V.O. Britt, M.P. Nemeth, Int. J. Solids Struct. 38, 1495 (2001)

    Article  Google Scholar 

  47. H. Matsunaga, J. Sound Vib. 225, 41 (1999)

    Article  Google Scholar 

  48. P. Mandal, C.R. Calladine, Int. J. Solids Struct. 37, 4509 (2000)

    Article  Google Scholar 

  49. S.K. Sahu, P.K. Datta, J. Sound Vib. 240, 117 (2001)

    Article  Google Scholar 

  50. L. Ravi Kumar, P.K. Datta, D.L. Prabhakara, Int. J. Struct. Stab. Dyn. 2, 409 (2002)

    Article  Google Scholar 

  51. L. Ravi Kumar, P.K. Datta, D.L. Prabhakara, Thin-Walled Struct. 42, 947 (2004)

    Article  Google Scholar 

  52. A. Khelil, Thin-Walled Struct. 40, 955 (2002)

    Article  Google Scholar 

  53. B.L.O. Edlund, Struct. Control Heal. Monit. Off. J. Int. Assoc. Struct. Control Monit. Eur. Assoc. Control Struct. 14, 693 (2007)

    Google Scholar 

  54. H. Ullah, Int. J. Numer. Methods Eng. 79, 1332 (2009)

    Article  MathSciNet  Google Scholar 

  55. S.M. Jun, C.S. Hong, Comput. Struct. 29, 479 (1988)

    Article  Google Scholar 

  56. B. Geier, K. Rohwer, Int. J. Numer. Methods Eng. 27, 403 (1989)

    Article  Google Scholar 

  57. L. Tong, T.K. Wang, Compos. Sci. Technol. 47, 57 (1993)

    Article  Google Scholar 

  58. F. Shadmehri, S.V. Hoa, M. Hojjati, Compos. Struct. 94, 787 (2012)

    Article  Google Scholar 

  59. J.B. Greenberg, Y. Stavsky, Compos. struct. 30, 399 (1995)

    Article  Google Scholar 

  60. N. Jaunky, N.F. Knight, D.R. Ambur, Am. Inst. Aeronaut. Astronaut. 98, 613 (1998)

    Google Scholar 

  61. C.T. Sambandam, B.P. Patel, S.S. Gupta, C.S. Munot, M. Ganapathi, Compos. Struct. 62, 7 (2003)

    Article  Google Scholar 

  62. T. Dey, L.S. Ramachandra, Int. J. Non-Linear. Mech. 64, 46 (2014)

    Article  Google Scholar 

  63. T. Dey, L.S. Ramachandra, Compos. Part B Eng. 60, 537 (2014)

    Article  Google Scholar 

  64. N. Asmolovskiy, A. Tkachuk, M. Bischoff, Eng. Comput. 32, 498 (2015)

    Article  Google Scholar 

  65. C. Demir, K. Mercan, Ö. Civalek, Compos. Part B Eng. 94, 1 (2016)

    Article  Google Scholar 

  66. V.R. Kar, S.K. Panda, Int. J. Mech. Sci. 115, 318 (2016)

    Article  Google Scholar 

  67. O. Civalek, Compos. Struct. 161, 93 (2017)

    Article  Google Scholar 

  68. R.D. Cook, D.S. Malkus, M.E. Plesha, R.J. Witt, Concepts and Applications of Finite Element Analysis, 4th edn. (Wiley, Singapore, 2004).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Civil Engineering, Veer Surendra Sai University of Technology, Burla, Odisha, 768018, India

    Gayatri Patel & Amar N. Nayak

Authors
  1. Gayatri Patel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Amar N. Nayak
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Amar N. Nayak.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Patel, G., Nayak, A.N. Static Stability Analysis and Design Aids of Curved Panels Subjected to Linearly Varying In-Plane Loading. J. Inst. Eng. India Ser. A 102, 565–589 (2021). https://doi.org/10.1007/s40030-021-00517-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40030-021-00517-0

Keywords

Search

Navigation