On The Normal Response And Buckling Load Of A Toroidal Shell Segment Pressurized By A Static Compressive Load

A. M. Ette; J. U. Chukwuchekwa; I. U. Udo-Akpan; G. E. Ozoigbo

doi:https://doi.org/10.14445/22315373/IJMTT-V65I10P503

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 65 | Issue 10 | Year 2019 | Article Id. IJMTT-V65I10P503 | DOI : https://doi.org/10.14445/22315373/IJMTT-V65I10P503

On The Normal Response And Buckling Load Of A Toroidal Shell Segment Pressurized By A Static Compressive Load

A. M. Ette, J. U. Chukwuchekwa, I. U. Udo-Akpan,G. E. Ozoigbo

Abstract

This investigation is concerned with analytical determination of the out-of-plane normal response, the associated Airy stress function and the static buckling load of an imperfect, finite but simply-supported toroidal shell segment that is statically pressurized. Regular perturbation procedures and asymptotic expansions are freely utilized. In the final analysis, a simple implicit equation for obtaining the static buckling load is obtained and the result is asymptotic in nature.

Keywords

Toroidal and Cylindrical shells, Static buckling, Airy Stress Function, Asymptotic and perturbation techniques.

References

[1] M. Steinand J. A. McElman, Buckling of segments of toroidal shells, AIAA Jnl.,1965, 3, 1704.
[2] J. W. Hutchison, Initial post buckling behavior of toroidal shell segment, Int. J. Solids Struct. 1967, 3, 97 -115.
[3] M. O. Oyesanya, Asymptotic analysis of imperfection sensitivity of toroidal shell segment modal imperfections, J. Nigerian Ass. Maths. Physics2002, 6, 197 – 206.
[4] M. O. Oyesanya, Influence of extra terms on asymptotic analysis of imperfection sensitivity of toroidal shell segment with random imperfection, Mechanics research Communications,2005, 32, 444 – 453.
[5] B. Kriegesman, M. Mohleand R. Rolfes, Sample size dependent probabilistic design of axially compressed cylindrical shells, Thin – Walled Structures2015, 96, 256 – 268.
[6] V. Hu andR. Burgueno Elastic post buckling response of axially loaded cylindrical shells with seeded geometric imperfection design, Thin – Walled structures 2014, 74, 222 – 231.
[7] T. Kubiak, Criteria of dynamic buckling estimation of Thin – walled structures, Thin – walled Structures 2007, 45, 888 – 892.
[8] T. Kubiak, Static and dynamic buckling of Thin – walled plate structures, Springer – Verlag, London, UK, 2013.
[9] T. A. Kolakowski, Buckling of Thin – walled composite structures with intermediate stiffeners, Composite Structures 2005, 69, 421 – 429.
[10] T. A. Kolakowski, Coupled dynamic buckling of Thin – walled composite columns with open cross – section, Composite Structures 2013, 95, 28 – 34.
[11] D. Lockharts and J. C. Amazigo, Dynamic buckling of externally pressurized imperfect cylindrical shells, J. of App. Mech., 1975, 42 (2), 316 – 320.
[12] J. C. Amazigo, Asymptotic analysis of the buckling of externally pressurized cylinders with random imperfection, Quart. Appl. Math. 1974, 32, 429 – 442.
[13] J. C. Amazigo and A. M. Ette, (On a two – small parameter differential equation with application to dynamic buckling, J. Nig. Math. Soc. 1987, 6, 90 – 102.
[14] B. Budiansky and W. J. Hutchinson, Dynamic buckling of imperfection – sensitive structures, Proceedings of 11th Int. Congr.Of Appl. Mech., Munich (ed. H. Gortler, 1964), Springer – Verlag 636 – 651, 1966.

Citation :

A. M. Ette, J. U. Chukwuchekwa, I. U. Udo-Akpan,G. E. Ozoigbo, "On The Normal Response And Buckling Load Of A Toroidal Shell Segment Pressurized By A Static Compressive Load," International Journal of Mathematics Trends and Technology (IJMTT), vol. 65, no. 10, pp. 15-26, 2019. Crossref, https://doi.org/10.14445/22315373/IJMTT-V65I10P503