Volume 5, Issue 1, March 2020, Page: 1-11
Perturbation Procedures in the Dynamic Analysis of a Toroidal Shell Segment Pressurized by a Step Load
Anthony Monday Ette, Department of Mathematics, School of Physical Sciences, Federal University of Technology, Owerri, Imo State, Nigeria
Joy Ulumma Chukwuchekwa, Department of Mathematics, School of Physical Sciences, Federal University of Technology, Owerri, Imo State, Nigeria
Williams Ifeanyichukwu Osuji, Department of Mathematics, School of Physical Sciences, Federal University of Technology, Owerri, Imo State, Nigeria
Atulegwu Chukwudi Osuji, Department of Mathematics, School of Physical Sciences, Federal University of Technology, Owerri, Imo State, Nigeria
Received: Nov. 22, 2019;       Accepted: Dec. 13, 2019;       Published: Jan. 17, 2020
DOI: 10.11648/j.ajmcm.20200501.11      View  59      Downloads  37
Abstract
This paper uses perturbation techniques in asymptotic procedures to determine the normal displacement, the associated Airy stress function and the dynamic buckling load of an imperfect, finite toroidal shell segment pressurized by a step load. The adoption of asymptotic and perturbation procedure is made possible by the presence of small non-dimensional parameter on which asymptotic expansions are made possible. It is assumed here that the imperfection can be regarded as the first term in the Fourier Sine series expansion. The buckling modes are also assumed to be strictly in the shape of the imperfection which is in turn given in the shape of the classical buckling mode. In the final analysis, a simple but implicit formula for determining the dynamic buckling load was obtained. The dynamic buckling load was related to the corresponding static buckling load and that relationship is independent of the imperfection parameter. It is observed, that this procedure, perhaps more than other ones, can be used to analyze relatively more complicated problems particularly where more demands and restrictions are placed on the imperfection parameter. The results are strictly and are valid as far as the imperfection parameter is relatively small compared to unity.
Keywords
Toroidal Shell, Airy Stress Function, Static and Dynamic Buckling, Asymptotic and Perturbation Technique
To cite this article
Anthony Monday Ette, Joy Ulumma Chukwuchekwa, Williams Ifeanyichukwu Osuji, Atulegwu Chukwudi Osuji, Perturbation Procedures in the Dynamic Analysis of a Toroidal Shell Segment Pressurized by a Step Load, American Journal of Mathematical and Computer Modelling. Vol. 5, No. 1, 2020, pp. 1-11. doi: 10.11648/j.ajmcm.20200501.11
Copyright
Copyright © 2020 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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