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The Scientific World Journal
Volume 2014 (2014), Article ID 240954, 10 pages
http://dx.doi.org/10.1155/2014/240954
Research Article

Collapse Pressure Analysis of Transversely Isotropic Thick-Walled Cylinder Using Lebesgue Strain Measure and Transition Theory

Department of Mathematics, Jaypee Institute of Information Technology, A-10, Sector 62, Noida 201307, India

Received 28 August 2013; Accepted 10 October 2013; Published 9 January 2014

Academic Editors: F. Berto, A. Di Schino, Y.-k. Gao, and F. Peeters

Copyright © 2014 A. K. Aggarwal et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The objective of this paper is to provide guidance for the design of the thick-walled cylinder made up of transversely isotropic material so that collapse of cylinder due to influence of internal and external pressure can be avoided. The concept of transition theory based on Lebesgue strain measure has been used to simplify the constitutive equations. Results have been analyzed theoretically and discussed numerically. From this analysis, it has been concluded that, under the influence of internal and external pressure, circular cylinder made up of transversely isotropic material (beryl) is on the safer side of the design as compared to the cylinders made up of isotropic material (steel). This is because of the reason that percentage increase in effective pressure required for initial yielding to become fully plastic is high for beryl as compared to steel which leads to the idea of “stress saving” that reduces the possibility of collapse of thick-walled cylinder due to internal and external pressure.