ANZIAM  J.  47 (2005), 121-130

Elastic plastic analysis of shallow shells---a new approach

J. Mazumdar   School of Mathematical Sciences   The University of Adelaide   Adelaide SA 5005   Australia   jmazumdar@maths.adelaide.au Also:   School of Electrical and Information Engineering   University of South Australia   Mawson Lakes Boulevard   Mawson Lakes SA 5095   Australia   Jagannath.Mazumdar@unisa.edu.au A. Ghosh   School of Mathematical Sciences   The University of Adelaide   Adelaide SA 5005   Australia     aghosh@maths.adelaide.au J. S. Hewitt   School of Mathematics and Statistics   University of South Australia   Mawson Lakes Boulevard   Mawson Lakes SA 5095   Australia     John.Hewitt@unisa.edu.au

and P. K. Bhattacharya   Department of Mathematics   Indian Institute of Technology   Delhi-110016   India

Abstract

A simple and efficient method for the analysis of the elastic-plastic bending of shallow shells is presented. The method is based upon the concept of contour lines of equal deflection on the surface of the shell, and uses Illyushin's theory of plastic deformation. As an illustration of the method, a technically interesting example of a shallow elliptic elastic dome is examined. Results are obtained for increasing loads and varying aspect ratios, and are illustrated graphically. The application of the method to other shell geometries is quite straightforward.

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