# American Institute of Mathematical Sciences

May  2007, 7(3): 643-650. doi: 10.3934/dcdsb.2007.7.643

## The hypercircle theorem for elastic shells and the accuracy of Novozhilov's simplified equations for general cylindrical shells

 1 Department of Civil Engineering, University of Virginia, Charlottesville, VA 22904-4742, United States

Received  September 2006 Revised  December 2006 Published  February 2007

The analog of the well-known Prager-Synge hypercircle theorem for three-dimensional, linearly elastic bodies is derived for the linear Sanders-Koiter theory of elastically anisotropic shells under surface and edge loads and then used to compute the accuracy of Novozhilov's simplified equations for an elastically isotropic general cylindrical shell. The key idea is to note that the Novozhilov equations are equivalent to the Sanders-Koiter equations with certain surface loads and distributed dislocations.
Citation: J. G. Simmonds. The hypercircle theorem for elastic shells and the accuracy of Novozhilov's simplified equations for general cylindrical shells. Discrete & Continuous Dynamical Systems - B, 2007, 7 (3) : 643-650. doi: 10.3934/dcdsb.2007.7.643
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