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

Pages: 643 - 650, Volume 7, Issue 3, May 2007

doi:10.3934/dcdsb.2007.7.643       Abstract        Full Text (152.6K)       Related Articles

J. G. Simmonds - Department of Civil Engineering, University of Virginia, Charlottesville, VA 22904-4742, United States (email)

Abstract: 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.

Keywords:  Hypercircle Theorem, accuracy of Novozhilov's cylindrical shell equations.
Mathematics Subject Classification:  Primary: 74K25; Secondary: 74B05.

Received: September 2006;      Revised: December 2006;      Published: February 2007.