Equilibrium of Heavy Elastic Cylindrical Shells

[+] Author and Article Information
C.-Y. Wang

Department of Mathematics, Michigan State University, E. Lansing, Mich. 48824

L. T. Watson

Department of Computer Science, Virginia Polytechnic Institute and State University, Blacksburg, Va. 24061

J. Appl. Mech 48(3), 582-586 (Sep 01, 1981) (5 pages) doi:10.1115/1.3157678 History: Received September 01, 1980; Revised March 01, 1981; Online July 21, 2009


An originally circular, heavy elastic shell rests on a horizonal surface. The equilibrium shape is governed by the heavy elastica equations. The solutions depend heavily on the parameter B, which represents the relative importance of density and perimeter length to flexural rigidity. There are four distinct cases. A perturbation analysis is obtained for small B while a similarity solution exists for large B. The general solution is obtained by accurate numerical integration using a least change secant update quasi-Newton method and a new homotopy method.

Copyright © 1981 by ASME
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