Optimal Forms of Shallow Shells With Circular Boundary, Part 3: Maximum Enclosed Volume

[+] Author and Article Information
R. H. Plaut

Department of Civil Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Va. 24061

L. W. Johnson

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

J. Appl. Mech 51(3), 536-539 (Sep 01, 1984) (4 pages) doi:10.1115/1.3167670 History: Received June 01, 1983; Revised October 01, 1983; Online July 21, 2009


In Parts 1 and 2, we determined optimal forms of shallow shells with respect to vibration and stability, respectively. In this final part, we consider a given load and find the shell form for which the volume between the base plane and the deflected shell is a maximum. As before, the shell is assumed to be thin, elastic, and axisymmetric, with a given circular boundary that is either clamped or simply supported. The material, surface area, and uniform thickness of the shell are specified. Both uniformly distributed loads and concentrated central loads are treated. In the numerical results, the maximum enclosed volume is on the order of 10 percent higher than that for the corresponding spherical shell.

Copyright © 1984 by ASME
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