Optimal Forms of Shallow Shells With Circular Boundary, Part 2: Maximum Buckling Load

[+] 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), 531-535 (Sep 01, 1984) (5 pages) doi:10.1115/1.3167669 History: Received June 01, 1983; Revised October 01, 1983; Online July 21, 2009


In Part 1, optimal forms were determined for maximizing the fundamental vibration frequency of a thin, shallow, axisymmetric, elastic shell with given circular boundary. Our objective in this part is to maximize the critical load for buckling under a uniformly distributed load or a concentrated load at the center. Again, the shell form is varied and the material, surface area, and uniform thickness of the shell are specified. Both clamped and simply supported boundary conditions are considered for the case of uniform loading, while one example is presented involving a concentrated load acting on a clamped shell. The optimality condition leads to forms that have zero slope at the boundary if it is clamped. The maximum critical load is sometimes associated with a limit point and sometimes with a bifurcation point. It is often substantially higher than the critical load for the corresponding spherical shell.

Copyright © 1984 by ASME
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