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RESEARCH PAPERS

Point Load on a Shallow Elliptic Paraboloid

[+] Author and Article Information
Kevin Forsberg

Lockheed Missiles and Space Company, Palo Alto, Calif.

Wilhelm Flügge

Stanford University, Stanford, Calif.

J. Appl. Mech 33(3), 575-585 (Sep 01, 1966) (11 pages) doi:10.1115/1.3625124 History: Received July 27, 1964; Revised September 07, 1965; Online September 15, 2011

Abstract

The present work is a study of a thin shallow shell having a specific type of deviation from axial symmetry, i.e., the portion of an elliptic paraboloid near its vertex. The singular solutions to the homogeneous shallow-shell equations are expressed as power series in terms of a parameter γ, which is a measure of the deviation of the shell geometry from axial symmetry. These singular solutions can be directly related to concentrated loading at the vertex of the shell. The solution converges in the range γ = 0 (sphere) to γ = 1/2 (cylinder). Detailed graphical results are presented for the stress resultants and radial deflection of a shell subjected to a point load at its vertex.

Copyright © 1966 by ASME
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