Self-Equilibrated Singular Solutions of a Complete Spherical Shell: Classical Theory Approach

[+] Author and Article Information
Nikolaos Simos

Earthquake Research Center, The City College of the City University of New York, New York, N.Y. 10031

Ali M. Sadegh

Department of Mechanical Engineering, The City College of the City University of New York, New York, N.Y. 10031

J. Appl. Mech 56(1), 105-112 (Mar 01, 1989) (8 pages) doi:10.1115/1.3176028 History: Received May 04, 1988; Revised July 21, 1988; Online July 21, 2009


The elastic response of a complete spherical shell under the influence of concentrated loads (normal point loads, concentrated tangential loads, and concentrated surface moments) which apply in a self-equilibrating fashion is obtained. The mathematical analysis incorporates the classical uncoupled system of equations for the transverse displacement W and a stress function F . The solution formulae for all three types of singular loading are in closed form and they are expressed in terms of complex Legendre and other elementary functions. The two latter portions of the analysis are associated with a multivalued stress function F which leads to a single-valued stress and displacement formulae. The intricacies of the solutions and their singular character are also discussed. Lastly, some representative shell problems are evaluated.

Copyright © 1989 by ASME
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