Deformation of Open Spherical Shells Under Arbitrarily Located Concentrated Loads

[+] Author and Article Information
J. P. Wilkinson

Dynamics, North American Aviation, Inc., Downey, Calif.

A. Kalnins

Department of Mechanics, Lehigh University, Bethlehem, Pa.

J. Appl. Mech 33(2), 305-312 (Jun 01, 1966) (8 pages) doi:10.1115/1.3625042 History: Received March 30, 1965; Revised July 06, 1965; Online September 15, 2011


An exact solution is derived for the Green’s function of an open rotationally symmetric spherical shell subjected to any consistent boundary conditions. The fundamental singularity of the Green’s function is expanded in series according to the addition theorems of Legendre functions, and the solution for a spherical shell subjected to an arbitrarily situated, harmonically oscillating, normal, concentrated load is obtained explicitly in terms of associated Legendre functions. The corresponding static Green’s function is obtained simply by setting the driving frequency equal to zero. Numerical results for the displacements and stress resultants of an example are presented in detail.

Copyright © 1966 by ASME
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