Axisymmetric Elasticity Solutions of Spherical Shell Segments

[+] Author and Article Information
H. S. Levine

Research Department, Grumman Aerospace Corporation, Bethpage, L. I., N. Y.

J. M. Klosner

Department of Applied Mechanics, Polytechnic Institute of Brooklyn, Brooklyn, N. Y.

J. Appl. Mech 38(1), 197-208 (Mar 01, 1971) (12 pages) doi:10.1115/1.3408743 History: Received April 07, 1969; Revised November 03, 1969; Online July 12, 2010


A series solution for the stresses and displacements of a spherical segment subjected to arbitrary axisymmetric surface tractions and edge boundary conditions is presented. A least-square point-matching technique is used to satisfy the specified edge conditions. The general solution for the axisymmetric case has been obtained by utilizing two sets of functions, namely, the Luré homogeneous functions and the full sphere functions used by Sternberg, Eubanks, and Sadowsky. In particular, solutions to the following problems have been obtained: (a) the spherical segment with a stress free edge subjected to a centrifugal force field; (b) the spherical segment subjected to an external pressure varying as cos2 N θ supported on a rigid surface with no shear resistance; and (c) the hemisphere having zero traction on its spherical surfaces subjected to edge shear stresses. The results are presented in graphic form, which demonstrate the boundary-layer effect. Heretofore solutions to these types of problems have been obtained by using shell theory approximations.

Copyright © 1971 by ASME
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