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 Lure´ 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 cos2N 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.
Axisymmetric Elasticity Solutions of Spherical Shell Segments
H. S. Levine,
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.
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Levine, H. S., and Klosner, J. M. (March 1, 1971). "Axisymmetric Elasticity Solutions of Spherical Shell Segments." ASME. J. Appl. Mech. March 1971; 38(1): 197–208. https://doi.org/10.1115/1.3408743
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