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.
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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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