The subject of this analysis is a homogeneous, isotropic, and elastic spherical dome of uniform thickness subjected to prescribed edge stresses at the end surface. Starting from three-dimensional equations of theory of elasticity, solutions of Navier’s equations and the characteristic equation are obtained. Eigenvalues are computed for various values of the thickness and radius ratio and their special features are analyzed. Coefficients of the nonorthogonal eigenfunction expansions are then determined through the use of a least-squares technique. Many numerical results are obtained and illustrated by figures. These results show that the method presented herein yields very satisfactory solutions. These solutions are fundamental to the understanding of thin shell theories.
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December 1977
Research Papers
Three-Dimensional Elasticity Solution and Edge Effects in a Spherical Dome
Shun Cheng,
Shun Cheng
Department of Engineering Mechanics, University of Wisconsin, Madison, Wisc.
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T. Angsirikul
T. Angsirikul
Menasco Co., Burbank, Calif.
Search for other works by this author on:
Shun Cheng
Department of Engineering Mechanics, University of Wisconsin, Madison, Wisc.
T. Angsirikul
Menasco Co., Burbank, Calif.
J. Appl. Mech. Dec 1977, 44(4): 599-603 (5 pages)
Published Online: December 1, 1977
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Received:
January 1, 1977
Online:
July 12, 2010
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Cheng, S., and Angsirikul, T. (December 1, 1977). "Three-Dimensional Elasticity Solution and Edge Effects in a Spherical Dome." ASME. J. Appl. Mech. December 1977; 44(4): 599–603. https://doi.org/10.1115/1.3424143
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