Three-Dimensional Elasticity Solution and Edge Effects in a Spherical Dome

[+] Author and Article Information
Shun Cheng

Department of Engineering Mechanics, University of Wisconsin, Madison, Wisc.

T. Angsirikul

Menasco Co., Burbank, Calif.

J. Appl. Mech 44(4), 599-603 (Dec 01, 1977) (5 pages) doi:10.1115/1.3424143 History: Received January 01, 1977; Online July 12, 2010


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.

Copyright © 1977 by ASME
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