Bending solutions that are uniformly valid in both shallow and nonshallow regions of a dome with arbitrary meridian are determined for edge loads that vary sinusoidally in the circumferential direction. The membrane and inextensional deformation solutions are obtained in terms of a function which satisfies a simple integral equation which eliminates the usual trial-and-error method of isolating the solutions that are regular at the apex. For a specific application, curves and formulas are obtained for the stresses and deformations of a dome with rigid rings clamped to the edges under the action of axial force, side force, and tilting moment.
Nonsymmetric Deformation of Dome-Shaped Shells of Revolution
C. R. Steele
Applied Mathematics Department, Lockheed Missiles & Space Company, Sunnyvale, Calif.
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Steele, C. R. (June 1, 1962). "Nonsymmetric Deformation of Dome-Shaped Shells of Revolution." ASME. J. Appl. Mech. June 1962; 29(2): 353–361. https://doi.org/10.1115/1.3640554
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