Research Article
Oct 1972
Linear Theory of Thin Rings
Publication: Journal of the Engineering Mechanics Division
Volume 98, Issue 5
Abstract
The equations governing small, elastostatic displacements of circular rings of arbitrary cross section are derived using the principle of virtual work. The equations are shown to be interpretable as the classical equations of equilibrium and the stress resultant-displacement equations. Of particular significant is the natural occurrence of the warping moment and its relation to the twisting moment. A method of solution is proposed in which the displacements of arbitrarily loaded ring segments are obtained in Fourier series using the method of Lagrange multipliers to account for the boundary conditions.
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Published In
Journal of the Engineering Mechanics Division
Volume 98 • Issue 5 • October 1972
Pages: 1031 - 1051
Copyright
© 1972 American Society of Civil Engineers.
History
Published in print: Oct 1972
Published online: Feb 3, 2021
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Authors
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Harry E. Williams
Prof. of Engrg., Harvey Mudd Coll., Claremont, Calif.
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