Linear Theory of Thin Rings

by Harry E. Williams, Prof. of Engrg.; Harvey Mudd Coll., Claremont, CA,

Serial Information: Journal of the Engineering Mechanics Division, 1972, Vol. 98, Issue 5, Pg. 1031-1051

Document Type: Journal Paper


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.

Subject Headings: Linear functions | Displacement (mechanics) | Arbitration | Equilibrium | Warpage | Load factors | Fourier analysis | Lagrangian functions

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