Snapping of Low Arches with Nonuniform Stiffness

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Abstract
Results in the form of critical load versus rise parameter are presented for two different types of symmetric stiffness distribution and three cross-sectional area to moment of inertia relations. Critical conditions are obtained through an approximate Ritz-type approach for both types of instability, limit point and unstable bifurcation. Exact solutions are obtained, whenever possible, which are used to provide a confidence factor for the approximate technique. Except for one special case, nonuniform stiffness geometries yield a stronger configuration than uniform stiffness geometries. In addition, for both nonuniform stiffness distributions considered, the more the stiffness is concentrated towards the center of the arch the stronger the arch.

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