Snapping of Low Arches with Nonuniform Stiffness

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.