Buckling of Shallow Arches with Supports that Stiffen when Compressed

Abstract

The snap-through instability of a uniform, shallow, elastic arch is considered. The arch has a sinusoidal shape and is subjected to a uniformly distributed load. As the load is increased, the flexural resistance of the supports is assumed to increase. In order to model this behavior, rotational springs act at the immovable arch ends, and their stiffnesses are assumed to be linear functions of the compressive thrust induced by the load. The effect of this support stiffening on the critical load is investigated. Both symmetric and asymmetric supports are treated. The critical load may be increased significantly due to support stiffening, especially if the initial flexural resistance is low.