Limit point instability of shallow arches under localized sinusoidal loading

Abstract

In the present study, the limit point buckling and postbuckling behaviors of sinusoidal, shallow arches with pinned supports subjected to localized sinusoidal loading, based on the Euler -Bernoulli beam theory, are numerically analyzed. There are some studies on the buckling of sinusoidal shallow arches under the effect of sinusoidal loading. However, in these studies, the sinusoidal loading acts along the horizontal projection of the entire shallow arch. No study has been found in the relevant literature pertaining to the stability of the shallow arches subjected to various lengths of sinusoidal loading. Therefore, the purpose of this paper is to contribute to the literature by examining the effect of the length of the localized sinusoidal loading and the initial rise of the shallow arch on the limit point buckling and postbuckling behaviors. Equilibrium paths corresponding to certain values of the length of the localized sinusoidal loading and various values of the initial rise parameter are presented. It has been observed that the length of the sinusoidal loading and the initial rise parameter affects the transition from no buckling to limit point instability remarkably. The deformed configurations of the sinusoidal shallow arch under localized loading regarding buckling and postbuckling states are illustrated, as well. The effects of the length of the localized sinusoidal loading on the internal forces of the shallow arch are investigated during various stages of the loading.