Bifurcation Analyses for Shallow Arches

An analysis based on Koiter's initial post-buckling theory is presented for the asymmetric buckling of clamped and pinned shallow arches, uniformly loaded. Based on a linear prebuckling state, the post-buckling analysis indicates that the asymmetric bifurcations occur as predicted by the exact theory, and that these bifurcations are generally unstable. A comparison is also made between the present shallow arch results and those obtained using a steep arch theory, and good agreement is shown over the expected range of agreement. Finally, it is shown that the Budiansky-Hutchinson formalism is a somewhat simpler approach to the post-buckling analysis than is Koiter's development.