An analytical study by energy methods of buckling of a thin ring subjected to equal, equally spaced concentrated loads

This thesis presents an analytical solution for evaluating the elastic buckling load of a thin ring subjected to an arbitrary number of equal, equally spaced, inwardly directed concentrated radial loads. Buckling is assumed to occur in a mode with as many lobes as loads. The Strain Energy method is used, utilizing an expression for hoop strain energy derived by Langhaar, Boresi and Carver. Verification of results was obtained for the case of two loads by comparison with well-established published works for rings subjected to distributed loading. For three and more loads, the results compared favorably with a published work for multi-lobed buckling of rings under uniform pressure. The reference work was experimentally confirmed only for the case of three-lobed buckling. It is concluded that the results are applicable for the cases of two and three loads. Experimental verification is advisable if the results are to be extended to rings with four or more loads.