Large post-buckling of heavy tapered elastica cantilevers and its asymptotic analysis - Wang, C.Y. (Archives of Mechanics, 2012)
Complete characteristics of the deformations of a tapered cantilever due to self weight are studied. Explicit stability criteria for pointy tapered columns and numerical results for the blunt columns are given. Asymptotic formulas for large deformations are derived, and the results compare well with those from numerical integration. It is found that the deformation depends heavily on a non-dimensional gravity parameter, the degree of taper and the cross sectional shape of the cantilever.