Stability of cantilever on elastic foundation under a subtangential follower force via shear deformation beam theories

Abstract

Abstract The static stability of clamped-free columns resting on elastic foundation is investigated under a nonconservative subtangential follower force. The higher-order shear deformation beam theories are applied to treat structural instability of a clamped-free rectangular and circular beam resting on Winkler foundation. Based on Engesser's assumption, a single governing equation is derived for divergence instability of Beck cantilever under a subtangential follower force. For different warping shapes of rectangular and circular cross-sections, the critical divergence buckling loads are determined. Static buckling still occurs for a cantilever column subjected to a subtangential follower force with small nonconservativeness parameter and dynamic flutter instability occurs for large nonconservativeness parameter. In a free space, a unified relationship with the Euler buckling loads is given explicitly for the case of a dead load, and the buckling load has an apparent reduction due to shear deformation with different warping of the cross-section. The obtained results further modify the Euler buckling formula to suit for the columns with a broad range of slenderness. Elastic foundation nearly linearly increases the buckling load and a nonconservativeness parameter also raises the divergence buckling load. For shorter columns, the classical buckling loads are significantly overestimated. The effects of slenderness, warping shapes, nonconservativeness parameter, and spring stiffness coefficient are analyzed.