Stability of a rigid sphere supported by a thin elastic column

摘要

The buckling of a rigid sphere supported by a thin elastic column as a mechanical model of a water tower is investigated. It is assumed that the column can suffer not only flexure as in classical elastica theory, but also compression and shear. The nonlinear equations describing the in-plane deformation are derived. It is shown that the critical load is determined from the linearized equilibrium equations. The post-critical shape of the column is obtained by numerical integration.