Power Law of Critical Buckling in Structural Members Supported by a Winkler Foundation

Abstract

In the fields of engineering, nanoscience, and biomechanics, thin structural members, such as beams, plates, and shells, that are supported by an elastic medium are used in several applications. There is a possibility that these thin structures might buckle under severe loading conditions; higher-order, complicated elastic buckling modes can be found owing to the balance of rigidities between the thin members and elastic supports. In this study, we have shown a new and simple ‘power law’ relation between the critical buckling strain (or loads) and rigidity parameters in structural members supported by an elastic medium, which can be modelled as a Winkler foundation. The following structural members have been considered in this paper: i) a slender beam held by an outer elastic support under axial loading, ii) cylindrical shells supported by an inner elastic core under hydrostatic pressure (plane strain condition), and iii) complete spherical shells that are filled with an inner elastic medium.