Elastic behavior of ring-on-foundation

Motivated by a practical flexible crashworthy structure that protects the bridge pile against ship collision, elastic behavior of a closed circular beam (i.e., a circular ring) attached to an elastic foundation (R-o-F, in short) is analyzed. Based on the curved beam theory, the governing equation for the bending deformation of the ring is derived, in combination with adequate boundary conditions. The elastic deformation of the R-o-F under concentrated loading is analytically obtained by solving the boundary value problem (BVP). From this solution the equivalent stiffness of the R-o-F is given in analytical form. Based on the analytical model, a non-dimensional parameter, defined by the ratio of the stiffness of the elastic foundation to the bending stiffness of the beam, is identified and found to dominate the behavior of R-o-F. The adequacy of the analytical results is verified by finite element simulations on the R-o-F model with various prescribed structural parameters. The identified non-dimensional parameter provides a valuable guidance to the design of the crashworthy structure.

► A flexible crashworthy protective structure is modeled as a ring-on-foundation (ROF). ► The mechanical behavior of the ROF is controlled by the stiffness ratio (λ=kR3/EI) between the foundation and the ring. ► The equivalent stiffness of the ROF is given explicitly as a function of λ. ► Good engineering design for the relevant crashworthy structures can be achieved by taking EI≈4kR3.