Plastic mechanism analysis of structural performances for stiffeners on bottom longitudinal web girders during a shoal grounding accident

• A theoretical model is proposed for shoal-grounding structural performances of stiffeners on bottom longitudinal girders.
• The existing deformation models of longitudinal girders are reviewed and discussed.
• A refined longitudinal girder model is proposed for structural performances in shoal grounding accidents.
• Fully contacted stiffeners and indirectly deformed stiffeners are observed and studied.
• The proposed model is verified of reasonable accuracy against LS-DYNA simulation results.

A theoretical model is introduced in this paper for structural performance of stiffeners on double-bottom longitudinal girders in a shoal grounding accident. Major emphasis is placed on establishing the characteristic deformation mechanism of stiffeners and identifying major energy dissipation patterns. Numerical simulations using the LS-DYNA nonlinear finite-element program were carried out to examine thoroughly the progressive deformation process during sliding deformation. Stiffener deformations were observed to fall into two categories: stiffeners fully contacted with the indenter, and stiffeners subjected to indirect deformation due to energy transfer from attached girders. Grounding performance of stiffeners is substantially influenced by that of the attached plating, and therefore a review of the existing deformation models of longitudinal girders (i.e. Simonsen 1997, Midtun 2006 and Hong 2008) was included. Hong's model of bottom girders was found not capable of representing the effects of stiffeners, and a new model of girders was thus developed. Based on observation of the numerical deformation process and the new analytical girder model, a kinematically admissible model of stiffeners on bottom longitudinal girders was built. Using the methods of plastic mechanism analysis, simplified analytical expressions for energy dissipation by girder-attached stiffeners, both fully contacted and noncontacted, were formulated, and equations for grounding resistance were subsequently obtained. The theoretical expressions agree favorably with results from nonlinear finite-element simulations and capture two significant characteristics of the problem: that energy varies little with indentation for stiffeners that fully contacting the indenter, and that energy is independent of slope angle for indirectly deformed stiffeners. The proposed theoretical model helps to predict analytically shoal grounding performance of stiffeners on longitudinal girders with reasonable accuracy.