Ultimate Strength Analysis of Ship Hull Girder Under Random Material and Geometric

A ship hull girder is a complex assembly of unstiffened/ stiffened plates, frames, etc. and is subjected to longitudinal bending, transverse bending, and torsion. The ultimate hull girder strength is the maximum bending capacity that a ship hull girder can sustain under longitudinal bending. For structural reliability analysis SRA, the uncertainties in ultimate hull girder strength must be estimated accurately. Due to the growing concern for safety of ships, lives at sea, and the marine environment, the International Association of Classification Societies IACS is considering a more refined set of rules. The deterministic estimation of ultimate hull girder strength under longitudinal bending started with the so-called direct method, e.g., Refs. 1‐3. The progressive collapse analysis of hull girders can be found in Refs. 4‐6. The above approaches do not typically consider the effect of initial imperfections, which include initial deflections and the residual welding stresses for the plating between two longitudinals. These imperfections occur due to poor workmanship, improper handling of cargo during loading and unloading, improper use of grab, slamming, etc. Guedes Soares 7 reviewed various design equations for the design of ship plates under the compressive load considering the effect of plate slenderness, initial distortions, residual stresses, and boundary conditions. A new design equation was proposed, which included all the variables, and also the uncertainty associated with the use of this equation was quantified. Further, an approximate method was proposed by Gordo and Guedes Soares 8 for load shortening curves of stiffened plates, accounting the plate and stiffener distortions and residual stresses. A similar study 9 also estimates the ultimate strength and effective width of attached plating considering plate initial deflection and residual stresses. The assessment of the ultimate strength of the ship hull girder 10 uses the approximate methods for load shortening curves given in Ref. 8. The present authors 11 analytically studied the effect of such initial imperfections on the ultimate hull girder strength analyzing a bulk carrier and a VLCC tanker. Bonello et al. 12 and Chryssanthopoulos 13 studied the effect of the random initial imperfections on the plates under axial compression. The references on the effects of initial imperfection on hull girder ultimate strength are very sparse. Kim 14 has estimated the ultimate strength of ten typical merchant ship hulls applying the idealized structural unit method ISUM. Paik and Thayamballi 15 also applied the ISUM approach to obtain hull girder ultimate strength, considering the effect of initial deflection and welding residual stresses. Harada and Shigemi 16 have performed a series of nonlinear FEM analysis for a double hull VLCC and a cape size bulk carrier to obtain the ultimate longitudinal strength in hogging and sagging conditions; nevertheless, such analyses can be computationally demanding and may be prohibitive in many situations. The initial deflections of a stiffened panel due to welding have been considered in Ref. 16 while uncertainty in the welding induced residual stress has been ignored. The yield strength and member thickness were varied systematically from +3 to 3 in the FEA model. Various available data on initial imperfections show that the initial deflections as well as residual welding stresses are random in nature. Moreover, they are likely to be correlated due to physical proximity, common material source, common welding practice, etc. The same holds for yield strength of different structural elements constituting the ship’s hull. In this paper, we extend our previous work 11,17 to incorporate randomness including correlation in the initial imperfections in the ship hull plating between stiffeners and yield strength of stiffeners. The results from this paper can lead to the realistic estimates of modeling uncertainty in the hull girder strength when randomness in the imperfection and the yield strength need to be taken into account. These additional uncertainties may be used to modify the design equation for new ships through appropriate partial factors. The proposed methodology is applied to a cape size bulk carrier and a double hull VLCC tanker that were used for the calibration of the hull girder longitudinal ultimate strength investigation in Ref. 18.