Research On Reliability Assessment Method Of Residual Strength Of Damaged Ships Under Combined Loads

In traditional ultimate strength assessment method for intact ship,only the vertical bending moment is generally considered,while the influence of other hull girder loads such as horizontal bending moment and torsion is ignored.For which,the maximum vertical bending moment is defined as the critical condition.However,for damaged ships,the horizontal bending moment can’t be neglected when the ship is in some oblique wave due to the change of the floating state of the hull after the water is injected into the tank.In which cases,if the ultimate strength assessment method of the intact ship is still applied to the damaged ship,only the vertical bending moment is considered for evaluating the residual strength,which may result in a dangerous evaluation result.Therefore,this paper aims to develop a reasonable reliability assessment method for the residual strength of damaged ships under combined loads,to achieve a more accurate evaluation results for safety of damaged ships.The main contents involved are introduced as follows:1)An improved Smith method for the calculation of residual strength of damaged ships is developed in this paper.For the traditional Smith method,the rotation of the actual axis of the asymmetrical section is not considered.For which,the force vector equilibrium criterion is introduced on the basis of the force equilibrium criterion in this paper.In the application of the two equilibrium criteria,the translation and the rotation of the neutral axis need to be determined through iterative process,and for which the multi-objective particle swarm optimization(MOPSO)algorithm is introduced.Thus,this paper proposed an improved Smith method considering the rotation of the neutral axis by applying the MOPSO algorithm.2)A fitting method for the limit state equation of the damaged ship under combined loads is proposed in this paper.Since the traditional explicit limit state equation is not suitable for damaged ships,a response surface method applying piecewise regression is used to fit the implicit limit state equation of the damaged ship.In this method,the limit state equation curve is segmentally fitted,and the weighted least square method is used to solve the undetermined coefficient.Besides,the value of each segment connection and the slope of the curve are equalized respectively to ensure the smoothness of the curve and the normal trend of the curve.3)The reliability assessment method for residual strength of damaged ships under combined loads is raised in this paper.When the damaged ship sails in the combined bending moment wave,the vertical load and the horizontal load suffered by the hull can be obtained by direct calculation.Based on the fitted limit state equation,the vertical residual strength and the horizontal residual strength of the damaged ship can be quickly located.After that,the distribution function of the loads and capacity are calculated separately.Considering the uncertainty and the variability of the loads and the residual strength,failure probability of the damaged ship can be obtained applying the Monte Carlo method for statistical sampling.In this research,it can be found as follows.Firstly,the traditional Smith method fails to consider the rotation of the neutral axis,which leads to large deviation of the calculation results.The improved Smith method effectively improves the calculation accuracy of the residual strength.Secondly,for the curve with high nonlinearity at the local point of the damaged ship,the explicit limit state equation has a poor fitting effect,and the implicit limit state equation based on the response surface method improves the fitting accuracy effectively.Finally,for some oblique wave conditions,compared with the reliability evaluation considering only the vertical bending moment,the probability of failure of the damaged ship is greater when considering the action of the combined load.Therefore,it is necessary to evaluate the reliability of the residual strength of damaged ships under combined loads.