Dynamic Response And Ultimate Strength Of Container Ship Hull Structures Under Slamming Loads

The buckling and ultimate carrying capability of ship structures are the very important factors for assessing the safety ship structures and have been widely studied by lots of researchers.In recent years,the size and traveling speed of the container ship are getting larger and larger,which leads to smaller stiffness of the hull girder.Therefore,slamming loads will have an apparent influence on the safety of ship structures.The dynamic buckling and dynamic ultimate strength of ship structures are more complex compared with static buckling and ultimate strength,because some factors such as time effect of loading,dynamic constitutive relationship and inertial effect,need to be considered.Therefore,it will be very significant to study the dynamic behavior of ship structures under slamming loading based on theoretical and numerical method.In terms of the above problems,the container ship is regarded as a research model in the present paper,and the following works were conducted:（1）The dynamic buckling of stiffened plates considering the elastically restrained edges subjected to in-plane impact loading is investigated.Navier’s double Fourier series is selected as a deflection function,then the large-deflection plate equations are solved by the Galerkin method and four-order Runge-Kutta method is used to solve the motion equations.An instance presented in the published literature has validated the correctness of the method.The method is extended to the research of the dynamic response of the stiffened plate with elastically restrained boundary condition.B-H buckling criterion is used to determine the critical dynamic buckling loads.The results show the rotational restraint stiffness usually ignored by previous researchers plays an important role in the dynamic response of the stiffened plate under in-plane impact loading,and the influence degree of rotational restraint stiffness on dynamic buckling loads and dynamic response increase along with the initial imperfection and pulse duration.The larger elastic rotational restraint stiffness will lead to the smaller dynamic response and larger critical dynamic buckling loading.For rectangular plates,the elastic rotational restraint edges can be simplified as clamped edges when nondimensional elastic rotational stiffness is larger than 20,while it can be simplified as clamped edges when nondimensional elastic rotational stiffness is lesser than 0.01.For stiffened plates,the elastic rotational restraint edges can be simplified as simply supported edges when nondimensional elastic rotational stiffness is larger than 20,while it can be simplified as simply supported edges when nondimensional elastic rotational stiffness is lesser than 0.5.（2）The elastic dynamic buckling of rectangular plates was studied in the previous chapter.It can be concluded that the rectangular plate still has the carrying capability after the dynamic buckling occurring.Therefore,it is necessary to study the dynamic ultimate strength of rectangular plates in order to access the dynamic ultimate carrying capacity of rectangular plates under dynamic loading.The extensive non-linear finite element（FE）analyses of the dynamic ultimate strength of the ship plate structures under uniaxial compressive load were presented.An empirical formula for predicting the dynamic ultimate compressive strength of ship plates,expressed in terms of the geometric dimensions of plates and impact speeds,was developed by curve fitting of FE results of 561 ship plates.The dynamic ultimate strength of a tested specimen is calculated based on the nonlinear finite element method,and the comparison with test results show the applicability of the present numerical method.The comparison between the proposed empirical formulation and the FEM results of 561 ship plates show the accuracy of curve fitting.The formula implicitly includes the effect of initial imperfections with an average level.The proposed formula was also applied to the outer bottom plates of container ships and oil tanker and a satisfactory agreement between the proposed formula and FE results was obtained.（3）The dynamic ultimate strength of rectangular plates under in-plane impact loading of which the speed keeps constant during the whole test process was studied and the corresponding empirical formula was derived.The dynamic loading was simplified as symmetrical half sine impact loading in the present paper in order to simulate the actual situation better.Then the velocity of two ends of the rectangular plate will change with the deformation and stress state.The dynamic ultimate compressive strength of isotropic imperfect rectangular plate with simply supported boundary conditions under intermediate-velocity impact based on Non-linear finite element method（FEM）was investigated.The initial imperfection which was assumed following the same shapes as its first transverse vibration mode with an average level was considered in the dynamic behavior analysis.The dynamic ultimate strength of rectangular plates obtained from FEM compared very well with the results of the published literature.The influences of parameters,such as impact duration,aspect ratio,plate thickness,and material yield stress were discussed to derive a reasonably accurate expression for predicting the dynamic ultimate compressive strength of rectangular plates.Results from the parametric study indicate that impact duration and aspect ratio have an important influence on the non-dimensional dynamic ultimate compressive strength of rectangular plates,while plate thickness and material yield stress have little effect.The obtained empirical formula was applied to the rectangular plates in existing ships,and the comparison of the dynamic ultimate compressive strength between the proposed formula and FE results show the applicability and good precision of the new empirical formula.（4）The whipping response of ship structures will be activated when traversing extreme waves,which usually cause buckling failure of decks and bottom plates under in-plane impact loads.For bottom stiffened plate structures,lateral loads are also needed to be considered.The stiffened plates are the most basic fundamental units as rectangular plates.Therefore,it is also very important to investigate the dynamic ultimate strength of stiffened plates under in-plane impact loading.Ship bottom stiffened plates usually subject to both in-plane slamming loading and lateral pressure from sea water.Therefore,An investigation is conducted on the dynamic ultimate strength of bottom stiffened plates of 10,000TEU container ship under uniaxial compression and lateral pressure.The dynamic ultimate strength of a tested specimen is calculated based on the nonlinear finite element method,and the comparison with test results shows the applicability of the present numerical method.The static ultimate strength of stiffened plate structures obtained with the numerical method is compared with an empirical formulation and the error is within the allowable range.Then,the influence of modes and magnitudes of initial imperfections,boundary conditions,lateral pressure,strain rate,and structural dimensions,on the dynamic ultimate strength are discussed.（5）Comparing with rectangular plates and stiffened plates,hull girders can represent the dynamic behavior of whole ships.The dynamic ultimate hull girder strength subjected to impact bending moment is completely different from the static ultimate hull girder strength.Because the dynamic material constitutive relationship and inertial effect need to be considered in the dynamic analysis.Nonlinear finite element method is used to obtain ultimate strength and nonlinear relationship between the bending moment and rotational angle of the hull girder,and the ultimate rotation(R_y0)was used as a failure criterion to estimate the dynamic ultimate strength of the container ship under impact bending moment.Slamming duration,the amplitude of impact bending moment and slamming impulse on the dynamic elastic-plastic response of the hull girder were estimated based on the nonlinear explicit finite element method.（6）With the development of global trade,ships become larger and faster.The threat of slamming should be considered for some ships with a large bow and high navigating speed,such as container ships.In terms of the studies on the slamming response of bow structure,the traditional method is based on American Bureau of Shipping,which by introducing the dynamic load factor,the equivalent static pressure that would cause the same maximum structural response as the dynamic slamming pressure is obtained.Then the dynamic response of bow structures subjected to slamming pressures was analyzed based on the quasi-static method and neglecting the time effect of dynamic loading.Therefore,the present paper introduces various influence parameters which are relevant to the dynamic response of the bow structure,including the amplitude of slamming pressures,impact duration,rise time of slamming pressures,load attenuation coefficient,the position of maximum slamming pressures and traveling speed of the slamming pressures over side shell of the bow flare.The dynamic behaviors of the large containership’s bow structures subjected to slamming pressures based on nonlinear finite element method.The influence of various influence parameters on the dynamic stress response of bow structures under slamming pressures was discussed in detail.The safety margin coefficient is presented to evaluate the safety performance of large container ships under slamming pressures.The obtained results contribute to help the naval architect to design a ship which has a stronger capacity of resisting slamming.The innovations of this thesis are listed as follows:（1）The rectangular plate and stiffened plate in the ship structures was usually supported by strong frames at the four edges,which offer a certain degree of elastical rotational restraint stiffness.The precise results of the dynamic buckling of ship plates are very hard to obtain based on the assumption of simply supported and clamped boundary conditions.However,the studies on the dynamic buckling of rectangular plates with elastical rotational restraint stiffness are very rare.Therefore,the rectangular plate and stiffened plate with elastically restrained edges were investigated based on the large-deflection plate theory in the present paper.The relationship between the critical dynamic buckling loading and the rotational restraint stiffness was obtained.Comparing with the critical dynamic buckling load of the ship plate with elastically restrained boundary conditions,the results of the ship plates with simply supported boundary conditions are smaller while the results are larger for clamped boundary conditions.（2）The rectangular plate still has the carrying capability after the elastic dynamic buckling occurred.Therefore,the studies on the dynamic ultimate strength of rectangular plates under in-plane slamming loading are very significant to strength against slamming design of ship structures.The dynamic ultimate strength of simply supported rectangular plates under in-plane slamming loading was investigated in the present paper.The influence of slamming duration,aspect ratio,material yield stress and plate thickness on the dynamic ultimate strength was discussed in detail.The empirical formula for predicting the dynamic ultimate strength of rectangular plates under in-plane slamming loading was established by data fitting for the lots of FE results,which is a simple equation expressed as aspect ratio,slamming duration,and static ultimate strength.（3）It is a good method to apply the static loading which is equivalent to dynamic loading to the finite element model of the bow structures to study the dynamic response of the bow structures under slamming pressures.However,this method neglects the dynamic behavior of structural response,which results in a certain degree of computing error.Including the time effect of loading,the dynamic stress response of the 10,000TEU container ship’s bow structures subjected to slamming pressures was studied in the present paper.Various influence parameters which are relevant to the dynamic response of the bow structure were analyzed deeply,including the amplitude of slamming pressures,impact duration,rise time of slamming pressures,load attenuation coefficient,the position of maximum slamming pressures and traveling speed of the slamming pressures over side shell of the bow flare.Proposed a safety margin coefficient for evaluating the safety performance of large container ships subjected to slamming pressures.The results show that when the dangerous values of some parameters appear simultaneously,the bow structure will yield to failure subjected to slamming pressures.