Research on Numerical Simulation of Ship-ice Collision Based on MD Nastran

ZHANG Ai-feng,SONG Yan-ping,SU Lin-fang

(Transportation Equipments and Ocean Engineering College,Dalian Maritime University,Dalian 116026,China)

0 Introduction

In recent years,the navigation passage for ship has transitorily appeared in summer arctic waters due to the sea ice melting with global warming.Thus,there has been a great interest in the navigation safety of ships in the region[1].Researchers put forward that the ice load should be taken into consideration in design stage and focus on the research for the structural integrity of vessel under ice loads.Up to now,most of study deal with the ship characteristics in the ice region,for example,how the hull breaks ice and how the broken ice acts on the hull.Few of experience are about the ship operations on the arctic sea.As a result,the computer simulation of such a complex process of ship-ice interation is very demanding.Wang Bo et al of ABS studied the deformation of ship structure and crushing ice in the process of ship-ice collisions using DYTRAN software[2].Rui Zong of Memorial University of Newfoundland carried out the nonlinear finite element analysis on ship-ice collision using Ls-Dyna,and then evaluated the local structure response of polar ship under the impact of ice load[3].Liu Zhenhui of Norwegian University of Science and Technology acquired a simplified formulation used to obtain the demand for energy dissipation in a ship-iceberg collision,and presented integrated numerical analysis of an iceberg collision with a foreship structure[4].However,the studies of ship-ice collision are limited.Currently,no work on numerical simulation of ship-ice collision based on MD Nastran is carried out.So the results of stress,strain and deformation during ship-ice collisions have been determined from collision simulations in this paper.

1 Load design scenario

In the collision process,the ship is assigned a forward speed to impact the wedgy edge of sea ice that is stationary.The collision scenario is shown in Fig.1.There will be an extrusion force on the hull,whose mechanics principle comes from the modified Popov collision model that is the pressurearea extrusion model colliding with wedgy edge and has been adopted by IACS Polar Class Rules[5].The assumption is that the kinetic energy of ship is completely transformed into crushing energy in the process of collision.It can maximize the ice damage(relative static of them),also can maximize the normal ice force on the ship structure.The energy equation of IACS Polar Class Rules will be obtained from Eq.(1)

Fig.1 The collision scenario of ship-ice interaction

The normal kinetic energy Knand the crushing energy of floe Ecrushare:

where Meis the effective mass(Me=Mship/C0,Mshipis ship displacement and C0is the mass reduction factor),vnis the normal velocity(vn=Vship·sinα·cosβ′,Vshipis the velocity of ship),Fnis the normal extrusion force on the bow,λnis the normal extrusion displacement of floe,and λnmis the maximum normal extrusion displacement.

Fig.2 The definition of contact area and angle

We write the normal contact area A and average pressure P[6]:

where P0is the ice pressure at 1 m2,ex is constant,the definition of α,β′and φ are shown in Fig.2[7].

We note that,if the normal extrusion displacement λnis known,the normal ice load Fncan be obtained from Eqs.(4)-(8):

The maximum value of the extrusion displacement is

Substituting the value of Vshipand Mshipinto Eq.(9),we have

Fncan be obtained if value of the relevant parameters is given and fais a shape factor,which shows the effect of bow shape on the ice force.The ex is specified as 0.1 in the IACS Polar Class Rules.P0is as shown in Tab.1 according to the ship ice class[3].

Tab.1 Ice pressure based on ice class from IACS

2 Numerical simulation

2.1 Finite element model

In this paper，a finite element analysis is performed to simulate the collision process between the bow of tanker and floe using MSC.Nastran SOL700,which fully integrates the fluid-structure coupling analysis function of MSC.Dytran and the structure analysis function of the LS-DYNA and can carry out the simulation analysis of various kinds of highly nonlinear transient events.The ice strengthening 107000 DWT Aframax tanker is chosen for the sample.The detailed finite element model for bow structure and the simple model for others of hull are used to avoid too much computing time due to the unnecessary element,as shown in Fig.3.

Fig.3 The FE model of arctic tanker

For simplicity,it is convenient but acceptable to model the sea ice sheet as a cuboid of 50×50×0.8 m3although the area of sea ice is very large in reality.Fig.4 shows the face A and face B of the ice are restrained with six degrees of freedom to simulate the infinite sea ice.

The ship-ice collision is a kind of very complex nonlinear transient response process under the impact load.Meanwhile,it is the fluid-solid coupling problem.There are three modeling approaches to deal with the fluid-solid coupling phenomenon in the field of ship collision,which is fluid-solid coupling method,additional mass method and the equivalent beam method.The first is high-precision but time-consuming;the third is the simplest but low-precision;the second is generally used modeling method.This paper adopts it in view of calculation accuracy and less calculation time.

Fig.4 The FE model of sea-ice

2.2 Material parameter

Because the elastoplastic constitutive relation is often used in metal material,the hull material parameter is defined by the ideal elastic-plastic model.It will occur larger values of the strain at a short time during ship-ice collisions,therefore the influence of strain rate sensitivity should be considered in the material model.Cowper-Symonds constitutive equation is chosen for dealing with the strain rate sensitivity in this paper[8-9].

where σdis the dynamic yield stress for the plastic strain rate ε,σyis the corresponding static yield stress,D and P are constant.

In general,the component will rupture when its plastic strain reaches the fracture strain value.It is difficult to determine a unified value because the material fracture strain is concerned with the behavior of the material itself and structure size.The fracture strain of the ship structure should be determined by steel grades according to the stipulation of NORSOK STANDARD N-004,as shown in Tab.2[10].The high-strength steel A32 and A36 are chosen for the steel of ship in this paper.

Tab.2 Fracture strain based on the steel grades

At present,a lot of researches are about the failure criterion of the sea ice.This paper assumes the ice material to be isotropy for the analysis effectively[11].It is generally believed that in engineering,the stress-strain relationship of sea ice is linear elastic and ice behaves in a brittle manner when its relative speed is greater than 2 cm/s and temperature is from-5°C to-25°C.So the elastic stress-strain relationship and the failure criterion in brittle zone should be included in the sea ice material model.Furthermore,the maximum plastic strain failure criterion is adopted for the ice material[12].The main material parameters of ship and sea ice are shown in Tab.3[13].

Tab.3 Material parameters

2.3 Calculation scheme

The ship is set to have a velocity of 5.14 m/s and vertically impacts the wedgy edge of floe.The velocity is set to be(3.634 5,0,3.634 5)by the initial velocity Tab of Loads/BCs module in MSC.Patran.The mass of ship model is different from the actual ship’s because of the simplification of model.For this reason,the mass and gravity center of model can be basically consistent with the actual ship by adjusting the density of model.As a result,the mass of ship and ice model include the added mass,to be 181 678 t and 1 980 t,respectively.

The interaction between different structures is accomplished by contact calculation in nonlinear dynamic simulation.MSC.Nastran SOL700 provides three contact types:point-surface contact,single surface contact and face-face contact.The face-face contact(master-slave surface contact)is generally used,which can simulate contact,separation,and the friction between two sides.

The examination of penetrating requires a large amount of time when conducting the dynamic calculation.The friction coefficient between the two contact bodies is 0.1 in this paper.Besides,the collision time is set for 2 seconds(time step 0.005 s).

3 Result analysis

3.1 Deformation

The deformation figure of bow structure can be acquired by the finite element analysis of working condition that has been set.Fig.5 shows different degrees of deformation and damage during the impact for the contact area and neighboring areas.It includes:membrane tensile deformation in the shell plating of bow because of the extrusion;conquassation and lateral extrusion deformation in the stringer and lateral extrusion deformation in the transverse webs.

At the same time,the force on the hull will impact sea ice in reverse to cause a certain degree of deformation of sea ice.Fig.6 shows failures of sea ice in the collision process,such as extrusion deformation,shearing and bend failure because of the different collision speed and angle between ship and ice.

The damage and deformation of sea ice after collision is shown in Fig.6.And parts of the unit were deleted by program due to the failure,which could not be involved in the calculation afterwards.

Fig.5 Deformation figure of bow structure

Fig.6 Deformation figure of sea ice

3.2 Stress and strain

The simulating calculation results indicate the stress nephogram changes of bow structure at each time step,as shown in Fig.7.

The material used for the arctic tanker is marine high strength steel A32(yield stress σY=315 MPa)in this paper,which is applied to side shell plating of the bow.It should be noted that the maximum stress of bow structures changes with time and has a downward trend after rising.However it is greater than yield stress.This phenomenon shows that it will occur the rise of stress and plastic deformation of structure under impact force during impact,meanwhile,the increase in energy associated with the deformation of the structure produces the unloading.As a result,stress value decreases.

Fig.8 The strain distribution of bow

The plastic strain of bow structures is shown in Fig.8.It should be noted that the plastic strain mainly concentrates in the contact area and adjacent area,which increases with time.Because the maximum plastic strain did not exceed the failure strain,no breakage occurs in the structures.

3.3 The analysis of collision process

The total energy is constant in the ship-ice collision.The kinetic energy of the ship will be partially converted into internal energy(elastic strain energy and plastic strain energy)and the damping energy,hourglass energy and friction energy,which is a small proportion in the total energy.The time-history curve of all kinds of energy in the process of ship-ice collision is shown in Fig.9.

Fig.9 Time-history curve of energy

Fig.10 Time-history curve of node stress

Fig.11 Time-history curve of node strain

The stress time-history curves(Fig.10)and strain time-history curves(Fig.11)were got after simulation for the node 7561,node 7557 and node 7558 of the collision zone is completed.Fig.10 shows that the stress curve of nodes is obviously nonlinear,which had several peaks in the process of collision.As described above,the plastic deformation in the process of collision absorbs parts of energy and leads to unloading.On the other hand,the shape of contact zone will constantly change because of the structure deforming and sea ice crushing during impact,so lead to the change of ship-ice interaction position and the peak pressure posi-tion.As shown in Fig.11,the increase of stress will lead to the plastic strain values rising at the same time.While the plastic strain of structure basically has reached the peak as the appearing of first stress peak value,which has a little change after that.

4 Conclusions

It is necessary to simulate the process of ship-ice collision using the numerical method in the current situation that lacks of the actual ship-ice collision data.In this study,a nonlinear dynamic finite element analysis based on MD Nastran was performed to identify the structure response during ship-ice collisions.It has widely significance to study the structure design and optimization of arctic ship.The local damage and plastic deformation of hull will occur if the impact velocity reaches a certain value.The following conclusions can be drawn from the numerical simulations:

(1)The deformation would occur in different structure components during the impact:the membrane tensile deformation in the shell plating;the conquassation and lateral extrusion deformation in the stringer and the lateral extrusion deformation in the transverse webs.

(2)The stress and plastic strain of bow structures changed with time.As a result of the analysis,the maximum stress exceeded yield stress and the plastic strain mainly concentrated in the contact area and adjacent area,which increased over time but did not exceed the failure strain.

(3)The stress curve showed obvious nonlinear characteristics in the process of collision,which illustrated that the load to the structures had transferring and unloading phenomenon in this process.

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