Numerical Simulations of the Damage Process of Double Cylindrical Shell Structure Subjected to an Impact

(China Ship Scientific Research Center,Wuxi 214082,China)

Numerical Simulations of the Damage Process of Double Cylindrical Shell Structure Subjected to an Impact

LIU Jun-jie,WAN Zheng-quan,QI En-rong,Wang Hui

(China Ship Scientific Research Center,Wuxi 214082,China)

Cylindrical shell structure is widely used in marine structure and submarine structure.In order to investigate the response of this structure under impact action and the effect of impact angle on response,the numerical simulation of a double cylindrical shell structure impacted by an object under different loading cases is carried out by MSC.Dytran,an analysis code for nonlinear,dynamic behavior of structure.The damage deformation and energy absorption of cylindrical shell structure as well as the impact force are analyzed in this paper.The results of the calculation are useful to the research and design work of cylindrical shell structure.

impact;double cylindrical shell structure;impact angle;numerical simulation

Biography：LIU Jun-jie(1978-),Male,Ph.D.student of CSSRC.

1 Introduction

Cylindrical shell structure is widely used in the marine structure and submarine structure.For example,the submarine is a typical double cylindrical shell structure which is composed of non-pressure hull and pressure hull.The impact and grounding accidents may happen during the period of submarine service which will lead to the submarine breakage,even sinking and personal casualty.The American “San Francisco” nuclear submarine suffered grounding accident in Jan.2005.Studying the response of cylindrical shell structure under an impact and investigating the damage mechanism of the structure will help improving the structure’s capacity of impact resistance.The impact is an instantaneous process and the deformation of structure members in contact region will jump from elastic form to plastic flow.The damage form in the region may be folding,buckling,tearing,and so on.This whole process is a complex nonlinear,transient response.With the rapid development of nonlinear FE technique,numerical simulation technique has been successfully used in many dynamic problems such as ship collision[1-2]and bullet biting[3].Some scholar used FEM to study the process of cylindrical shell structure impacted by an object[4].The MSC.Dytran,a analysis code for nonlinear,dynamic behavior of structure,is adopted in this paper.The FE model of double cylindrical shell structure impacted by an object is built and the impacting process in different loading cases is simulated.In order to compare the damage degree between single cylindrical shell and double cylindrical shell,the calculation of these two kinds of structures impacted by an object in certain angle is carried out.Through the analysis and study for the numerical simulation results,the damage mechanism of the double cylindrical shell structure and influence of different structure member to the whole structure’s capacity of impact resistance are proposed.The research results in this paper will be of use in cylindrical structure’s impact resistance design.

2 FE model

The program,MSC.Patran is adopted to build the FE model of double cylindrical shell structure impacted by an object.The striking object has a half-ball head and cylindrical body.The FE model of the object presented in Fig.1 is meshed with QURD4 and material is defined as MATRIG.The model has 13 640 nodes and 13 638 elements.

The double cylindrical shell structure is composed of outer shell,inner shell,joint plate and stiffener.The FE model of cylindrical structure presented in Fig.2 is meshed with QURD4 and material is defined as elastoplastic DMATEP.The strain sensitivity is considered and the region contacted with the object is fine meshed in this model.The whole model has 43 824 nodes and 44 424 elements.There are 12 joint plates in the circle and each plate has 12°included angle.

The initial conditions in this simulation are the circle center of object head which is in the middle between two frames of cylindrical shell structure and the distance between two objects is 0.15m,the initial velocity of the object is 75m/s along its axial direction.The boundary conditions are that the two sides of the cylindrical structure are fixed.

In order to study the influence of impact angle to cylindrical shell structure’s damage,7 loading cases i.e.7 object impact angles are considered to the numerical simulation.The def-inition of each loading case is presented in Fig.3.

3 Calculation results and analysis

The Adaptive Master-Slave Surface Contact Arithmetic is adopted for the impact calculation.The surface of double cylindrical shell structure is defined as Master Surface and the surface of object is defined as Slave Surface.The whole time of calculation is 0.045 seconds except case No.7 is 0.06 seconds.A series of calculation results can be obtained from processor MSC.Patran which can reflect the common phenomena and basic rules during the damage process of double cylindrical shell structure impacted by the object.

3.1 The damage and deformation in the impact region

Under different loading cases,the equivalent stress distribution and deformation of double cylindrical shell structure at last time step are shown in Fig.4.We can find that the damage and deformation are different.In case No.1,after penetrating the outer shell of impacted body,the object impacted inner shell for no contacting with joint plate and stiffener directly.The inner shell was torn slightly but not penetrated;in cases No.2 and No.3,the object penetrated the outer shell of impacted body as well,but because the angle of case No.3 shown in Fig.3 is larger than that of case No.2,that means the object contacted with joint plate and stiffener in case No.3 more sufficiently than in case No.2,as well as the energy absorption of joint plate and stiffener were more too,the damage and deformation of inner shell were smaller as shown in Fig.5.The inner shell in these two cases deformed but had no fracture;in case No.4,the object did not penetrate the outer shell of impacted body but bounced.The impact induced deformation of double cylindrical shell structure and friction happened obviously between object and outer shell;In case No.5 to case No.7,the object did not contact with joint plate and stiffener directly and different damage was formed.In the former two cases,the object penetrated the outer shell of impacted body and had friction with the inner shell but no penetrating.The outer shell had not been penetrated and the object bounced just like the case No.4.

Comparing case No.5 with No.2 as well as No.6 with No.3,we can find the damage of inner shell in former cases is severer than in later cases.Then the conclusion can be obtained that the joint plate and stiffener have protection to inner shell.

From the results of calculation,we can find that the damage and deformation of double cylindrical shell structure are concerned with the impact angle under the condition that the initial velocity of object,as well as the parameters of both object and cylindrical structure is certain.The impact angle has a critical value Kangle,while the impact angle is greater than Kangle,the object will bounce instead of penetrating the outer shell of cylindrical structure.In this paper,the value of Kangleis between 30°and 60°.

3.2 The kinetic energy loss and conversion of object

The process of double cylindrical shell structure impacted by an object satisfies the conservation of energy.The initial kinetic energy of the object is converted into the following four types of energy during the impacting process:the remaining kinetic energy of the object after the process,the elastoplastic deformation energy and kinetic energy of double cylindrical shell structure,the thermal energy as a result of friction between the structures and the energy loss of hourglass phenomenon.

The curves of object’s kinetic energy loss and cylindrical structure’s elastoplastic deformation energy vs.time have been obtained from the calculation under different loading cases,as shown in Fig.5.In cases No.1,No.2,No.3,No.5 and No.6,the kinetic energy of the object had been exhausted and the object stopped moving at 45ms.At that moment,the outer shell of cylindrical structure had been penetrated by object and the inner shell deformed differently but no penetration.In cases No.4 and No.7,after simulations were finished,the object still had certain values of kinetic energy,this is because the object failed to penetrate the outer shell of cylindrical structure and occurrence of bounce,object changing the direction of its movement.From the curves shown in Fig.5,we can see that the kinetic energy loss of object mainly changed in the deformation energy of cylindrical shell structure,the kinetic energy of cylindrical structure is very small,can be neglected.

In cases No.1 to No.7,the deformation energy of cylindrical shells structure accounting for the kinetic energy loss of the object are about the percentage:86.16%,84.97%,90.91%,67.82%,76.05%,68.78%and 71.46%.Comparing case No.2 with No.5,case No.3 with No.6,we can see that the values of No.2 and No.3 are greater than those of No.5 and No.6,this is because after penetrating outer shell of cylindrical structure,the object contacted with joint plates and stiffeners directly in former two cases while not in later two cases,the deformation of joint plate and stiffener are more sufficient in former two cases.The values of case No.1 to No.3 are greater than those of cases No.4 to No.7,this is because the energy exhausted by friction are more in cases No.4 to No.7 than in cases No.1 to No.3.

To compare the energy absorption efficiency of outer shell with that of inner shell of cylindrical structure,case No.1 is taken into account.Under the conditions that outer shell was penetrated while inner shell was not,the deformation energy of inner shell is 55.67 percent of the whole deformation energy of cylindrical structure.The outer shell still has large deformation space while inner almost has none.We can find the inner shell is the main energy absorption unit in this double cylindrical shell structure.

3.3 Impact force

Three cases No.1,No.3 and No.6 were selected for this study.Under the three selected cases,the curves of impact force vs.time can be obtained from the calculation,as shown in Fig.6.It is obvious that the impact force has non-linear characteristics.Different loading cases and different stages of impact,the double cylindrical shell structure has different deformation and impact force.Each discharge of impact force represents yield or failure of a certain unit.In Fig.6,the discharge of impact force at point 1 stands for the fracture of outer shell.The discharge of impact force at point 2 in cases No.1,No.3 and No.6 stands for the yield or failure of inner shell,the yield and deformation of joint plate and stiffener,the yield and deformation of inner shell,respectively.From the Fig.6,we can find the value of impact force at point 1 is different in each loading case;this means the value is concerned with the impact direction and angle.We can see that the value of impact force at point 2 is greater than that at point 1;this means the value is concerned with the structure parameters too,for example material and plate thickness,etc..

4 Comparison of simulation results between single and double cylindrical shell structure

The process of single cylindrical shell structure impacted by an object had been calculated in Ref.[5].In order to compare the damage mechanism between single and double cylindrical shell structure impacted by object,impact angle in case No.6 was selected to the numericalsimulation ofsingle cylindrical shell structure with same parameters impacted process.

The equivalent stress distribution and deformation of single cylindrical shell structure at simulation time 45ms are shown in Fig.7 which are similar to those of outer shell in double one.The deflection of object in single one is smaller than that in double one,because the object in single did not contact with any units after penetrating the shell,while did in double one,the friction changed the movement direction of the object.

The energy curves of single,double cylindrical shell structure impacted by the object are shown in Fig.8.The curves Ⅰ,Ⅱ,Ⅲ,Ⅳ and Ⅴ represent respectively,kinetic energy of object impacting single cylindrical shell structure EKS,deformation energy of single cylindrical shell structure EDS,kinetic energy of object impacting double cylindrical shell structure EKD,deformation energy of outer shell and inner shell in double cylindrical shell structure EDD1,EDD2.When the calculation is finished,the values are EKS=1 638 700J,EDS=1 136 700J,EKD=22 961J,EDD1=1 548 100J and EDD2=707 930J.Obviously,the energy absorption capacity of double cylindrical shell structure is greater than that of single one.

The impact force curves of single,double cylindrical shell structure impacted by object are shown in Fig.9.The curvesⅠandⅡrepresent respectively impact force during single and double cylindrical shell structure impacted process.We can find the maximum impact force is similar when outer shell is fractured in two kinds of structure,this means whether single or double shell does not influence the value of impact force of outer shell.

5 Conclusions

(1)The damage of cylindrical shell structure has obvious localized deformation.The deformation of whole cylindrical structure is very small and the damage is concentrated in the contact region.

(2)The damage and deformation are different under different loading cases.The influence of joint plate and stiffener to the impact resistant ability of cylindrical shell structure is different under different loading cases.The damage form of unit may be folding,buckling,tearing,and so on.

(3)The impact angle has a critical value Kanglewhen the parameters of object and cylindrical structure are certain.Once the impact angle is greater than the Kangle,the object will bounce instead of penetrating the outer shell of double cylindrical shell structure.

(4)The kinetic energy loss of object has become a major conversion of the deformation of cylindrical shell structures during the impact process.In this process,the local inertia of damaged unit is very small and its local kinetic energy can be neglected,the plastic deformation of the cylindrical structure adsorbed large amount of kinetic energy of object.The effect of energy absorption capacity of cylindrical structure is concerned with the impact angle of object.The energy absorption capacity of double cylindrical shell structure is greater than that of single one,as well as that of inner shell greater than outer shell.

(5)The impact force has non-linear characteristics.The time course of impact force curve has an obvious non-linear characteristics and each discharge of impact force represents yield or failure of a certain unit.The value of impact force is related to the direction,angle and the parameters(material,thickness,etc)of cylindrical shell structure,while has nothing to do with its structural form(single shell or double shell).

[1]Wang Zili,Gu Yongning.Numerical simulations of ship/ship collisions[J].Explosion and Shock Waves,2001,21(1):29-34.(in Chinese)

[2]Fan Bin,Wang Lin.Study on ship-bridge collision and protection structure of bridge[J].Journal of East China Shipbuilding Institute(Natural Science Edition),2005,19(4):1-5.(in Chinese)

[3]He Tao,Wen Heming.Computer simulations of the penetration of metal targets by spherical-nosed projectiles[J].Explosion and Shock Waves,2006,26(5):456-461.(in Chinese)

[4]Tan Dali,Mei Zhiyuan,Chen Weiran.Collision mechanism analysis for rib-stiffened cylinder under water pressure condition[J].Journal of Ship Mechanics,2008,12(4):635-641.(in Chinese)

[5]Liu Junjie,Wan Zhengquan,Qi Enrong.Study on simulation of damage process of ring-stiffened cylindrical shell impacted by object[J].Steel Construction,2008,23(115):32-35.

双层圆柱壳受物体撞击损伤过程数值仿真

刘俊杰，万正权，祁恩荣，王 辉

（中国船舶科学研究中心，江苏 无锡 214082）

圆柱壳是海洋工程结构物和潜体中广泛采用的结构单元，为了研究其在物体撞击作用下的响应以及撞击角度对撞击响应的影响，文中采用大型非线性动态响应分析程序MSC.Dytran，分不同撞击角度，对双层圆柱壳结构受射弹撞击过程进行了数值仿真，研究分析了圆柱壳结构的损伤变形、能量吸收及撞击力的变化情况。文中的计算结果对圆柱壳结构物的抗撞击分析研究及合理的结构设计有参考价值。

撞击；双层圆柱壳结构；撞击角度；数值仿真

U661.43

A

刘俊杰（1978-），男，中国船舶科学研究中心博士生，研究方向为舰艇碰撞结构安全性研究；

王 辉（1976-），男，中国船舶科学研究中心高级工程师。

U661.43

A

1007-7294（2010）06-0660-10

date：2010-02-05

万正权（1962-），男，中国船舶科学研究中心研究员，博士生导师；

祁恩荣（1965-），男，中国船舶科学研究中心研究员；