Scholarly article on topic 'Effects of the rebounding of a striking ship on structural crashworthiness during ship-ship collision'

Effects of the rebounding of a striking ship on structural crashworthiness during ship-ship collision Academic research paper on "Materials engineering"

CC BY
0
0
Share paper
Academic journal
Thin-Walled Structures
OECD Field of science
Keywords
{"Ship collision" / "Bow-side interaction" / "Structural crashworthiness" / "Striking ship's rebounding" / "Resistance to penetration" / "Finite element experiment"}

Abstract of research paper on Materials engineering, author of scientific article — Aditya Rio Prabowo, Dong Myung Bae, Jung Min Sohn, Ahmad Fauzan Zakki, Bo Cao, et al.

Abstract The purpose of this paper is to study the rebounding phenomenon of a striking ship and its effect on the structural crashworthiness of the struck ship. Pioneer works on ship collision and mathematical formulations to assess energy after collision are described to summarize the behaviour of the ship structure under collision between ships in various scenarios. A benchmark study is conducted using laboratory tests of the resistance to penetration of a stiffened plate to validate the methodology of the present work, which uses finite element methods to model a series of dynamic collision scenarios. The setting and configuration of a full-scale collision analysis is introduced, along with the configurations of the defined scenarios. External and internal ship collision parameters are considered as parameters that will affect structural behaviour prior to and after ruptures. The results of the evaluation indicate that in the event of a side collision, the striking ship can either fully stuck or rebounding phenomena. These phenomena produce significant differences in term of internal energy and crushing force, which are included as crashworthiness criteria. The type of striking ship, as well as its velocity, significantly affects the rebounding of the striking ship and behaviour of the struck ship. A notable gap between medium and high-carbon steels is not found during observations of the structural crashworthiness accounting for structure materials. Finally, other criteria for assessing the mechanisms and effects of rebounding during a collision are summarized, i.e. kinetic energy, acceleration, and extent of damage.

Academic research paper on topic "Effects of the rebounding of a striking ship on structural crashworthiness during ship-ship collision"

Contents lists available at ScienceDirect

Thin-Walled Structures

journal homepage: www.elsevier.com/locate/tws

Full length article

Effects of the rebounding of a striking ship on structural crashworthiness during ship-ship collision

Aditya Rio Prabowoa,!\ Dong Myung Baeb, Jung Min Sohnb, Ahmad Fauzan Zakkic, Bo Caod, Joung Hyung Choa

a Interdisciplinary Program of Marine Convergence Design, Pukyong National University, Pusan, South Korea b Department of Naval Architecture and Marine Systems Engineering, Pukyong National University, Pusan, South Korea c Department of Naval Architecture, Diponegoro University, Semarang, Indonesia d China Shipbuilding Industry Economic Research Center, Beijing, China

CrossMark

ARTICLE INFO

ABSTRACT

Keywords: Ship collision Bow-side interaction Structural crashworthiness Striking ship's rebounding Resistance to penetration Finite element experiment

The purpose of this paper is to study the rebounding phenomenon of a striking ship and its effect on the structural crashworthiness of the struck ship. Pioneer works on ship collision and mathematical formulations to assess energy after collision are described to summarize the behaviour of the ship structure under collision between ships in various scenarios. A benchmark study is conducted using laboratory tests of the resistance to penetration of a stiffened plate to validate the methodology of the present work, which uses finite element methods to model a series of dynamic collision scenarios. The setting and configuration of a full-scale collision analysis is introduced, along with the configurations of the defined scenarios. External and internal ship collision parameters are considered as parameters that will affect structural behaviour prior to and after ruptures. The results of the evaluation indicate that in the event of a side collision, the striking ship can either fully stuck or rebounding phenomena. These phenomena produce significant differences in term of internal energy and crushing force, which are included as crashworthiness criteria. The type of striking ship, as well as its velocity, significantly affects the rebounding of the striking ship and behaviour of the struck ship. A notable gap between medium and high-carbon steels is not found during observations of the structural crashworthiness accounting for structure materials. Finally, other criteria for assessing the mechanisms and effects of rebounding during a collision are summarized, i.e. kinetic energy, acceleration, and extent of damage.

1. Introduction

Technological developments have given various communities the opportunity to expand their observations of ocean resources, as commodities and materials such as crude oil, natural gas, fish, etc. are in demand globally. In these conditions, marine structures such as ships become vital, for supplying offshore activity or even transporting export-import products. Furthermore, serious attention has been paid to improvements in ship safety [1] and structure [2]. During operational and stand-by modes, a ship can be subjected to various loads, which must be resisted to ensure that the objective of ship is fulfilled and the safety of crew, passenger, cargo, and ship itself can be guaranteed. Analyses are conducted before the ship is accepted for construction; these analyses assess the stress and strength of the structure. For such an analysis, information is required on loads, and an initial structural scantling design must be available. The output of the structural analysis is the structural response, defined in terms of stresses, deflections, and

strengths. Then, the estimated response is compared to the design criteria [3]. However, other loads that cannot be resisted may occur accidentally, which can cause remarkable casualties on the ship and its surroundings. A collision creates an accidental load that is always linked with negative consequences, such as those resulting from the terrible accident of the Doña Paz in the Philippines, in which only 26 out of more than 1400 passengers were reported to have survived. In other cases of collision, environmental damage may occur, such as oil leakage from a tanker vessel [4]. In addition to being an accidental load, collision is also classified as an impact phenomenon whose occurrence involves significant nonlinearities. Collision scenarios may be limitless, depending on the various influences from materials, structures, etc.

In this work, an observation of structural behaviours affected by several parameters involved in ship collision is conducted. A series of impact scenarios are defined to estimate the behaviour of the struck ship during and after impact by the striking ship. Crashworthiness

* Corresponding author. E-mail address: aditya@pukyong.ac.kr (A. Rio Prabowo).

http://dx.doi.org/10.10Wj.tws.2017.02.022

Received 6 June 2016; Received in revised form 19 January 2017; Accepted 23 February 2017

0263-8231/ © 2017 The Authors. Published by Elsevier Ltd.

This is an open access article under the CC BY license (http://creativecommons.Org/licenses/BY/4.0/).

Fig. 1. Experiment preparation for the penetration on the stiffened plate: (a) laboratory instrument [13] and (b) technical drawing of the stiffened plate (illustration is made based on description of [13]).

(a) (b)

Fig. 2. Numerical model of the penetration experiment: (a) perspective view which shows the indenter on the top of the plate and (b) stiffener on the lower part of the plate.

Fig. 3. Force tendency against displacement of the indenter. Verification is conducted by comparing the present work to results of the penetration experiment by [13].

criteria are summarized, and further predictions are presented in the evaluation of results.

Fig. 4. Comparison of with previous method to validate ship grounding analysis. The experiment result by [37] is presented as verification of the present work.

2. Literature reviews of impact engineering and analysis

2.1. Pioneer works of impact engineering

Collision is classified as an accidental load and impact which can occur in various scenarios that lead to remarkable damage. In marine and ocean structures, this phenomenon is observed to evaluate safety

Fig. 5. Damage contour on the panel in event of penetration by the indenter: (a) penetration experiment [13] and (b) numerical simulation.

Table 1

Principal dimension of the striking ship.

Dimension component Striking-I Striking-II

Length over all (m) 67.50 144.50

Breadth (m) 12.80 19.80

Draught (m) 3.00 5.60

Depth (m) 3.90 10.20

Table 2

Principal dimension and scantling of the Ro-Ro ship.

Variable Value

Principal dimension

Length over all (m) 85.92

Breadth (m) 15.00

Draught(m) 4.30

Depth (m) 10.40

Scantling

Main frame (mm) L 150x90x9

Web frame (mm) T 300x9 + 125x12

Deck beam (mm) L 125x75x9

Strong beam (mm) T 350x10 + 150x16

Side shell 12 (lower than car deck) and 10 (upper than car deck)

Inner shell 10

Main deck 8

Middle deck 8

Car deck 15

Tank top 12

aspects. Nonlinear behaviour is expected during its occurrence, for example in ship collision. A method for structural analysis under ship collision was introduced by Paik and Seo [5] which is considered as development of practical techniques for finite element modelling in observing collision and grounding phenomena [6-8]. Relationships of structural behaviour in event of ship-ship collision subjected to different external parameters, e.g. angle and velocity have been presented after twentieth century until recently by researchers, such as Zheng et al. [9], Tabri [10], Pill [11], and Prabowo [12]. These studies are needed to be continued sustainably in order to provide tendency of structural behaviour under impact as development of ship design and structure is also conducted rapidly.

preparation. However, the result can be considered very good and in further analysis and observation can be deployed as benchmark reference. Previous penetration tests [13,14] of Alsos, Amdahl, and Hopperstad at Norwegian University of Science and Technology (NTNU), Bae et al. with implementation of laboratory testing and material characterization based on specimen of an actual collision accident on finite element simulation [15], and correlation of material characteristics and ship survivability under collision by Ringsberg [16] are several pioneer studies in collision and material experiments.

: 47.2RT + 0.5 ^ (ht2) : Ca0/' V-6

: C1.5 Ö0/1'5teq1'5

Serious attention has been paid to collision and other forms of impact, such as grounding up to this day using several calculation methods which actually correlate with the mentioned methods. In time period approximately 40 years since 1958 when Minorsky introduced energy formula [17], empirical method had been developed by Vaughan [18], Woisin [19], Lu and Callidine [20], Paik [21] and Zhang [22]. Their formulas are presented in mathematical forms in Eqs. 1 to 6. Analytical equations are also considered reliable in predicting structural behaviour under collision as presented by Pedersen [23,24], Kierkegaard [25], Hysing [26] and Scharrer [27].

-- Po-L [Emp + (5.0 - L)L16]0-5 = 22.4-Po [EimpL ]05

: 263ß[1.0 + 0.88(è/D)106]-[L/300]2-20

(8) (9)

E = 47.2RT + 32.7

The formulation in ship collision is expanded by Liu and Amdahl [28] using Stronge's assumption [29] in contact between two rigid entities for ice-structure interaction which this topic is also recently studied by Bae et al. [30] on a chemical tanker. Proposed analytical expressions of Pedersen are presented in Eqs. 7-9. As indicated in previous paragraph, the involvement of numerical method in assessing ship structure under impact is also considered in pioneer works. High influence from technology development makes this method is deployed in wide spectrum of science and technology analyses. A comprehensive application of finite element method in ship and collision is presented in next section.

RT =2 PNLNtN + PnLntn (2)

E = 93RT + 33A (3)

Development of structure and design will always consistent with safety that makes analysis of collision impact on marine structure is extended to material response in experiencing the impact. Study on material-level behaviour for ship structure can be conducted by laboratory experiment and simulated further by numerical method. This kind of study is indeed expensive in term of time and material

2.2. Review on numerical experiment for collision phenomena

Advance developments of impact engineering, especially in ship collision are not independent from the improvement of computational instrument which is considered as good calculation method in estimating structural behaviour and material response under various forms of load. Deployment computer to calculate a phenomenon is generally called by numerical experiment - simulation. As indicated by its name, this method is defining real phenomena (physical data i.e. geometry,

Table 3

Proposed failure strain versus mesh size by Germanischer Lloyd [38].

Stress state One dimension structure Two dimension structure

0.079 0.056

Be 0.760 0.540

Element type Beam-Truss Shell-Plate

property, etc.) into the numerical information and then is solved by certain code, for example finite element. This method is judged by researchers suitable for analysis on collision and grounding. The produced results have satisfactory with calculation by other methods such as empirical formulae [15], simplified expression [31], and even laboratory experiment [13]. After methodology for large-scale simula-

tion is verified by benchmark particulars, the numerical result can be considered as reliable result. This method allows preparation in physical test and experiment can be pressed as low as possible and failure in the experiment can be re-conducted after several refinements.

However, despite of its positive characteristics, challenge rises to obtain numerical solution in reasonable time process. It cannot be denied that time is essential in every method of research, as well as in this method. An accurate result may be obtained by making detail geometry and property as physical reference during pre-processor stage is conducted. This assumption is relative and not always true in numerical study. Bathe [32] specifically described for finite element method that mathematical (numerical) model should fulfil two main criteria in terms of effectiveness and reliability. Proper consideration in deploying overall ship model is recommended to be conducted before

Table 4

Material properties of the proposed steel.

Material Steel grade Yield strength Ultimate strength Elastic modulus Density Poisson's ratio

(Pa) (Pa) (Pa) (kg/m3) (-)

Medium-carbon 1030 4.40X108 5.25X108 2.10X1011 7850 0.30

High-carbon 1080 4.80X108 8.00X108

HSLA AH32 3.15X108 4.70X108

1.8x10° 1.6x10° 1.4x10° 1.2x10° P 1.0x10'

S 8.0x10 c

e 6.0x10' 4.0x10s 2.0x10s 0.0

-------Striking 1. Cons. Velocity - 3 m/s ----Striking 1, Jnil. Velocity - 3 in/s ......Striking 2, Cons. Velocity - 3 m/s Striking 2, Init. Velocity T 3 m/s

0.00 0.05 0.10 0.15 0.20 0.25 0.30

Time (s)

Fig. 8. Result of internal energy for different applied velocity's characteristic on the striking ship.

5.0x10 4.5x10° 4.0x10° 3.5x10° 3.0x10°

2.0x10 2 1.5x10°-1.0x10°-5.0x10s 0.0

-------Striking 1 Cons. Velocity - 3 m/s

----Striking 1 Init. Velocity — 3 m/s Cons. Velocity _ 3 nr/s

Striking 2

-----Striking 2 Init. Velocity = 3 m/s / >: f : i? \ P ■ : : ,/ j \ •'•-„.-■•■•'7 .v.

/ v ft I..., /•-' rf : y' ■ri \ ' A. /

i J J --- r vi,«.i-y v ^ v '

J ¿' \

0.00 0.05 0.10 0.15 0.20 0.25 0.30

Time (s)

Fig. 9. Tendency of striking force during collision process. Distinction is spotted for different velocity type.

pre-processor stage is performed, since this stage often requires man-hours in making model, defining material part, etc. The other reason is also stated by Bathe that by numerical analysis, user cannot predict the response of physical problem exactly because it is impossible to reproduce even in the most refined mathematical model. Therefore, several researchers in their early works, specifically in collision [33,34] and grounding [35,36], only deployed a partition using a ship region that would be observed under impact instead of full model. As indicated in previous paragraph, to ensure numerical solution of this research method, benchmark is needed. Based on the review, a study which is conducted by several methods to provide satisfactory verification of experiment or investigation. Combination between investigation and real phenomena laboratory test, with deploying numerical experiment in further evaluation is preferred as conducted in several pioneer works. Validation using empirical formula and simplified method is also

Fig. 10. Internal energy for ten velocities of the striking-I. Rupture is estimated occur on 9-10 m/s.

proved can produce good agreement with other methods. 2.3. State-of-the-art

The previous subsection described pioneering impact engineering works, as well as the implementation of numerical experiments for modelling ship collision. Review based on the presented references concludes that collision analysis is continuously performed to fulfil demand of safety (survivability) during ship operational. Both testing and modelling were used to study and adequately verify the contribution of materials [16]. The behaviour of structures and materials under collision (especially between two ships) can be predicted by other methods, such as empirical formulae [15,34] and analytical methods [31]. Several analyses indicate that during a collision between ships, the striking ship (which penetrates the other ship in a collision) is assumed to be completely-stuck on the struck ship at the end of the collision process. By assessing defined assumptions in pioneer studies, complete-stuck phenomenon can be considered to possibly occur under certain conditions, as follows:

1. The striking ship has a constant velocity. Therefore, during the penetration process, the striking ship can penetrate up to the designated target location without being influenced by the inner structure of the struck ship.

2. The striking ship is significantly larger than the struck ship. However, this factor is relative, as there is another possibility in this assumption, which is that the striking ship will capsize at the end of collision process.

3. A side collision scenario is applied, and the struck ship is set to stand still under impact.

These assumptions are convenient to use, as it is reasonable to assume that this is the worst case for the struck ship, especially in a side collision scenario where the striking ship continues to penetrate the side structure of the struck ship. Nevertheless, this definition ignores the fact that a ship is designed and built to be simultaneously strong and

Fig. 11. Extent of damage on the struck ship after collision with the striking-I. Two velocities are affecting the rupture on side shell before the striking ship experiences rebounding.

Fig. 12. Crushing force of the collision scenario with the striking-I. The characteristic of rebounding can be estimated in conditions of prior to rupture and after to rupture.

Fig. 13. Behaviour of internal energy under collision with the striking-II. Rupture is estimated already occur in velocity 6 m/s as larger ship is deployed in the experiment.

Z 3.00x10'

U. 2.25x10 -

" I 'I -

Ж/. : ii liV'i ' ' '

.,','> - S.?, « «;{г.! 4> .

й ¡ЗШ'Й^Л 'Н. •

» i^i"'Tuvlkrtv, »m ^ Л|/ 1 1 у v , ■

а.' ; " V \YY-

$ I ! --

-----6 m/s

----7 m/s

----8 m/s

-----9 m/s

10 m/s

4 \ Ь'У'О \\ "ft"1'

—i—

Time (s)

Fig. 14. Crushing force in five scenarios with the striking-II acts as the indenter. Overall fluctuation indicates satisfaction is achieved that higher velocity will affect internal energy as well as the experienced force.

Time (s)

Fig. 15. Crushing force in collision with the striking-II for different applied material.

5x10 -

È5 3x10s-

a3 с LU

1 2x10s

.....-.....-................................

! -------Floor

! - - Center girder

• -------Tank top

; -------Side shell

-------Main frame

-------Web frame (1 part)

* -------Web frame (- part)

0.15 Time (s)

Fig. 16. Internal energy for each part on the lower part as applied by the high-carbon steel. Side shell refers to the outer shell. This term is used since no inner shell in the lower part.

flexible. In an assessment where the striking ship continues to perform a crushing process during collision, the produced results only provide strength characteristics, while the flexural ability of the struck ship to

Fig. 17. Tendency of internal energy on the upper part which involves more members in side collision.

resist penetration is neglected. In order to develop new considerations of collisions between two ships, this work has been conducted to estimate the structural crashworthiness of a struck ship under a dynamic collision scenario with respect to the rebounding phenomenon of the striking ship after penetration occurs. The contributions of structural and material parts in a collision is considered as an internal parameter, while collision velocity and the striking ship represent external factors. Different striking ships are deployed to consider the relationship between ship dimension and penetration location. Crashworthiness criteria, including energy, force, acceleration, and damage are evaluated and discussed.

3. Methodology verification: on the resistance of stiffened panels to penetration damage

3.1. Experiment preparation

The numerical simulation methodology in this work will be validated with a benchmark study to ensure that the method can produce reliable results. The study is performed by changing the mesh with respect to collision force and indenter displacement in order to verify the numerical method. This study is conducted based on experiments by using a resistance panel subjected to the penetration of a rigid indenter [13] at the Norwegian University of Science and Technology (NTNU). In the experiment, the stiffened panel (representing the side structure of the struck ship) is set to be laterally impacted by the conical indenter, which acts as the striking ship in the case of a full-scale collision analysis (Fig. 1). The penetration experiment will be modelled by numerical methods; the setup of the virtual model is shown in Fig. 2.

In the numerical experiment, the finite element method will be used to conduct a penetration test with varying meshing configurations for the involved structures, which are approximately 10x10 mm and 15x15 mm. Contact is strictly modelled between the rigid conical entity (the indenter) and the structural members of the stiffened plates. A plastic-kinematic material is implemented for the stiffened plate (the target structure); this material has density p = 7850 kg/mm3, Poisson's ratio v = 0.3, yield strength ay = 260 MPa, and Young's modulus Ex = 210 GPa. Strain rate effects are included in the material model using Cowper-Symonds parameters Ccs = 4000 (1/s) and Pcs = 5.0. The results from the numerical model are summarized, along with force tendency and damage contours of the stiffened plate after the penetration test.

Striking-I: AH32

Striking-!!: AH32

Fig. 18. Damage extent by different material type based on the target location respecting the ship size.

Fig. 19. Kinetic energy of collision with the striking-I in different applied velocities.

Table 5

Structural response during collision with the striking-I. Displacement refers to the outer shell.

Velocity Displacement (m)

Rebound

(m/s) Side shell Main frame Web frame Tank top Car deck (m)

1 0.00549 0.00868 0.00000 0.00002 0.00406 0.06119

2 0.02461 0.03142 0.00418 0.00067 0.01065 0.15435

3 0.04742 0.05388 0.02805 0.00149 0.02945 0.22569

4 0.06906 0.07950 0.04817 0.00207 0.03436 0.29191

5 0.08848 0.10280 0.07417 0.00215 0.04397 0.38931

6 0.11140 0.12920 0.09349 0.00219 0.05390 0.41689

7 0.13370 0.15530 0.11210 0.00129 0.04689 0.47608

8 0.16110 0.18590 0.13630 0.01756 0.05233 0.52439

9 0.22440 0.28320 0.16550 0.01854 0.06406 0.25322

10 0.31050 0.35630 0.17310 0.02549 0.07476 0.20159

3.2. Simulation results

The results from the present work will be compared first with those from the penetration experiment, then with the results of similar simulations, in order to verify the grounding analysis [37]. Comparison will cover force magnitude during contact between the target structure and rigid indenter, and damage contour on the plate during penetra-

tion. During the verification of the model with the results of the penetration experiment (Fig. 3), it could be concluded that the force results were in good agreement with both of the experimental results and the results of previous work done with models of various mesh sizes (Fig. 4). Although there was a difference in magnitude after the force decreased, the overall tendencies allowed us to conclude that the displacement when the force reached its approximate maximum point was satisfactory, with a difference of less than 0.025 m between the experiment and simulation.

Similar deformation contour (Fig. 5) on the plate during got penetrated by the indenter completed the evaluation. Based on these results, good correlation with the experimental results is achieved as well as in comparison with the verification results of grounding analysis. The present method is successfully validated and can be used for the full-scale collision analysis in further section.

4. Ship collision

4.1. Principal dimension and engineering model

In this work, a series of collision scenarios between two ships are considered, and deployed in the simulation. The ships are defined as follows: the struck ship is the penetrated target, and the striking ship acts as the indenter in the event of ship collision. A deformable structure is applied to the Ro-Ro ship (the struck ship), while rigid characteristics are implemented for the two striking ships, which are a passenger ship and a cargo reefer. These striking ships are chosen by considering their size relative to the struck ship: the passenger ship is smaller and the cargo reefer is larger. The principal dimensions of the striking ships are presented in Table 1, and the scantling configuration of the struck ship is given in Table 2. Numerical models are shown in Fig. 6. Since different striking ships are used, the passenger ship will be denoted as the striking-I and cargo reefer denoted as the striking-II in further analysis.

£f (le) = £g + £e

In the numerical experiment, ship models will be deployed as the involved ships, and will be analysed in several scenarios by explicit finite element (FE) codes LS-DYNA to estimate the structural crash-worthiness of those ships in the event of a collision. As a highlight of the collision scenario, varying velocities will be modelled for the movement of the striking ships to the designated target location on the struck ship,

Table 6

Structural response during collision with the striking-II. Displacement includes shells and decks.

Velocity

Displacement (m)

Rebound

(m/s) Outer shell Inner shell Deck (m)

Side shell Main frame Web frame Side shell Main frame Web frame Main deck Middle deck Car deck

6 m/s 0.28540 0.34250 0.17120 0.11430 0.11430 0.00011 0.06497 0.01106 0.01106 0.09840

7 m/s 0.30770 0.46300 0.23000 0.00294 0.00294 0.00294 0.06522 0.00517 0.00517 0.07343

8 m/s 0.52230 0.60350 0.36000 0.04583 0.04583 0.04583 0.09221 0.03219 0.00218 0.12414

9 m/s 0.54280 0.63490 0.45060 0.10030 0.10030 0.10030 0.07499 0.04434 0.01369 0.06089

10 m/s 0.80990 1.04400 0.69290 0.10820 0.10820 0.10820 0.06333 0.07575 0.01697 0.09264

Table 7

Damage mode on side shell in collision with Striking-I.

Time (s)

Fig. 20. Kinetic energy on collision scenario using the striking-II as the indenter.

0.15 0.20

Time (s)

21. Acceleration of the struck ship during collision with applied velocity 10 m/s.

which is restrained by the centreline. Fixation is applied to all transverse frames at the end of the struck ship model. In the same location, axial displacement is applied on the shell plating. When contact between two ships occurs, dynamic stress will be produced on the deformable structure as different parameters are applied in each scenario. Several responses are estimated to take place with respect to the applied parameters for both the striking and struck ship. As previously described, ship collision is a very complex process. It involves significant force, extensive damage contours, and crushing of structural members. Rupture is unavoidable in certain cases, and the entire process is highly nonlinear. Unwanted phenomena in such a dynamic system can occur in the form of hourglass and shear locking phenomena. The fully integrated Belytschko-Tsay element formulation

Striking 1

Velocity (m/s) Damage on side shell (in length)

Tearing (m) Plastic (m) Folding (m)

1 0.0000 0.7804 0.0000

2 0.0000 1.8789 0.0000

3 0.0000 3.4565 0.0000

4 0.0000 3.5199 0.0000

5 0.0000 4.9240 0.5192

6 0.0000 5.5185 0.8150

7 0.0000 5.8337 1.4010

8 0.0000 5.5619 1.9158

9 1.3831 4.9595 2.2843

10 1.9435 4.5347 2.7270

Table 8

Damage mode on side shell in collision with Striking-II.

Type Velocity (m/s) Damage on side shell

Tearing (m) Plastic (m) Folding (m)

Striking 2 6 1.3387 5.1236 1.9963

7 1.9803 4.9111 2.0698

8 2.2733 5.6496 1.9739

9 2.7616 4.6931 2.0359

10 3.0840 4.1722 1.1493

is implemented as a countermeasure for all model scenarios. A plastic-kinematic material is applied on the struck ship—the failure criterion for this type of material is defined based on the failure recommendations of Germanischer Lloyds [38], as shown in Eq. (10) and Table 3. The mesh sensitivity of the overall model is determined to be in the range of 5-10 in terms of element length-to-thickness (ELT) ratio. As two ships undergo contact in a collision process, their friction properties must be defined. Typically, static coulomb friction coefficients in the range 0.2-0.4 are adopted for steel-on-steel contact. Therefore, a coefficient of 0.3 will be implemented for the FE configuration in this work. Further details of the engineering model (i.e. material properties, ship velocities, and target location) will be described in next subsection.

4.2. Scenario configuration

A series of collision scenarios are defined for the present work in this subsection. The applied parameters in the analyses are considered based on external and internal parameters relative to the struck ship. In terms of external parameters, the velocity and size of the striking ship are considered. Several implemented material properties (based on chemical composition and differences in structural arrangement as affected by the target location) are determined as the internal parameters. This consideration is applied to the simulation based on a review of the mechanics of ship collisions [22], where the external parameters are evidenced to contribute significantly to the crushing of

A Rio Prabowo et aL Table 9

Displacement and damage during collision with the striking-I. Results refer to the outer shell.

Material type Displacement (m)

Side shell Main frame Web frame Tank top

1030 0.3105 0.3563 0.1731 0.0255

1080 0.2713 0.3226 0.1505 0.0213

AH32 0.4035 0.5680 0.4858 0.0226

involved structures. Ships with several structure material and shipbuilding arrangement may be subjected to impact loading, which leads to an assessment of the crashworthiness of a ship structure with several internal configurations (i.e. material and structural arrangement) against side collision.

In the present work, the striking ships are assigned specific velocities in the range of 1-10 m/s. Constant and initial characteristics are defined to demonstrate the contribution of ship velocity to struck and rebounding phenomena in a side collision scenario. In order to evaluate the capability of the struck ship to resist collision impact in various situations, the velocity range is expanded, so that velocities higher than the recorded velocity of the striking ship are included in the analysis. For another external parameter (as described in the previous subsection) two striking ships are determined based on their size relative to the struck ship. The effect of ship size on structural behaviour under impact will be observed and discussed. The size affects the target location of each striking ship, which is illustrated in Fig. 7 with the assumption that during a collision process, the involved ships are fully loaded. Thus, the ships mould until they reach maximum draught. The internal parameters of the struck ship are implemented with consideration of the steel material according to the carbon composition. There are three steels (including medium-carbon, highcarbon, and high-strength low-alloy (HSLA)) that are used on the deformable structure. The strength properties of these materials are presented in Table 4. In the proposed material model, the strength properties of the three steels will be applied along with the calculated failure strain with respect to mesh size. The structural capability under the influence of several materials will be assessed against collision with the striking ships. On the other hand, besides affecting draught (the larger ship has a higher draught), the dimensions of the striking ships also contribute to the target location in the vertical direction, which has a different structural arrangement. Striking-I, which is smaller than the struck ship, impacts the lower part of the side structure of the struck ship. This part is defined to be the side structure between the car deck and tank top. Striking-II is larger than both the struck ship and striking-I, and it impacts the upper part of the struck ship. This part is determined to be the side structure between the main and car decks, where an inner shell is also installed. The ship crashworthiness of the upper and lower parts (which have significantly different structures) subjected to the defined collision scenarios are evaluated and discussed.

5. Structural crashworthiness at the collision

5.1. Applied velocity

The applied velocity results are presented in this subsection. As described in the scenario configuration, the possibility of the striking ship being completely stuck on the target ship exists, and can occur during collision, especially during a side collision. However, the flexibility of the side hull of the struck ship provides another possibility, in which rebounding may happen. Two velocity types were calculated. Their tendencies, shown in Fig. 8 indicate that for cases with the same parameters i.e. velocity, involved ships, experiment time and other material and structure configurations, different results are obtained. The experiment, which was conducted using a constant velocity, produced an internal that increases continuously during a collision

Damage on side shell (in length) Rebound

Car deck Tearing (m) Plastic (m) Folding (m) (m)

0.0748 1.9435 4.5347 2.7270 0.2016

0.0734 1.7576 4.5997 3.6206 0.2192

0.0805 2.7698 3.0084 2.2173 0.0675

event. This behaviour matches the applied characteristics of the striking ship, which was set to constantly penetrate the struck ship during collision. In comparison with previous work [31,34,39,40] that used FE calculations, simplified expressions, and model tests, the energy tendencies in the present work are in good agreement. The initial velocity characteristics, on the other hand, indicated that the energy increases to certain level and decreases after reaching a peak point. This tendency is influenced by the elastic characteristics of the material and structure of the struck ship. During the initial penetration, the striking ship continuously penetrated the struck ship, moving with kinetic energy.

As penetration occurred during the collision process, the struck ship absorbed kinetic energy, and the movement of the striking ship stopped at the point at which internal energy reached a maximum. This point represents the amount of energy needed to deform or even destroy the target structure using maximum penetration. After that, the internal energy decreased, indicating that no further penetration or crushing process was occurring. However, in this situation, the striking ship was not stuck; that is, it remained in the same position at which maximum penetration occurred. The elastic properties of the applied material provide flexibility to the struck ship—it is widely known that ships are designed to satisfy two criteria, strength and flexibility. Flexibility cannot be ignored, as a ship will experience various dynamic loads. Considering only the criteria of strength can lead a ship to remarkable failure, caused (for example) by sagging and hogging. In the kinetic energy collision results (presented in a later discussion), flexibility produces a rebounding phenomenon in which the striking ship bounces back after collision. This event occurred as the kinetic energy of the striking ship, which was completely absorbed by the struck ship, tended to deflect to the opposite direction from the approach direction of the striking ship. A phenomenon of the deflected striking ship that reached the maximum penetration (in this moment it has zero kinetic energy and its movement is stopped) to opposite direction from the approach direction is called rebounding. A good correlation is also shown in terms of crushing force (Fig. 9) during collision. The striking ship which using the constant velocity was found capable to perform extensive crushing onto deeper penetration than the initial velocity. High-fluctuation of the crushing force was observed take place along collision period and it completely stuck in the end of impact. The similarity of the characteristics of the two velocities is apparent only for very short durations (approximately 0.03 s). After this time period, the crushing force of the ship with a constant velocity continuously increased; the ship with an initial velocity also increased, but not with the same significant tendency shown by the ship with the constant velocity. Based on this evaluation, it can be concluded that rebounding phenomena can possibly occur during a side collision scenario between two ships; this result demonstrates that the crashworthiness of the target structure can significantly differ during rebounding of the striking ship.

5.2. Striking ship

This section presents an evaluation of how the striking ship continues to influence the structural behaviour of a ship under collision. Several velocities are implemented for the movement of the striking ships towards their designated target locations, based on the sizes of the ships. Indications of rebounding are clearly shown by the internal

6 ^ JS

u tf w

"a cu T3

a o "¿0

M ^ N & ^ 00 ^ ^ CN

^ CO ^ & ^T (N O (N &

energy during collision at velocities between 1 and 8 m/s in a collision scenario between striking-I and the struck ship. The tendencies in Fig. 10 indicate that over a collision period of 0.075-0.10 s, the striking ship stopped for a moment before experiencing rebounding in the opposite direction. After exceeding a velocity of 8 m/s, the internal energy does not produce a significant rising and reducing in the form of the hill-shape-like tendency given by 4-8 m/s. In conformation with the extent of the damage, it is observed that for a velocity of 9 m/s, the side shell was torn by the striking ship. A tear on the side structure of the striking ship was explicitly observed, as presented in Fig. 11. A good correlation was observed at the moment of side plating failure between the internal energy and the extent of crushing force (Fig. 12), reaching its peak point according to the applied velocity. The higher the striking velocity of the ship, the higher the force that is experienced. For the applied parameters, the tearing that occurred when the side plating ruptured influenced the force to significantly decrease over a short time. The conclusion of this behaviour is different from for the collision that occurs before the side plating ruptures.

In the eight initial scenarios, the force decreases after collision, with an applied velocity of 9-10 m/s. In terms of velocities lower than those that produce rupture, the lowest velocity (1 m/s) produces almost no movement in term of internal energy. It is found that the characteristic of very low velocity (in this case can be represented by 1 m/s) in collision with respect to rebounding phenomenon is hard to be observed in term of the internal energy. Therefore, for this velocity, evaluation is performed on the crushing force behaviour. In term of force, it is concluded that the force level for 1 m/s is the lowest of the proposed velocities. However, the time period for the force experienced by the struck ship is the longest in the category of no-plating-rupture velocity. For collision velocities in this category, rebounding also takes place. However, since the striking ship moves slowly, the rebounding process takes more time, which makes this behaviour occur over a longer period than for ships moving at higher velocities, for which rupture occurs on the side plating. The characterization of structural responses to collision load can also be estimated from force. As velocity in this scenario increases, the force gradually increases over a time period of 0-0.20 s. The faster rate of increase will affect the period of decreasing force in cases where rupture does not occur. This rhythm indicates that the faster the applied velocity, the earlier the striking ship experiences rebounding.

During collision with the larger ship (striking-II), the struck ship experienced tearing earlier than it did in the scenario with striking-I. The present collisions indicate that side plating ruptures begin during collisions at a velocity of 6 m/s, occurring on the upper part of the struck ship. The internal energy in Fig. 13 shows similar tendencies with the energy during rupture in collision with striking-I. From observations of internal energy, it can be estimated that a larger striking ship will produce a smaller rebounding distance than a smaller ship moving with the same velocity. Energy characteristics indicate that there is very little increase at the point at which the internal energy reaches a maximum and then immediately decreases. Hill-shape-like behaviour is unlikely to be found in scenarios where a ship that is larger than the struck ship is used as the indenter.

Higher velocities produce higher levels of internal energy—this response is defined as the energy that is needed to deform or even crush the involved objects for various collision cases. As presented in the literature review, the amount of destroyed volume for the involved structure is predicted to be equally perpendicular to energy. A larger destroyed volume also affects force fluctuation (Fig. 14) and the tendency that "the tendency of a larger destroyed component to produce more fluctuation" is confirmed. The crushing force for the striking-II scenarios shows that in the initial collision, the tendencies of all velocities are similar, with different magnitudes. In the time range from 0-0.1 s, the side plating does not experience rupture. However, after 0.1 s, the force fluctuates in different patterns for each velocity. This behaviour occurs similarly for several applied velocities, however,

Fig. 22. Damage of the inner shell under side collision

Table 11

Five-highest-magnitude of velocity that is applied on the striking-I. Velocities in range 710 m/s are denoted as expanded magnitude respecting recorded velocities by [41].

Applied velocity Recorded in operation

(m/s) (knot) (knot)

6 [similar to recorded data] 11.6631 Average: 10.30 Maximum: 11.80

7 [expanded] 13.6069

8 [expanded] 15.5508

9 [expanded] 17.5946

10 [expanded] 19.4384

the extent of penetration will be different (this penetration is followed by the rupture of structural members within the struck ship). Based on these results, it can be predicted that in a scenario where tearing occurs on the struck ship, the energy and force will be larger than for the applied velocity response that produces the greatest rebounding (refers to subsection 5.4).

5.3. Structure material

Material is an important and inseparable part of ship structure. The application of material to the side structure of a ship can be considered to be a reasonable option for increasing resistance against ship collision. When implementing side structure materials, it can be concluded from crushing force (Fig. 15) characteristics that medium- and high-carbon steels have similar capacities for resisting collision. It has been demonstrated that an approximately 8% difference in yield strength does not significantly affect structural capabilities. However, a significant distinction is observed between plain-carbon and alloy steels. During the structural rupture occurring at 0.06 s, the low-alloy steel experienced a force magnitude that was 30% lower than that of the high-carbon steel. According to this study, it can be concluded that with a strength gap of 28%, the crushing force shows a significant difference, while the gap indicates that percentage difference of the yield strength and crushing force in the maximum point between two different materials is similar (in this discussion the yield strength differs by

of the striking-II which is the largest ship in this work.

28% and difference of the force magnitude in the peak is 30%). With respect to structural arrangements, it can be concluded that the upper structure has a more complex arrangement than the lower structures, as three decks and an inner shell are installed at that location. Taking both the energy formulation and the previous discussion of the internal energy-crushing force relationship, it can be predicted that the internal energy that is required to destroy the lower part will be smaller than that required to destroy the upper part. The energy results for the lower and upper parts are consecutively presented in Figs. 16 and 17 (for each part connected to the side structure). An evaluation of the internal energy indicates that the outer shell contributed dominantly to side collision resistance. The energy level tendencies suggest that the statement "collision to the upper part involves more structural members and leads to higher energy" has been satisfactorily demonstrated.

Extent of damage is presented in Fig. 18 that indicates correlation between the energy and force is successfully confirmed by the occurred damage on the side structure. The material with higher strength will produce less tearing length. Similarity in the force tendency of plain-carbon steel material is shared in term of damage contour.

5.4. Overall discussion on rebounding of the striking ship

In a collision process between two ships, the striking ship may experience rebounding due to the elastic properties of the ship structure and applied material. As briefly discussed for applied velocity, the striking ship experiences a zero-movement state when the kinetic energy (Fig. 19) is reduced to a low point. After passing this state, the striking ship rebounds in the opposite direction relative to the approach direction of earlier penetration.

This phenomenon is verified by the characteristics of the kinetic energy, which increases after collision at 0.1 s. The rebound of the striking ship also provides a distinction between two groups: prior-to-rupture and after-rupture. In the first group, the striking ship fails to penetrate the side shell until the maximum peak internal energy and crushing force point is reached. In this group, the tendency of the striking ship to experience rebounding is clear, with the kinetic energy increasing quite significantly after the zero-movement state. However,

in the second group, where failure occurs, the time at which the striking ship experiences this state is late, and kinetic energy does not rise to as high a value as the previous group. Almost all of the initial kinetic energy is converted to internal energy, which in this situation destroys the side structure of the struck ship. The rebounding distance is presented in Tables 5 and 6, with the displacement of related members on the struck ship for different striking ships. More complex structures are involved in the collision with the striking-II, and rebounding distance in certain scenarios is not linear with velocity. This scenario is highly affected by the rupture of the struck ship. As previously described, satisfaction in velocity-rebounding relations is achieved for the prior-to-rupture group. The complexity of the structure that is affected by more-involved members makes the failure of each member happen at a different time. This demonstrates that ship collision involves nonlinear phenomena, as dynamic responses do not always provide a linear correlation between applied parameters and estimated results. The rebounding behaviour of the upper structure is confirmed by the tendency of the kinetic energy (Fig. 20) for the highest velocity. The kinetic energy for a velocity of 10 m/s is observed to be lower than for the collision with an applied velocity of 8 m/s, after the zero-movement state is passed by both velocities.

With respect to the striking ship, based on displacement of structural members, it can be estimated that striking-II, as the largest ship in the present work, will contribute larger structural responses in terms of acceleration and damage mode than striking-I. As shown in Fig. 21, the upper structure experienced larger fluctuations in term of acceleration than the lower structure. The double hull structure on the upper part is indicated to provide higher resistance during penetration by the striking ship. Damage modes on the struck ship with respect to applied velocity are given in Tables 7 and 8 for striking-I and striking-II, respectively. Based on this data, striking-II has successfully penetrated the side shell with an initial velocity 6 m/s, while (as described in previous discussions) the rupture of the side shell during collision with striking-I occurs later, at an applied velocity of 9 m/s. The correlation between velocity and damage mode is similar to that observed for tearing mode.

This statement is also supported by the structural behaviour when different material types are used for the struck ship (Tables 9 and 10). Low-alloy steel, which has the lowest yield strength, produced the largest tearing of all proposed materials. A tearing length difference of more than approximately 35% was observed in comparison with the high-carbon steel. The rebounding distance in these collision scenarios also shows good agreement with material strength—the higher-strength material will produce a longer rebounding distance.

Crashworthiness can be defined as the ability of a structure to protect its cargo, passengers, crew, or other valuable entities during an impact. Depending on the nature of the impact and the objects involved, several criteria are used to determine the crashworthiness of a structure. In this work, energy, force, acceleration, and damage are presented and discussed. Accounting for crashworthiness and safety, the inner shell is an important component, as it acts as a final defence against side collision. On ships that carry goods that are dangerous when spilled in the ocean (such as crude oil and nuclear products), a double hull system is implemented. The installation of an inner shell is also expanded to the Ro-Ro ship presented in this work. Therefore, besides a discussion of the abovementioned crashworthiness criteria, it is also important to observe the condition of the inner shell after a collision process. It should be ensured that the inner shell is not breached by the striking ship, and that it does not experience significant damage.

The conditions of both the outer and inner shell are presented in Fig. 22. The results are taken based on a collision with striking-II, which is the largest of the deployed ships. The representation of these results, describing the worst scenarios in this study, is selected based on the internal energy, crushing force, experienced acceleration, and extent of damage. In previous discussions it has been concluded that striking-II

produces higher energy levels and force fluctuations, more intense acceleration, and larger tearing on the struck ship. However, as shown, the condition of the inner shell is good-no tearing is found, and all major damage (e.g. plate tearing, folding, and plastic deformation) is experienced by the outer shell. This tendency is already implicitly described by the internal energy and crushing force that only one significant rising of the energy and maximum fluctuation of the force is only found which indicates that penetration only occurs on the outer shell in early collision. The inner shell is verified to be safe until the end of collision process as the later tendency only presents small rising that represents the striking ship experiences rebounding phenomenon. Before the striking ship reaches the inner shell, its kinetic energy is absorbed by the outer shell; this is verified by the immense damage found in this component. The elastic characteristics of the side structure cause the striking ship to rebound in the opposite direction, which indicates that the inner shell is successfully protected against side collisions in all proposed scenarios in this work. On the lower part, where only an outer shell is installed, tearing is found. However the tearing phenomenon occurs at a higher velocity than the recorded maximum velocity [41] for striking-I. The highest magnitude is found to be approximately 11.8 knots with an average of 10.3 knots. It can be concluded that if the recorded velocities (Table 11) are applied with striking-I, and side collision (with consideration of the striking ship's rebounding) occurs, then the struck ship will not experience tearing. As is described in previous discussions, during a side collision with striking-I, tearing begins when a velocity of 9 m/s is applied to the striking ship. Based on this discussion and using the aforementioned evaluation criteria, it can be concluded that the struck ship has crashworthiness against side collisions, with respect to the rebounding of the striking ship when internal and external parameters are applied to collision scenarios.

6. Conclusions

This paper presented a study of crashworthiness criteria assessed during rebounding phenomena occurring on striking ships. A benchmark study was conducted to ensure that the numerical methodology deployed in this work was capable of producing reliable results. External and internal ship collision parameters were defined to cover adequate scopes for the parameters influencing collision between two ships, accounting for side impact. Important responses in assessing structural crashworthiness (such as energy, force, acceleration, and extent of damage) have been discussed.

The results of a series of collision scenarios are summarized in this section. In the initial discussion, it was demonstrated that structural crashworthiness during rebounding phenomena occurring on the struck ship was different than it was for fully stuck cases. During rebounding, internal energy was observed increase to a peak, and then decrease to a certain point; that is, it demonstrated hill-shape-like behaviour. This tendency was evaluated differently for fully stuck cases in which energy increased continuously. The rebounding distance of the striking ship was reduced during occurrences of side shell rupture. With respect to other parameters, the velocity and striking ship appear to have the most influence of all parameters during ship collision, especially when the extent of damage and rebounding distance are considered. The size of the striking ship is found to directly affect the target location on the struck ship. In discussion, it is concluded that this parameter will affect an internal parameter (namely, structural arrangement), as significant difference, especially in the vertical direction, influences the positions of the colliding struck and striking ships. The largest striking ship (striking-II) impacts the upper structure, which has more structural members than the lower part, which collides with striking-I. There is a good correlation between internal energy and crushing force for all proposed scenarios. The extent of damage during the internal parameter, i.e. structure material is applied on both of the upper and lower parts suggests good agreement that the rebounding distance is equally

perpendicular with the strength of the material. In the same discussion, it can be concluded that there is no significant difference in term of crashworthiness during collision between medium- and high-carbon steels. It is recommended that medium-carbon steel be used as a structural material, since high-carbon materials are more expensive. Because of the carbon content, this steel is difficult to bend or form, especially for a passenger ship, which is dominated by curved shapes.

The conclusion of rebounding phenomena occurs after the striking ship experiences a zero-movement state in a side collision scenario. In this situation, the kinetic energy of the collision is completely absorbed by the struck ship. As applied material on the struck ship has elastic properties, the absorbed energy is deflected in the opposite direction, so that the striking ship undergoes rebounding. This is confirmed by the fact that kinetic energy rises again after the zero-movement state has been passed. The rebounding of the striking ship is obtained reach its farthest distance in one-velocity before rupture occurs (if tearing occurs in the 9 m/s, then the farthest distance will occur in the 8 m/s). This conclusion is summarized with the assumption the striking ship is applied by the rigid body. Considering that rebounding is reduced when rupture occurs, it can be estimated that when a deformable striking ship is deployed, the rebounding distance will be lower than it is in a scenario using a rigid striking ship. This phenomenon occurs because the kinetic energy is absorbed not only by the struck ship, but also by the striking ship. This kinetic energy is converted into internal energy that destroys both deformable structures, which is confirmed by the fact that damage occurs on both the struck and striking ship. In this situation, a fully stuck scenario is possible for the striking ship. Verification of the rebounding mechanism described in this study is obtained from Newton's third law of motion that for every action (i.e., the penetration of the struck ship), there is an opposite reaction (i.e., the rebound of the striking ship). The kinetic energy during rebounding does reach the value of the initial penetration, because most of the energy has been converted to plastically deform or even destroy the struck ship as a part of the collision process. The rebounding mechanism discussed in this work can be considered in further studies, especially for collision analyses involving a bulbous bow on the striking ship. Sustainable impact engineering studies for marine structures are highly encouraged, and it is recommended that researchers plan for the verification of an experimental methodology before main analysis is conducted.

Acknowledgement

This work was successfully presented and published with the support from BK21 plus MADEC Human Research Development Group, South Korea. This work was successfully carried out in the Laboratory of Ship Structure and Vibration Analysis, Department of Naval Architecture and Marine Systems Engineering, Pukyong National University, South Korea. Best gratitude is addressed to Dr. Eng. Ahmad Fauzan Zakki and Dr. Eng. Deddy Chrismianto from Department of Naval Architecture, Diponegoro University, Indonesia for their support in preparing and obtaining technical drawing, specimen material and experiment procedure.

References

[1] F. Goerlandt, P. Kujala, On the reliability and validity of ship-ship collision risk analysis in light of different perspectives on risk, Saf. Sci. 62 (2014) 348-365.

[2] C. Fang, P.K. Das, Survivability and reliability of damaged ships after collision and grounding, Ocean Eng. 32 (2005) 293-307.

[3] T. Lamb, Ship design and construction, Soc. Nav. Archit. Mar. Eng. (SNAME) 1 (2003).

[4] T.L. Yip, W.K. Talley, D. Jin, The effectiveness of double hulls in reducing vessel-accident oil spillage, Mar. Pollut. Bull. 62 (2011) 2427-2432.

[5] J.K. Paik, J.K. Seo, A method for progressive structural crashworthiness analysis under collision and grounding, Thin-Walled Struct. 45 (2007) 15-23.

[6] J.K. Paik, Practical techniques for fine element modelling to simulate structural crashworthiness in ship collisions and grounding (Part I: theory), Ships Offshore

Struct. 2 (2007) 69-80.

[7] J.K. Paik, Practical techniques for fine element modelling to simulate structural crashworthiness in ship collisions and grounding (Part II: verification), Ships Offshore Struct. 2 (2007) 81-85.

[8] O. Kitamura, FEM approach to the simulation of collision and grounding damage, Mar. Struct. 15 (2002) 403-428.

[9] Y. Zheng, S. Aksu, D. Vassalos, C. Tuzcu, Study on side structure resistance to ship-ship collisions, Ships Offshore Struct. 2 (2007) 273-293.

[10] K. Tabri, Influence of coupling in the prediction of ship collision damage, Ships Offshore Struct. 7 (2012) 47-54.

[11] I. Pill, K. Tabri, Finite element simulations of ship collisions: a coupled approach to external dynamics and inner mechanics, Ships Offshore Struct. 6 (2011) 59-66.

[12] A.R. Prabowo, D.M. Bae, J.M. Sohn, B. Cao, Energy behaviour on side structure in event of ship collision subjected to external parameters, Heliyon 2 (2016) e00192.

[13] H.S. Alsos, J. Amdahl, On the resistance to penetration of stiffened plates, Part I -Experiments, Int. J. Impact Eng. 36 (2009) 799-807.

[14] H.S. Alsos, J. Amdahl, O.S. Hopperstad, On the resistance to penetration of stiffened plates, Part II - Numerical analysis, Int. J. Impact Eng. 36 (2009) 875-887.

[15] D.M. Bae, A.R. Prabowo, B. Cao, A.F. Zakki, G.D. Haryadi, Study on collision between two ships using selected parameters in collision simulation, J. Mar. Sci. Appl. 15 (2016) 63-72.

[16] J.W. Ringsberg, Characteristics of material, ship side structure response and ship survivability in ship collision, Ships Offshore Struct. 5 (2010) 51-66.

[17] V.U. Minorsky, An analysis of ship collision with reference to protection of nuclear power ship, J. Ship Res. 3 (1958) 1-4.

[18] H. Vaughan, Bending and tearing of plate with application to ship-bottom damage, Nav. Archit. 3 (1958) 97-99.

[19] G. Woisin, Design against collision, Schiff Hafen 31 (1979) 1059-1069.

[20] G. Lu, C.R. Callidine, On the cutting of a plate by a wedge, Int. J. Mech. Sci. 32 (1990) 293-313.

[21] J.K. Paik, Cutting of a longitudinally stiffened plate by a wedge, J. Ship Res. 38 (1994) 340-348.

[22] S. Zhang, The Mechanics of Ship Collision (Ph.D. thesis), Department of Naval Architecture and Offshore Engineering, Technical University of Denmark, Lyngby, Denmark, 1999.

[23] P.T. Pedersen, S. Valsgaard, D. Olsen, S. Spangenberg, Ship impacts: bow collisions, Int. J. Impact Eng. 13 (1993) 163-187.

[24] P.T. Pedersen, Ship Crushing Load Studies, East Bridge, The Storeb^lt Publication, Korsor, Denmark, 1998.

[25] H. Kierkegaard, Ship Collision with Icebergs (Ph.D. thesis), Department of Ocean Engineering, Technical University of Denmark, Lyngby, Denmark, 1993.

[26] T. Hysing, Damage and penetration analysis - safety of passenger/RoRo vessels, DNV Report No. 95-0419, Norway, 1995.

[27] M. Scharrer, C. Ostegaard, Safety of passenger/RoRo vessels - analysis of collision energies and hole sizes, GL Report No. FL96.009, Germany, 1996.

[28] Z. Liu, J. Amdahl, A new formulation of the impact mechanics of ship collisions and its application to a ship-iceberg collision, Mar. Struct. 23 (2010) 360-384.

[29] W.J. Stronge, Impact Mechanics, Cambridge University Press, Cambridge, UK, 2004.

[30] D.M. Bae, A.R. Prabowo, B. Cao, J.M. Sohn, A.F. Zakki, Q. Wang, Numerical simulation for the collision between side structure and level ice in event of side impact scenario, Lat. Am. J. Solids Struct. 13 (2016) 2691-2704.

[31] S. Haris, J. Amdahl, Analysis of ship-ship collision damage accounting for bow and side deformation interaction, Mar. Struct. 32 (2013) 18-48.

[32] K.J. Bathe, Finite Element Procedures, Prentice Hall, New Jersey, US, 1996.

[33] A.R. Prabowo, D.M. Bae, J.M. Sohn, A.F. Zakki, Evaluating the parameter influence in the event of a ship collision based on the finite element method approach, Int. J. Technol. 4 (2016) 592-602.

[34] O. Ozguc, P.K. Das, N. Barltrop, A comparative study on the structural integrity of single and double skin bulk carriers under collision damage, Mar. Struct. 18 (2005) 511-547.

[35] Z. Yu, Z. Hu, G. Wang, Plastic mechanism analysis of structural performances for stiffeners on bottom longitudinal web girders during a shoal grounding accident, Mar. Struct. 40 (2015) 134-158.

[36] O.V.E. Sormunen, M. Korgesaar, K. Tabri, M. Heinvee, A. Urbel, P. Kujala, Comparing rock shape models in grounding damage modelling, Mar. Struct. 50 (2016) 205-223.

[37] A. AbuBakar, R.S. Dow, Simulation of ship grounding damage using the finite element method, Int. J. Solids Struct. 50 (2013) 623-636.

[38] Germanischer Lloyd, Development of explanatory notes for harmonized SOLAS Chapter II-1, Int. Marit. Organ. (IMO) (2003).

[39] E. Lehmann, J. Peschmann, Energy absorption by the steel structure of ships in the event of collisions, Mar. Struct. 15 (2002) 429-441.

[40] J.K. Paik, P.T. Pedersen, Modelling of the internal mechanics in ship collisions, Ocean Eng. 23 (1996) 107-142.

[41] Marine Traffic, Dharma Ferry 3, <www.marinetraffic.com>, accessed in the 2 January 2017.

Glossary

A: : area of tearing

b: : width of the bridge pier in contact with the ship side

C: : constant value in the range 0.9-3.5

D: : moulded depth of the vessel

E: : absorbed energy

Ejmp: : energy to be absorbed by the crushing bow Pside'- : broadside collision load

h: : height of broken or heavily deformed longitudinal members RT : volume of destroyed members

LN: : length of damage on the striking ship t& : thickness of damage on the striking ship

Ln: : length of damage on the struck ship teq : equivalent plate thickness

L: length of perpendicular/275: tn : thickness of damage on the struck ship

L: : ship length ts- thickness of the members

le: : individual element length thickness of the plate

l: : length of the cut factor accounting for the stiffening system of the ship

Po: : reference collision load equal to 210 MN eg. : uniform strain

Pbow: : maximum bow collision load Se'- : necking strain

PN: : depth of damage on the striking ship tfQ. : flow stress of the material

Pn: : depth of damage on the struck ship