Comparing Structural Casualties of the Ro-Ro Vessel Using Straight and Oblique Collision Incidents on the Car Deck

Journal of Marine Science and Engineering

Article Comparing Structural Casualties of the Ro-Ro Vessel Using Straight and Oblique Collision Incidents on the Car Deck

Aditya Rio Prabowo 1,* , Dong Myung Bae 2 and Jung Min Sohn 2,* 1 Department of Mechanical Engineering, Universitas Sebelas Maret, Surakarta 57126, Central Java, Indonesia 2 Department of Naval Architecture and Marine Systems Engineering, Pukyong National University, Busan 48513, Korea; [email protected] * Correspondence: [email protected] (A.R.P.); [email protected] (J.M.S.)

Received: 24 April 2019; Accepted: 6 June 2019; Published: 11 June 2019

Abstract: Roll on-roll off (Ro-Ro) ship is the preferable vessel for public transportation and also as a medium to distribute several commodities. Its operations are a straightforward process but traffic management is quite delicate, especially for cross-route. Moreover, maritime incidents sometimes occur, causing significant casualties and in the case of the Ro-Ro, collision with other ship is a possible threat with the ability to trigger immense damages. This research, therefore, was conducted to assess the structural casualties of a Ro-Ro vessel under collision. This was modelled with respect to a ship involved in a certain incident in Indonesia in the latest decade, and the designed collision problems were calculated using the finite element approach. The collision angle was selected as the main input parameter with the straight collision of angle 90◦ and oblique collision with different angles applied to the scenario. The results found the collision energy due to structural destruction to have distinct pattern and peak value under oblique cases with lower values observed for straight collision for all scenarios. It is, however, recommended that energy should be taken as an initial parameter in further investigation of structural damage and response contour.

Keywords: maritime incidents; straight and oblique collisions; ﬁnite element approach; energy ratio; rupture strain

1. Introduction Transportation has been playing an important role in human society, and industrial development since the first industrial revolution took place more than two centuries ago. It started with the use of the animal as the driving force followed by the application of diesel engine in inland, aerospace, and water transportation. Furthermore, human interaction also experiences massive progress, for example, the use of a mobile phone makes it more convenient to communicate over long distances compared to the conventional methods of communication. This was followed by the evolution of these phones to become smart leading to easy business transactions, trading and several other forms of interaction. For the purpose of this study, transportation mode is focused because it requires carrying subjects from one location to the other based on designated missions, for example, it is possible to transport humans and commodities using a public vehicle which is classified as an inland transportation mode. However, most archipelago countries are faced with the challenges of obtaining another transportation mode to transport people on the island and this led to the use of water transportation mode by the public, thereby, making it become one of the highest maritime business potentials in these countries. Consequently, roll on-roll off (Ro-Ro) ship was considered the most suitable vessel in this situation due to its capability to convey a large number of vehicles, passengers, and commodities at the same time to cross the sea or strait.

J. Mar. Sci. Eng. 2019, 7, 183; doi:10.3390/jmse7060183 www.mdpi.com/journal/jmse J. Mar. Sci. Eng. 2019, 7, x 2 of 15

business potentials in these countries. Consequently, roll on-roll off (Ro-Ro) ship was considered the J.most Mar. Sci. suitable Eng. 2019 vessel, 7, 183 in this situation due to its capability to convey a large number of vehicles,2 of 15 passengers, and commodities at the same time to cross the sea or strait. The Ro-Ro ship is a vessel with the cargo wheeled or loaded/unloaded on board, in a vehicle or The Ro-Ro ship is a vessel with the cargo wheeled or loaded/unloaded on board, in a vehicle or other platforms equipped with wheels. The first ships to be classified under this category were the other platforms equipped with wheels. The first ships to be classified under this category were the Ferry equipped with railways to allow the transport of train carriages between the margins of the Ferry equipped with railways to allow the transport of train carriages between the margins of the rivers considered too wide for bridges. The use of the Ro-Ro concept in merchant ships started in the rivers considered too wide for bridges. The use of the Ro-Ro concept in merchant ships started in late 1940s, early 1950's and mainly in the short-sea routes, such as inter-island route through the strait the late 1940s, early 1950’s and mainly in the short-sea routes, such as inter-island route through the in archipelago countries. It became a significant vital transportation mode and a traffic connector. strait in archipelago countries. It became a significant vital transportation mode and a traffic connector. Furthermore, Figure 1 shows how the infrastructures for Ro-Ro spread on the islands of Indonesia Furthermore, Figure1 shows how the infrastructures for Ro-Ro spread on the islands of Indonesia thereby making domestic water traffic of the country to be very high. This is also influenced by the thereby making domestic water traffic of the country to be very high. This is also influenced by the use use of the strait between the islands as international route, especially from East Asian countries such of the strait between the islands as international route, especially from East Asian countries such as as South Korea, Japan and China and Southeast Asia including Singapore to reach Australia [1–3]. South Korea, Japan and China and Southeast Asia including Singapore to reach Australia [1–3].

Balikpapan Banda Aceh 10 trajectories Ternate 2 trajectories 8 vessels 16 trajectories 2 ports 2 vessels Batam Bitung 8 vessels 7 trajectories 5 trajectories 3 ports 8 vessels Pontianak 3 vessels Biak 2 ports 10 trajectories 1 port Sorong 7 trajectories Singkil 3 vessels 4 trajectories 7 vessels 18 trajectories 3 vessels 4 vessels Luwuk Padang Batulicin 11 trajectories 4 trajectories 2 trajectories 6 vessels 2 vessels 3 vessels 1 port Ambon 2 ports Surabaya Bajoe 10 trajectories 3 trajectories 10 vessels 3 vessels 1 trajectory 5 ports Bakauheni 2 ports 1 vessel 2 ports 1 trajectory 1 port Merak Merauke Jepara 8 trajectories 1 trajectory Ketapang 2 trajectories 2 vessels 6 vessels 1 trajectory Kupang 2vessels 1 port 2 vessels 21 trajectories 2 ports 7 vessels 3 ports Figure 1. Location of port infrastructure across Indonesia territory (based on information in Ref. [4]). Figure 1. Location of port infrastructure across Indonesia territory (based on information in ref. [4]). With due consideration for the traffic situation of archipelago countries through the use of IndonesiaWith as due a representative, consideration it for is mandatorythe traffic tosituation ensure shipof archipelago safety during countries daily operation. through the However, use of theIndonesia most serious as a represent threat wasative, observed it is mandatory to be the possible to ensure occurrence ship safety of during impact loaddaily due operation to several. However, causes, andthe themost data serious recently threat released was byobserved Allianz to [5 ]be indicated the possible collision occurrence and grounding of impact to be load the mostdue to frequent. several Thecauses high, and number the data of casualtiesrecently released as a result by Allianz of these [5] usually indicated vary, collision but they and are gro allunding usually to triggered be the most by thefrequent structural. The rupturehigh number of the of load casualties [6–9], and as thisa result makes of these it important usually tovary conduct, but they an analysis are all usually on the subject.triggered Therefore, by the structural the objective rupture of this of study the load was to[6– investigate9], and this the makes collision it important phenomenon to conduct of impact an loadanalysis involving on the two subject. ships using Therefore, a numerical the objective approach, of i.e., this nonlinear study was finite to element investigate method the (NLFEM). collision Thisphenomenon method was of impact considered load suitableinvolving for two this ships case sinceusing thea numerical analytical approach method, is i.e. limited, nonlinear in term finite of materialelement aspectmethod and (NLFEM). structural This complexity method andwas becauseconsidered the idealizedsuitable for phenomena this case since were inthe large analytical scale involvingmethod is several limited parameters. in term of Furthermore,material aspect the and comparison structural of thecomplexity structural and parameters because basedthe idealized on the NLFEMphenomena analysis were was in discussedlarge scale as involving a contact several scenario parameters. is designed Furthermore, by varying collision the comparison angle. of the structural parameters based on the NLFEM analysis was discussed as a contact scenario is designed 2. Literature Reviews: Ro-Ro and Maritime Incidents by varying collision angle. The first time Ro-Ro was introduced to the public, it was intended to transport train carriages between2. Literature the margins Reviews: of Ro the-Ro rivers and consideredMaritime Incidents too wide for bridges in Scotland and, for its effective operation,The first the vesseltime Ro was-Ro equipped was introduced with railways. to the public, However, it was the warintended experienced to transport across train the European carriages continentbetween the affected margins the rapidof the developmentrivers considered of technology, too wide for water bridges transportation in Scotland inclusive. and, for its Moreover, effective theoperation, World War the II vessel motivated was the equipped improvement with ofrailways. Ro-Ro vessel However, to be morethe war adaptable experienced as landing across vessel the forEuropean military continent equipment affected and this the is rapid presently development being used of fortechnology, both military water and transportation offshore industries inclusive. as theMoreover, Landing the Craft World Tank War (LCT). II motivated After the war, the theimprovement previously of modified Ro-Ro vessel Ro-Ro to was be converted more adaptable for other as operation schemes like merchant ship MV Virginia Beach. Furthermore, in order to fulfill several objectives in maritime industries, Ro-Ro vessel was modified to provide several other types such as: J. Mar. Sci. Eng. 2019, 7, 183 3 of 15

Ro-Ro passenger (Ro-Pax) It has a large deck, and limited passenger facilities (less than passenger • ferries) and its superstructures cover part of the deck. Pure car carriers It is designed for only one purpose, which is to efficiently transport cars or other • types of vehicles such as bus, truck, etc. According to Wärtsillä, the largest deep-sea car carriers in service has the ability to convey up to 8000 car equivalent units [10]. Lift on-lift off (Lo-Lo) This is similar to freight, but it has a different mechanism compared to • general container vessel. The container vessel usually performed their loading and unloading with a port/harbor facility, while Lo-Lo conducts the process with the use of an onboard crane.

Identification of loss and risk during a vessel operation is very important in maritime industries, especially to a company’s financial and insurance policy and misconduct in this aspect has the ability to lead a company to bankruptcy due to the occurrence of certain accidents in the fleet. This phenomenon is rising as several accidents in the maritime environment have been proved to be an initial trigger for massive losses such as iceberg-ship impact case of the Titanic [11], large scale oil spill accident of the Sea Empress [12], death toll in the Sewol’s sinking [13], environmental destruction and species extinction after the Exxon Valdez ran aground and spilled oil [14], Halifax explosion accident in Canada with death estimation reached 2000 people [15,16], and massive financial loss for passenger compensation, ship evacuation and environment restoration in grounding case of the Costa Concordia [17]. From all these, collision and grounding appear to be the highest cause of vessel losses in the category of accidental loads. Furthermore, from a calculated data of 2018, Allianz [18] showed 90% of global trades/commodities are transported by shipping, and this reflects the contributions of several types of ships to the sustainability of global economy and growth. However, despite its positive value, there are several challenges in its operations. Tables1 and2 shows the number of total loses per region from 2008–2017, and Southeast Asia region holds the largest spot, exceeding the East Mediterranean and the Black Sea. Advance assessment in 2017 also pointed out accidental loading was the main cause of largest ships lost as shown in Table3, with three out of ten largest cases found in Indonesia and Philippines, and observed to have involved bulk carrier and passenger vessels.

Table 1. Review of total losses by top 10 regions: 2008–2017 [18].

Region Loss Total (ship) South China, Indochina, Indonesia, and the Philippines 252 East Mediterranean and the Black Sea 169 Japan, Korea, and North China 126 British Isles, North Sea, England Channel and Bay of Biscay 89 Arabian Gulf and approaches 62 West African Coast 51 West Mediterranean 48 East African Coast 34 Russian Arctic and Bering Sea 29 Bay of Bengal 28 Other 241 Total 1129 J. Mar. Sci. Eng. 2019, 7, 183 4 of 15

Table 2. Total losses during 2017 accounting for accident regions [18].

Region Loss Total Tendency South China, Indochina, Indonesia and Philippines 30 6 ↑ East Mediterranean and Black Sea 17 2 ↓ British Isles, North Sea, England Channel and Bay of Biscay 8 = Arabian Gulf and approaches 6 3 ↑ Japan, Korea, and North China 6 5 ↓ South Atlantic and East Coast of South America 5 1 ↑ West Mediterranean 4 = West African Coast 3 = Baltic 2 2 ↑ Bay of Bengal 2 1 ↓ Other 11 4 ↓ Total 94 4 ↓

Table 3. List of the largest ships lost in 2017 [18].

Ship Name Size (GT) Accident Date Description Sank after water filled the vessel hull Stellar Daisy 148431 March 31 through a crack in approximately 3700 km off the coast of Uruguay Theresa Arctic 43414 June 2 Grounded on reefs off Kilifi, Kenya Melite 39964 July 26 Grounded at Pulau Laut, Indonesia Emerald Star 33205 October 13 Sank off the coast of the Philippines Fire broke out approximately 400 Maersk Pembroke 31333 August 22 km off the Isles of Scilly.

3. Pioneer Work Related to Impact Loading in the Maritime Environment The efforts are classified into active and passive major groups as introduced by Törnqvist [19] and Prabowo [20]. The active group is conducting research to support ships during their operations and interactions with other facility and infrastructure in order to avoid accidental phenomena. The navigation system is one the popular field in this group and series of researches are dedicated to improve and expand the capability of radar, communication instrument, gyrocompass, etc, such as the works conducted by Perera and Mo [21], Yoo [22] and An [23]. On the contrary, the passive group focuses on the assessment of structural performance during and after accidents, and the prediction of casualties/loss on the involved parties. However, this work was considered a fundamental aspect in developing marine technology as the results of the assessment and prediction in this group are adopted as reference data for the active group to improve navigation as well as mitigation for ship and other marine structures. Several scholars such as Amdahl [24], Soares [25], Pedersen [26] and Prabowo [27] concentrated their research in this field with varieties of researches, as many as the active group. The main motive of these works was to understand the accidental load/event, such as the reoccurrence of collision, grounding, and explosion despite the achievement of major progress of navigational instruments. Furthermore, this group was mainly analyzed through the use of numerical analysis (FEM), analytical formula, and empirical approach. The FEM is considered the most developed method compared to others in terms of size, large scale structure, proper ship modeling including the boundary condition, and loading scheme. Moreover, in terms of the considered parameter, more aspects are inputted into the model to idealize the complexity of an accidental model in very specific details. With respect to the works previously mentioned, the analytical formula and empirical approach are currently considered in the analysis as comparison and validation of the numerical calculation. J. Mar. Sci. Eng. 2019, 7, 183 5 of 15 J. Mar. Sci. Eng. 2019, 7, x 5 of 16 calculation.Similarly, the Simi mainlarly, motive the main of this motive analysis of this form analysis is that both form methods is that both referred methods to pioneer referred experimental to pioneer experimentaltest with better test accuracy with better as the accuracy phenomena as the were phenomena physically were investigated. physically investigated.

4. Analysis Analysis P Preparationreparation and M Modellingodelling C Conﬁgurationonfiguration

4.1. Vessel Vessel geometry Geometry Two vesselsvessels were used in this study with the Ro-RoRo-Ro used as the struck vessel and cargo as the striking vesselvessel asas shown shown in in Figure Figure2. The2. The struck struck ship ship was was idealized idealized as a deformableas a deformable body body with anwith inner an innerstructural structural arrangement arrangement such as such inner as shell, inner frame, shell, and frame, girder. and On girder. the contrary, On the thecontrary, striking the vessel striking was vesseldeﬁned was as a defined rigid body as modelled a rigid body on bow modelled geometry on without bow geometry inner structure. without These inner assumptions structure. These were assumptionsimplemented were to focus implemented the damage to observation focus the damage on the struckobservation vessel. on Furthermore, the struck vessel. by deploying Furthermore, a rigid bystriking deploying vessel, a therigid worst striking damage vessel, was the estimated worst damage due to itswas inability estimated to undergo due to its deformation inability to and undergo cause deformationlarger damage and than cause a deformable larger damage striking than ship. a deformable striking ship.

Upper deck Δ Middle deck Δ Upper side hull Car deck Core region - ratio 8 Lower side hull Δ Inner bottom plate Intermediate region - ratio 9

Δ Baseline

Inner bottom plate

Far region - ratio 10

(a)

Striking vessel - ratio > 10

Car deck

Lower side hull Core region - ratio 8 Inner bottom plate Far region - ratio 10 (b)

FigureFigure 2. The 2. geometryThe geometry of the of idealized the idealized struck struck vessel vessel:: (a) B (oxesa) Boxes highlight highlight the mesh the mesh configuration conﬁguration on the on side hull,the sideand hull,(b) Detail and ( bof) Detailmeshing of meshingon the inner on thestructure inner structureand the striking and the vessel. striking vessel.

Based on these conﬁgurations,configurations, other settings were demanded on the deformable structures to ensure the the rupture rupture are are well well captured. captured. In Inthis this case, case, the the discretion discretion of large of large model model was wasan important an important task totask be to conducted be conducted,, and andafter after several several works works in inthe the fields ﬁelds of ofimpact impact engineering engineering and and crashworthiness, crashworthiness, such as [20, [20,28], the implementation implementation of meshing size based on the ratio ratio of of element element length length and and member member thickness isis provenproven capable capable of of producing producing good good results. results. The The same same strategy strategy was was applied applied in this in workthis work with with the finest-smallest mesh of ratio 8 at the core, largest ratio 10 at the far, and ratio 9 at the

J. Mar. Sci. Eng. 2019, 7, 183 6 of 15 the finest-smallest mesh of ratio 8 at the core, largest ratio 10 at the far, and ratio 9 at the intermediate region of contact. Moreover, since the striking vessel was modelled as a rigid object, the larger mesh was used to increase the efficiency of the calculation process conducted through nonlinear finite element (NLFE) ANSYS LS-DYNA. Furthermore, the large structures underwent discretization into more than 70,000 element number, and explicit methodology was chosen to calculate configuration due to its effectiveness in estimating the characteristics of impact engineering [29].

4.2. Material Settings The two vessels were embedded with a material model, and the strain-dependent plastic-kinematic material formulation presented in Equation (1) [29] was applied to idealize the steel properties on the numerical model. The strain-dependent characteristic was considered because of its relation to the rupture criterion. Furthermore, as described in the previous discussion, immense structural damage is one of the casualty forms mostly observed during and after the occurrence of an accidental load. Therefore, it was necessary to define a condition when the material could be considered to have fail or ruptured and for the purpose of this study, a rupture value of 0.2 was selected. Besides failure, the Cowper–Symonds values were also defined on the material as its nonlinearity was expected since the analysis has the ability to make the material surpass yield point, therefore, value C = 3200/s and P = 0 were applied on the mathematical expression. However, when compared with mild steel, the value in this work is higher considering the material type selected, high-strength low-alloy (HSLA) steel (yield stress σY = 440 MPa, density ρ = 7850 kg/mm, Poisson ratio ν = 0.3, hardening parameter n = 0 and elastic modulus E = 210,000 MPa), and effect of the impact to material behaviour.

 . ! 1   ε P  e f f σ = 1 +  σ + βE ε (1) Y  C  0 P P

. where σY is the yield stress, ε is the strain rate, C and P are the Cowper–Symonds strain rate parameters, σ0 is the initial yield stress, β is the hardening parameter, Ep is the plastic-hardening modulus, E is the e f f elastic modulus, and εp is the eﬀective plastic strain.

4.3. Boundary Conditions The accidental load was defined as the collision between two vessels with the striking vessel hitting the designated target on the struck vessel’s side shell. Specifically, the target was placed on the car deck of the Ro-Ro below the upper and middle decks. However, in order to investigate several structural performances of the card deck, different collision angles, 60◦, 90◦, and 120◦, were applied on the scenario configuration according to the Cartesian coordinate system. Even though the 60◦ and 120◦ are actually the same degrees in different quadrants, different results were expected due to the curve geometry of the struck vessel. The collision geometry of the NLFE analysis is presented in Figure3. J.J. Mar. Mar. Sci. Sci. Eng. Eng. 20192019,, 77,, x 183 7 of 16 15 J. Mar. Sci. Eng. 2019, 7, x 7 of 16

Collision angle: 60º Collision angle: 90º Collision angle: 120º Collision angle: 60º Collision angle: 90º Collision angle: 120º

Striking Striking Striking Striking vessel Striking vessel vessel Striking vessel vessel vessel

Struck vessel Struck vessel Struck vessel Struck vessel

Struck vessel Struck vessel

Figure 3. A variety of collision angle applied to the scenarios. Figure 3. AA variety variety of collision angle applied to the scenarios.

During vessel collision, the the striking speed speed applied applied was was 12 12 knots or approximately 6 6 m/s m/s with During vessel collision, the striking speed applied was 12 knots or approximately 6 m/s with restrained rotational displacements. The The struck struck vessel vessel was was made made constant constant (not (not moving) moving) with the restrained rotational displacements. The struck vessel was made constant (not moving) with the fixationfixation attach attacheded on on the the edge edge of ofdecks, decks, inner inner bottom bottom plate, plate, and andside sidetransverse transverse frame. frame. Moreover, Moreover, since fixation attached on the edge of decks, inner bottom plate, and side transverse frame. Moreover, since collisionsince collision is the is main the main subject subject of this of thisstudy, study, contact, contact, involving involving frictions, frictions, is isan an inevitable inevitable phenomenon. phenomenon. collision is the main subject of this study, contact, involving frictions, is an inevitable phenomenon. Therefore, automatic contact surface surface-to-surface-to-surface model was used t too idealize the interaction of surface Therefore, automatic contact surface-to-surface model was used to idealize the interaction of surface geometry between between the the struck struck and and striking striking vessel vessel,, and and the the values values of offriction friction coefficient coefficient were were set setat μ atk geometry between the struck and striking vessel, and the values of friction coefficient were set at μk =µ k0.57= 0.57 and and μs =µ 0.74s = 0.74 for kinematic for kinematic and andstatic static values values respectively. respectively. = 0.57 and μs = 0.74 for kinematic and static values respectively. 5. Structural Structural A Assessmentsssessments 5. Structural Assessments 5.1. Internal Internal energy Energy 5.1. Internal energy TThehe structural assessment of the struck vessel was first first conducted by observing behaviours of The structural assessment of the struck vessel was first conducted by observing behaviours of the internal energy, whichwhich waswas includedincluded inin thethe crashworthinesscrashworthiness criteria. The graph below illustrates the internal energy, which was included in the crashworthiness criteria. The graph below illustrates the numbers of of structural structural members members destroyed destroyed o onn impact impact as as well well as as the the level level of of the the expected expected damage. damage. the numbers of structural members destroyed on impact as well as the level of the expected damage. Figure 44 showsshows thethe collisioncollision angleangle 6060°◦ to have produced the highest energy level,level, followed by 120◦° Figure 4 shows the collision angle 60° to have produced the highest energy level, followed by 120° and 90 °◦,, consecutively. consecutively. The The results results also also indicated indicated that that the the destruction of of the struck vessel in oblique and 90°, consecutively. The results also indicated that the destruction of the struck vessel in oblique collision 60 60◦°lasts lasts longer, longer which, which may may be important be important background background regarding regarding high energy high pattern. energy Through pattern. collision 60° lasts longer, which may be important background regarding high energy pattern. Throughthe representation the representation of the internal of the energy internal at energy the end at of the the end collision of the acollision shown ina show Figuren 5in, a Figure parabolic 5, a Through the representation of the internal energy at the end of the collision a shown in Figure 5, a parabolicshape was shape produced was produced when the collisionwhen the angle collision was angle in its vertexwas in orits lowestvertex point.or lowest point. parabolic shape was produced when the collision angle was in its vertex or lowest point. 18000 18000 Case: vessel collision Case: vessel collision Target: car deck 15000 Target: car deck 15000 Method: NLFE analysis Method: NLFE analysis Collision angle: Collision angle: 12000 60o 12000 60o 90o 90o 9000 120o 9000 120o

6000 6000

Internal Energy [kJ] Energy Internal

Internal Energy [kJ] Energy Internal 3000 3000

0 0 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 Penetration [mm] Penetration [mm] Figure 4. Summary of the internal energy based on the proposed cases. Figure 4. Summary of the internal energy based on the proposed cases. Figure 4. Summary of the internal energy based on the proposed cases.

J.J. Mar.Mar. Sci.Sci. Eng.Eng. 20192019,, 77,, 183x 88 ofof 1516

17000 y = 3.1533x2 - 583.23x + 40106 16500 R2 = 1 16000 15500 15000

14500

14000 Case: vessel collision Internal Energy [kJ] Energy Internal Target: car deck 13500 Collision angle: 13000 Current results Polynomial trend-line 12500 50 60 70 80 90 100 110 120 130 Collision Angle [deg.] Figure 5. Pattern of the internal energy on a variety of collision angle. Figure 5. Pattern of the internal energy on a variety of collision angle. This phenomenon suggested that during side collision, the side hull is more prone to oblique collisionThis than phenomenon a perpendicular suggested one orthat perfect during T-collision. side collision, This statementthe side hull is founded is more on prone the less to oblique energy collision than a perpendicular one or perfect T-collision. This statement is founded on the less energy observed in the angle 90◦, which shows that less damaged structure occurred after the collision process. observed in the angle 90°, which shows that less damaged structure occurred after the collision 5.2.process. Energy Ratio This is the proportion of the total energy in a system to the initial energy, as shown in the 5.2. Energy ratio mathematical expressions in Equations 2 and 3. However, if the left-hand side falls below the right hand,This it is possibleis the proportion to conclude of that the energytotal energy is being in absorbed a system artificially, to the initial perhaps energy by, anas hour-glassing shown in the phenomenon,mathematical whichexpressions may occurin Equations due to major 2 and damage3. However, of the if idealized the left-hand structures. side falls This below fundamental the right calculationhand, it is possible was matched to conclude with the that results energy in is Figure being6 whereabsorbed the artificially, ratio was found perhaps not by to an be h perfectlyour-glassing one sincephenomenon, some energy which was may affected occur by due an to hourglass. major damage However, of the a veryidealized satisfying structures. condition This was fundamental indicated ascalculation the final resultswas matched for all cases with exceed the results 95%, andin Figure the hourglass 6 where proportionthe ratio was less found than 5%. notA to more be perfectly specific discussionone since someon hourglass energy is was presented affected in by the an next hourglass sub-section.. However, a very satisfying condition was indicated as the final results for all cases exceed 95%, and the hourglass proportion less than 5%. A + + + + + = 0 + 0 + more specific discussion Eonkin hourglassEint Esi is Epresentedrw Edamp inE thehg nextEkin subE-intsection.Wext (2)

Etotal 0 0 E +E +E +Eratio+E= +E = E +E +W (3)(2) kin int si rw damp 0 hg+ kin int ext Etotal Wext where E is the current kinetic energy, E is the current internal energy, E is the current sliding kin int Etotal si interference energy (including friction),EratioE =is0 the current rigid wall energy, E is the current(3) rw E +W damp total ext0 0 damping energy, Ehg is the current hourglass energy, Ekin is the initial kinetic energy, Eint is the initial 0 kin int si internalwhere E energy, is theW currentext is the kinetic external energy work,, EEratio is isthe the current energy internal ratio, and energyEtotal, isE the is initialthe current total energy.sliding interference energy (including friction), Erw is the current rigid wall energy, Edamp is the current damping energy, Ehg is the current hourglass energy, E0kin is the initial kinetic energy, E0int is the initial internal energy, Wext is the external work, Eratio is the energy ratio, and E0total is the initial total energy.

J. Mar. Sci. Eng. Eng. 2019, 7, x 183 9 of 1516

J. Mar. Sci. Eng. 2019, 7, x 9 of 16 1.0 1.0

0.9 0.9

0.8 0.8 Case:Case: vessel vessel collision collision Target: car deck 0.70.7 Target: car deck Method:Method: NLFE NLFE analysis analysis CollisionCollision angle: angle:

Energy Ratio [-] Energy

Energy Ratio [-] Energy 0.60.6 60 60o o o 90 90o o 0.50.5 120 120o

0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 Penetration [mm] Penetration [mm]

FigureFigure 6. Ratio6. Ratio of of the the internal internal energy to to the the kinetic kinetic energy energy during during collisions. collisions. Figure 6. Ratio of the internal energy to the kinetic energy during collisions. 5.3. Hourglass5.3. Hourglass Phenomenon phenomenon 5.3. HourglassHourglassHourglass phenomenon is a is behaviour a behaviour of of a a numerical numerical model model to to be be deformed deformed in innon non-physical-physical ways ways or or geometricallygeometricallyHourglass due is due to a thetobehaviour the excessive excessive of artiﬁcially artificially a numerical applied model load. load. to As As be initially initially deformed predicted predicted in in non the in-physical discussion the discussion ways of orof the energy ratio, a very small part of the energy was artificially absorbed by hourglass and the results thegeometrically energy ratio, due a veryto the small excessive part ofartificially the energy applied was artiﬁcially load. As initially absorbed predicted by hourglass in the and discussion the results of presented in Figures 7–9 show compatibility with the prediction, even though it is minor. presentedthe energy in ratio, Figures a very7–9 small show part compatibility of the energy with was the artificially prediction, absorbed even though by hourglass it is minor. and the results presented in Figures 7–9 show compatibility with the prediction, even though it is minor. 1000 Target: car deck 1000 Collision angle: 60o Target: car deck 800 Structure member: o Collision Lower angle: side 60 shell 800 Structure Middle member: deck 600 Lower Car deck side shell Middle Upper deckside shell 600 Deck girder 400 Car deck Upper side shell Deck girder 400 [kJ] Energy Hourglass 200

Hourglass Energy [kJ] Energy Hourglass 200 0 0 500 1000 1500 2000 2500 Penetration [mm] 0 Figure 7. Hourglass energy of the collision angle 60◦. 0 Figure500 7. Hourglass energy1000 of the collision1500 angle 60°. 2000 2500

Penetration [mm]

Figure 7. Hourglass energy of the collision angle 60°.

J. Mar. Sci. Eng. 2019, 7, x 10 of 16

J. Mar.J. Sci.Mar. Eng. Sci. Eng.2019 2019, 7, 183, 7, x 10 of 1610 of 15 600 Target: car deck 600 Collision angle: 90o 500 Target: car deck CollisionStructure angle:member: 90o 500 Structure Lower member: side shell 400 LowerMiddle sidedeck shell 400 MiddleCar deck deck 300 CarUpper deck side shell Deck girder 300 Upper side shell Deck girder 200

Hourglass Energy [kJ] Energy Hourglass 200 100

Hourglass Energy [kJ] Energy Hourglass 100 0 0 500 1000 1500 2000 0 0 500 Penetration1000 [mm] 1500 2000

Penetration [mm] Figure 8. Hourglass energy of the collision angle 90°. Figure 8. Hourglass energy of the collision angle 90◦. Figure 8. Hourglass energy of the collision angle 90°. 1000 Target: car deck 1000 o Target:Collision car angle: deck 120 800 CollisionStructure angle:member: 120o 800 Structure Lower member: side shell LowerMiddle sidedeck shell 600 MiddleCar deck deck 600 CarUpper deck side shell UpperDeck girder side shell 400 Deck girder 400

Hourglass Energy [kJ] Energy Hourglass 200 Hourglass Energy [kJ] Energy Hourglass 200 0 0 500 1000 1500 2000 0 0 500 Penetration1000 [mm] 1500 2000

Figure 9. Hourglass energyPenetration of the collision [mm] angle 120◦. Figure 9. Hourglass energy of the collision angle 120°. The summary of the designed collision cases indicated the T-collision shown in Figure8 to Figure 9. Hourglass energy of the collision angle 120°. have produced the lowest hourglass energy compared to the oblique cases in Figures7 and9. However, a detail observation has the ability to identify the most contributing member in the hourglass phenomenon. Furthermore, the tendency of the car deck was observed to have produced the highest level, followed by the lower side hull, deck girder, upper side, and middle decks, respectively. It was especially found that the upper side and middle decks have extremely low hourglass with approximation in the range of 0–50 kJ. Moreover, associating the result of this subsection with the expected damage pattern after vessel collision showed a higher level of damage is experienced by a J. Mar. Sci. Eng. 2019, 7, x 11 of 16

The summary of the designed collision cases indicated the T-collision shown in Figure 8 to have produced the lowest hourglass energy compared to the oblique cases in Figures 7 and 9. However, a detail observation has the ability to identify the most contributing member in the hourglass phenomenon. Furthermore, the tendency of the car deck was observed to have produced the highest level, followed by the lower side hull, deck girder, upper side, and middle decks, respectively. It was especially found that the upper side and middle decks have extremely low hourglass with J.approximation Mar. Sci. Eng. 2019 ,in7, 183the range of 0–50 kJ. Moreover, associating the result of this subsection with11 of the 15 expected damage pattern after vessel collision showed a higher level of damage is experienced by a member during impact and the possibility of hourglass occurrence increase for this member. member during impact and the possibility of hourglass occurrence increase for this member. However, However, this leads to a very low energy value with no effect on the reliability of the present this leads to a very low energy value with no effect on the reliability of the present calculation. Therefore, calculation. Therefore, there is need to consider an alternative to fully neutralize the hourglass in very there is need to consider an alternative to fully neutralize the hourglass in very high dynamic and high dynamic and nonlinear simulation and this can be achieved through the development of a fully nonlinear simulation and this can be achieved through the development of a fully integrated element integrated element formulation in the deformable body as conducted in [30–32]. formulation in the deformable body as conducted in [30–32]. 5.4. Rupture strain 5.4. Rupture Strain As defined in the numerical configuration, rupture is experienced by a material when the As defined in the numerical configuration, rupture is experienced by a material when the ultimate ultimate strain is exceeded due to accidental load. In case of the vessel collisions, the strain strain is exceeded due to accidental load. In case of the vessel collisions, the strain distribution on the distribution on the struck vessel reached a quite long extent in oblique collisions of 60° and 120° as struck vessel reached a quite long extent in oblique collisions of 60◦ and 120◦ as shown in Figures 10 shown in Figures 10 and 11. The strain observed indicated that the earlier contact of the side part of and 11. The strain observed indicated that the earlier contact of the side part of the striking vessel the striking vessel and struck vessel occurred before the tip of the striking vessel hit the target. This and struck vessel occurred before the tip of the striking vessel hit the target. This pattern is very pattern is very different compared to the T-collision, as shown in Figure 12. This illustration showed different compared to the T-collision, as shown in Figure 12. This illustration showed the opening on the opening on the struck vessel was perfect with the tip of the striking vessel which penetrated the the struck vessel was perfect with the tip of the striking vessel which penetrated the target straight to target straight to the transverse direction. Therefore, due to more local damage on the struck vessel, the transverse direction. Therefore, due to more local damage on the struck vessel, the internal energy the internal energy and hourglass for angle 90° were lower than the oblique cases. and hourglass for angle 90◦ were lower than the oblique cases.

J. Mar. Sci. Eng. 2019, 7, x 12 of 16 Figure 10. Contours of the strain near the car deck: Angle 60◦. Figure 10. Contours of the strain near the car deck: Angle 60°.

Figure 11. Contours of the strain near the car deck: Angle 120◦. Figure 11. Contours of the strain near the car deck: Angle 120°.

Figure 12. Contours of the strain near the car deck: Angle 90°.

The observation of the damage pattern showed the most side frame on the oblique collision 120° was folded on the lower part while the upper part was crushed and pushed on the direction of the striking angle. Furthermore, the curved geometry on the fore-peak section made the crushing pattern of two oblique collisions different even though the angle size is the same according to the Cartesian diagram. In terms of the damage extent, the collision in 60° caused longer tear on the connection of the car deck and lower side shell influenced by deeper penetration. Moreover, the calculation of the penetration in the same depth predicted the damage length to be similar in terms of size.

5.5. Critical stress The stress in the current structural assessment was conducted to investigate the total number of members affected due to the car deck. According to the critical stress presented by von-Mises formulation in Figures 13–15, the affected members for the three cases were similar, and they include car deck (main target), girder, lower hull, upper hull, and middle deck. However, despite these similarities, high-stress intensity occurred quite extensive on the lower hull of the collision case 90°. It is, therefore, possible to come up with the estimation that the collision would continue, and the part covered by high stress would experience the earliest rupture, and the element removed in the calculation. It was also noted that the oblique collisions and T-collision have a quite distinct extent in terms of damage and stress with the former having the tendency to form an incision rather than deep- focus penetration produced by the latter on the struck vessel.

J. Mar. Sci. Eng. 2019, 7, x 12 of 16

J. Mar. Sci. Eng. 2019, 7, 183Figure 11. Contours of the strain near the car deck: Angle 120°. 12 of 15

Figure 12. Contours of the strain near the car deck: Angle 90◦. Figure 12. Contours of the strain near the car deck: Angle 90°. The observation of the damage pattern showed the most side frame on the oblique collision 120◦ was foldedThe observation on the lower of the part damage while thepattern upper showed part wasthe most crushed side and frame pushed on the on oblique the direction collision of 120° the strikingwas folded angle. on Furthermore,the lower part the while curved the geometryupper part on was the fore-peakcrushed and section pushed made on the the crushing direction pattern of the ofstriking two oblique angle. Furthermore, collisions diff erentthe curved even thoughgeometry the on angle the fore-peak size is the section same accordingmade the crushing to the Cartesian pattern diagram.of two oblique In terms collisions of the damagedifferent extent, even though the collision the angle in 60 size◦ caused is the longersame according tear on the to connectionthe Cartesian of thediagram. car deck In andterms lower of the side damage shell influencedextent, the bycollision deeper in penetration. 60° caused Moreover,longer tear theon calculationthe connection of the of penetrationthe car deck in and the lower same side depth shell predicted influenced the damage by deep lengther penetration. to be similar Moreover, in terms the of calculation size. of the penetration in the same depth predicted the damage length to be similar in terms of size. 5.5. Critical Stress 5.5. CriticalThe stress stress in the current structural assessment was conducted to investigate the total number of membersThe stress aff ectedin the duecurrent to thestructural car deck. assessment According was to conducted the critical to stressinvestigate presented the total by von-Misesnumber of formulationmembers affected in Figures due 13 –to15 the, the car affected deck. members According for theto threethe critical caseswere stress similar, presented and they by includevon-Mises car deckformulation (main target), in Figures girder, 13–15, lower the hull, affected upper members hull, and fo middler the three deck. cases However, were similar, despite theseand they similarities, include high-stresscar deck (main intensity target), occurred girder, quite lower extensive hull, uppe on ther lowerhull, and hull middle of the collision deck. However, case 90◦. Itdespite is, therefore, these possiblesimilarities, to come high-stress up with intensity the estimation occurred that quite the extens collisionive on would the lower continue, hull andof the the collision part covered case 90°. by highIt is, stresstherefore, would possible experience to come the earliestup with rupture, the estimation and the that element the removedcollision would in the calculation.continue, and It was the alsopart notedcovered that by the high oblique stress collisions would experience and T-collision the earliest have arupture, quite distinct and the extent element in terms removed of damage in the and stress with the former having the tendency to form an incision rather than deep-focus penetration calculation.J. Mar. Sci. Eng. It 2019 was, 7 also, x noted that the oblique collisions and T-collision have a quite distinct extent13 of in 16 producedterms of damage by the latterand stress on the with struck the vessel.former having the tendency to form an incision rather than deep- focus penetration produced by the latter on the struck vessel.

Figure 13. Critical stress (von Mises formulation) of the collision Angle 60◦. Figure 13. Critical stress (von Mises formulation) of the collision Angle 60°.

Figure 14. Critical stress (von Mises formulation) of the collision angle 90°.

Figure 15. Critical stress (von Mises formulation) of the collision angle 120°.

The inflicted damage due to a variety of penetration styles influenced the stress contour on the side hull. Moreover, the oblique collisions in Figures 13 and 15 caused stress distribution to the longitudinal direction of the struck vessel, while the T-collision in Figure 14 caused high-stress intensity on the lower part of the hull opening which was explicitly distributed on the lower side

J. Mar. Sci. Eng. 2019, 7, x 13 of 16 J. Mar. Sci. Eng. 2019, 7, x 13 of 16

Figure 13. Critical stress (von Mises formulation) of the collision Angle 60°.

J. Mar. Sci. Eng. 2019Figure, 7, 183 13. Critical stress (von Mises formulation) of the collision Angle 60°. 13 of 15

Figure 14. Critical stress (von Mises formulation) of the collision angle 90°. Figure 14. Critical stress (von Mises formulation) of the collision angle 90◦. Figure 14. Critical stress (von Mises formulation) of the collision angle 90°.

Figure 15. Critical stress (von Mises formulation) of the collision angle 120◦. Figure 15. Critical stress (von Mises formulation) of the collision angle 120°. The inﬂicted damage due to a variety of penetration styles inﬂuenced the stress contour on the side hull. Moreover,The inflicted theFigure obliquedamage 15. Critical collisionsdue to stress a variety in (von Figures Mises of penetrat 13 formul and 15ionation) caused styles of the stressinfluenced collision distribution angle the stress 120°. to the contour longitudinal on the directionside hull. of Moreover, the struck the vessel, oblique while collisions the T-collision in Figures in Figure 13 and 14 15 caused caused high-stress stress distribution intensity onto the the lowerlongitudinalThe part inflicted of thedirection hull damage opening of duethe whichtostruck a variety wasvessel, explicitly of penetratwhile distributedtheion T-collision styles oninfluenced thein Figure lower the side14 stress caused hull, contour including high-stress on the its localsideintensity components,hull. Moreover,on the lower such the as part shelloblique of andthe collisions frame.hull opening This in conditionFi whichgures 13was indicated and explicitly 15 thecaused distributed hull stress part was distributionon in the a critical lower to stateside the beforelongitudinal the larger direction tearing of occurred the struck and vessel, a deeper while penetration the T-collision was expected in Figure to lead 14 tocaused the same high-stress pattern intensity on the lower part of the hull opening which was explicitly distributed on the lower side on the side hull. A similar case is found on the 120◦ collision angle with the red contours spotted on the connection between the car deck and side hull. However, this spot was not a complete failure during an interaction between two ships, and the stress was intact at the end of the collision process. Therefore, the tearing length may reach this spot if a larger part of the striking bow penetrates the struck ship on impact.

6. Conclusions This research was dedicated to investigating structural responses of the Ro-Ro vessel during a series of accidental load designed using a vessel-to-vessel collision with the angle varied in the calculation, and the analysis was conducted through the use of nonlinear finite element (NLFE) analysis. The results obtained indicated internal energy of the oblique collision case to be superior to the T-collision case, and this was verified by observing the damage level of the rupture strain and critical stress. Moreover, more local damage was produced in the T-collision case, which caused fewer casualties on the struck vessel. Besides physical behaviour, verification of the calculation process of the J. Mar. Sci. Eng. 2019, 7, 183 14 of 15 current work was also conducted by investigating energy ratio, and a very small portion of the energy was found to have been absorbed artificially. Hourglass phenomenon was expected, and higher damaged members in the simulation were found to have the capability to produce higher hourglass possibility. Therefore, these findings showed energy ratio and hourglass energy to be important criteria, especially in the structural assessment of accidental load in the maritime environment, and they are recommended to be included as validation criteria in NLFE calculation considering that accidental load causes high nonlinearities. However, implementation of the current method and verification are also viable to be used in any assessment related to impact or accidental load on structures. Therefore, future work in this field should extend collision investigation by involving other angles and conduct a comparative study with a head-to-head collision case. It should also provide a concise and precise description of the experimental results, interpretation as well as the experimental conclusions to be drawn.

Author Contributions: All the authors contributed equally to the paper’s preparation. Funding: This research was an independent project without grant funding based on the collaboration of Laboratory of Design and Computational Mechanics, Universitas Sebelas Maret, Indonesia and Laboratory of Ship Structure and Vibration Analysis, Pukyong National University, South Korea. Conﬂicts of Interest: The authors declare no conﬂict of interest.

References

1. Rusli, M.H.M. Maritime Highways of Southeast Asia: Alternative Straits? RSIS Commentaries, Nanyang Technological University: Singapore, 2012. 2. ERIA. Sea lane security in the selected EAS countries. In Sea Lane Security of Oil and Liquefied Natural Gas in the EAS Region; ERIA Research Project Report 2015-14; Kimura, S., Morikawa, T., Singh, S., Eds.; ERIA: Jakarta, Indonesia, 2016; pp. 41–55. 3. Prabowo, A.R.; Bae, D.M.; Cho, J.H.; Sohn, J.M. Analysis of structural crashworthiness and estimating safety limit accounting for ship collisions on strait territory. Lat. Am. J. Sol. Struct. 2017, 14, 1594–1613. [CrossRef] 4. ASDP. Map (Trajectories). ASDP Indonesia Ferry, Jakarta. 2019. Available online: https://www.indonesiaferry. co.id/en/komersil (accessed on 17 February 2019). 5. Allianz. Safety and Shipping Review 2017; Allianz Global Corporate and Specialty: Munich, Germany, 2017. 6. Geffroy, A.G.; Longère, P.; Leblé, B. Fracture analysis and constitutive modelling of ship structure steel behaviour regarding explosion. Eng. Fail. Anal. 2011, 18, 670–681. [CrossRef] 7. Prabowo, A.R.; Muttaqie, T.; Sohn, J.M.; Harsritanto, B.I.R. Investigation on structural component behaviours of double bottom arrangement under grounding accidents. Theor. Appl. Mech. Lett. 2019, 9, 50–59. [CrossRef] 8. Kujala, P.; Goerlandt, F.; Way, B.; Smith, D.; Yang, M.; Khan, F.; Veitch, B. Review of risk-based design for ice-class ships. Mar. Struct. 2019, 63, 181–195. [CrossRef] 9. Prabowo, A.R.; Bae, D.M.; Sohn, J.M.; Zakki, A.F.; Cao, B.; Wang, Q. Analysis of structural damage on the struck ship under side collision scenario. Alex. Eng. J. 2018, 57, 1761–1771. [CrossRef] 10. Babicz, J. Wärtsilä, Encyclopedia of Ship Technology; Wärtsilä Corporation: Helsinki, Finland, 2015. 11. Labib, A.; Read, M. Not just rearranging the deckchairs on the Titanic: Learning from failures through Risk and Reliability Analysis. Saf. Sci. 2013, 51, 397–413. [CrossRef] 12. Law, R.J. Chapter 35—The Sea Empress Oil Spill, 1996. In Oil Spill Science and Technology; Gulf Professional Publishing: Cambridge, MA, USA, 2011; pp. 1109–1117. 13. Park, S.H.; Pham, T.Y.; Yeo, G.T. The Impact of ferry disasters on operational efficiency of the South Korean Coastal Ferry Industry: A DEA-Window Analysis. Asian J. Shipp. Logist. 2018, 34, 248–255. [CrossRef] 14. Morris, B.F.; Loughlin, T.R. Chapter 1—Overview of the Exxon Valdez Oil Spill 1989–1992. In Marine Mammals and the Exxon Valdez; Elsevier: Amsterdam, The Netherlands, 1994; pp. 1–22. 15. Carter, P.L. The Halifax Explosion a century later: Lessons for our time. Am. J. Surg. 2018, 215, 772–774. [CrossRef][PubMed] 16. Amyotte, P.R. Some myths and realities about dust explosions. Proc. Saf. Environ. Prot. 2014, 92, 292–299. [CrossRef] J. Mar. Sci. Eng. 2019, 7, 183 15 of 15

17. Giustiniano, L.; Cunha, M.P.E.; Clegg, S. The dark side of organizational improvisation: Lessons from the sinking of Costa Concordia. Bus. Horiz. 2016, 59, 223–232. [CrossRef] 18. Allianz. Safety and Shipping Review 2018; Allianz Global Corporate and Specialty: Munich, Germany, 2018. 19. Törnqvist, R. Design of Crashworthy Ship Structures; Technical University of Denmark: Lyngby, Denmark, 2003. 20. Prabowo, A.R. Crashworthiness Assessment of Ship Structures under Collision and Grounding; Pukyong National University: Busan, Korea, 2018. 21. Perera, L.P.; Mo, B. Ship performance and navigation data compression and communication under autoencoder system architecture. J. Ocean Eng. Sci. 2018, 3, 133–143. [CrossRef] 22. Yoo, S.L. Near-miss density map for safe navigation of ships. Ocean Eng. 2018, 163, 15–21. [CrossRef] 23. An, K. E-navigation services for Non-SOLAS ships. Int. J. e-Navig. Mar. Econ. 2016, 4, 13–22. [CrossRef] 24. Moan, T.; Amdahl, J.; Ersdal, G. Assessment of ship impact risk to offshore structures—New NORSOK N-003 guidelines. Mar. Struct. 2019, 63, 480–494. [CrossRef] 25. Chen, B.Q.; Liu, B.; Soares, C.G. Experimental and numerical investigation on the influence of stiffeners on the crushing resistance of web girders in ship grounding. Mar. Struct. 2019, 63, 351–363. [CrossRef] 26. Liu, B.; Pedersen, P.T.; Zhu, L.; Zhang, S. Review of experiments and calculation procedures for ship collision and grounding damage. Mar. Struct. 2018, 59, 105–121. [CrossRef] 27. Prabowo, A.R.; Muttaqie, T.; Sohn, J.M.; Bae, D.M. Nonlinear analysis of inter-island RoRo under impact: Effects of selected collision’s parameters on the crashworthy double-side structures. J. Braz. Soc. Mech. Sci. Eng. 2018, 40, 248. [CrossRef] 28. Alsos, H.S.; Amdahl, J. On the resistance of tanker bottom structures during stranding. Mar. Struct. 2007, 20, 218–237. [CrossRef] 29. ANSYS. ANSYS LS-DYNA User’s Guide; ANSYS, Inc.: Canonsburg, PA, USA, 2019. 30. ANSYS. ANSYS Mechanical APDL Element Reference; ANSYS, Inc.: Canonsburg, PA, USA, 2019. 31. Prabowo, A.R.; Cho, H.J.; Byeon, J.H.; Bae, D.M.; Sohn, J.M. Investigation of impact phenomena on the marine structures: Part I—On the behaviour of thin-walled double bottom tanker during rock-structure interaction. IOP Conf. Ser. J. Phys. Conf. Ser. 2017, 953, 012003. [CrossRef] 32. Prabowo, A.R.; Sohn, J.M.; Bae, D.M.; Harsritanto, B.I.R. Crashworthiness assessment of double-hull tanker structures under ship grounding actions. MATEC Web Conf. 2018, 195, 04008. [CrossRef]

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).