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Evaluating structural crashworthiness and progressive failure of double hull tanker under accidental grounding: bottom raking case

Aditya Rio Prabowo / Hyun Jin Cho
  • Interdisciplinary Prog. Marine Convergence Design, Pukyong National University, Pusan, South Korea
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/ Seung Geon Lee
  • Dept. Naval Architecture and Marine Systems Engineering, Pukyong National University, Pusan, South Korea
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/ Seung Jun Baek
  • Dept. Naval Architecture and Marine Systems Engineering, Pukyong National University, Pusan, South Korea
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/ Jung Hoon Byeon
  • Interdisciplinary Prog. Marine Convergence Design, Pukyong National University, Pusan, South Korea
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/ Dong Myung Bae
  • Dept. Naval Architecture and Marine Systems Engineering, Pukyong National University, Pusan, South Korea
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/ Jung Min Sohn
  • Corresponding author
  • Interdisciplinary Prog. Marine Convergence Design, Pukyong National University, Pusan, South Korea
  • Dept. Naval Architecture and Marine Systems Engineering, Pukyong National University, Pusan, South Korea
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/ Bangun IR Harsritanto
Published Online: 2018-07-27 | DOI: https://doi.org/10.1515/eng-2018-0024

Abstract

Remarkable consequences of maritime accident can be various, including structural damage, loss of life and marine pollution. During an accidental phenomenon, such as ship grounding, the amount of oil spillage indicates casualties’ extent of surrounding sea water. Effort to provide protection for sea environment against such event has been conducted actively by developing navigational instruments, and passively using structural development and assessment. The accidental grounding is, however, a very complicated process with high sensitivity to given factors during its occurrence. Variety in ship type, location, obstruction etc. affected by advance improvement in naval technology, invites sustainable analysis for structural crashworthiness and failure to produce evaluation data.

This work aims to perform an assessment on double hull tanker subjected accidental grounding with oceanic seabed as the obstruction. Fundamental concept of bottom raking is used to design grounding scenario using numerical experiment. Non-Linear Finite Element Method (NLFEM) is deployed to idealise tanker structure and obstruction geometry. The selected crashworthiness criteria in grounding are summarised to provide structural prediction in moment double hull members are experiencing crushing process. Influence of geometrical parameters’ variation to progressive failure is presented with contribution of double bottom members to structural behaviour in final part. Result data of the current work can be a reasonable reference to understanding double bottom performance in grounding, especially in raking case. Insight of such accidental phenomenon is very useful in further effort to minimise grounding consequences.

Keywords: ship grounding; double hull tanker; seabed geometry; Non-Linear Finite Element Method (NLFEM); crashworthiness criteria; progressive failure

1 Introduction

Safety for carrier shipping has been a concern since initial notable accidents occurred and caused immense damage and casualty for structure, environment and industry, such as Titanic (1912), Herald of Free Enterprise (1987), Exxon Valdez (1989) and Estonia (1994) [1]. Accidental phenomena in sea is closely related to vessel loss, which recent statistic of Allianz indicates that more than 240 cases appeared as wrecked, stranded and grounded ships between 2007-2016 [2]. It also can be concluded, based on the statistical data in same reference, that grounding emerges at the second place on the top ten causes of loss. Ensuring a shipping from such dangerous phenomenon is, however, a very complicated task considering non-linearity of the accidental grounding. It involves structural connection failure, longitudinal girder crushing and transverse floor penetration, while interaction of seabed and various structure members happens at the same time. Considering the input factors/parameters, the demand to update hull evaluation may occur due to development in ship and structural types. Fundamental estimation and technical description of target location and involved seabed obstruction also possibly influence the grounding outcome. Thus, sustainable analyses using various of these parameters are required for evaluating performance of dangerous carriers, such as a tanker. Adequate reference data regarding structural crashworthiness and progressive failure are noted as important results in order to develop design and scheme to minimise grounding casualties, e.g. oil spillage.

This study is addressed to conduct an evaluation on double hull tanker when it encounters ship grounding in a shipping. Several structural members are determined as the target, and selected seabed geometries are designed to be used as the obstruction in contact with ship structure. Crashworthiness criteria are used to describe and predict structural behaviour in responding grounding impact. Structural failure and damage extent are also discussed in this work considering remarkable crushing process will occur on the ship structure.

2 Numerical strategy for simulating non-linear phenomena

2.1 Implicit methodology

Basic mathematical equation for most structural dynamic problems of a mechanical system is described as the spatial discretization of virtual work. From this basic equation, the structural problem is categorized into two different classes, namely linear and non-linear phenomena. In the linear phenomena, the internal force is linearly proportional to the displacement, while the stiffness remains constant (Equation 1). On other hand, the internal force is no longer in proportional state as displacement, and stiffness is dependent to the updated displacement. Therefore, time integration scheme should be applied to the non-linear semi-discrete form in Equation 2, which represents a non-linear system of simultaneous algebraic equations, and any time integration operator may be used in association with the Newton-Rhapson iterative algorithm. Other methodologies, namely the Newmark and generalised HHT-α are also alternative methods in calculating structural dynamic problems [3].

[M]{u¨(t)}+[C]{u˙(t)}+[K]{u(t)}={Fa(t)}(1)

[M]{u¨(t)}+[C]{u˙(t)}+{Fi(t)}={Fa(t)}(2)

where [M] is the structural mass matrix; [C] is the structural damping matrix; [K] is the structural stiffness matrix; {ü (t)} is the nodal acceleration vector; { (t)} is the nodal velocity vector; {u (t)} is the nodal displacement vector; {Fi (t)} is the internal load vector and {Fa (t)} is the applied load vector.

The characteristic of implicit method in solving linear problems is unconditionally stable for certain integration parameters. To support this process, the time step size will vary to satisfy accuracy requirement. Conversely, in calculating non-linear problems (it is defined as condition of time-dependent dynamic load; analysis is causing large component deformations and involved material exceeds the proportional limit and in non-linear state in observed phenomenon [4, 5, 6]), a series of linear approximation using Newton-Raphson method is used, thus each time step may have many equilibrium iterations. Furthermore, it needs inversion of the non-linear dynamic equivalent stiffness matrix, which is very costly. Small iterative time steps may be required to achieve convergence. For numerical simulation using ANSYS LS-DYNA [7], convergence tool are provided, nevertheless convergence is not guaranteed for highly non-linear problems, such as collision and grounding.

2.2 Explicit methodology

In terms of the time integration, the explicit method uses a central difference strategy. The accelerations are evaluated at time t are given by mathematical expression in Equation 3. After that, the velocities and displacements are evaluated (see Equations 4 and 5). Geometry of the subject is updated by adding the recent displacement increments to the initial geometry/condition as presented in Equation 6.

{at}=[M]1({Ftext}{Ftint})(3)

{vt+Δt/2}={vtΔt/2}+{at}Δtt(4)

{ut+Δt}={ut}+{vt+Δt/2}Δtt+Δt/2(5)

{xt+Δt}={x0}+{ut+Δt}(6)

where [M] is the structural mass matrix; {Ftext} is the applied external and body force vector; {Ftint} is the internal force vector; {at} is the acceleration at time t; {vt} is the velocity at time t; {ut} is the displacement at time t; {x0} is the initial geometry; { xt } is the updated geometry at time t and Δttis the difference in time of at time t compared to the initial/selected condition.

Characteristic of the explicit methodology for non-linear problems, such as collision and grounding, is described as follows: the mass matrix is assumed lump, which required only simple inversion; the equations are uncoupled so that they can be solved directly; the stiffness matrix is not requires (in implicit methodology, this process is needed); convergence check are not required as the equations are uncoupled and the time step should be very small [7]. Based on these descriptions, the explicit methodology is considered more suitable for calculating non-linear phenomena, such as collision [8, 9, 10] and grounding [11, 12, 13]. An adequate attention is given to inversion of the stiffness matrix. Since this process is not required, computational cost can be reduced. Furthermore, convergence check is not conducted, and lighten computational instrument in calculation process. Finally, characteristic of very small time steps is matched with the nature of the collision and grounding as non-linear phenomena. They take place in very short time process, thus very small time step is required in numerical analysis for these non-linear phenomena.

3 Finite element model and configuration

3.1 Double bottom tanker

The idealised ship is modelled based on a 17000 ton class oil/chemical tanker embedded by double side structure, which the principal particulars of the ship are presented as follows: Length Loa = 144 m; Breadth B = 22.6 m; Depth H = 12.5 m; Draft T = 9.2 m and Gross Tonnage GT: 11000 ton.

As grounding is defined as contact between bottom part of ship and oceanic seabed, ship modelling is focused on the double bottom structures. Structural members of the double bottom are idealised as an arrangement of plated structures using thin shell element with fully integrated version of the Belytschko-Tsay shell element formulation (EF no. = 12) incorporated in finite element codes ANSYS LS-DYNA [7]. The ship geometry for grounding analysis is shown in Figure 1.

Numerical geometry of the double bottom structures for grounding analysis.
Figure 1

Numerical geometry of the double bottom structures for grounding analysis.

Structural members are divided into smaller elements according to recommendation of the element-length-to-thickness (ELT) ratio with value in range 5-10 [14, 15]. This meshing methodology was previously applied in accidental collision simulation using FEM, and comparison with empirical and analytical methods successfully produced a satisfactory [16, 17]. Material properties of a general marine steel are inputted on plastic-kinematic material (Equation 7) to be applied on the ship structure. The steel properties is presented in Table 1 with assumption the material has kinematic hardening (hardening number β = 0) and acts as strain-rate dependent. The strain rate 3200 is selected for Cowper-Symonds parameters C considering large damage extent will occur on the ship structure [18, 19]. Related to grounding damage, the material is assumed to experience fracture when the ultimate fracture strain is surpassed due to excessive loads. This fracture criterion is given to the deformable steel material with the determined value for steel fracture f = 0.2 [20, 21].

Table 1

Material properties of the ship structures.

σY=1+(ε˙C)1p(σ0+βEpεpeff)(7)

where σY is the yield strength; ϵ̇ is the strain rate; C and P are the Cowper-Symonds strain rate parameters; σ0 is the initial yield strength; β is the hardening number; Epis the plastic hardening modulus and εpeff is the effective plastic strain.

3.2 Obstruction geometry

Besides the ship structures, seabed needs to be defined as the obstruction for grounding analysis. The geometry is considered based on conical, rock and shoal. Conical configuration is adopted based on previous work of Zilakos et al. [22] in simulating grounding action. The assumed rock is designed based on a 2nd polynomial expression (Equation 8 and example geometries in Figure 2). This rock type has a characteristic smaller radius on the lower surface compared to its maximum height [23, 24, 25]. In the current work, modified geometry will be used with the radius is designed to be larger than the maximum height. The rock will be denoted as polynomial rock to give different notation since the conical geometry also to be applied by material properties of seabed rock. The shoal geometry is designed based on seafloor description by Alsos and Amdahl [14] which indicates this geometry is a very different obstruction and the upper surface of the is relative larger than the rock. This geometry is called by idealised shoal in comparative discussion for structural crashworthiness against the selected geometries.

Example of designed rock geometry according to a 2nd polynomial expression with constant y – radius.
Figure 2

Example of designed rock geometry according to a 2nd polynomial expression with constant y – radius.

z=y2a(8)

where z is the height variable; y is the radius variable and a is the form variable.

Obstruction geometries for this study are summarised in Figure 3, which applied material properties is adopted from the pyroxene mineral rock on the oceanic crustal formation. The geometry is assumed to be rigid with no deformation is not expected during interaction with the ship structure. The rigid material properties are shown in Table 2 including constraint parameter for the obstruction.

Selected obstruction geometries applied in grounding analysis: (a) conical rock in previous work [22], (b) polynomial rock and (c) idealised shoal. The unit is determined to be in mm.
Figure 3

Selected obstruction geometries applied in grounding analysis: (a) conical rock in previous work [22], (b) polynomial rock and (c) idealised shoal. The unit is determined to be in mm.

Table 2

Material properties of the selected obstructions.

4 Preparation of grounding scenario

During interaction between the ship and obstruction, uniform velocity Vu = 10 m/s is applied on the obstruction to move to several targets on the ship to model bottom raking case. The target is selected on structural members of the double bottom, i.e. side girder and space between girders. The objective is to obtain behaviour data regarding significance of the structural arrangements’ variety (with and without strengthening by the girder) on the double bottom. As indicated in Table 2, the obstruction is only allowed to move on the longitudinal direction (Z displacement) with all rotational movements restrained. The boundary condition is attached on the lower surface of the obstruction, while the ship is set to be fixed on the centerline by applying constraint on the end of the inner bottom and bottom plates (Figure 4). Besides target location, the obstruction will be varied according to the selected geometries. Results of structural crashworthiness are summarized, especially progressive failure on the double bottom and performance of the structural members contacted with the obstruction in the grounding.

Illustration of boundary condition (left side) and grounding process (right side). The ship and obstruction are highlighted by arrows on the side view.
Figure 4

Illustration of boundary condition (left side) and grounding process (right side). The ship and obstruction are highlighted by arrows on the side view.

5 Results and discussion

5.1 Effect of target location to the crashworthiness and fracture behaviours

The investigation is conducted by evaluating crashworthiness criteria and structural behaviours during the selected grounding factors are applied on the analysis. The target location presented (Figure 5), in terms of the internal energy criterion, significant difference with the girder strengthening structures produced higher absorbed strain energy than without the girder strengthening. Notable difference approximately 41% in the end of the ship grounding analysis. However, this difference did not occur in an instant, but in progressive process as advance displacement of the obstruction on the double bottom. In the initial impact, the energy for all proposed locations showed similarity (in displacement range 0-1 m). Since girder deformation became remarkable, the destroyed members’ volume increased so that the internal energy for the side girders I and II rose and achieved higher maximum value than spaces between two girders.

Results of the internal energy for the proposed target locations on the double bottom.
Figure 5

Results of the internal energy for the proposed target locations on the double bottom.

The difference of maximum value between side girder and space between girders could also be concluded as the amount of girder contribution against accidental ship grounding with raking case. An interesting phenomenon was spotted on the similarity and diversity for the spaces and girders, consecutively. The space between girders, including side girder-side girder and center girder-side girder showed good similarity as no remarkable during obstruction displacement. Nevertheless, the energy for the girders did not share this fluctuation, with notable difference for these targets were evidenced since obstruction displacement reached 2 m. Based on these findings, it could be concluded that for grounding to the side girder II, other structural members contributed significantly and did not exist on near the side girder I. This observation on the structural arrangement indicated that transverse web on side part of the double bottom acted as an additional member that strengthened the structure. Thus, increment of the internal energy on the side girder II was influenced by damaged volume of this member.

Besides predicting the energy criterion, progressive failure is possibly predicted by assessing structural resistance (crushing force) for all directions. As presented in Figure 6, high fluctuation in the initial ship-obstruction contact reflected the nature of ship grounding as an impact phenomenon. High resistance occurred as shock of the structure in experiencing high-level-short-time load type. Progressive failure of the first intersection consisting stiffener, floor and plate happened until obstruction displacement 0.5-0.8 m. A high fluctuation occurred approximately on the displacement 1 m as remark of the beginning of stiffener indentation. The progressive structural fracture appeared as separation of the stiffener-bottom plate connection. Since the displacement direction and stiffener were located on same longitudinal direction (Y axis), structural resistance showed stability. A high fluctuation, but much lower than the initial one in displacement range 3-3.5 m, appeared as the second intersection was breached. After this point, structural resistance between the second and third intersections tended to be higher than before the second intersection got penetrated. This phenomenon occurred as the space sizes between these intersection was different. The tank between the second and third intersections was predicted smaller in longitudinal length so that the third intersection delivered structural resistance during stiffener and bottom plate were indented.

Structural resistance and progressive failure during ship grounding to center-side girder space.
Figure 6

Structural resistance and progressive failure during ship grounding to center-side girder space.

Force behaviours also indicated the direction of damage extent on the structure when the double bottom interacted with the obstruction. It was found that bottom raking case caused remarkable fluctuation on the longitudinal and vertical directions (FX and Fz, respectively). Estimation of major damage was concluded on this direction dominated by indentation of the bottom plate and longitudinal stiffener. Damage on the transverse direction, as presented in FY, only showed notable fluctuation when the initial separation of the stiffener-plate connection which the plate was flapped back due to penetration by the conical rock (Figure 7a). The damage extent was considered similar with description of the braided cut by Simonsen [26], such that the bottom plate separates as in the clean curling cut, but the deformed flaps fold back and forth.

Damage extent after conical rock penetration: (a) girder space and (b) longitudinal girder.
Figure 7

Damage extent after conical rock penetration: (a) girder space and (b) longitudinal girder.

Affected by the longitudinal girder, Figure 7b indicated that the experienced stress in grounding to the side girder produced longer and larger stress expansion range. In the end of the penetration spot, the bottom plate after the third intersection was already influenced by the stress while in grounding to the girders’ space, the stress contour on the same spot was minor. Furthermore, the stress amount for the girder strengthening structure reached higher maximum level than structure without girder. Confirmation of the internal energy and structural resistance on the selected target location was successfully presented by stress-damage contour after grounding.

Related to the crashworthiness of the girder strengthening structure, progressive failure on the double bottom (Figure 8) presented similarity tendency compared to ship grounding on the center-side girder space. However, the overall structural resistance after the first intersection was breached concluded that the longitudinal girder provided better resistance against grounding action in raking case. Structural stability in experiencing impact was also observed as more uniform and stable during initial impact to the ship occurred in displacement range 0-0.5 m than girder structure without girder. Accounting for structural connection, it was noted that during indentation T-connection of girder and plate, higher fluctuation of the structural resistance took place (approximately more than 30%) indicating girder connection was stronger than the stiffener-plate connection.

Structural resistance and progressive failure during ship grounding to side girder.
Figure 8

Structural resistance and progressive failure during ship grounding to side girder.

Fracture behaviour of the structural members was also reflected on the stress fluctuation when the obstruction penetrated the double bottom. In terms of the transversal members (Figure 9), the floors indicated similar maximum stress level before it went down and as the obstruction left a structure in penetration. Validity of the structural behaviour was presented by early high fluctuation for the transverse floor I as the first intersection was indented. Reduction in stress of the transverse floor I was followed by increment of stress on the transverse floor II on the second intersection during the occurrence of the crushing process at this location. Different fluctuation behaviour was observed on the longitudinal members (Figure 10). The fluctuation was relative high for almost all obstruction displacement. The main cause of this phenomenon was predicted due to the position of the structural members, which same with the obstruction movement in the ship grounding. The bottom plate existed on the XY plane while the longitudinal stiffener on the XZ plane, which both of them overlap with the displacement direction of the obstruction on the X direction. This behaviour was considered contradictive compared to the transversal members, e.g. transverse floor existed on the YZ plane. High fluctuation was occurred and directly followed by sudden reduction of the von Mises stress. Based on these results, it could be concluded that gradual fluctuation in terms of the stress on the structural members was highly affected with movement of the ship or obstruction in grounding.

Behaviour of failure stress (von Mises criterion) for transversal members on the double bottom.
Figure 9

Behaviour of failure stress (von Mises criterion) for transversal members on the double bottom.

Failure stress (von Mises criterion) of longitudinal members in the ship grounding.
Figure 10

Failure stress (von Mises criterion) of longitudinal members in the ship grounding.

Since the beginning of mechanical estimation for ship grounding, concern has been addressed to bending deformation on the lower part of the ship bottom. Analytical theory on Simonsen’s research [26] regarding major fracture on the bottom plate was evidenced in this research using NLFEM. The effective strain data was taken based on element member near fractured part. It was predicted based on tendency in Figure 11 that the bottom plate experienced significant fracture than other members on double bottom. Strain behaviour of this member increased to the point where the fracture strain limit was selected. Compared to other members, experienced strain by the bottom was 20% higher than floor and girder. In other part of same research by Simonsen [26] using experimental test and recent work for re-modelling a series of grounding test [27], result of the current numerical analysis reached good satisfactory especially for structural resistance (crushing force) behaviour for horizontal (in line with indenter movement) and vertical direction. Furthermore, high fluctuation behaviour was also found on these analyses during the transverse floor and intersection were breached.

Strain level compared to the selected ultimate strain limit in grounding analysis.
Figure 11

Strain level compared to the selected ultimate strain limit in grounding analysis.

5.2 Crashworthy and casualty of the double bottom accounting for obstruction geometry

In this discussion, very different geometrical model compared to the previous section, would be deployed as the obstruction in the grounding analysis. The polynomial rock (Figure 12) which has gradual increment in height, produced several fluctuations in the initial penetration as fracture on the first intersection occurred gradually from the lower part (bottom plate) to upper (Z axis) and forward (X axis) directions. The force experienced significant reduction approximately in displacement 1 m due to indentation by maximum height of the obstruction was surpassed. Starting for this point, force began to increase again, but in gradual tendency until the indentation causing T-connection of girder and plate was broken. As high fluctuation occurred for the FY, it could be predicted that the girder got deflected to transversal direction. Increments of the FXand Fz continued until the second intersection was breached. Compared to the conical rock, the force due to penetration of the polynomial rock was considered higher with approximately more than 50%. The structural resistance after breaching of this intersection was also higher than grounding action with the conical rock. Meanwhile, the idealised shoal (Figure 13) provided higher tendency of structural resistance than the polynomial rock. However, maximum force level was spotted very few than the rock. Stable fluctuation dominated overall accidental grounding to the shoal. Based on comparison with results of the polynomial rock and conical obstruction, it could be summarized that the behaviour of structural resistance (presented by the crushing force) reflected the progressive indentation on the target during any impact phenomenon. The idealised shoal and conical rock, which had a larger impact angle, produced stable crushing fluctuation between two intersections as the obstructions caused massive damage in forms of large open cut on the lower double bottom. Structural members of the lower part were crushed and wiped during advanced stages of penetration, larger the geometrical angle, more stable the crushing process and structural resistance. Small angle and gradual characteristics on the polynomial rock produced more fluctuation with clear force increment along the obstruction displacement. Based on this behaviour, vertical penetration of the double bottom was minor, but extensive stress would occur on large part of the ship breadth. It was also noted by comparing two obstructions possessing large geometrical angle, closer the angle to 90°, more stable crushing process would likely take place on the structure for the raking case.

Structural resistance of the double bottom impacted by the selected obstruction: polynomial rock.
Figure 12

Structural resistance of the double bottom impacted by the selected obstruction: polynomial rock.

Structural resistance of the double bottom impacted by the selected obstruction: idealised shoal.
Figure 13

Structural resistance of the double bottom impacted by the selected obstruction: idealised shoal.

Contribution of broad contact surface could be considered as the most influencing factor of obstruction geometry. This factor can be observed on the structural acceleration of the involved double bottom’s members in experiencing ship grounding. Acceleration of the polynomial rock (Figure 14) was concluded lower than the idealised shoal (Figure 16). On the intense fluctuation parts (indicating crushing process of the first and second intersections), the maximum acceleration level of the shoal was higher by approximation 40% than the rock. Even during the penetration between two intersections, the fluctuation of the shoal was still superior to the rock. Specifically, based on data of specific involved members on the double bottom, the longitudinal members existed in the XZ plane experienced larger amount of the acceleration than the transverse members. Tendency of the results was closely correlating to the movement direction and impact surface in this direction. Therefore, acceleration was more influenced by side surface of the obstruction than the upper surface during ship grounding in raking case. The side surface of the idealised shoal was firmer due to larger angle on it than the polynomial rock, so that overall acceleration for the shoal would be higher. It would be interesting and highly recommended to quantify relation between surface area and various crashworthiness criteria under variety of grounding actions.

Structural acceleration under grounding action. The selected obstruction: polynomial rock.
Figure 14

Structural acceleration under grounding action. The selected obstruction: polynomial rock.

Structural acceleration under grounding action. The selected obstruction: idealised shoal.
Figure 15

Structural acceleration under grounding action. The selected obstruction: idealised shoal.

Internal energy of the double bottom accounting for geometrical variety of the obstruction.
Figure 16

Internal energy of the double bottom accounting for geometrical variety of the obstruction.

Overall results of the acceleration shared same tendency with the internal energy criterion (Figure 16), which the idealised shoal produced higher damage extent on the double bottom structure compared to the polynomial rock. The energy difference was varying as advance obstruction displacement in grounding but in similar percentage, i.e. in range of 32-35%. For the same target location, both obstructions produced similar energy tendency with most significant increment occurred during the intersections’ crushing in displacement 0.5 and 3.25 m. Tendency of the internal energy evidenced match with the damage extent criterion. Damage of the polynomial rock (Figure 17) indicated less vertical penetration on the lower structure with the double bottom was deflected to Z axis. In this grounding, significant tearing indentation only occurred on the transverse floor I. However, large part of the double bottom was affected by stress contours, especially in direction to the ship breadth. Contrast to this tendency, the idealised shoal (Figure 18) produced remarkable opening on the bottom plate. Characteristic of the tearing was also considered different than grounding to a conical rock, which more match with stable or clean curling cut. In this tearing type, the plate is separated in front of obstruction (connection of the bottom plate and transverse floor I), and it undergoes rolls and folds to the same side during penetration by obstruction.

Damage-stress contours on the double bottom during impacted by the polynomial rock. Based on this illustration, wide contours occurred on large part of the ship breadth.
Figure 17

Damage-stress contours on the double bottom during impacted by the polynomial rock. Based on this illustration, wide contours occurred on large part of the ship breadth.

Damage-stress contours on the double bottom during impacted by the idealised shoal. The contours indicated the stress expansion was shrinking into smaller area.
Figure 18

Damage-stress contours on the double bottom during impacted by the idealised shoal. The contours indicated the stress expansion was shrinking into smaller area.

6 Conclusions

This work presented a series of grounding analysis of a double hull tanker to produce structural crashworthiness and progressive failure data. The analysis was successfully conducted by the non-linear finite element method (NLFEM) to process several designed grounding scenarios. Selected grounding factors were involved to the scenarios, and discussion was addressed to structural behaviour subjected to these factors.

Results of the internal energy and damage extent accounting for the target location provided strong indication of girder’s contribution to the amount of damaged volume. More stable fluctuation of the structural resistance observed on the girder strengthening structures. Besides these criteria, progressive failure was successfully predicted bf assessing von Mises stress on the involved structural members. Confirmation of the members’ influence to the grounding damage was presented by strain behaviour. Regarding this factor, it is encouraged to perform a sustainable future work to summary contribution of transverse web on the girder crushing during side grounding. On the obstruction factor, geometrical parameters, i.e. obstruction angle and impact surface, were dominating structural damage on the double bottom. Global tendencies of force, acceleration, energy and damage extent criteria concluded that the most remarkable casualties occurred due to grounding to the idealised shoal. Specific observation to measure gap of the damage volume concluded that the shoal caused approximately 35% more damage to the double bottom than the rock in the end of the ship grounding. Current study was successfully summarized characteristic of the crashworthiness criteria on the impacted structures, which can be reasonable references for further assessments. Based on discussion for this factor, it was noted that the crashworthiness criteria of individual members (local tendency) involved in impact, e.g. accidental grounding and collision, was important to be observed to provide complete assessment in terms of global behaviour on the impacted structures.

Acknowledgement

This work was financially supported by grant from BK21 plus MADEC Human Research Development Group, South Korea. Authors would like to acknowledge Department of Naval Architecture and Marine Systems Engineering, Pukyong National University for supporting instrument of numerical experiment.

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About the article

Received: 2017-12-21

Accepted: 2018-04-18

Published Online: 2018-07-27


Citation Information: Open Engineering, Volume 8, Issue 1, Pages 193–204, ISSN (Online) 2391-5439, DOI: https://doi.org/10.1515/eng-2018-0024.

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© 2018 A. R. Prabowo et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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