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A combined numerical and semi-analytical collision damage assessment procedure
Marine Structures 28 (2012) 101–119
Contents lists available at SciVerse ScienceDirect
Marine Structures journal homepage: www.elsevier.com/locate/ marstruc
A combined numerical and semi-analytical collision damage assessment procedure Sören Ehlers a, *, Kristjan Tabri b a b
Dept. of Marine Technology, Norwegian University of Science and Technology, Otto Nielsens vei 10, 7491 Trondheim, Norway Dept. of Civil Engineering, Faculty of Mechanical Engineering, Tallinn University of Technology, Estonia
a r t i c l e i n f o
a b s t r a c t
Article history: Received 21 October 2011 Received in revised form 23 March 2012 Accepted 5 May 2012
Ship collisions are increasingly simulated with numerical methods predicting the structural damage, respectively the ships’ safety, in such accidental event. The latest analyses techniques can take the non-linear structural behaviour and the motions of the colliding vessels into account, however using time-consuming numerical models. Hence, a single dynamic collision can be analysed with a fair degree of accuracy, but at high computational cost. Therefore, this article presents a combined numerical and analytical procedure to assess ship collision damage with significantly lower computational cost. Numerical quasi-static collision simulations estimate the non-linear structural behaviour for a given vessel colliding at selected vertical locations. This provides the force versus penetration curves, which thus depends on the structural arrangement at the striking location. Hence, the semi-analytical collision analysis is calibrated based on these structural resistance curves in order to estimate the change in available energy for structural deformation considering different longitudinal striking locations and angles. As a result, the collision damage, respectively penetration depth and length, can be estimated for vessels of different dimensions and mass ratio’s subjected to various collision situations if the presented procedure is applied. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Collision damage Internal mechanics External dynamics Coupling
* Corresponding author. Tel.: þ47 73 59 5596, þ47 91 89 7748 (mobile); fax: þ47 73 59 5697. E-mail address: [email protected] (S. Ehlers). 0951-8339/$ – see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.marstruc.2012.05.005
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1. Introduction Accidental limit state analyses are of utmost importance, because the structure should be able to tolerate the service load at a reasonably safe level in the post-accidental condition. However, a ship collision accident can easily cause a limit state with undesirable damage and consequently loss of life and ship loss. Furthermore, in recent years approximately 20% of all serious and very serious accidents are collision accidents. Typically such collision accidents can occur under various collision scenarios, respectively ship types colliding, ship velocities and striking angles. Hence, this article is concerned with the assessment of the collision damage under various scenarios in a fast and accurate manner. A classic approach to analyse ship collisions is the separate evaluation of the vessels motions, external dynamics, and the structural response, internal mechanics; see [1]. In such a decoupled analysis the energy to be absorbed in structural deformations is evaluated with a calculation model for external dynamics, where this energy is evaluated based on the law of momentum conservation; see for example [2]. However, this energy is the only outcome of the external dynamics analysis and the exact ship motions are not evaluated. Furthermore, the extent of the penetration associated with this energy is evaluated by comparing it to the area under the force-penetration curve obtained from the analysis of internal mechanics. Hence, the accuracy of the decoupled analysis depends on the level of precision on assuming the penetration path a priori. However, the latter can only be done rather precisely for symmetric collision, where the striking ship collides under a right angle at the amidships of the initially motionless struck ship with only few motion components being excited [3]. In conclusion, in order to analyse the collision damage of non-symmetric ship collisions, the penetration path needs to be evaluated in parallel with the ship motions, i.e. a coupled damage assessment approach is needed. External dynamics primarily evaluate the ship motions under the action of external forces; see for example [4,5] for time domain simulations and [6,7] for finite element-based simulations. However, the external dynamics requires input from the internal mechanics to evaluate the magnitude of the contact force and the extent of deformation. These internal mechanics analyses are commonly carried out in a quasi-static fashion for a collision incident [8]. Internal mechanics simulations of collision accidents are often done using the finite element method, because this numerical method is flexible and widely applicable for complex structures [9]. These simulations contain highly non-linear structural deformations, including rupture. Therefore, the finite element analyses of ship collision incidents require the input of the local strain and stress relation until failure. Furthermore, the analyses need to be reliable and realistic in order for the collision strength of the side structure of the ship to be predicted accurately. In conclusion, the aim of this paper is to present the current state of the art numerical collision simulation approach considering rupture of the shell plating according to [10] and the fully dynamic semi-analytical simulation of the ships motions occurring during a ship collision according to [11]. As a result, both methods will be linked through the numerically obtained force, respectively normalized traction, versus penetration curve in a combined procedure, see Fig. 1. Thus by adopting this procedure the energy available for structural deformations as well as the damage extend for various collision locations, striking angles and collision velocities can be analysed. Compared to a fully coupled numerical simulation using the finite element method (FEM) this procedure is significantly less time consuming and results in low computational cost. The procedure will be presented for a selected case study with an initially motionless struck vessel. However, its generic features allow for easy adaptation to different striking and struck vessels as well as collision locations and scenarios. Furthermore, the current procedure differs from other simplified collision models, such as SIMCOL, DAMAGE or DTU model for example, as we require FE simulations for calibration. Hence, even though this procedure is more time expensive compared to other simplified models, it is not limited to certain structural configurations and damage mechanism as found in the other models. Thus, the presented approach can also account for, i.e., novel crashworthy structures in a variety of collision scenarios once their force versus penetration curve is obtained for a single collision scenario.
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Fig. 1. Overview of the combined numerical and analytical collision damage assessment procedure.
1.1. Scenario description The collision risk increases in dense traffic zones, especially if there is a profound cross traffic, see Fig. 2. This cross traffic zone can be found between Helsinki and Tallinn in the Baltic Sea, where the passenger traffic between the two capitals is crossing with the eastbound and westbound oil and cargo traffic. Therefore, the potential striking ships, primarily tankers, travel in East–West or
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Fig. 2. Dense cross traffic zone in the Baltic Sea.
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West–East direction, whereas the potential struck ships, primarily ROPAX vessels, travel in South– North or North–South direction. Therefore, the presented procedure will concern a collision between a striking tanker and an initially motionless struck ROPAX. The latter will result in a slight overestimation of the transverse extent of damage while underestimating the longitudinal damage extent. 2. A combined numerical and semi-analytical collision damage assessment procedure This chapter combines the research work according to Ehlers [10] and Tabri [11] and introduces a combined numerical and semi-analytical procedure to assess ship collision damage. Hence, this combination will allow for an accurate estimation of the structural damage as well as the accurate estimation of the available collision energy. Furthermore, due to the fast analytical computations and the reasonable extrapolation of the numerical results this procedure is computationally less expensive when compared to fully coupled simulations using FEM. Therefore, the non-linear finite element method is only used to simulate the ship collision for a pre-defined vessel struck at pre-selected vertical striking positions by a rigid indenter perpendicular at the amidships. This provides the force versus penetration curve, respectively the structural collision resistance, in terms of a normalized traction versus penetration curve. The semi-analytical collision analysis will than utilize this characteristic traction versus separation curve to estimates the change in available energy for structural deformation considering different longitudinal striking locations and angles. 2.1. The reference striking and struck vessel In order to present the feasibility of the procedure a reference ROPAX vessel is chosen following the scenario description presented in Fig. 2 together with one potential striking tanker. The main particulars are: L ¼ 188.3 m, B ¼ 28.7 m, T ¼ 6 m, Cb ¼ 0.63 and ice class 1 AS. The scantlings are obtained from an actual new building; see Fig. 3. Hence, the main particulars of the struck ROPAX vessel and the stricking tanker together with their hydromechanical properties are given in Table 1. The nondimensional kxx for ROPAX vessel is therefore 0.038, and 0.25 for kyy and kzz. The non-dimensional values for the Tanker follow analogously being 0.032 and 0.25. A principal definition of the collision event is presented in Fig. 4. 2.2. Quasi-static numerical collision simulation The solver LS-DYNA version 971 is used for the collision simulations. The ANSYS parametric design language is used to build the finite element model of the reference ROPAX vessel according to Fig. 3 and Table 1. The three-dimensional model is built between two transverse bulkheads spaced at 26.25 m, see Fig. 5, and the translational degrees of freedom are restricted at the plane of the bulkhead locations. The remaining edges are free. The structure is modelled using quadrilateral Belytschko-Lin-Tsay shell elements with four nodes and 5 integration points through their thickness. The characteristic elementlength in the contact region is 50 mm to account for the non-linear structural deformations, such as buckling and folding. The element-length dependent material relation and failure criterion according to [10] is utilized for the simulations; see Fig. 6. Therein, also the validity range of the strain versus stress relation for elements larger than 25 mm is shown. Furthermore, the validity of this constant strain failure criterion presented in Fig. 6b, which is obtained for plates with a thickness of 4 mm and 6 mm, is given in [12] for thick plates as found in the present ROPAX vessel. In the current collision simulations the failure strain is assigned to the entire model according to the characteristic elementlength in the contact region for simplicity. Additionally, a comparison discussing the applicability and influence of this material relationship including failure for collision simulations is presented in [13]. Standard LS-DYNA hourglass control and automatic single surface contact (friction coefficient of 0.3) is used for the simulations; see [14]. The collision simulations are displacement-controlled. The rigid bow, see Fig. 7, is moved into the ship side structure at a constant velocity of 10 m/s. This velocity is reasonably low so as not to cause inertia effects resulting from the ships’ masses, see [15]. Furthermore,
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Fig. 3. Main frame of the struck ROPAX vessel.
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Table 1 Properties of the ships used in the analysis. Ship
L [m]
B [m]
T [m]
Cb [–]
Vol [m3]
Mass [t]
kxx [m]
kyy [m]
kzz [m]
ROPAX Tanker
188 190
28.7 24
6 12
0.62 0.8
20 078 43 776
20 178 46 082
7.175 6.00
47 47.50
47 47.50
the rigid indenter results in the maximum energy absorption of the side structure alone, which is needed for a comparison and can be considered conservative and thereby suitable for a fast prediction. The resulting force versus penetration curves, with their distinct peaks at outer and inner hull failure, is shown in Fig. 8. Therein, it can be seen that the simulations are carried out for the two most probable draft variations, respectively vertical striking location. The corresponding damage indicating the state of outer and inner hull rupture for the striking location close to the first deck, namely FE max, is shown in Fig. 9 as an example. The second striking location is located closer to the tank top, namely FE min. 2.3. Dynamic semi-analytical collision simulation The numerical assessment of the force versus penetration curve presented above is computationally expensive and thus, not always applicable to study a large number of collision scenarios. Here we present an approach that benefits from the numerical simulations and can be applied to simulate a large number of scenarios. The approach is based on a semi-analytical collision simulation model of [16]. This semi-analytical simulation model uses a simplified approach to evaluate the structural resistance in ship collisions. When two non-conforming bodies are brought into contact they initially touch each other at a single point or line. As the contact proceeds and the bow penetrates further into the struck ship, the contact interface expands. To predict the shape of the contact interface – denoted by S* as in Fig. 10 – the geometries of the colliding bodies are to be defined. Therefore, the geometry, position, and orientation of the intruding bow of the striking ship is defined as surface S and similarly, the struck ship is approximated as a plane P. The shape of the contact surface S* is based on the geometry and the relative position of the ships. The contact force at each time step is obtained by integrating the normal and tangential tractions over the contact surface between the colliding bodies. The normal traction p is equal to the known
Fig. 4. Definition of the collision event (LC – eccentricity between the initial contact point and the origin of the coordinate system that locates at the centre of gravity of the ship, b – collision angle).
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Fig. 5. FEM model and striking location.
maximum normal stress on the surface of the deformed side structure. The tangential traction q is based on the Coulomb friction law stating the proportionality between tangential and normal traction components. Thus, the total contact force Fc consists of normal force Fp and tangential force Fq and is evaluated as
FC ¼ FAp þ FAq ¼
RR S
¼ p
pnAQ dS þ
ZZ S
RR S
A
qlQ dS ¼
A nAQ þ mq lQ dS
RR S
pnAQ dS þ
RR S
mq plAQ dS (1)
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Fig. 6. Strain versus stress relation for mild steel (a) and failure strain versus element-length (b) [10].
A
where nAQ is an unit normal at integration point Q pointing outside the bulb and lQ describes the direction of the traction force component. Superscript A indicates that a value is defined in the local coordinate system of the striking ship (superscript B stands for the struck ship). Elaborate derivation of the above equation is presented in [16]. The surface tractions p and q describe the structural resistance the penetrating bow experiences on its surface. These obviously depend on the structural configuration of the struck ship and on the relative position between the ships i.e. on the penetration depth. This dependence can be calibrated by looking at the numerically evaluated force-penetration curve in Fig. 8. Only the normal traction is to be calibrated due to the assumed proportionality between the traction components in Eq. (1). The value of traction p and its variation as a function of penetration has to assure that the semianalytical simulation model considers a similar force-penetration curve as evaluated in numerical simulations. The traction curve used in the semi-analytical simulations is depicted in Fig. 11 together
Fig. 7. Rigid intender, respectively bow.
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Fig. 8. Resulting force-penetration curves.
with the numerically obtained traction curve for FE min and FE max. The numerical traction is obtained in a straightforward fashion with LS-DYNA using the *DATABASE_BINARY_INTFOR output option for the instantaneous contact pressure between the tip of the bow (r ¼ 0.126 m) and the ship structure. Hence, the resulting force-penetration curve using this simplified traction curve in the semi-analytical collision simulations is shown with a bold line in Fig. 12 and compared to the numerical results. Furthermore, Fig. 12 includes semi-analytical calculations for collisions angles, b, of 15, 30 and 45 , which are carried out using the characteristic traction curve from Fig. 11. In Fig. 13 the resulting energypenetration curve are presented for all collision angles and compared to the numerically evaluated results. Therein, it can be seen that both force and energy are predicted well until the critical inner hull fracture is reached. Initially the traction p is constant (line AB) and the total contact force increases as the contact surface increases. After the tearing of the outer plating the resistance drops significantly (line BC). The traction remains constant at relatively low value (CD) until the penetrating bow contacts with the inner hull (DE) that locates at 6.05 m from the outer hull. The inner hull presents significant resistance until it’s tearing (FG) after which the resistance gain drops to relatively low level (GH). The resulting force- and energy-penetration curve is positioned between the FE max and FE min curves. Therefore, the simplified analysis as calibrated here does not distinguish between two different drafts.
3. Results of the coupled collision damage procedure The semi-analytical model is applied to assess the accidental damage in different collision scenarions. Effect of collision velocity, angle and eccentricity is studied. The collision angle b and eccentricity LC are defined in Fig. 4. The results of the coupled numerical and analytical collision damage procedure are presented in Figs. 14–19 for the vessels presented in Table 1. The influence of the striking angle, see Fig. 4, on the available energy for structural deformations with collision velocity as a variable for the
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Fig. 9. Example of the resulting damage for FE max (outer and inner hull rupture).
striking locations at midships is presented in Fig. 14. Therein, it can be seen that the highest velocity results in the highest available energy for structural deformation. Furthermore, it can be seen that nonright angle collisions excite ship motions and thereby reduce the available deformation energy. Additionally, the influence of the excited motions, respectively available deformation energy, as well as transverse and longitudinal penetration of the vessel, as a result of non-symmetric striking locations for a given collision velocity can be seen in Figs. 15–17 respectively. Consequently, Figs. 18 and 19 presents the influence of the striking location on the transverse and longitudinal penetration for a given collision velocity respectively. 4. Discussion The results of the combined numerical and analytical collision damage assessment procedure clearly indicate that an uncoupled simulation approach does not satisfy for non-symmetric collision and various scenarios. Hence, even though the present approach assumes a somewhat averaged structural behaviour of the ROPAX vessel, it is capable of assessing the penetration depth and length for various collision scenarios. Thereby it remains safely on the conservative side, because the typically
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Fig. 10. Surface tractions acting at the penetrating bow [15].
Fig. 11. Traction p as a function of penetration.
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Fig. 12. Force-penetration curve obtained with semi-analytical approach (a. b ¼ 0 , b. b ¼ 15 , c. b ¼ 30 and d. b ¼ 45 ).
higher resistance of a bulkhead and a deformable bow is not included. The influence of the latter on the numerical force versus penetration curve was however analysed using a deformable bow; see Fig. 20. Even though the deformations are substantial, the typically stiff behaviour of a conventionally stiffened bow results in small changes of the resulting collision force versus penetration curve; see Fig. 21, and therefore the choice of a rigid bow for the presented comparative collision simulations is well justified. Consequently, the emphasises of this articles lies with the assessment procedure, therefore, it can easily be adopted to different ship types and structures through a new initial set of FEM-based force versus penetration curves for the ship in question. Additionally, the accuracy of the force versus penetration curves is believed to be very good due to the high accuracy achieved with the employed material model including failure; see [13]. In the future, this can further be strengthened with a full three-dimensional coupled numerical simulation according to [7] as applied by [17] for large-scale collision experiments. However, it can be seen clearly that an uncoupled approach would be capable of predicting the symmetric collision damage sufficiently, see also [3], whereas only the coupled approach can assess the energy available for structural deformations and ship motions simultaneously. Concerning the presented case study, when looking at the transverse penetration in the evaluated scenarios, Figs. 16 and 18, it can be concluded that in most of the simulated scenarios the inner hull will be penetrated. The
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Fig. 13. Energy-penetration curve obtained with semi-analytical approach (a. b ¼ 0 , b. b ¼ 15 , c. b ¼ 30 and d. b ¼ 45 ).
Fig. 14. Influence of striking angle on available energy for structural deformations with collision velocity as a variable (LC ¼ const ¼ 0).
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Fig. 15. Influence of striking location on available energy for structural deformations with collision location as a variable (v0 ¼ const ¼ 7 m/s).
penetration depth exceeds the distance of 6.05 m between the outer and inner hull in most of the scenarios. In means of longitudinal penetration the collisions below a 45 angle are the most critical; see Figs. 17 and 19. Knowing the damage lengths at different eccentricities helps to assess whether a certain scenario will damage more than a single watertight compartment.
Fig. 16. Influence of striking angle on transverse penetration with collision velocity as a variable (LC ¼ const ¼ 0).
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Fig. 17. Influence of striking angle on longitudinal penetration with collision velocity as a variable (LC ¼ const ¼ 0).
In conclusion, while the numerical simulation using FE analysis did not describe any specific collision scenario, the simulations with semi-analytical models always reflect a certain scenario with defined ship masses, velocities, collision locations and striking angles. Thereby, the result is a scenario specific damage description. Furthermore, the computational time for a FE-based damage assessment is usually several hours compared to less than 3 min for one semi-analytical simulation. Hence, due to the time efficiency of the semi-analytical approach a large number of collision scenarios can be assessed, allowing the identification of most critical scenarios or certain threshold parameters such as critical collision velocity resulting in the tearing of the inner hull of the struck ship.
Fig. 18. Influence of striking location on transverse penetration (depth) with collision location as variable (v0 ¼ const ¼ 7 m/s).
S. Ehlers, K. Tabri / Marine Structures 28 (2012) 101–119
Fig. 19. Influence of striking location on longitudinal penetration with collision location as variable (v0 ¼ const ¼ 7 m/s).
Fig. 20. Deformable bow.
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Fig. 21. Rigid versus deformable bow collision force versus penetration curves.
5. Conclusion A combined numerical and semi-analytical collision damage assessment procedure according to Ehlers [10] and Tabri [11] has been presented. The resulting procedure is capable of analysing the energy available for structural deformations as well as the damage extent for various collision locations, striking angles and collision velocities. Compared to a fully coupled numerical simulation using FEM this procedure is significantly faster. Furthermore, this damage assessment procedure allows for easy adaptation to different striking and struck vessels as well as collision locations and scenarios. Thereby, this approach extends the information obtained with a single FE-simulation to actual collision scenarios and thus, to detect possible critical scenarios and thereby to develop new safety measures, such as improved structural arrangements. Additionally, the presented model can be updated to include the forward speed of the struck vessel, but the effect of this forward speed on the traction versus penetration curve is still to be studied and validated. Furthermore, if the current assumption of a rigid intender does not hold true for the future analysis in question, than this could however be overcome in the future utilizing the presented procedure, e.g. by inclusion of the indenter deformation in the traction–separation curve. Acknowledgements The research work of Kristjan Tabri has been financially supported by the European Social Fund (grant agreement no. MJD110). This support is kindly appreciated. References [1] Minorsky VU. An analysis of ship collision with reference to protection of nuclear power plants. J Ship Res 1959;3:1–4. [2] Pedersen PT, Zhang S. On impact mechanics in ship collisions. Mar Struct 1998;11:429–49. [3] Tabri K, Broekhuijsen J. Influence of ship motions in the numerical prediction of ship collision damage. In: 3rd Int. Conf. on Mar. Struct. – MARSTRUCT; 2011. p. 391–7. [4] Petersen MJ. Dynamics of ship collisions. Ocean Eng 1982;9:295–329.
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[5] Tabri K, Broekhuijsen J, Matusiak J, Varsta P. Analytical modelling of ship collision based on full-scale experiments. Mar Struct 2009;22:42–61. [6] Le Sourne H, Donner R, Besnier F, Ferry M. External dynamics of ship-submarine collision. In: 2nd Int. Conf. Collision and Grounding of Ships, ICCGS, Denmark; 2001. p. 137–44. [7] Pill I, Tabri K. Finite element simulations of ship collisions: a coupled approach to external dynamics and inner mechanics. In: 2nd Int. Conf. on Mar. Struct. – MARSTRUCT; 2009. p. 103–9. [8] ISSC. Int. ship and offshore structures congress. In: Collision and grounding, committee V.1, vol. 2; 2006. [9] ICCGS. In: Ehlers S, Romanoff J, editors. 5th Int. Conf. on Collision and Grounding of Ships; 2010. p. 263. [10] Ehlers S. Material relation to assess the crashworthiness of ship structures, Doctoral dissertation, Helsinki University of Technology; 2009. Available at: http://lib.tkk.fi/Diss/2009/isbn9789522481443/. [11] Tabri K. Dynamics of ship collisions. Doctoral dissertation. Aalto University; 2010. Available at: http://lib.tkk.fi/Diss/2010/ isbn9789522482730/. [12] Ehlers S. A procedure to optimize ship side structures for crashworthiness. J Eng Marit Environ 2009;224:1–12. [13] Ehlers S. The influence of the material relation on the accuracy of collision simulations. Mar Struct 2010;23:462–74. [14] Hallquist JO, LS-DYNA. Keyword User’s Manual. Version 971. Livermore Software Technology Corporation; 2007. [15] Konter A, Broekhuijsen J, Vredeveldt A. A quantitative assessment of the factors contributing to the accuracy of ship collision predictions with the finite element method. In: 3rd Int. Conf. Collision and Grounding of Ships, ICCGS, Japan; 2004. p. 17–26. [16] Tabri K, Varsta P, Matusiak J. Numerical and experimental motion simulations of non-symmetric ship collisions. J Mar Sci Tech 2010;15:87–101. [17] Ehlers S, Tabri K, Romanoff J, Varsta P. Numerical and experimental investigation on the collision resistance of the X-core structure. J Ships Offshore Struct Spec Issue Collision Grounding; 2010:1–9.
Contents lists available at SciVerse ScienceDirect
Marine Structures journal homepage: www.elsevier.com/locate/ marstruc
A combined numerical and semi-analytical collision damage assessment procedure Sören Ehlers a, *, Kristjan Tabri b a b
Dept. of Marine Technology, Norwegian University of Science and Technology, Otto Nielsens vei 10, 7491 Trondheim, Norway Dept. of Civil Engineering, Faculty of Mechanical Engineering, Tallinn University of Technology, Estonia
a r t i c l e i n f o
a b s t r a c t
Article history: Received 21 October 2011 Received in revised form 23 March 2012 Accepted 5 May 2012
Ship collisions are increasingly simulated with numerical methods predicting the structural damage, respectively the ships’ safety, in such accidental event. The latest analyses techniques can take the non-linear structural behaviour and the motions of the colliding vessels into account, however using time-consuming numerical models. Hence, a single dynamic collision can be analysed with a fair degree of accuracy, but at high computational cost. Therefore, this article presents a combined numerical and analytical procedure to assess ship collision damage with significantly lower computational cost. Numerical quasi-static collision simulations estimate the non-linear structural behaviour for a given vessel colliding at selected vertical locations. This provides the force versus penetration curves, which thus depends on the structural arrangement at the striking location. Hence, the semi-analytical collision analysis is calibrated based on these structural resistance curves in order to estimate the change in available energy for structural deformation considering different longitudinal striking locations and angles. As a result, the collision damage, respectively penetration depth and length, can be estimated for vessels of different dimensions and mass ratio’s subjected to various collision situations if the presented procedure is applied. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Collision damage Internal mechanics External dynamics Coupling
* Corresponding author. Tel.: þ47 73 59 5596, þ47 91 89 7748 (mobile); fax: þ47 73 59 5697. E-mail address: [email protected] (S. Ehlers). 0951-8339/$ – see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.marstruc.2012.05.005
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S. Ehlers, K. Tabri / Marine Structures 28 (2012) 101–119
1. Introduction Accidental limit state analyses are of utmost importance, because the structure should be able to tolerate the service load at a reasonably safe level in the post-accidental condition. However, a ship collision accident can easily cause a limit state with undesirable damage and consequently loss of life and ship loss. Furthermore, in recent years approximately 20% of all serious and very serious accidents are collision accidents. Typically such collision accidents can occur under various collision scenarios, respectively ship types colliding, ship velocities and striking angles. Hence, this article is concerned with the assessment of the collision damage under various scenarios in a fast and accurate manner. A classic approach to analyse ship collisions is the separate evaluation of the vessels motions, external dynamics, and the structural response, internal mechanics; see [1]. In such a decoupled analysis the energy to be absorbed in structural deformations is evaluated with a calculation model for external dynamics, where this energy is evaluated based on the law of momentum conservation; see for example [2]. However, this energy is the only outcome of the external dynamics analysis and the exact ship motions are not evaluated. Furthermore, the extent of the penetration associated with this energy is evaluated by comparing it to the area under the force-penetration curve obtained from the analysis of internal mechanics. Hence, the accuracy of the decoupled analysis depends on the level of precision on assuming the penetration path a priori. However, the latter can only be done rather precisely for symmetric collision, where the striking ship collides under a right angle at the amidships of the initially motionless struck ship with only few motion components being excited [3]. In conclusion, in order to analyse the collision damage of non-symmetric ship collisions, the penetration path needs to be evaluated in parallel with the ship motions, i.e. a coupled damage assessment approach is needed. External dynamics primarily evaluate the ship motions under the action of external forces; see for example [4,5] for time domain simulations and [6,7] for finite element-based simulations. However, the external dynamics requires input from the internal mechanics to evaluate the magnitude of the contact force and the extent of deformation. These internal mechanics analyses are commonly carried out in a quasi-static fashion for a collision incident [8]. Internal mechanics simulations of collision accidents are often done using the finite element method, because this numerical method is flexible and widely applicable for complex structures [9]. These simulations contain highly non-linear structural deformations, including rupture. Therefore, the finite element analyses of ship collision incidents require the input of the local strain and stress relation until failure. Furthermore, the analyses need to be reliable and realistic in order for the collision strength of the side structure of the ship to be predicted accurately. In conclusion, the aim of this paper is to present the current state of the art numerical collision simulation approach considering rupture of the shell plating according to [10] and the fully dynamic semi-analytical simulation of the ships motions occurring during a ship collision according to [11]. As a result, both methods will be linked through the numerically obtained force, respectively normalized traction, versus penetration curve in a combined procedure, see Fig. 1. Thus by adopting this procedure the energy available for structural deformations as well as the damage extend for various collision locations, striking angles and collision velocities can be analysed. Compared to a fully coupled numerical simulation using the finite element method (FEM) this procedure is significantly less time consuming and results in low computational cost. The procedure will be presented for a selected case study with an initially motionless struck vessel. However, its generic features allow for easy adaptation to different striking and struck vessels as well as collision locations and scenarios. Furthermore, the current procedure differs from other simplified collision models, such as SIMCOL, DAMAGE or DTU model for example, as we require FE simulations for calibration. Hence, even though this procedure is more time expensive compared to other simplified models, it is not limited to certain structural configurations and damage mechanism as found in the other models. Thus, the presented approach can also account for, i.e., novel crashworthy structures in a variety of collision scenarios once their force versus penetration curve is obtained for a single collision scenario.
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Fig. 1. Overview of the combined numerical and analytical collision damage assessment procedure.
1.1. Scenario description The collision risk increases in dense traffic zones, especially if there is a profound cross traffic, see Fig. 2. This cross traffic zone can be found between Helsinki and Tallinn in the Baltic Sea, where the passenger traffic between the two capitals is crossing with the eastbound and westbound oil and cargo traffic. Therefore, the potential striking ships, primarily tankers, travel in East–West or
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Fig. 2. Dense cross traffic zone in the Baltic Sea.
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West–East direction, whereas the potential struck ships, primarily ROPAX vessels, travel in South– North or North–South direction. Therefore, the presented procedure will concern a collision between a striking tanker and an initially motionless struck ROPAX. The latter will result in a slight overestimation of the transverse extent of damage while underestimating the longitudinal damage extent. 2. A combined numerical and semi-analytical collision damage assessment procedure This chapter combines the research work according to Ehlers [10] and Tabri [11] and introduces a combined numerical and semi-analytical procedure to assess ship collision damage. Hence, this combination will allow for an accurate estimation of the structural damage as well as the accurate estimation of the available collision energy. Furthermore, due to the fast analytical computations and the reasonable extrapolation of the numerical results this procedure is computationally less expensive when compared to fully coupled simulations using FEM. Therefore, the non-linear finite element method is only used to simulate the ship collision for a pre-defined vessel struck at pre-selected vertical striking positions by a rigid indenter perpendicular at the amidships. This provides the force versus penetration curve, respectively the structural collision resistance, in terms of a normalized traction versus penetration curve. The semi-analytical collision analysis will than utilize this characteristic traction versus separation curve to estimates the change in available energy for structural deformation considering different longitudinal striking locations and angles. 2.1. The reference striking and struck vessel In order to present the feasibility of the procedure a reference ROPAX vessel is chosen following the scenario description presented in Fig. 2 together with one potential striking tanker. The main particulars are: L ¼ 188.3 m, B ¼ 28.7 m, T ¼ 6 m, Cb ¼ 0.63 and ice class 1 AS. The scantlings are obtained from an actual new building; see Fig. 3. Hence, the main particulars of the struck ROPAX vessel and the stricking tanker together with their hydromechanical properties are given in Table 1. The nondimensional kxx for ROPAX vessel is therefore 0.038, and 0.25 for kyy and kzz. The non-dimensional values for the Tanker follow analogously being 0.032 and 0.25. A principal definition of the collision event is presented in Fig. 4. 2.2. Quasi-static numerical collision simulation The solver LS-DYNA version 971 is used for the collision simulations. The ANSYS parametric design language is used to build the finite element model of the reference ROPAX vessel according to Fig. 3 and Table 1. The three-dimensional model is built between two transverse bulkheads spaced at 26.25 m, see Fig. 5, and the translational degrees of freedom are restricted at the plane of the bulkhead locations. The remaining edges are free. The structure is modelled using quadrilateral Belytschko-Lin-Tsay shell elements with four nodes and 5 integration points through their thickness. The characteristic elementlength in the contact region is 50 mm to account for the non-linear structural deformations, such as buckling and folding. The element-length dependent material relation and failure criterion according to [10] is utilized for the simulations; see Fig. 6. Therein, also the validity range of the strain versus stress relation for elements larger than 25 mm is shown. Furthermore, the validity of this constant strain failure criterion presented in Fig. 6b, which is obtained for plates with a thickness of 4 mm and 6 mm, is given in [12] for thick plates as found in the present ROPAX vessel. In the current collision simulations the failure strain is assigned to the entire model according to the characteristic elementlength in the contact region for simplicity. Additionally, a comparison discussing the applicability and influence of this material relationship including failure for collision simulations is presented in [13]. Standard LS-DYNA hourglass control and automatic single surface contact (friction coefficient of 0.3) is used for the simulations; see [14]. The collision simulations are displacement-controlled. The rigid bow, see Fig. 7, is moved into the ship side structure at a constant velocity of 10 m/s. This velocity is reasonably low so as not to cause inertia effects resulting from the ships’ masses, see [15]. Furthermore,
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Fig. 3. Main frame of the struck ROPAX vessel.
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Table 1 Properties of the ships used in the analysis. Ship
L [m]
B [m]
T [m]
Cb [–]
Vol [m3]
Mass [t]
kxx [m]
kyy [m]
kzz [m]
ROPAX Tanker
188 190
28.7 24
6 12
0.62 0.8
20 078 43 776
20 178 46 082
7.175 6.00
47 47.50
47 47.50
the rigid indenter results in the maximum energy absorption of the side structure alone, which is needed for a comparison and can be considered conservative and thereby suitable for a fast prediction. The resulting force versus penetration curves, with their distinct peaks at outer and inner hull failure, is shown in Fig. 8. Therein, it can be seen that the simulations are carried out for the two most probable draft variations, respectively vertical striking location. The corresponding damage indicating the state of outer and inner hull rupture for the striking location close to the first deck, namely FE max, is shown in Fig. 9 as an example. The second striking location is located closer to the tank top, namely FE min. 2.3. Dynamic semi-analytical collision simulation The numerical assessment of the force versus penetration curve presented above is computationally expensive and thus, not always applicable to study a large number of collision scenarios. Here we present an approach that benefits from the numerical simulations and can be applied to simulate a large number of scenarios. The approach is based on a semi-analytical collision simulation model of [16]. This semi-analytical simulation model uses a simplified approach to evaluate the structural resistance in ship collisions. When two non-conforming bodies are brought into contact they initially touch each other at a single point or line. As the contact proceeds and the bow penetrates further into the struck ship, the contact interface expands. To predict the shape of the contact interface – denoted by S* as in Fig. 10 – the geometries of the colliding bodies are to be defined. Therefore, the geometry, position, and orientation of the intruding bow of the striking ship is defined as surface S and similarly, the struck ship is approximated as a plane P. The shape of the contact surface S* is based on the geometry and the relative position of the ships. The contact force at each time step is obtained by integrating the normal and tangential tractions over the contact surface between the colliding bodies. The normal traction p is equal to the known
Fig. 4. Definition of the collision event (LC – eccentricity between the initial contact point and the origin of the coordinate system that locates at the centre of gravity of the ship, b – collision angle).
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Fig. 5. FEM model and striking location.
maximum normal stress on the surface of the deformed side structure. The tangential traction q is based on the Coulomb friction law stating the proportionality between tangential and normal traction components. Thus, the total contact force Fc consists of normal force Fp and tangential force Fq and is evaluated as
FC ¼ FAp þ FAq ¼
RR S
¼ p
pnAQ dS þ
ZZ S
RR S
A
qlQ dS ¼
A nAQ þ mq lQ dS
RR S
pnAQ dS þ
RR S
mq plAQ dS (1)
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Fig. 6. Strain versus stress relation for mild steel (a) and failure strain versus element-length (b) [10].
A
where nAQ is an unit normal at integration point Q pointing outside the bulb and lQ describes the direction of the traction force component. Superscript A indicates that a value is defined in the local coordinate system of the striking ship (superscript B stands for the struck ship). Elaborate derivation of the above equation is presented in [16]. The surface tractions p and q describe the structural resistance the penetrating bow experiences on its surface. These obviously depend on the structural configuration of the struck ship and on the relative position between the ships i.e. on the penetration depth. This dependence can be calibrated by looking at the numerically evaluated force-penetration curve in Fig. 8. Only the normal traction is to be calibrated due to the assumed proportionality between the traction components in Eq. (1). The value of traction p and its variation as a function of penetration has to assure that the semianalytical simulation model considers a similar force-penetration curve as evaluated in numerical simulations. The traction curve used in the semi-analytical simulations is depicted in Fig. 11 together
Fig. 7. Rigid intender, respectively bow.
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Fig. 8. Resulting force-penetration curves.
with the numerically obtained traction curve for FE min and FE max. The numerical traction is obtained in a straightforward fashion with LS-DYNA using the *DATABASE_BINARY_INTFOR output option for the instantaneous contact pressure between the tip of the bow (r ¼ 0.126 m) and the ship structure. Hence, the resulting force-penetration curve using this simplified traction curve in the semi-analytical collision simulations is shown with a bold line in Fig. 12 and compared to the numerical results. Furthermore, Fig. 12 includes semi-analytical calculations for collisions angles, b, of 15, 30 and 45 , which are carried out using the characteristic traction curve from Fig. 11. In Fig. 13 the resulting energypenetration curve are presented for all collision angles and compared to the numerically evaluated results. Therein, it can be seen that both force and energy are predicted well until the critical inner hull fracture is reached. Initially the traction p is constant (line AB) and the total contact force increases as the contact surface increases. After the tearing of the outer plating the resistance drops significantly (line BC). The traction remains constant at relatively low value (CD) until the penetrating bow contacts with the inner hull (DE) that locates at 6.05 m from the outer hull. The inner hull presents significant resistance until it’s tearing (FG) after which the resistance gain drops to relatively low level (GH). The resulting force- and energy-penetration curve is positioned between the FE max and FE min curves. Therefore, the simplified analysis as calibrated here does not distinguish between two different drafts.
3. Results of the coupled collision damage procedure The semi-analytical model is applied to assess the accidental damage in different collision scenarions. Effect of collision velocity, angle and eccentricity is studied. The collision angle b and eccentricity LC are defined in Fig. 4. The results of the coupled numerical and analytical collision damage procedure are presented in Figs. 14–19 for the vessels presented in Table 1. The influence of the striking angle, see Fig. 4, on the available energy for structural deformations with collision velocity as a variable for the
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Fig. 9. Example of the resulting damage for FE max (outer and inner hull rupture).
striking locations at midships is presented in Fig. 14. Therein, it can be seen that the highest velocity results in the highest available energy for structural deformation. Furthermore, it can be seen that nonright angle collisions excite ship motions and thereby reduce the available deformation energy. Additionally, the influence of the excited motions, respectively available deformation energy, as well as transverse and longitudinal penetration of the vessel, as a result of non-symmetric striking locations for a given collision velocity can be seen in Figs. 15–17 respectively. Consequently, Figs. 18 and 19 presents the influence of the striking location on the transverse and longitudinal penetration for a given collision velocity respectively. 4. Discussion The results of the combined numerical and analytical collision damage assessment procedure clearly indicate that an uncoupled simulation approach does not satisfy for non-symmetric collision and various scenarios. Hence, even though the present approach assumes a somewhat averaged structural behaviour of the ROPAX vessel, it is capable of assessing the penetration depth and length for various collision scenarios. Thereby it remains safely on the conservative side, because the typically
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Fig. 10. Surface tractions acting at the penetrating bow [15].
Fig. 11. Traction p as a function of penetration.
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Fig. 12. Force-penetration curve obtained with semi-analytical approach (a. b ¼ 0 , b. b ¼ 15 , c. b ¼ 30 and d. b ¼ 45 ).
higher resistance of a bulkhead and a deformable bow is not included. The influence of the latter on the numerical force versus penetration curve was however analysed using a deformable bow; see Fig. 20. Even though the deformations are substantial, the typically stiff behaviour of a conventionally stiffened bow results in small changes of the resulting collision force versus penetration curve; see Fig. 21, and therefore the choice of a rigid bow for the presented comparative collision simulations is well justified. Consequently, the emphasises of this articles lies with the assessment procedure, therefore, it can easily be adopted to different ship types and structures through a new initial set of FEM-based force versus penetration curves for the ship in question. Additionally, the accuracy of the force versus penetration curves is believed to be very good due to the high accuracy achieved with the employed material model including failure; see [13]. In the future, this can further be strengthened with a full three-dimensional coupled numerical simulation according to [7] as applied by [17] for large-scale collision experiments. However, it can be seen clearly that an uncoupled approach would be capable of predicting the symmetric collision damage sufficiently, see also [3], whereas only the coupled approach can assess the energy available for structural deformations and ship motions simultaneously. Concerning the presented case study, when looking at the transverse penetration in the evaluated scenarios, Figs. 16 and 18, it can be concluded that in most of the simulated scenarios the inner hull will be penetrated. The
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Fig. 13. Energy-penetration curve obtained with semi-analytical approach (a. b ¼ 0 , b. b ¼ 15 , c. b ¼ 30 and d. b ¼ 45 ).
Fig. 14. Influence of striking angle on available energy for structural deformations with collision velocity as a variable (LC ¼ const ¼ 0).
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Fig. 15. Influence of striking location on available energy for structural deformations with collision location as a variable (v0 ¼ const ¼ 7 m/s).
penetration depth exceeds the distance of 6.05 m between the outer and inner hull in most of the scenarios. In means of longitudinal penetration the collisions below a 45 angle are the most critical; see Figs. 17 and 19. Knowing the damage lengths at different eccentricities helps to assess whether a certain scenario will damage more than a single watertight compartment.
Fig. 16. Influence of striking angle on transverse penetration with collision velocity as a variable (LC ¼ const ¼ 0).
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Fig. 17. Influence of striking angle on longitudinal penetration with collision velocity as a variable (LC ¼ const ¼ 0).
In conclusion, while the numerical simulation using FE analysis did not describe any specific collision scenario, the simulations with semi-analytical models always reflect a certain scenario with defined ship masses, velocities, collision locations and striking angles. Thereby, the result is a scenario specific damage description. Furthermore, the computational time for a FE-based damage assessment is usually several hours compared to less than 3 min for one semi-analytical simulation. Hence, due to the time efficiency of the semi-analytical approach a large number of collision scenarios can be assessed, allowing the identification of most critical scenarios or certain threshold parameters such as critical collision velocity resulting in the tearing of the inner hull of the struck ship.
Fig. 18. Influence of striking location on transverse penetration (depth) with collision location as variable (v0 ¼ const ¼ 7 m/s).
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Fig. 19. Influence of striking location on longitudinal penetration with collision location as variable (v0 ¼ const ¼ 7 m/s).
Fig. 20. Deformable bow.
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Fig. 21. Rigid versus deformable bow collision force versus penetration curves.
5. Conclusion A combined numerical and semi-analytical collision damage assessment procedure according to Ehlers [10] and Tabri [11] has been presented. The resulting procedure is capable of analysing the energy available for structural deformations as well as the damage extent for various collision locations, striking angles and collision velocities. Compared to a fully coupled numerical simulation using FEM this procedure is significantly faster. Furthermore, this damage assessment procedure allows for easy adaptation to different striking and struck vessels as well as collision locations and scenarios. Thereby, this approach extends the information obtained with a single FE-simulation to actual collision scenarios and thus, to detect possible critical scenarios and thereby to develop new safety measures, such as improved structural arrangements. Additionally, the presented model can be updated to include the forward speed of the struck vessel, but the effect of this forward speed on the traction versus penetration curve is still to be studied and validated. Furthermore, if the current assumption of a rigid intender does not hold true for the future analysis in question, than this could however be overcome in the future utilizing the presented procedure, e.g. by inclusion of the indenter deformation in the traction–separation curve. Acknowledgements The research work of Kristjan Tabri has been financially supported by the European Social Fund (grant agreement no. MJD110). This support is kindly appreciated. References [1] Minorsky VU. An analysis of ship collision with reference to protection of nuclear power plants. J Ship Res 1959;3:1–4. [2] Pedersen PT, Zhang S. On impact mechanics in ship collisions. Mar Struct 1998;11:429–49. [3] Tabri K, Broekhuijsen J. Influence of ship motions in the numerical prediction of ship collision damage. In: 3rd Int. Conf. on Mar. Struct. – MARSTRUCT; 2011. p. 391–7. [4] Petersen MJ. Dynamics of ship collisions. Ocean Eng 1982;9:295–329.
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[5] Tabri K, Broekhuijsen J, Matusiak J, Varsta P. Analytical modelling of ship collision based on full-scale experiments. Mar Struct 2009;22:42–61. [6] Le Sourne H, Donner R, Besnier F, Ferry M. External dynamics of ship-submarine collision. In: 2nd Int. Conf. Collision and Grounding of Ships, ICCGS, Denmark; 2001. p. 137–44. [7] Pill I, Tabri K. Finite element simulations of ship collisions: a coupled approach to external dynamics and inner mechanics. In: 2nd Int. Conf. on Mar. Struct. – MARSTRUCT; 2009. p. 103–9. [8] ISSC. Int. ship and offshore structures congress. In: Collision and grounding, committee V.1, vol. 2; 2006. [9] ICCGS. In: Ehlers S, Romanoff J, editors. 5th Int. Conf. on Collision and Grounding of Ships; 2010. p. 263. [10] Ehlers S. Material relation to assess the crashworthiness of ship structures, Doctoral dissertation, Helsinki University of Technology; 2009. Available at: http://lib.tkk.fi/Diss/2009/isbn9789522481443/. [11] Tabri K. Dynamics of ship collisions. Doctoral dissertation. Aalto University; 2010. Available at: http://lib.tkk.fi/Diss/2010/ isbn9789522482730/. [12] Ehlers S. A procedure to optimize ship side structures for crashworthiness. J Eng Marit Environ 2009;224:1–12. [13] Ehlers S. The influence of the material relation on the accuracy of collision simulations. Mar Struct 2010;23:462–74. [14] Hallquist JO, LS-DYNA. Keyword User’s Manual. Version 971. Livermore Software Technology Corporation; 2007. [15] Konter A, Broekhuijsen J, Vredeveldt A. A quantitative assessment of the factors contributing to the accuracy of ship collision predictions with the finite element method. In: 3rd Int. Conf. Collision and Grounding of Ships, ICCGS, Japan; 2004. p. 17–26. [16] Tabri K, Varsta P, Matusiak J. Numerical and experimental motion simulations of non-symmetric ship collisions. J Mar Sci Tech 2010;15:87–101. [17] Ehlers S, Tabri K, Romanoff J, Varsta P. Numerical and experimental investigation on the collision resistance of the X-core structure. J Ships Offshore Struct Spec Issue Collision Grounding; 2010:1–9.