Comparison of residual strength-grounding damage index diagrams for tankers produced by the ALPS/HULL ISFEM and design formula method

Transcription

1 csnk, 2013 Int. J. Naval rchit. Ocean Eng. (2013) 5:47~61 Compason of residual strength-gunding damage index diagrams for tankers pduced y the LPS/HULL ISFEM and design formula method Do Kyun Kim 1,2, Han yul Kim 1, Mohd Hail Mohd 1,3 and Jeom Kee Paik 1 1 Lloyd s Register Foundation Research Centre of Excellence (The Ship and Offshore Research Institute), Pusan National University, usan, Korea 2 Graduate Schl of Engineeng Mastership, Pohang University of Science and Technology, Pohang, Korea 3 Matime Technology Department, Universiti Malaysia Terengganu, Terengganu, Malaysia STRCT: This study compares the Residual ultimate longitudinal strength gunding Damage index (R-D) diagrams pduced y two analysis methods: the LPS/HULL Intelligent Supersize Finite Element Method (ISFEM) and the design formula (modified Paik and Mansour) method used to assess the safety of damaged ships. The compason includes four types of doule-hull l tankers:, framax, and. The R-D diagrams were calculated for a sees of 50 gunding scenaos. The diagrams were efficiently sampled using the Latin Hypercue Sampling (LHS) technique and comprehensively analysed ased on ship size. Finally, the two methods were compared y statistically analysing the differences etween their gunding damage indices and ultimate longitudinal strength predictions. The findings pvide a useful example of how to apply the ultimate longitudinal strength analysis method to gunded ships. KEY WORDS: Gunding damage; R-D diagram; Residual ultimate longitudinal strength; Gunding damage index; Doule hull l tankers. NOMENCLTURES css sectional area oginal area of the inner ottom oginal area of the outer ottom reduced (damaged) area of the inner ottom reduced (damaged) area of the outer ottom ship readth doule side width D ship s depth h doule ottom height I moment of inertia L ship length M u ultimate hull girder ending moment M uo ultimate hull girder ending moment at intact condition 2 R coefficient of determination r 1 readth of the ottom of the ck r 2 readth of the tip of the ck α correction factor φ angle of the ck Corresponding author: Jeom Kee Paik jeompaik@pusan.ac.kr

2 48 Int. J. Naval rchit. Ocean Eng. (2013) 5:47~61 INTRODUCTION Ships are vulnerale to vaous accidents such as gunding, collision, fire and explosion in addition to age-related degradation such as corsion, fatigue cracking and localised dents. This study investigates the residual ultimate longitudinal strength of doule-hull l tankers suject to gunding damage. Gunding or collision accidents continue to occur despite concerted efforts to prevent them. recent example is the Costa Concordia cruise ship, which was gunded on 13 January Numeus studies have een performed in relation to gunding or collision accidents, including the assessment of damage to ships (Wang et al., 2002; Paik et al., 2003; Kim, 2013), damage prediction (Simonsen and Fis-Hansen, 2000; Simonsen et al., 2009), structural consequences (Zhang, 2002; Zhang and Suzuki, 2006), hull girder collapse (Pedersen, 1994; Paik et al., 1998; Wang et al., 2000), damage scenaos (wn, 2002; Samuelides et al., 2008; Paik et al., 2012), modelling (Ta et al., 2009; Paik, 2007a; Paik, 2007) and structural designs (Paik, 2003; Samuelides et al., 2009). Research on gunding accidents conducted y Pedersen (2010), Nguyen et al. (2011) and Hong and mdahl (2012) may also e referred. Recently, Paik et al. (2012) pposed a new concept, the R-D diagram, for accurately evaluating the safety of damaged ships using the design formula method (Paik et al., 2013) to predict the residual ultimate longitudinal strength of ships damaged y gunding. The method is ased on the presumed stress distution of the mid-ship section (Hughes and Paik, 2010). Nevertheless, vaous alternative analysis methods, such as the idealized structural unit method (ISUM or SMITH method), the non-linear finite element method (NLFEM), the intelligent supersize finite element method (ISFEM) and others can also e used to identify the accuracy and efficiency of structural safety. While Paik et al. (2012) applied the design formula (analytical) method, this study focuses on the differences etween the ISFEM (LPS/HULL) (LPS/HULL, 2012) and the design formula methods (modified Paik and Mansour method or modified P-M method) (Paik et al., 2013) in assessing the safety of damaged ship structures. The results fm the two methods are compared to determine the most practical appach. Tale 1 indicates the main differences etween previous studies and present study. ased on the calculated results, an R-D diagram is estalished and the values for the gunding damage index () and residual ultimate hull girder strength are compared. Tale 1 The main differences etween previous studies and the present study. Previous (Paik et al., 2012) Present Damage type Gunding Gunding Target structure Doule-hull l tankers Doule-hull l tankers Structural analysis method Design formula method Intelligent supersize FEM Definition of ship structure charactestics Charactesation of damage parameters Pailistic identification of damage parameters Selection of damage scenaos Definition of damage index for selected damage scenaos Sampling technique Calculation of residual strength for selected damage scenaos Development of the diagram compang the residual strength with the damage index Fig. 1 The general pcedure for the development of the R-D diagram (Paik et al., 2012).

3 Int. J. Naval rchit. Ocean Eng. (2013) 5:47~61 49 PROCEDURE FOR THE DEVELOPMENT OF THE RESIDUL STRENGTH DMGE INDEX DIGRM Paik et al. (2012) pposed a new concept for evaluating damaged structures, the R-D (Residual strength Damage index) diagram. Fig. 1 shows the general pcedure for the development of an R-D diagram. ased on this pcedure, R-D diagrams of doule-hull l tankers (Paik et al., 2012) using the design formula (modified P-M) method, ulk carers (Park et al., 2012), and container ships (Kim et al., 2012a) have een estalished using the ISFEM (LPS/HULL) method. θ r tan φ 2 = r1-2h 2 r 2 H θ H r 1 r 2 0 aseline r 1 r 2 = 0 Fig. 2 Nomenclature for lunt and sharp ck shapes (Paik et al., 2012). Paility density p1 p1 f ( ) = 10. ( ) Mean = 00 COV = 06 p 1 = Gunding damage location in the ship s readth direction p 1 / Paility density p2 f ( ) = D p2 p ( ) D D p2 11. ( 01. < 03. ) D Mean = COV = 75 v 2 = Gunding damage height (vertical penetration extent) p 2 /D Fig. 3(a) Paility density distution of the location of Fig. 3() Paility density distution of the gunding damage ( p 1 ) in the direction of the ship s height of gunding damage ( p 2 ), normalised readth, normalised y ship readth (IMO, 2003). y ship depth (IMO, 2003). Paility density p3 p ( ) p3 p3 = 04 03< 09 p3 p ( 0. 9 < 1. 0) f ( ). (.. ) Mean = COV = 23 p 3 = Gunding damage readth (transverse extent) p 3 / Fig. 3(c) Paility density distution of the readth Fig. 3(d) Paility density distution of of gunding damage ( p 3 ), normalised the assumed angle of the ck ( p 4 ) y ship readth (IMO, 2003). (Paik et al., 2012). The aove pcedure can e summased as follows. fter defining the dimensions, geometry and mateal pperties of the target ship structures, the gunding damage parameters should e identified as follows and as shown in Fig. 2 (Paik et al., 2012).

4 50 Int. J. Naval rchit. Ocean Eng. (2013) 5:47~61 p 1 : gunding location in the direction of the ship s eam. p 2 : height (H) of ck penetrating into the ottom of the hull in the direction of the ship s depth. p 3 : readth ( r 1 ) of the ottom of the ck at the elevation corresponding to the ship s aseline and readth ( r 2 ) of the tip of the ck. p : angle of the ck (φ ). 4 The previous study adopted the paility density distutions pvided y the IMO (2003) as reasonale gunding damage scenaos in terms of damage location ( p 1 ), damage height (or penetration) ( p 2 ) and damage readth ( p 3 ), as shown in Figs. 3(a) to (c). Figs. 3(a) to 3(c) show the IMO s paility density distutions for the gunding damage parameters and Fig. 3(d) illustrates the distution of the assumed angles of the cks. These figures are also employed in this study and the same assumptions used in Paik et al. (2012) are used in this study to select a reasonale numer of damage scenaos using the LHS technique (Ye, 1998). This technique takes into consideration economic factors such as computational cost limitations. The expatiation of LHS is omitted, ut can e found in Ye (1998). Once the gunding damage parameters (including damage location and extent) have een defined, the residual ultimate longitudinal strength analysis and identification of the gunding damage index () pceed simultaneously. Normally, gunding in doule-ottomed structures occurs in oth the outer-ottom and the inner-ottom structures. Therefore, the should identify the extent and location of gunding damage for oth the inner and outer ottom structures, as shown in Eq. (1). It includes a correction factor (α ) to reflect the contution of the inner ottom structure to the ultimate longitudinal strength of the ship (Paik et al., 2012). = + α (1) TRGET STUCTURES ND PPLIED METHODS This study examines four types of representative doule-hull l tankers:, framax, and, as shown in Fig. 4 with their pncipal dimensions. The css-sectional data are also presented in Tale 2. Tale 2 Css-sectional data of target structures. Ship type (m 2 ) Vertical I (m 4 ) Hozontal N.. (m) framax Note: = sectional area, I = moment of inertia, N.. = neutral axis position fm aseline. Figs. 5 (design formula method) and Figs. 6 (ISFEM) show the analysis models for doule-hull l tankers. In ef, the design formula (modified P-M) method is ased on either the plate-stiffener comination (PSC) model or the plate-stiffener separation (PSS) model. Figs. 5(a) to (d) show the PSC models for four doule-hull l tankers; the figures for the PSS model are omitted here. Design formula pvides a 2-dimensional representation ut ISFEM adopts a 3-dimensional representation. The important fact to note is that the assumed stress distutions are along the mid-ship section (presumed stress distution-ased method), as shown in Fig. 7. However, this method cannot deal with interactions etween local and gloal failure.

5 Int. J. Naval rchit. Ocean Eng. (2013) 5:47~61 51 z z framax D h L = m = m D = 25 m -2 = 2.08 m h = 2.15 m /D = 1.56 y D h L = m = m D = 20 m -2 = 2.35 m h = 2.40 m /D = 2.09 y (a) class. () framax class. z z D L = 260 m = m D = m -2 = 2.45 m h = 2.55 m /D = 2.07 D L = m = 58.0 m D = 29.0 m -2 = 2.40 m h = 3.00 m /D= 2.00 h y h y (c) class. (d) class. Fig. 4 Configuration of the mid-ship sections of four types of doule-hull l tankers and their pncipal dimensions (Kim et al., 2012c) (a) class () framax class. (c) class. (d) class. Fig. 5 Design formula (modified P-M) models assemled using the plate-stiffener comination (PSC) models for the four types of doule-hull l tankers (Paik et al., 2013).

6 52 Int. J. Naval rchit. Ocean Eng. (2013) 5:47~61 (a) class. () framax class. (c) class. (d) class. Fig. 6 Intelligent-supersize FEM (LPS/HULL) models for the four types of doule-hull l tankers (LPS/HULL, 2012). The ISFEM method (LPS/HULL) is only used for PSS geometc modelling and is ased on a numecal formulation with closed form solutions. Therefore, it pvides oth 2-dimensional and 3-dimensional outputs and can deal with interactions etween local and gloal failure. Hence, LPS/HULL is suitale for analysing pgressive hull collapse. More details on the features of these two methods can e found in Paik and Thayamalli (2003) and Hughes and Paik (2010). Yielded at tensiled part Linear elastic aund N.. uckling collapsed at compressed part Fig. 7 Schematic view of presumed stress distution-ased method (Hughes and Paik, 2010).

7 Int. J. Naval rchit. Ocean Eng. (2013) 5:47~ ending moment(gnm) PSC PSS NSYS LPS/HULL ICS CSR Modified Paik-Mansour formula method Curvature(1/km) Fig. 8 Previous enchmark result for a typical doule-hull as illustrated in Fig. 4(d) (Paik et al., 2013). efore analysing the ultimate hull girder strength, enchmark research was performed for vaous types of vessels y Paik et al. (2013), as shown in Fig. 8. This figure shows the analysis results for a typical doule-hull l tanker. The ISFEM method (LPS/HULL) was recently applied to vaous types of ship structures to analyse and identify their structural capacity (Kim et al., 2012; 2012c; Park et al., 2012). DEVELOPMENT OF R-D DIGRMS ND COMPRISON OF THE TWO METHODS In this section, R-D diagrams are estalished using oth the ISFEM (LPS/HULL) and the design formula (modified P-M) method to validate the applicaility of oth analysis methods. gain, the analysis results are compared in a step-y-step pcess. The details of oth methods can e found in Paik and Thayamalli (2003) and Hughes and Paik (2010). The compason etween the design formula (modified P-M) method (Paik et al., 2013) and ISFEM (LPS/HULL) (LPS/HULL, 2012) method egins with the following steps: 1) define the correction factor; 2) determine the ; and 3) estalish the R-D diagram. Define the correction factor The correction factor (α ) can e determined y the ratio of the slopes of the ultimate longitudinal strength ehaviour in the inner and outer ottom structures for the vaous damage cases, as shown in Eq. (2). α = θi / θ O, (2) where θ and I θ O are the slopes of the ultimate longitudinal strength versus the curves of the amount of gunding damage for the respective inner and outer ottoms. Figs. 9 to 12 illustrate the compason results for the calculated correction factors of doule-hull l tankers.

8 54 Int. J. Naval rchit. Ocean Eng. (2013) 5:47~61 hogging LPS/HULL sagging LPS/HULL LPS/HULL Slope α Slope α O I LPS/HULL Slope α Slope α O I / or / (a) condition. / or / () condition. Fig. 9 Vaation in the ultimate longitudinal strength of a class doule-hull l tanker with the amount of gunding damage to the outer and inner ottom. framax hogging LPS/HULL framax sagging LPS/HULL LPS/HULL Slope α Slope α O I LPS/HULL Slope α Slope α O I / or / (a) condition. / or / () condition. Fig. 10 Vaation in the ultimate longitudinal strength of an framax class doule-hull l tanker with the amount of gunding damage to the outer and inner ottom. hogging LPS/HULL sagging LPS/HULL LPS/HULL Slope α Slope α O I O I LPS/HULL Slope α Slope α / or / (a) condition. / or / () condition. Fig. 11 Vaation in the ultimate longitudinal strength of a class doule-hull l tanker with the amount of gunding damage to the outer and inner ottom.

9 Int. J. Naval rchit. Ocean Eng. (2013) 5:47~61 55 hogging LPS/HULL sagging LPS/HULL LPS/HULL Slope α Slope α O I LPS/HULL Slope α Slope α O I / or / / or / (a) condition. () condition. Fig. 12 Vaation in the ultimate longitudinal strength of a class doule-hull l tanker with the amount of gunding damage to the outer and inner ottom. Tale 3 shows the correction factors otained fm the results of Figs. 9 to 12. Generally, the trend of the correction factors pduced y the ISFEM (LPS/HULL) method show an upward tendency compared with the design formula (modified P-M) method. Tale 3 Compason of correction factors. Correction factor LPS / HULL LPS / HULL framax Note: LPS/HULL = analysis method ased on ISFEM, = analysis method ased on design formula method. Determine the Using the pncipal dimensions illustrated in Fig. 4, together with the IMO s paility density distutions and assumptions of the ck s shape using the LHS technique, four types of gunding damage parameters for 50 gunding damage scenaos are defined and shown in Tale 4. The gunding damage indices for 50 gunding damage scenaos are calculated ased on the otained damaged parameters under vertical ending moments ased on the values fm Eqs. (1) and (2) and Tale 3. The results for the calculation of values are covered in the discussion section. Estalish the R-D diagram In this section, R-D diagrams are developed ased on the calculated residual ultimate longitudinal strength and gunding damage indices. Figs. 13(a) to (d) show the developed R-D diagrams otained using a curve-fitting method. Figs. 14 and 15 show the R-D diagrams for all doule-hull l tankers using oth the ISFEM (LPS/HULL) and the design formula (modified P-M) method.

10 56 Int. J. Naval rchit. Ocean Eng. (2013) 5:47~61 Tale 4 The four gunding damage parameters for 50 gunding damage scenaos (Paik et al., 2012). Scenao p 1 p 2 p 3 p D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D

11 Int. J. Naval rchit. Ocean Eng. (2013) 5:47~61 57 LPS/HULL framax LPS/HULL (Gunding damage index) = (Gunding damage index) = (a) class. () framax class. LPS/HULL LPS/HULL (Gunding damage index) = (c) class. Fig. 13 The R-D diagrams for the doule-hull l tanker. (Gunding damage index) = (d) class. hogging framax LPS/HULL hogging framax = R 2 = 618 (Gunding damage index) = = R 2 = 830 (Gunding damage index) = (a) Design formula (modified P-M) method (Paik et al., 2012). () Intelligent-supersize FEM (LPS/HULL). Fig. 14 The otained R-D diagrams for the doule-hull l tankers under the hogging ending moment.

12 58 Int. J. Naval rchit. Ocean Eng. (2013) 5:47~61 framax LPS/HULL framax = R 2 = 455 (Gunding damage index) = (a) Design formula (modified P-M) method (Paik et al., 2012). = R 2 = 708 (Gunding damage index) = () Intelligent-supersize FEM (LPS/HULL). Fig. 15 The otained R-D diagrams for the doule-hull l tankers under the sagging ending moment. = R 2 = 830 = R 2 = 708 = R 2 = 618 LPS/HULL (a) condition () condition. Fig. 16 Compason etween the R-D diagrams for doule-hull l tankers pduced y the intelligent-supersize FEM (LPS/HULL) and those pduced y the design formula (modified P-M) method. = R 2 = 455 LPS/HULL Generally, the R-D diagrams otained y the design formula (modified P-M) method underestimate the residual ultimate longitudinal strength of doule-hull l tankers in oth the hogging and sagging conditions, compared with ISFEM (LPS/ HULL). The results can e found in Figs. 16(a) and (). DISCUSSIONS Figs. 17 and 18 show the statistical results ased on the otained outputs. Two parameters, the and the residual ultimate ending moment ( M u ), were assessed y consideng the vertical hogging and sagging moments. The aim of this study was to compare the residual ultimate ending moment capacity calculated y these two methods. The gunding damage indices were also compared, as shown in Figs. 17(a) and (). s mentioned in Paik et al. (2013), l tanker structures can e modelled using the design formula (modified P-M) method using the plate-stiffener separation model (PSS), and those under a hogging moment can e modelled using the plate-stiffener comination (PSC) model. The ISFEM (LPS/HULL) method uses the PSS modelling technique. compason of the results otained y these two techniques under the same conditions is shown in Figs. 17() and 18(). PSS modelling is adopted with the design formula (modified P-M) method and ISFEM (LPS/HULL) in sagging conditions.

13 Int. J. Naval rchit. Ocean Eng. (2013) 5:47~ () 1.2 Mean : 999 S-D : 188 COV : () 1.2 Mean : 683 S-D : 523 COV : framax 0.3 framax () LPS/HULL () LPS/HULL (a) condition. () condition. Fig. 17 The deviation etween the gunding damage indices () otained y the design formula method and the intelligent-supersize FEM. (a) condition. () condition. Fig. 18 The deviation etween the residual ultimate longitudinal strength analysed y the design formula method and the intelligent-supersize FEM. In contrast, Figs. 17(a) and 18(a) illustrate the results of the analysis ased on PSC modelling (design formula method) and PSS modelling (ISFEM). In this case, the results are somewhat different. The results for the sagging moment conditions are more general using oth analysis methods. Fig. 17() indicates that ISFEM pduces a etter result than the design formula method. However, the results of the design formula method are pessimistic fm a designer s perspective. Finally, oth of these two methods can e applied to analyse gunding damage to doule-hull l tanker structures. The compason results will e useful for assessing the safety of damaged ships using the aovementioned methods.

14 60 Int. J. Naval rchit. Ocean Eng. (2013) 5:47~61 CONCLUDING REMRKS Ship gunding accidents frequently occur despite continual efforts to prevent them. To pduce salvage plans or to save human lives, safety assessment guidelines that include reliale accident scenaos are needed. Vaous methods for estimating the safety of damaged ship structures have een pposed. mong them, analysis methods (e.g., the design formula method) and numecal methods (e.g., intelligent supersize FEM) have een compared to determine the residual ultimate longitudinal strength of gunded ship structures. This study compared and vefied the applicaility of the aovementioned methods. To select realistic gunding damage scenaos, the Residual ultimate longitudinal strength - gunding Damage index (R-D) diagram appach was applied to the ISFEM (LPS/HULL) and design formula (modified P-M) method. The otained R-D diagrams were compared in terms of their residual ultimate longitudinal strength and gunding damage index () predictions under vertical ending moments. Future research will also consider collision damage, among other types. CKNOWLEDGEMENTS This study was undertaken y Lloyd s Register Foundation (LRF) Research Centre of Excellence (The Ship and Offshore Research Institute) at Pusan National University, Korea. Lloyd's Register Foundation supports the advancement of engineengrelated education, and funds research and development that enhances safety of life at sea, on land and in the air. The research was supported y the asic Science Research Pgram thugh the National Research Foundation of Korea (NRF) and funded y the Ministry of Education, Science, and Technology (Grant no.: K E ). The first author (D.K. Kim) is now with the Graduate Schl of Engineeng Mastership (GEM) at Pohang University of Science and Technology (POSTECH). REFERENCES LPS/HULL, computer pgram for pgressive collapse analysis of ship hulls. DRS Defense Solutions, dvanced Mane Technology Center, Stevensvill, MD, US ( wn,.j., Collision scenaos and pailistic collision damage. Mane Structures, 15(4-5), pp Hong, L. and mdahl, J., Rapid assessment of ship gunding over large contact surfaces. Ships and Offshore Structures, 7(1), pp Hughes, O.F. and Paik, J.K., Ship structural analysis and design. The Society of Naval rchitects and Mane Engineers, New Jersey, US. IMO, Revised intem guidelines for the appval of alternative methods of design and construction of l tankers. Mane Envinment Ptection Committee of the Organization y Resolution MEPC 110(49), International Matime Organization, London, UK. Kim, D.K., Condition assessment of damaged ships and ship-shaped offshore structures. PhD. Pusan National University. Kim, D.K., Kim, H.., Zhang, X., Pedersen, P.T., Kim, M.S. and Paik, J.K., 2012a. Development of a relationship etween residual ultimate longitudinal strength and gunding damage index diagram for container ships. Pceedings of 31 st International Conference on Ocean, Offshore and rtic Engineeng (OME 2012). Rio de Janei, razil 1-6 July Kim, D.K., Park, D.K., Kim, H.., Seo, J.K., Kim,.J., Paik, J.K. and Kim, M.S., The necessity of applying the common corsion addition rule to container ships in terms of ultimate longitudinal strength. Ocean Engineeng, 49, pp Kim, D.K., Park, D.K., Park, D.H., Kim, H.., Kim,.J., Seo, J.K. and Paik, J.K., 2012c. Effect of corsion on the ultimate strength of doule hull l tankers Part II: hull girders. Structural Engineeng and Mechanics, 42(4), pp Nguyen, T.H., Garrè, L., mdahl, J. and Leira,.J., Monitong of ship damage condition dung stranding. Mane Structures, 24(3), pp

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