Scantling optimization ropax ship

UNIVERSITY OF LIÈGE ANTWERP MARITIME ACADEMY FACULTY OF APPLIED SCIENCE HOGERE ZEEVAART SCHOOL DEPARTMENT OF ARGENCO – ANAST MASTER THESIS SCANTLING OPTIMIZATION ROPAX SHIP Tri Dung NGUYEN Promoter: Prof Dr Philippe RIGO Academic year 2009 – 2010 Acknowledgements First of all, I would like to express my warmest appreciation to Prof Philippe RIGO and Prof Michel HOGGE, Dean of the faculty of Applied Science who granted me a scholarship for this study of Naval architechture in ANAST, university of Liège Furthermore, I would be grateful to Prof Philippe RIGO for his instruction and encouragement during my study I also would like to especially thank Dr Adrian CONSTANTINESCU and Dr Eugen PIRCALABU who provided me various advice and helpful comments at the most difficult time of my working for this thesis Additionally, I would like deeply thank all Professors and Professor Assistants of university of Liège and ANAST who gave me a lot of knowledge and many interesting lectures During one year of studying in university of Liège, Belgium, I have greatly benefited from the friendship and association with many classmates I would like to thank all students in my class for their support in various aspects I always keep in my mind the beautiful memories about them Finally, I would like to express my whole-hearted gratitude to my family for all their loves and support for my life Liège, May 16th 2009 i Summary The usual method of structural design is an indirect trial – and – error approach (rules – based design) The designers intuitively choose the dimensions and then determine if the design satisfying the constraints The designs are revised repeatedly while still satisfying the constraints Such an approach does not necessarily yield the most economical or least weight design In order to obtain a best design, the structural engineers have to recur to structural optimization methods Structural design is always defined during the earliest phases of a project It is thus not difficult to understand why a preliminary design stage optimization tool is attactive The problem in this moment is to minimize a predetermined utility function, such as the cost or the weight under the constraints that the failure probability of the structure will not exceed several certain allowable values Ship scantling always poses numerous problems to designers Floating structures are indeed complex, generally composed of strongly stiffened plates, deck plates, bottom plates and sometimes intermediate decks, frames, bulkheads, etc The stiffening system is also particularly sophisticated Therefore an optimization tool at preliminary stage featuring flexibility, modeling speed and user-friendliness may provide precious help to designers They can start directly with an automatic search for optimum scantling As the above statements, the principal mission of this study is to utilize LBR-5, the optimization software to obtain the optimum scantlings of ROPAX ship with the initial scantlings as follows: - Verify the dimesions of model in input data, Modelize the frames in double bottom, Calculate the internal loads – wheeled loads following the BV rules, Verify the load cases for ROPAX ship with hull girder loads and local loads, Determine the structural constraints from BV rules as well as geometrical and equality constraints, Structural analysis the stresses of initial scantling, Run the LBR-5 to obtain the optimum scantling with respect of construction cost or structural weight Estimate the optimal solution and propose the recommended scantling Concerning the above tasks, this report is presented within four chapters - Chapter “The background of ship structure design”, Chapter “Scantling optimization and LBR-5 software for stiffened structures”, Chapter “Scantling optimization of the Ropax ship”, Chapter “Conclusion” ii Table of Contents Chapter THE BACKGROUND OF SHIP STRUCTURE DESIGN 1.1 Introduction 1.1.1 Rationally based structural design versus rules-based design 1.1.2 Preliminary design versus detailed design 1.2 Loads acting on a ship structure 1.2.1 Time duration 1.2.2 Local and global loads 1.2.3 Hull girder loads calculation 1.2.4 Local loads calculation 1.2.5 Load cases 14 1.2.6 Ship Motions and Accelerations 16 1.3 Stresses and checking criteria 18 1.3.1 Introduction 18 1.3.2 Stress and deflection components 18 1.3.3 Stress calculation 21 1.3.4 Checking criteria 26 Chapter SCANTLING OPTIMIZATION AND LBR-5 SOFTWARE FOR STIFFENED STRUCTURES 28 2.1 Introduction 28 2.2 Scantling optimization procedure 28 2.3 Failure modes classification 31 2.3.1 Stiffened panel failure modes 33 2.3.2 Frame failure modes 33 2.3.3 Hull girder collapse modes 34 2.4 Introduction of LBR-5 34 2.4.1 The OPTI module 36 2.4.2 The COST module 36 2.4.3 The CONSTRAINT module 37 Chapter SCANTLING OPTIMIZATION OF ROPAX SHIP 38 3.1 Main specification of the ROPAX ship 38 3.2 Modelize the midship section 38 3.3 Loads acting on Ropax structure 46 3.3.1 The hull girder global loads 46 3.3.2 The local loads 47 3.4 The constraints of optimization 56 3.5 Cost and productivity data 60 iii 3.6 The results of scantling optimization 61 Chapter CONCLUSIONS 86 REFERENCES 88 APPENDICES i Appendix 1: General arrangement and amidship drawing of Ropax ship i Appendix 2: Longitudinal stress calculation ii Appendix 3: Phenomena of each load case iii Appendix 4: Non-uniform pressures on decks due to wheeled loads ix Appendix 5: Equivalent angle to bulb profile stiffeners x iv Table of Figures Figure – Direct structural analysis flow chart Figure – Sign conventions for shear forces Q and bending moments M Figure – Distribution factor FQ Figure – Still water pressure Figure – Wave pressure for each load cases according to BV [5] 11 Figure – Wheeled loads – Distribution of vehicles on a primary supporting member [5] 13 Figure – Wheeled loads distance between two consecutive axles [5] 13 Figure – Wheeled loads distance between axles of two consecutive vehecles [5] 13 Figure – Wave loads in load case “a”, “b”, “c” and “d” according to BV [5] 15 Figure 10 – Definition of stress components 19 Figure 11 – Primary, secondary and tertiary structural response 20 Figure 12 – A standard stiffened panel 20 Figure 13 – Behavior of an elastic beam under shear force and bending moment 22 Figure 14 – Element of plate structure and components of bending stress resultants 24 Figure 15 – Torsional shear flow 25 Figure 16 – The moment – curvature curve (M - Φ) 30 Figure 17 – Structural modeling of the structure and its components 31 Figure 18 – Modes of failures by buckling of a stiffened panel 32 Figure 19 – Basic configuration of the LBR-5 model and database presentation 35 Figure 20 – General organisation flow chart of a structure optimization process 35 Figure 21 – Chart of the LBR-5 model with CONSTRAINT, COST and OPTI modules 37 Figure 22 – The double bottom of a common Ropax ship (web frame – every 2800 mm) 39 Figure 23 – The modelled frame in double bottom 39 Figure 24 – Equivalent angle profile 40 Figure 25 – The central girder with frames on both sides 40 Figure 26 – The midship section and the double bottom model in LBR5 43 Figure 27 – The partial 3D model 45 Figure 28 – The partial model in LBR5 45 Figure 29 – The wheeled loads in load case “a“ and “c“ 51 Figure 30 – The wheeled loads in load case “b“ 51 Figure 31 – The wheeled loads in load case “d“ 52 Figure 32 – The equivalent pressure 53 Figure 33 – The test of the transformation between uniform and non-uniform pressure 54 Figure 34 – The stresses in plate at x = 8.4 (m) by uniform pressure 55 Figure 35 – The stresses in plate at x = 8.4 (m) by non-uniform pressure 55 Figure 36 – The stresses in plate at x = L/2 = 16.8 (m) by uniform pressure 55 Figure 37 – The stresses in plate at x = L/2 = 16.8 (m) by non-uniform pressure 56 Figure 38 – The Von Mises stress in plate from structural analysis 62 Figure 39 – The Von Mises stress in frames at WFJ from structural analysis 64 Figure 40 – Objective curve of cost optimization 65 Figure 41 – Objective curve of weight optimization 66 v Figure 42 – Objective curve of cost optimization with the frames on panel 10, 23 and 14 are high tensile steel 67 Figure 43 – Objective curve of weight optimization with the frames on panel 10, 23 and 14 are high tensile steel 68 Figure 44 – Flow chart of one step optimization procedure 72 Figure 45 – Flow chart of multi-steps optimization procedure 72 Figure 46 – Optimum plate thickness in cost multi step optimization 77 Figure 47 – Optimum frame web height in cost multi step optimization 78 Figure 48 – Optimum stiffener spacing in cost multi step optimization 79 Figure 49 – Optimum stiffener web height in cost multi step optimization 80 Figure 50 – Optimum plate thickness in weight multi step optimization 82 Figure 51 – Optimum frame web height in weight multi step optimization 83 Figure 52 – Optimum stiffener spacing in weight multi step optimization 84 Figure 53 – Optimum stiffener web height in weight multi step optimization 85 vi Chapter The background of ship structure desgin Chapter THE BACKGROUND OF SHIP STRUCTURE DESIGN 1.1 Introduction Analysis and Design are two words that are very often associated Sometimes they are used indifferently one for the other even if there are some important differences between performing a design and completing an analysis Analysis refers to stress and strength assessment of the structure Analysis requires information on loads and needs an initial structural scantling design Output of the structural analysis is the structural response defined in terms of stresses, deflections and strength Then, the estimated response is compared to the design criteria Design for structure refers to the process followed to select the initial structural scantlings and to update these scantlings from the early design stage (bidding) to the detailed design stage (construction) To perform analysis, initial design is needed and analysis is required to design This explains why design and analysis are intimately linked, but are absolutely different Design also relates to topology and layout definition Ship structural design is a challenging activity Hence Hughes states: “The complexities of modern ships and the demand for greater reliability, efficiency, and economy require a scientific, powerful, and versatile method for their structural design.” Ship structural analysis and design is a matter of compromises: - Compromise between accuracy and the available time to perform the design This is particularly challenging at the preliminary design stage A 3D Finite Element Method (FEM) analysis would be welcome but the time is not available For that reason, rule-based design or simplified numerical analysis has to be performed - To limit uncertainty and reduce conservatism in design, it is important that the design methods are accurate On the other hand, simplicity is necessary to make repeated design analyses efficient The results from complex analyses should be verified by simplified methods to avoid errors and misinterpretation of results (checks and balances) - Compromise between weight and cost or compromise between least construction cost, and global owner live cycle cost (including operational cost, maintenance, etc.) 1.1.1 Rationally based structural design versus rules-based design There are two kinds of school to perform analysis and design of ship structure The first one, the oldest, is called rule-based design It is mainly based on the rules defined by the classification societies Hughes states that: “In the past, ship structural design has been largely empirical, based on accumulated experience and ship performance, and expressed in the form of structural design codes or rules Chapter The background of ship structure desgin published by the various ship classification societies These rules concern the loads, the strength and the design criteria and provide simplified and easy-to-use formulas for the structural dimensions, or “scantlings” of a ship This approach saves time in the design office and, since the ship must obtain the approval of a classification society, it also saves time in the approval process.” The second school is the Rationally Based Structural Design; it is based on direct analysis Hughes, who could be considered as a father of this methodology, further states: “There are several disadvantages to a completely “rulebook” approach to design First, the modes of structural failure are numerous, complex, and interdependent With such simplified formulas the margin against failure remains unknown; thus one cannot distinguish between structural adequacy and over-adequacy Second, and most important, these formulas involve a number of simplifying assumptions and can be used only within certain limits Outside of this range they may be inaccurate For these reasons there is a general trend toward direct structural analysis.” In ship design, classification societies preferred to offer updated rules resulting from numerical analysis calibration In addition, for new vessel types or non-standard dimension, direct procedure is the only way to assess the structural safety Therefore it seems that the two schools have started a long merging procedure Classification societies are now encouraging and contributing greatly to the development of direct analysis and rationally based methods Ships are very complex structures compared with other types of structures They are subject to a very wide range of loads in the harsh environment of the sea Progress in technologies related to ship design and construction is being made daily, at an unprecedented pace The majority of ship designers strive to develop rational and optimal designs based on direct strength analysis methods using the latest technologies in order to realize the shipowner’s requirements in the best possible way When carrying out direct strength analysis in order to verify the equivalence of structural strength with rule requirements, it is necessary for the classification society to clarify the strength that a hull structure should have with respect to each of the various steps taken in the analysis process, from load estimation through to strength evaluation In addition, in order to make this a practical and effective method of analysis, it is necessary to give careful consideration to more rational and accurate methods of direct strength analysis The flow chart given in figure gives an overview of the analysis as defined by a major classification society Note that a rationally based design procedure requires that all design decisions (objectives, criteria, priorities, constraints…) must be made before the design starts This is a major difficulty of this approach 1.1.2 Preliminary design versus detailed design For a ship structure, structural design consists of two distinct levels: the Preliminary Design and the Detailed Design about which Hughes states: Chapter The background of ship structure desgin Figure – Direct structural analysis flow chart “The preliminary determines the location, spacing, and scantlings of the principal structural members The detailed design determines the geometry and scantlings of local structure (brackets, connections, cutouts, reinforcements, etc.) Preliminary design has the greatest influence on the structure design and hence is the phase that offers very large potential savings This does not mean that detail design is less important than preliminary design Each level is equally important for obtaining an efficient, safe and reliable ship During the detailed design there also are many benefits to be gained by applying modern methods of engineering science, but the applications are different from preliminary design and the benefits are likewise different Since the items being designed are much smaller it is possible to perform full-scale testing, and since they are more repetitive it is possible to obtain the benefits of mass production, standardization and so on In fact, production aspects are of primary importance in detail design Also, most of the structural items that come under detail design are similar from ship to ship, and so in-service experience provides a sound basis for their design In fact, because of the large number of such items it would be inefficient to attempt to design all of them from first principles Instead it is generally more efficient to use design codes and standard designs that have been Chapter Scantling Optimization ROPAX Ship ` Figure 52 – Optimum stiffener spacing in weight multi step optimization 84 Chapter Scantling Optimization ROPAX Ship ` Figure 53 – Optimum stiffener web height in weight multi step optimization 85 Chapter Conclusions Chapter CONCLUSIONS Special initial details are modeled this study, for example, the frame is shared by the concerning panels in double bottom The hull girder bending moments acting on ship are calculated in accordance with BV rules, particularly, the Ropax ship is solicited more in hogging condition because the still water bending moment due to distributed weight on board is hogging moment Therefore, the structure is more dangerous or has the higher stresses if the Ropax ship is subject to the wave bending moment in hogging condition Local pressures are distributed non-uniformly along OX and OY axis such as the inertia pressures transformed from wheeled loads applied on decks This load depends on the arrangement of vehicles on decks and the load cases given by BV rules In upright condition, the wheeled loads in load case “b” which is influenced by pitch motion are non-uniformly distributed along OX axis but constant in OY direction In inclined condition, the rolling motion affects the wheeled loads in load case “d” and makes it variable in both of directions The wheeled loads on deck are divided into two kinds of pressure The first type is the uniform distributed pressure along OX axis and the second type is localized pressure (Ploc) The Ploc is obtained as the maximum value for all load cases The equality constraint is applied to the frame web thickness of panels locating in double bottom In addition, the stiffenes equivalent to bulb profile one violate the geometrical constraints, for example, stiffener web height and the flange breadth or the frame web height not suit its thickness and frame flange width in initial dimension The structural constraints compared with stresses in structure is the Von Mises stresses in plate at x = L/2 (175 N/mm2 for mild steel and 243 N/mm2 for high strength steel) and the Von Mises stresses in frame at web-flange junction abd in stiffener flange at x = L/2 (192 N/mm2 for mild steel and 267 N/mm2 for high strength steel) Besides, the structural constraint of minimum thickness to avoid the plate buckling and the constraint of ultimate strength of stiffened panel are imposed on structure as well as the structural constraints for stiffeners are also applied (Tab 34) The stresses in frames of initial scantling exceed the allowable stresses (Fig 39) So it is stated that the initial design cannot used in reality and the initial scantling is changed after the first iteration of optimization In general, the optimization is convergent when optimizing with all design varibles and the stresses are verified in structural analysis that they satisfy the structural constraints The optimum solutions are discussed carefully and the recommended scantling chosen is the solution of the cost and weigh multi step optimization (Tab 43) with the objective values are smaller that that of the one step optimization and the material ability is used almost 86 Chapter Conclusions The solutions of weight and cost optimization are compared together (Tab 43) This study as well as the application of LBR5 for other ship, i.e FSO barge shows that the cost optimization gives out the best cost and makes the weight increasing a little from the optimum weight, i.e 5.24% for one step optimization; 4.16% for multi-step one in this study and about to 2% for FSO barge while the weight optimization provides the best weight but creates the quite large difference of cost as 5.58% for one step optimization, 7.99% for multi-step one for Ropax ship and to 18 % for FSO barge [2] The recommended solution is the scantling of weight and cost multi step optimization The optimum cost is 789742 (€) and the weight is 606.917 (T) for the cost optimization and the optimum weight is 582.696 (T) and the cost is 852880 (€) for the weight optimization Observing the scantling of weight and cost optimization carefully (Tab 46 & 48) I see that the solver gives out the thickness of plate, the web height of stiffeners and frames as small as possible in weight optimization to reduce the weight of structure while the number of stiffener and frame are increased to satisfy the allowable stress on the other hand the stiffener and frame spacing becomes shorter On the contrary, the cost of structure composed of the cost of basic materials (plates, bars, ect.), the cost of consumables necessary for construction process (energy, welding, ect.) and the cost of labour used for building of the entire structure can be decreased sufficiently by reducing the cost of consumables and labour To that the number of stiffener and frame will become smaller so the stiffener and frame spacing will be larger whilst the dimension of plate (thickness), stiffener and frame (web height) is increased to satify the allowable stress That is why the frame spacing and the frame web height of weight optimization is smaller than those of cost optimization It is the same with the stiffeners For the plate thickness, it is larger in cost optimization and smaller in weight optimization (Fig 46 to 53) 87 References REFERENCES [1] Philippe RIGO and Enrico Rizzuto, Analysis and design of ship structure, 2002, chapter 18 [2] Philippe RIGO, A module-oriented tool for optimum design of stiffener structures-Part I, Mar Struct 2001; 14(6): 611-29 [3] Philippe RIGO, Scantling optimization based on convex linearizations and a dual approach-Part II, Mar Struct 2001; 14(6): 631-49 [4] Philippe RIGO, An integrated software for scantling optimization and least production cost, Ship technology research vol 50 – 2003 [5] Bureau Veritas, Steel ships, November 2008 edition - http://erules.veristar.com [6] Jeom K Paik and Alaa E Mansour, A simple formulation for predicting the ultimate strength of ships In J Mar Sci Technol (1995) 1: 52-62 [7] M K Rahman and M Chowdhury, Estimation of ultimate longitudinal bending moment of ships and box girders In Journal of ship research, vol 40, no 3, Sept 1996, pp 244-257 [8] Heba W Leheta and Alaa E Mansour, Reliability-based method for optimal structural design of stiffened panels, Marine Structures 10 (1997); 323-352 88 Appendix APPENDICES Appendix 1: General arrangement and amidship drawing of Ropax ship i Appendix Appendix 2: Longitudinal stress calculation SEAKING HYDROSTATIC SYSTEM 2009-02-26 TIME 20.20 RO-PAX IMPROVE CONDITION NO ===================== Cargo Condition 100% Consumables LONGITUDINAL STRESS CALCULATION -NO DIST SHEAR BENDING DRAFT FORCE MOMENT -94.600 0.000 0.0 8.041 -91.280 170.620 242.6 8.019 -87.960 414.830 1211.7 7.997 -84.640 662.512 2996.5 7.976 -81.320 908.656 5603.8 7.954 -78.000 1140.503 9005.6 7.932 -74.400 1447.839 13685.5 7.909 -70.800 1664.785 19300.4 7.885 -67.200 1833.912 25599.7 7.862 10 -63.600 1961.071 32433.9 7.838 11 -60.000 2044.199 39645.1 7.815 12 -56.400 2081.469 47073.8 7.791 13 -52.800 2175.782 54694.7 7.768 14 -50.560 2186.639 59574.0 7.753 15 -48.320 2159.838 64441.5 7.738 16 -46.080 2112.189 69218.2 7.724 17 -43.840 2052.431 73874.0 7.709 18 -41.600 1981.396 78382.7 7.695 19 -34.880 1941.656 91493.1 7.651 20 -28.160 1800.347 104374.0 7.607 21 -21.440 1295.063 114760.6 7.563 22 -14.720 746.535 121587.9 7.519 23 -8.000 178.769 124647.4 7.475 24 2.080 -601.030 122404.8 7.409 25 12.160 -1309.486 112594.4 7.343 26 22.240 -1862.491 96316.9 7.278 27 32.320 -2158.959 75681.4 7.212 28 42.400 -2135.151 53589.9 7.146 29 50.240 -1822.978 37494.2 7.095 30 58.080 -1387.441 25300.0 7.043 31 65.920 -1116.700 15342.4 6.992 32 73.760 -807.661 7596.5 6.941 33 81.600 -399.758 2682.1 6.890 34 84.480 -286.844 1647.8 6.871 35 87.360 -191.240 913.7 6.852 36 90.240 -115.209 426.5 6.833 37 93.120 -55.173 132.2 6.815 38 96.000 0.000 0.0 6.796 MAXIMUM SHEAR FORCE = MAXIMUM BENDING MOMENT = 2186.639 ( 124827.7 ( Inf%) AT A DISTANCE OF = -50.560 Inf%) AT A DISTANCE OF = -5.689 ii Appendix Appendix 3: Phenomena of each load case Distributed pressures on load case 'a1' iii Appendix Distributed pressures on load case 'b1' iv Appendix Distributed pressures on load case 'c+' v Appendix Distributed pressures on load case 'd+' vi Appendix Distributed pressures on load case 'a2' vii Appendix Distributed pressures on load case 'b2' viii Appendix A Appendix 4: Non-uniform m pressures on n decks due to o wheeled loads ix Appendix Appendix 5: Equivalent angle to bulb profile stiffeners H T H T α α eqv H eqv B eqv FT mm mm eqv H eqv B eqv FT mm mm 60 2.3 55.48 22.90 4.52 240 10 215.91 42.82 24.09 80 1.6 73.30 22.77 6.70 240 11 215.91 43.82 24.09 80 1.6 73.30 24.40 6.70 240 12 215.91 44.82 24.09 80 1.6 73.30 26.04 6.70 260 10 233.74 45.81 26.26 100 1.2 91.13 22.11 8.87 260 11 233.74 46.81 26.26 100 1.2 91.13 23.34 8.87 260 12 233.74 47.81 26.26 100 1.2 91.13 24.57 8.87 280 10.5 251.57 49.29 28.43 120 108.96 20.91 11.04 280 11 251.57 49.79 28.43 120 108.96 21.91 11.04 280 12 251.57 50.79 28.43 120 108.96 22.91 11.04 280 13 251.57 51.79 28.43 140 6.5 126.78 24.40 13.22 300 11 269.39 52.78 30.61 140 126.78 24.90 13.22 300 12 269.39 53.78 30.61 140 126.78 25.90 13.22 300 13 269.39 54.78 30.61 140 10 126.78 27.90 13.22 320 11.5 287.22 56.26 32.78 160 144.61 27.88 15.39 320 12 287.22 56.76 32.78 160 144.61 28.88 15.39 320 13 287.22 57.76 32.78 160 144.61 29.88 15.39 320 14 287.22 58.76 32.78 160 11.5 144.61 32.38 15.39 340 12 305.04 59.75 34.96 180 162.43 31.87 17.57 340 13 305.04 60.75 34.96 180 162.43 32.87 17.57 340 14 305.04 61.75 34.96 180 10 162.43 33.87 17.57 340 15 305.04 62.75 34.96 180 11.5 162.43 35.37 17.57 370 12.5 331.78 64.72 38.22 200 8.5 180.26 35.35 19.74 370 13 331.78 65.22 38.22 200 180.26 35.85 19.74 370 14 331.78 66.22 38.22 200 10 180.26 36.85 19.74 370 15 331.78 67.22 38.22 200 11 180.26 37.85 19.74 370 16 331.78 68.22 38.22 200 11.5 180.26 38.35 19.74 400 13 358.52 69.70 41.48 200 12 180.26 38.85 19.74 400 14 358.52 70.70 41.48 220 198.09 38.84 21.91 400 15 358.52 71.70 41.48 220 10 198.09 39.84 21.91 400 16 358.52 72.70 41.48 220 11 198.09 40.84 21.91 430 14 385.26 75.18 44.74 220 11.5 198.09 41.34 21.91 430 15 385.26 76.18 44.74 220 12 198.09 41.84 21.91 430 17 385.26 78.18 44.74 240 9.5 215.91 42.32 24.09 430 20 385.26 81.18 44.74 x ... CONSTRAINT, COST and OPTI modules 37 Chapter Scantling optimization of ROPAX ship Chapter SCANTLING OPTIMIZATION OF ROPAX SHIP 3.1 Main specification of the ROPAX ship The main characteristics Length... (orange frames) 42 Chapter Scantling optimization of ROPAX ship Figure 26 – The midship section and the double bottom model in LBR5 43 Chapter Scantling optimization of ROPAX ship Panel 17 18 19 20... 37 Chapter SCANTLING OPTIMIZATION OF ROPAX SHIP 38 3.1 Main specification of the ROPAX ship 38 3.2 Modelize the midship section 38 3.3 Loads acting on Ropax structure