Global Strenght Analysis in Head Waves, for an Offshore Support Vessel

Global Strenght Analysis in Head Waves, for an Offshore Support Vessel Mihaela Costache, & George Jagite Naval Architecture Faculty, University "Dunarea de Jos" of Galati, Romania ARTICLE INFO Volume 3 Number 4/2014 Issue 8 DOI: 10.15590/ajase/ Received: Sep 14, 2014 Accepted: Sep 19, 2014 Revised: Sep 24, 2014 Published: Sep 26, 2014 E-mail for correspondence: mihaela.costache86@yahoo.com ABSTRACT The main topic of this paper is the 3D-FEM global strength analysis of a offshore supply vessel (OSV) under the following loads: still water and equivalent quasi-static head waves pressure, eigen ship and cargo weight. Two loading cases are selected for this analysis: full loading condition and ballast condition. The 3D-FEM (Finite Element Method) model extends over the whole ship length, the floating and trim equilibrium condition, in vertical plane, are obtained using eigen iterative numerical procedures. The buckling and yielding criteria are used to compare the numerical results with the allowable values according to classification societies. Key words: global ship strength, 3D-FEM, equivalent quasi-static head waves Source of Support: European Union ( POSDRU/159/1.5/S/132397-ExcelDOC ), Conflict of Interest: Declared. How to Cite: Costache M and Jagite G. 2014. Global Strenght Analysis in Head Waves, for an Offshore Support Vessel Asian Journal of Applied Science and Engineering, 3, 73-88. This article is is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. Attribution-NonCommercial (CC BY-NC) license lets others remix, tweak, and build upon work non-commercially, and although the new works must also acknowledge & be non-commercial. INTRODUCTION I n order to increase the accuracy of the global strength analysis of ship structure, a major step is to use the 3D-FEM full ship length models (Lehmann 1998, Rozbicki et al. 2001, Domnisoru 2006), instead of models extended only over several cargo holds (Hughes 1988, Domnisoru 2001, Servis et al. 2003). In this study, the global strength analysis is carried on a offshore supply vessel, that operates in Black Sea. Two main loading cases are selected for this analysis (full loading condition and ballast condition) under equivalent quasi-static head waves. To obtain the equilibrium parameters eigen program codes (Jagite et Domnisoru 2014) are used. Siemens PLM - FEMAP software is used for preprocessing and post-processing and NX Nastran software is used to carry out the analysis. Asian Business Consortium AJASE Aug 2014 Vol 3 Issue 8 Page 73

THE THEORETICAL MODELS FOR THE ANALYSIS OF SHIP STRENGTH The main advantages of the 3D-FEM analysis compared as to the classical method based on 1D-girder models are: the floating and trim equilibrium position is obtained at still water and equivalent quasi-static head waves, with no restrictions due to the ship hull form; the 3D stress and deformation distributions are obtained, predicting the domains with higher risk; compared as to the models developed on several cargo holds a reduced number of boundary conditions are used; the real ship 3D structure is taken into account; compared as to the 1D models, the 3D-FEM models include also the transversal structures which cannot be considered in 1D girder models, these are based only on longitudinal structures. In the following are presented the main steps for the global strength analysis, based on 3D- FEM ship model, extended over whole length. The 3D-FEM mesh of the ship hull structure The first step of the ship strength analysis includes the generation of the 3D-FEM-hull model. The mesh can be generated automatically, using auto-mesh options that are usual included in the FEM programs or it can be done manually. In the 3D-FEM models, all structural members have been modeled according to their original shape using the following types of elements: plate element defined by four nodes each with six degrees of freedom; bar elements defined by two nodes, six degrees of freedom per node; mass elements defined by one node. The boundary conditions of the 3D-FEM model The next step of analysis includes the generation of the boundary conditions for the 3D- FEM hull model, Full extend over the ship length, that are of two types: the vertical support condition at two nodes disposed at the ship hull structure extremities (on the central line), noted ND aft at aft end and ND fore at fore end; due to the symmetry of the ship structure and the symmetry of the loads the model was developed only on one side and symmetry boundary conditions are applied at the nodes located on the central line of the ship; The two nodes ND aft and ND fore are used as objective function at the veritical equilibrium conditions, at still water or equivalent quasi-static head waves, the vertical reaction force have to become zero. The loading conditions: The numerical analysis based on 3D-FEM model This third step of the global strength analysis contains the modeling of the load conditions and the effective numerical structure analysis of the 3D-FEM model. The next type of loads acts over the ship hull structure: the gravity load from the eigen hull structure weight and other mass components of the displacement (these masses are modeled with concentrated mass elements), except the cargo weight; the cargo load, considered as local hydrostatic pressure over the ship structure; Asian Business Consortium AJASE Aug 2014 Vol 3 Issue 8 Page 74

the equivalent quasi-static wave pressure load for the following cases: h w=0 (still water) and h w 0, according the statistical values from classifications societies (Bureau Veritas 2014), using an iterative procedure for the free floating and trim condition equilibrium, implemented with eigen program code (Jagite et Domnisoru 2014) developed in API (Femap programming interface). Figure 1 contains the flow chart of the eigen API program code. The height of the equivalent wave is calculated according to Bureau Veritas Rules: h h w w where L 4.1 crw 25 3/ 2 300 L 10.75 c 100 c Rw [m] for L<90m; Rw [m] for 90 L 300; = {1.00 9.00 0.75 0.66 0.60} is navigation coefficient. Figure 1. Flow chart of eigen API program file Asian Business Consortium AJASE Aug 2014 Vol 3 Issue 8 Page 75

The iterative procedure contains two main steps: the free floating condition, having as objective numerical function the sum of vertical reaction forces at the two nodes, from the ship extremities, RT3eq RT3aft RT3 fore 0 ; the free trim and floating condition having as objective numerical function the vertical reaction forces at each two nodes, from the ship extremities, RT3aft 0, RT3fore 0; The numerical results evaluation This step of the global ship strength analysis based on 3D-FEM models is obtained the following numerical results: the free floating and trim equilibrium parameters, draughts (average, aft draught and fore draught) and trim angle; the stress and deformations over the whole ship hull length, and also the prediction of the higher risk domains. Shear force and bending moment distribution along whole ship length is calculated with the following relation: Ft i FA nod FR nod FM nod ; xinod. xxi1. i Az Rz Mz M i nod x x F nod F nod F nod xinod. xxi1 nod. z Z FAx nod FRx nod FMx nod M Ay nod M Ry nod M My nod where: F A - applied force; F R - force reaction; F M - multi force; M A - applied moment; M R - moment reaction; M M - multi moment; Z - elevation of reference plane to calculate the moment. The yielding ratio and buckling ratio were used as checking criteria. The yielding ratio is calculated according to Bureau Veritas Rules using eigen program codes. YR VM ; Master Master Ry R M ; R y 235 k Asian Business Consortium AJASE Aug 2014 Vol 3 Issue 8 Page 76 2 2 2 ; 1/ 2 3 ; VM x y x y where k is the material coefficient (for grade A steel, R eh =235 N/mm 2, k=1) and, are partial safety factors. The buckling ratio is calculated using SDC Verifier ver.3.6 software (www.sdcverifier.com). The buckling per panel is verified according to Det Norske Veritas rules for: longitudinally uniform compression; transverse compression; shear forces; biaxially loaded plates with shear. R ; M

THE OSV SHIP 3D-FEM MODEL In this study is considered a offshore supply vessel (OSV) ship. The main dimensions of the ship are presented in Table I. Table I. The OSV ship main characteristics Length overall L OA 62.20 m Length between perpendiculars L BP 59.80 m Breadth B 13.60 m Draught T 4.50 m Depth D 5.40 m Service speed v s 11.00 knots The two loading conditions selected for this study are: full loading condition and ballast condition. Hereafter are presented the mass distribution for each case and also the lightship distribution. Figure 2. Lightship distribution Figure 3. Full loading condition. Mass distribution Figure 4. Ballast condition. Mass distribution Asian Business Consortium AJASE Aug 2014 Vol 3 Issue 8 Page 77

The 3D-FEM model was built according to classification societies rules, global coarse mesh with mesh dimension around 600 mm, one element between stiffeners. Three type of elements were used: plate elements, bar elements and mass elements. Table II. The 3D-FEM model characteristic Nodes 8435 Elements 17092 Properties 46 Materials 1 Figure 5. 3D-FEM model extending over whole ship length Figure 6. 3D-FEM model - side shell Figure 7. 3D-FEM model - main deck Figure 8. 3D-FEM model - double bottom Figure 9. 3D-FEM model - longitudinal bulkhead Asian Business Consortium AJASE Aug 2014 Vol 3 Issue 8 Page 78

Figure 10. 3D-FEM model - transverse bulkhead and web frames In the table III are presented the characteristics of the material used for 3D-FEM model, mild steel (grade A). Table III. Material characteristics Young modulus 206000 N/mm 2 Poison coefficient 0.3 Transversal modulus 79231 N/mm 2 Density 7850 Kg/m 3 Yield limit 235 N/mm 2 The boundary conditions applied to the 3D-FEM model are presented in the Table IV. The TX, TY and TZ are the translation along X, Y and Z axis and the RX, RY and RZ are the rotations around X, Y and Z axis. Table IV. Boundary conditions applied to 3D-FEM model Boundary condition TX TY TZ RX RY RZ Center line symmetry PD X X Aft node NDaft X X Fore node NDfore X Figure 11. Boundary conditions on 3D-FEM model Asian Business Consortium AJASE Aug 2014 Vol 3 Issue 8 Page 79

Figure 12. Boundary conditions on extremities of the ship (aft - left, fore - right) Numerical Analysis of the Global Strength of the Ship Hull The numerical analysis is focused on the global ship hull structure strength. The external equivalent quasi-static head waves pressure, with height h w=0-6m, 1m step is applied on the 3D-FEM model, using an iterative procedure for the vertical plane equilibrium condition. Based on Bureau Veritas Rules the equivalent quasi-static wave height for this ship is h w = 5.84 m. The 3D-FEM model is analyzed under equivalent wave loads both for wave crest and wave through. For each loading condition 15 load cases were analyzed, here after are presented the equilibrium parameters for full loading condition. Taft represents the aft draught and Tfore represents the fore draught. Table V. Equilibrium parameters for full loading condition Wave crest Wave through Hw [m] Taft [m] Tfore [m] Taft [m] Tfore [m] 0.00 4.500 4.500 4.500 4.500 1.00 4.500 4.500 4.380 4.620 2.00 4.500 4.500 4.269 4.729 3.00 4.500 4.500 4.170 4.830 4.00 4.500 4.500 4.079 4.919 5.00 4.500 4.500 3.990 5.010 5.84 4.500 4.500 3.930 5.067 6.00 4.500 4.500 3.919 5.079 In the figures Figure 13 - Figure 16 are presented the shear force and the bending moment distribution along whole ship length for full loading condition (FL) for both wave crest and though. In the figures Figure 17 - Figure 28 are presented the yielding ratio and buckling ratio distribution along whole ship length for full loading condition(fl) for both wave crest and though. Asian Business Consortium AJASE Aug 2014 Vol 3 Issue 8 Page 80

Figure 13. FL, shear force distribution, wave crest Figure 14. FL, shear force distribution, wave through Figure 15. FL, bending moment distribution, wave crest Figure 16. FL, bending moment distribution, wave through Figure 17. FL, Yielding ratio distribution on side shell, wave crest Figure 18. FL, Yielding ratio distribution on side shell, wave through Figure 19. FL, Yielding ratio distribution on main deck, wave crest Figure 20. FL, Yielding ratio distribution on main deck, wave through Figure 21. FL, Yielding ratio distribution on double bottom, wave crest Figure 22. FL, Yielding ratio distribution on double bottom, wave through Asian Business Consortium AJASE Aug 2014 Vol 3 Issue 8 Page 81

Figure 23. FL, Buckling ratio distribution on side shell, wave crest Figure 24. FL, Buckling ratio distribution on side shell, wave through Figure 25. FL, Buckling ratio distribution on main deck, wave crest Figure 26. FL, Buckling ratio distribution on main deck, wave through Figure 27. FL, Buckling ratio distribution on double bottom, wave crest Figure 28. FL, Buckling ratio distribution on double bottom, wave through Hereafter are presented the results obtained for ballast load condition. Table VI. Equilibrium parameters for ballast condition Wave crest Wave through Hw [m] Taft [m] Tfore [m] Taft [m] Tfore [m] 0.00 2.600 2.480 2.600 2.480 1.00 2.415 2.473 2.550 2.690 2.00 2.210 2.426 2.480 2.860 3.00 1.950 2.350 2.365 3.000 4.00 1.740 2.212 2.280 3.080 5.00 1.475 2.045 2.150 3.130 5.84 1.118 1.906 1.960 3.167 6.00 1.050 1.880 1.900 3.175 In the figures Figure 29 - Figure 32 are presented the shear force and the bending moment distribution along whole ship length for ballast loading condition (B) for both wave crest and though. In the figures Figure 33 - Figure 44 are presented the yielding ratio and buckling ratio distribution along whole ship length for ballast loading condition(b) for both wave crest and though. Asian Business Consortium AJASE Aug 2014 Vol 3 Issue 8 Page 82

Figure 29. B, shear force distribution, wave crest Figure 30. B, shear force distribution, wave through Figure 31. B, bending moment distribution, wave crest Figure 32. B, bending moment distribution, wave through Figure 33. B, Yielding ratio distribution on side shell, wave crest Figure 34. B, Yielding ratio distribution on side shell, wave through Figure 35. B, Yielding ratio distribution on main deck, wave crest Figure 36. B, Yielding ratio distribution on main deck, wave through Figure 37. B, Yielding ratio distribution on double bottom, wave crest Figure 38. B, Yielding ratio distribution on double bottom, wave through Asian Business Consortium AJASE Aug 2014 Vol 3 Issue 8 Page 83

Figure 39. B, Buckling ratio distribution on side shell, wave crest Figure 40. B, Buckling ratio distribution on side shell, wave through Figure 41. B, Buckling ratio distribution on main deck, wave crest Figure 42. B, Buckling ratio distribution on main deck, wave through Figure 43. B, Buckling ratio distribution on double bottom, wave crest Figure 44. B, Buckling ratio distribution on double bottom, wave through For the equivalent quasi-static wave height h w = 5.84 m the yielding ratio and buckling ratio distribution is presented, for wave crest and through, both for full loading and ballast condition. Figures 45-52, Full loading condition, wave crest; Figures 53-60, Full loading condition, wave through; Figures 61-68, Ballast condition, wave crest; Figures 69-76, Ballast condition, wave through; Full loading condition, wave crest, h w = 5.84 m Figure 45. FL, wave pressure Figure 46. FL, vertical deflection [mm] Asian Business Consortium AJASE Aug 2014 Vol 3 Issue 8 Page 84

Figure 47. FL, side shell - yielding ratio Figure 48. FL, side shell - buckling ratio Figure 49. FL, main deck - yielding ratio Figure 50. FL, main deck - buckling ratio Figure 51. FL, double bottom - yielding ratio Figure 52. FL, double bottom - buckling ratio Full loading condition, wave through, h w = 5.84 m Figure 53. FL, wave pressure Figure 54. FL, vertical deflection [mm] Figure 55. FL, side shell - yielding ratio Figure 56. FL, side shell - buckling ratio Asian Business Consortium AJASE Aug 2014 Vol 3 Issue 8 Page 85

Figure 57. FL, main deck - yielding ratio Figure 58. FL, main deck - buckling ratio Figure 59. FL, double bottom - yielding ratio Figure 60. FL, double bottom - buckling ratio Ballast condition, wave crest, h w = 5.84 m Figure 61. B, wave pressure Figure 62. B, vertical deflection [mm] Figure 63. B, side shell - yielding ratio Figure 64. B, side shell - buckling ratio Figure 65. B, main deck - yielding ratio Figure 66. B, main deck - buckling ratio Asian Business Consortium AJASE Aug 2014 Vol 3 Issue 8 Page 86

Figure 67. B, double bottom - yielding ratio Figure 68. B, double bottom - buckling ratio Ballast condition, wave trough, h w = 5.84 m Figure 69. B, wave pressure Figure 70. B, vertical deflection [mm] Figure 71. B, side shell - yielding ratio Figure 72. B, side shell - buckling ratio Figure 73. B, main deck - yielding ratio Figure 74. B, main deck - buckling ratio Figure 75. B, double bottom - yielding ratio Figure 76. B, double bottom - buckling ratio Asian Business Consortium AJASE Aug 2014 Vol 3 Issue 8 Page 87

CONCLUSIONS Based on the numerical results, from the global strength analysis for the offshore supply vessel, it results the following conclusions: the maximum vertical deflections are smaller as the admissible value for both loading cases (maximum vertical deflection is w max = 65.95 mm < w adm = L/500 =119.6 mm); the maximum value for yielding criteria, for full loading condition, 0.897 located on side shell, is lower than the admissible value, considering the maximum wave height h w =6m; the maximum value for buckling criteria, for full loading condition, 0.827 located on side shell, is lower than the admissible value, considering the maximum wave height h w =6m; the maximum value for yielding criteria, for ballast condition, 0.409 located on side shell, is lower than the admissible value, considering the maximum wave height h w =6m; the maximum value for buckling criteria, for ballast condition, 0.551 located on main deck, is lower than the admissible value, considering the maximum wave height h w =6m; using the 3D-FEM models, it makes possible to obtain the global stress distribution over the structure, predicting also the domains with higher risk. ACKNOWLEDGEMENTS The authors appreciated the support provided by the Prof. Dr. Leonard Domnisoru. This work has been accomplished using NX Nastran FEMAP software, and has been funded by European Union under the project POSDRU/159/1.5/S/132397-ExcelDOC. REFERENCES Bathe, K.J. 1990. Finite Elementen Methoden. Berlin: Springer Verlag BV. 2014. Bureau Veritas Rules for Classification of Steel Ships DNV. 2014, Det Norske Veritas Rules, DNV-RP-C201, Buckling Strength of Plated Structures Domnisoru, L. 2001. The finite element method applied in shipbuilding. Bucharest: The Technical Publishing House Domnisoru, L. 2006. Structural analysis and hydroelasticity of ships. Galati: University "Dunarea de Jos" Press Guedes Soares, C. 1999. Special issue on loads on marine structures. Marine Structures 12(3):129-209 Hughes, O.F. 1988. Ship structural design. A rationally-based, computer-aided optimization approach. New Jersey: The Society of Naval Architects and Marine Engineering Ioan, A., Popovici, O., Domnisoru, L. 1998. Global ship strength analysis. Braila: Evrika Publishing House Jagite, G., Domnisoru, L., 2014. Ship Structural Analysis with Femap API program codes. Naval Architecture Faculty, University "Dunarea de Jos" Galati, Romania Lehman, E. 1994. Matrizenstatik. Hamurg: Technischen Universitat Hambourg - Hamburg Lehman, E. 1998. Guidelines for strength analysis of ship structures with the finite element method. Hamburg: Germanischer Lloyd Register Rozbicki, M., Das Purnendu, K., Crow, A. 2001. The preliminary finite element modeling of a full ship. International Shipbuilding Progress. Delft 48(2):213-225 SDC Verifier ver 3.6, www.sdcverifier.com Servis, D., Voudouris, G., Samuelides, M., Papanikolaou, A. 2003. Finite element modeling and strength analysis of hold no. 1 of bulk carriers. Marine Structures 16:601-626 Siemens PLM - FEMAP -- 0 -- AJASE!!! Speedy publication service, Online archives, Paperless, web-based peer review system, Open access policy, Indexing in world known citation databases, Global circulation, Broad international readership and authorship, Online submission system, Minimum publication charge Asian Business Consortium AJASE Aug 2014 Vol 3 Issue 8 Page 88

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