Phân tích sức bền giới hạn kết cấu tàu dầu bằng phương pháp phần tử hữu hạn phi tuyến

conomy have the most important position in the whole design of ship structures. In this paper, ultimate strength of ship hull has been calculated by using the finite-element software. The modeling method which is suitable for ultimate strength calculation is gained. At the same time, ultimate loading capacity’s variation of series bulk carriers with length is gained. Finally the effective way of increasing ultimate loading capacity of river-to-sea ships has been obtained through changing thickness and material properties of key component of ship structure. It provides references for the design of river-to-sea ships. Keywords: Ultimate strength; analysis; hull oil tanker; bending mo - ment; ship structure. Tóm tắt Trong phân tích sức bền giới hạn kết cấu thân tàu, tính kinh tế và tính an toàn của kết cấu luôn có vai trò quan trọng trong việc tính toán, thiết kế kết cấu. Trong bài báo này, phần mềm phân tích phần tử hữu hạn ABAQUS được sử dụng để phân tích, tính toán sức bền giới hạn của kết cấu tàu. Mô hình hóa kết cấu thân tàu để tính toán sức bền giới của tàu dầu đáy đơn, đồng thời xác định tải trọng giới hạn của một số con tàu chở dầu với kích thước khác nhau. Kết quả phân tích, tính toán làm cơ sở để đưa ra giải pháp nâng cao khả nĕng chịu tải của kết cấu thông qua việc thay đổi độ dày và đặc tính vật liệu của thành phần kết cấu chính của tàu. Kết quả nghiên cứu là tài liệu tham khảo cho việc tính toán, thiết kế tàu pha sông biển. Từ khóa: Sức bền giới hạn; phân tích; tàu dầu; mô - men uốn; kết cấu tàu. transverse ultimate strength and torsional ultimate strength. The focus of the ultimate strength research of different ship types is different, but the ultimate strength of hull girder is usually the longitudinal ultimate strength. The ultimate longitudinal strength of a ship have been traditionally designed to evaluated by comparing the maximum stress of the cross section of the hull under the action of the vertical composite bending mo - ment with the allowable stress value. Its essence is based on the linear theory of elasticity. Caculation and analysis of ultimate strength of ship hull is an important part of ship structure design. The ship hull is the typical thin-walled structure which consists of stiffened plates, box girder and 1. INTRODUCTION Ultimate strength analysis of ship structure is based on is the classical theory of elasticity for a long time. But with the analysis method improved, people are beginning to realize that the influence of buckling, yield and post-buckling of component must be considered. There are four main methods: nonlinear finite element method, direct calculation method ideal, structure element method, gradually failure analysis method. The ultimate strength of ship hull can be broadly divided into longitudinal ultimate strength, Reviewers: 1. Assoc. Prof. Dr. Phan Anh Tuan 2. Dr. Ngo Huu Manh NGHIÊN CỨU KHOA HỌC 64 Tạp chí Nghiên cứu khoa học, Trường Đại học Sao Đỏ, ISSN 1859-4190, Số 3 (70) 2020 transvered stiffened web frames. The ultimate strength of the ship hull depends on these structure member. The ship hull structure is very complicated three-dimensional thin-wallstructure. In analysis and design of ship structure, the ultimate strength analysis is an essential stage, which usually gives an assessment result of the structural safety condition [1]. Paik et al (2009 and 2010) [2, 3] used nonlinear finite element to calculate ultimate strength of plate structure and stiffened-plate under the effect of vertical pressure. The research object is outer bottom plate and stiffened-plate structures of 100,000 ton. Paik [4] et al. Study characteristics of buckling and ultimate strength of plate sttructure under bending mo - ment and combined loads. Paik [5] et al. also studied the elastic buckling of simply supported plates, studied considered the influence of residual stress on the elastic buckling of the plate under the combined action of shear stress, biaxial compressive stress and lateral compressive stress. Come up with a formula for elastic buckling equation of simply supported plate. Yao [6] calculated the buckling and ultimate strength of the plate under uniaxial compressive stress, considered the influence of welding residual stress and initial deformation. Nishiliara [7], Shi GuiJie [8], Van Tan Vu [9] built up four box girder model: single bottom tanker, double bottom tanker, bulk carrier, container carrier. Author conducted longitudinal bending tests and calculations on a series of steel box girder, and obtained the relationship of ultimate bearing capacity under different scale ratios. In this paper uses the universal finite element software ABAQUS as the calculation tool to calculate the ultimate strength of a single-hull oil tanker, and compares it with the literature value to verify the effectiveness of the software and the parameter settings that should be paid attention to when calculating. The bulk carrier performs ultimate strength calculation to predict the ultimate bearing capacity of the hull girder under two dangerous conditions: sagging bending mo - ment and hogging bending mo - ment. 2. CALCULATION OF ULTIMATE LONGITUDINAL STRENGTH OF SHIP HULL GIRDER 2.1. Geometric and material properties In this paper, a single hull oil tanker (Fig 1) will be taken as the calculation object for research. Fig 1. Mid-ship section of bulk carrier The dimension and material properties of open box girder model are shown in Table 1. Table 1. Dimensions and material properties of the model No Dimension (mm) Type sy(MPa) 1 480×32 flat steel 313,6 2 797×15+200×33 T 313,6 3 447×11,5+125×22 T 313,6 4 549×11,5+125×22 angle bar 235,2 5 597×11,5+125×22 angle bar 235,2 6 597×11,5+125×22 angle bar 235,2 7 647×11,5+125×22 angle bar 235,2 8 350×25,4 angle bar 235,2 9 646×12,7+150×25 angle bar 235,2 10 697×12,7+150×25 angle bar 235,2 11 747×127+150×25 angle bar 313,6 12 747×12,7+180×25 angle bar 235,2 13 797×14+180×25 T 235,2 14 847×14+180×25 angle bar 313,6 15 847×14+180×32 T 235,2 16 847×15+180×25 angle bar 313,6 17 847×15+200×25 angle bar 313,6 18 897×15+200×25 angle bar 253,2 19 945×16+200×25 angle bar 235,2 20 897×15+200×25 angle bar 313,6 21 797×15+180×25 angle bar 313,6 22 347×11,5+125×22 angle bar 313,6 23 300×11,5+100×16 angle bar 313,6 24 397×25 angle bar 313,6 25 300×11,5+100×16 angle bar 313,6 LIÊN NGÀNH CƠ KHÍ - ĐỘNG LỰC 65Tạp chí Nghiên cứu khoa học, Trường Đại học Sao Đỏ, ISSN 1859-4190, Số 3 (70) 2020 No Dimension (mm) Type sy(MPa) 26 370×16 angle bar 313,6 27 230×12,7 angle bar 235,2 28 230×12,7 angle bar 235,2 29 300×25 angle bar 253,2 30 425×25 angle bar 313,6 31 370×16 angle bar 313,6 32 397×11,5+100×25 T 313,6 Yield stress of the material: s = 313,6 N/mm2. Young’ smodulus: E = 2,1e5N/mm2. Poisson’s ratio g = 0,3. 2.2. Selection of model This paper calculate the ultimate strength bending mo - ment of a series of ships hull structure. The hull structure is extremely complicated. Therefore, it is necessary to use a simplified and effective model when performing ultimate strength analysis. This studying assumes that the laterally strong bones of the hull are strong enough so that the overall damage of the plate frame will not occur. Therefore, it is necessary to use a simplified and effective model when performing ultimate strength analysis. This studying assumes that the laterally strong bones of the hull are strong enough so that the overall damage of the plate frame will not occur. The hull plates and longitudinal frames are modeled by plate elements. 2.3. Nonlinear finite element mesh modeling The quality of mesh size division is an important step to ensure the ultimate strength calculation results. The mesh size form is directly related to the accuracy of the calculation and the calculation time. The mesh density in a finite element model is an important topic because of its relationship to accuracy. Generally, the denser mesh size is, the closer the calculation result is to the true value, but the calculation time is also rapidly increasing. Therefore, it is particularly important to adopt reasonable element division when calculating the ultimate strength of ship girder. In order to investigate the influence of element grid division on the ultimate strength of ship structure. This paper divides the finite element model into three models for different element densities (one frame spacing, 1/2 frame spacing, 1/4 frame spacing, each limited. The element model is shown in Fig 2, Fig 3, Fig 4. The effect of mesh density on the ultimate strength of the actual ship are 23.268 element, 22.074 element, and 22.068. From this mesh density, it can be seen that the refinement from one one frame spacing to 1/2 frame spacing reduce significantly the calculation value of the limit bending mo - ment. When refined to 1/4 frame spacing, the calculated value of the ultimate bending mo - ment changes very little, but the time consumed in the calculation is greatly increased. Therefore, when the mesh density of the calculation model is relatively loose, the dense mesh can indeed be effective improve the calculation accuracy. But when the mesh is dense enough, continuing to refine the model mesh has little effect on the calculation results, and will cause unnecessary increase in computer time. Fig 2. Finite element model for one frame spacing model Fig 3. Finite element model for 1/2 frame spacing model Fig 4. Finite element model for 1/4 frame spacing model NGHIÊN CỨU KHOA HỌC 66 Tạp chí Nghiên cứu khoa học, Trường Đại học Sao Đỏ, ISSN 1859-4190, Số 3 (70) 2020 2.4. Boundary conditions Boundary conditions also have an impact on the calculation results of ultimate strength. In this section use the multi-point constraint (MPC) function provided in of the finite element model for boundary conditions [8, 9]. Assume that the rigid end face rotates around the neutral axis, and gradually increase the bending mo - ment value; apply a rigid fixed .There are two different boundary conditions for simply supported: (1) Simply supported, all nodes on the end face restrain the displacement of the ship in the length direction Uz= 0, the depth displacement Uy = 0 of the node restraint on the upper and lower slabs, and the node restrains the ship on the side slab Displacement in the width direction Ux = 0; (2) Rigidly fixed, constraining 6 degrees of freedom of all nodes on the end face. 3. CALCULATION RESULT OF A SERIES OF REAL SHIP MODELS This paper, ABAQUS software was usedfor ultimate strength alanysis of bulk carrier structure. 3.1. Analysis of a 80 m bulk carrier The mid-ship section structure are shown in Fig 5. The frame spacing is 2.800 mm, the Young’s modulus is E = 2,1×105N/mm2, and the Poisson’s ratio: g = 0,3. Fig.5. Mid – ship section of 80 m bulk carrier Table 2. Dimensions and material characteristics of 80 m bulk carrier structure No Dimension (mm) Type s (MPa) 1 140×90×12 angle bar 235,2 2 125×80×12 angle bar 235,2 3 160×100×12 angle bar 235,2 4 100×63×7 angle bar 235,2 5 125×80×10 angle bar 235,2 6 180×10 angle bar 235,2 The finite element model of an 80 m bulk carrier is shown in Fig 6. The calculation results of the ultimate bending mo - ment are as follows: Fig 7 shows the sagging bending mo - ment - deformation (rotation angle) curve in the model. The calculated ultimate bending mo - ment value of the middle arch is 2,8 × 1011N.mm; Fig 8 shows the hogging bending mo - ment - deformation (rotation angle) curve of the model. The calculated of ultimate bending mo - ment value is 2,44 × 1011N.mm. Fig 6. Finite element model of 80 m bulk carrier Fig.7. Sagging bending mo - ment-deformation curve Fig 8. Hogging bending mo - ment - deformation curve LIÊN NGÀNH CƠ KHÍ - ĐỘNG LỰC 67Tạp chí Nghiên cứu khoa học, Trường Đại học Sao Đỏ, ISSN 1859-4190, Số 3 (70) 2020 3.2. Analysis of 110m bulk carrier Fig 9. Mid – ship section of 110 m bulk carrier Table 3. Dimensions and material characteristics of 110 m bulk carrier structure No Dimension (mm) Type s(MPa) 1 160×100×12 angle bar 235,2 2 140×90×14 angle bar 235,2 3 180×110×14 angle bar 235,2 4 110×70×7 angle bar 235,2 5 140×90×12 angle bar 235,2 6 180×10 angle bar 235,2 The finite element model of an 80 m bulk carrier is shown in Fig 10. The calculation results of the ultimate bending mo-ment are as follows: Fig 11 shows the sagging bending mo - ment-deformation (rotation angle) curve in the model. The calculated ultimate bending mo-ment value of the middle arch is 5,32 × 1011N.mm; Fig 12 shows the hogging bending mo-ment-deformation (rotation angle) curve of the model. The calculated of ultimate bending mo-ment value is 5,03 × 1011N.mm. Fig.10. Finite element model of 110 m bulk carrier Fig 11. Sagging bending mo-ment-deformation curve Fig 12. Hogging bending mo-ment-deformation curve 3.3. Analysis of 140 m bulk carrier Fig 13. Mid – ship section of 140 m bulk carrier Table 4. Dimensions and material characteristics of 140 m bulk carrier structure No Dimension (mm) Type s(MPa) 1 160×100×16 angle bar 235,2 2 160×100×14 angle bar 235,2 3 200×125×14 angle bar 235,2 4 110×70×10 angle bar 235,2 5 160×100×12 angle bar 235,2 6 180×10 angle bar 235,2 NGHIÊN CỨU KHOA HỌC 68 Tạp chí Nghiên cứu khoa học, Trường Đại học Sao Đỏ, ISSN 1859-4190, Số 3 (70) 2020 The finite element model of an 140 m bulk carrier is shown in Fig 14. The calculation results of the ultimate bending mo-ment are as follows: Fig 15 shows the sagging bending mo-ment-deformation (rotation angle) curve in the model. The calculated ultimate bending mo-ment value of the middle arch is 1,06×1012N.mm; Fig 16 shows the hogging bending mo-ment-deformation (rotation angle) curve of the model. The calculated of ultimate bending mo-ment value is 9,55×1011N.mm. Fig 14. Finite element model of 140 m bulk carrier Fig 15. Sagging bending mo-ment-deformation curve Fig 16. Hogging bending mo-ment-deformation curve Table 5. Relation between the ultimate strength and ship length (×1011N.mm) Ultimate strength status 80 m 110 m 140 m Sagging bending mo-ment 2,44 5,03 9,55 Hogging bending mo-ment 2,8 5,32 10,6 4. CONCLUSION This paper used the finite element software ABAQUS as the calculation tool to calculate the ultimate strength of a single-hull oil tanker, and compares it with the literature values. The effect of meshing density, boundary conditions, and initial loading ratio coefficients on the hull girder were analysed. In addition, the ultimate strength calculation of a series of bulk carriers is carried, and the ultimate load-bearing capacity of the hull girder under two dangerous conditions of sagging and hogging bending mo-ment. The ultimate strength calculation of a series of hull oil tanker structure were analysed, The ultimate strength of the hull girder under two dangerous conditions of sagging bending mo- men-deformation, and hogging bending mo-men- deformation were analysed. The ultimate strength calculation show that, the ultimate bending mo- men increases with the increase of the ship length, and the ultimate bending mo-ment of the middle arch is always greater than the ultimate sagging mo-ment. When the length of the ship is less than 110 m, the ultimate bending mo-ment increases with the length of the ship. The relationship is linear. When the length of the ship is greater than 110 m, the growth rate of the limit bending mo-ment was obviously accelerated. REFERENCES [1] IACS (2012), Common Structure Rules for Bulk Carriers [S]. [2] Paik J K, Seo J K (2009), Nonlinear finite element method models for ultimate strength analysis of steel stiffened-plate structures under combined biaxial compression and lateral pressure actions - Part I: Plate elements[J], thin- Walled Structures, 47: 1008-1017. [3] JeomKee Paik (2010), Large deflection behavior and ultimate strength of stiffened panels [C], The Society of Naval Architects and Marine Engineers. LIÊN NGÀNH CƠ KHÍ - ĐỘNG LỰC 69Tạp chí Nghiên cứu khoa học, Trường Đại học Sao Đỏ, ISSN 1859-4190, Số 3 (70) 2020 [4] JeomKee Paik, Bong Ju Kim, Jung Kwan Seo (2008), Methods for ultimate limit state assessment of ships and ship-shaped offshore structures: Part I—Unstiffened plates [J], Ocean Engineering, 35: 261–270. [5] JeomKee Paik, Bong Ju Kim, Jung Kwan Seo (2008), Methods for ultimate limit state assessment of ships and ship-shaped offshore structures: Part II stiffened panels [J], Ocean Engineering, 35: 271–280. [6] Yao T, Fujikubo M, Yanagihara D, et al (1998), Influence of welding imperfections on buckling/ ultimate strength of ship bottom plate subjected to combined biaxial thrust and lateral pressure [A], Thin-Walled Structures, Research and Development, 2nd International Conference on Thin-walled Structures, 425- 432. [7] Nishihara S (1984), Ultimate Longitudinal Strength of Midship Cross Section. Naval Arvh. And Ocean Engine, (22), 200-214. [8] Shi Gui-jie, Wang De-yu (2012), Residual ultimate strength of open box girders with cracked damage [J], Ocean Engineering, 43: 90–101. [9] Van Tan Vu, Wei Guo Wu (2014), Nonlinear Finite Element Method Ultimate Strength Analysis of Open Box Girders, International journal of advanced materials research, Vol 919, PP:177-182. Vu Van Tan - Training and research process: Dr Vu Van Tan is a Dean of Mechanical Engineering Department, Sao Do University, Hai Duong, Vietnam. He studied doctoral courses at School of Transportation, Wuhan University of Technology, Wuhan, Hubei, China. He is doing research in Ship structural analysis and design. - Mobile phone: 0911.422.658 - Email: vutannnn@gmail.com AUTHORS BIOGRAPHY