NGHIÊN CỨU KHOA HỌC Structural optimization of ship structures based on structural analysis using nonlinear finite element method Phân tích, tối ưu hóa kết cấu tàu bằng phương pháp phần tử hữu hạn phi[.]
NGHIÊN CỨU KHOA HỌC Structural optimization of ship structures based on structural analysis using nonlinear finite element method Phân tích, tối ưu hóa kết cấu tàu phương pháp phần tử hữu hạn phi tuyến Vu Van Tan Email: vutannnn@3mail.com Sao Do University Received date: 16/5/2022 Accepted date: 22/6/2022 Published date: 30/6/2022 Abstract In this paper, ultimate strength and structural optimization of river-to-sea ships has been calculated by using the finite-element software, mainly to analyze under different working conditions of sagging and hogging bending moment Each component of the river-to-sea ship is thickened separately, and the effectiveness of increasing the ultimate strength is measured by the percentage of weight increase and the percentage of ultimate strength increase, and the most effective method to improve the ultimate strength of the river-to-sea ship is obtained And by changing the material distribution between the plate and the longitudinals, a series of calculations are carried out to obtain the safety range of the ultimate strength, and finally provide a reference for the design of the stan dard ship type directly from the river-to-sea ship Keywords: Ultimate strength; analysis; ultimate bending moment; river-to-sea ship; ship structure Tóm tat Trong báọ này, phương pháp phần tử hữu hạn phi tuyến sử dụng để tính tốn, phân tích tối ưu hóa độ bền kết cấu tàu pha sông biển tác dụng mô men uốn (sangging and hogging) Chi tiết kết cấu tàu có chiều dày khác nhau, tính tốn tối ưu hóa kết cấu, tiến hành thay đổi độ dày kết cấu dựa kết phân tích việc tăng sức bền giới hạn tính tỷ lệ phần trăm tăng cùa độ bền giới hạn kết cấu Đây là phương pháp hiệu để tính tốn, phân tích tối ưu hóa sức bền giới hạn kết cấu tàu pha sông biển Và cách thay đổi phân bố vật liệu chi tiết tấm, tiến hành phân tích, tính tốn khả làm việc an toàn kết cấu sở phân tích sức bền giới hạn đưa kết tham chiếu cho việc phân tích, tính tốn thiết kế kết cấu tàu pha sông biển Từ khóa: Sức bền giới hạn; phân tích; mơ men uốn giới hạn; tàu pha sông biển; kết cấu tàu INTRODUCTION The hull girder under load mainly includes bending moment, torque, hydrostatic pressure, hydrodynamic pressure, cargo load and so on The hull girder un der the combined action of multiple load groups will affect the ultimate strength of the hull girder From the above research results, it can be seen that the ultimate strength of the hull structure will be affected by various loads But usually the longitudinal and vertical ultimate strength of hull girder is the focus of research When the ship is sailing in oblique waves, large torsional de formation can occur, and the structure of the river-tosea direct ship has a large opening This feature can improve the torsional rigidity of the river-to-sea ship At this time, the hull is in the vertical bending moment and torque Under the joint action, it is very likely to fail and collapse Owen F Hughes and Farrokh Mistree developed a large-scale ship structure optimization system, which Reviewer: Assoc Prof Dr Phan Anh Tuan Dr Ngo Huu Manh 50 is a finite element analysis method for optimization de sign and an optimization method for structure design that can effectively solve large-scale structures that can effectively solve nonlinear constraints [1] Among them, the optimization method is solved by a new se quential linear programming method Its character istic is that when the nonlinear constraint function is expanded according to the Taylor series, it retains the linear approximation method of the second-order term This method is very effective for solving large-scale, nonlinear structural optimization problems In recent years, due to the continuous maturity of largescale finite element analysis software and the continu ous improvement of the intelligence of structural analy sis modules, engineers reliance on mathematical tools and the workload of programming have been greatly reduced Finite element-based optimization has been widely used In actual engineering A large number of finite element optimization papers closely related to the actual structure of the project have been published continuously, making the structural optimization design once again a new hot spot [2, 3, 4, 5], In this paper, ultimate strength and structure optimiza tion of river-to-sea ships has been calculated by US- Tạp chí Nghiên cứu khoa học, Trường Đại học Sao Đỏ, Số (77) 2022 LIÊN NGÀNH KHÍ - ĐỘNG Lực ĩng the finite-element software, mainly to analyze un der different working conditions of sagging and hogging bending moment By changing the material distribution between the plate and the longitudinals, a series of cal culations are carried out to obtain the safety range of the ultimate strength and finally provide a reference for the design of the standard ship type directly from the river-to-sea ships OTIMIZATION CALCULATION 2.1 Geometric and Material properties In this paper, a hull oil tanker (Fig.1) will be taken as the calculation object for research The dimension and material properties of ships are shown in Table Type No Dimension (mm) 22 347x11.5+125x22 angle bar 313.6 23 300x11.5+100x16 angle bar 313.6 24 397x25 angle bar 313.6 25 300x11.5+100x16 angle bar 313.6 26 370x16 angle bar 313.6 27 230x12.7 angle bar 235.2 28 230x12.7 angle bar 235.2 29 300x25 angle bar 253.2 30 425x25 angle bar 313.6 31 370x16 angle bar 313.6 32 397x11.5+100x25 T (Mpa) 313.6 Yield stress of the material: Ơ = 313.6 N/mm2 Young’s modulus: E = 2.1 e6N/mm2 Poisson’s ratio Y = 0.3 2.2 Initial finite element model analysis Figure Midship section of bulk carrier Table Dimensions and material properties of the model No Dimension (mm) Type Ơ (Mpa) 480x32 flat steel 313.6 797x15+200x33 T 313.6 This paper calculate the ultimate bending moment of a series of ships, and the hull structure is extremely complicated, the calculation of the entire ship is very time-consuming Therefore, it is necessary to use a simplified and effective model when performing ulti mate 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 only possible to model the hull structure of the ship with a length of 5.100mm between the transverse frame of the ship, and the hull plates and longitudinal frames are modeled by plate elements Calculation of the ultimate strength of the whole ship is very time-consuming, therefore, it is necessary to use a simplified model when performing an ultimate strength analysis In this paper, the 12.400 ton river-to-sea ships hull is used as the ultimate strength analysis model Based on the initial finite element model, and by changing the plate thickness and material properties in key areas, a scheme for improving the ultimate strength of the riverto-sea ships structural is obtained 447x11.5+125x22 T 313.6 549x11.5+125x22 angle bar 235.2 597x11.5+125x22 angle bar 235.2 597x11.5+125x22 647x11.5+125x22 angle bar angle bar 235.2 350x25.4 angle bar 235.2 646x12.7+150x25 angle bar 235.2 10 697x12.7+150x25 angle bar 235.2 11 747x127+150x25 angle bar 313.6 12 747x12.7+180x25 angle bar 235.2 13 797x14+180x25 T 235.2 14 847x14+180x25 angle bar 313.6 15 847x14+180x32 T 235.2 16 847x15+180x25 angle bar 313.6 17 847x15+200x25 angle bar 313.6 2.2.1 Working conditions and boundary conditions 18 897x15+200x25 angle bar 253.2 19 945x16+200x25 angle bar 235.2 20 897x15+200x25 angle bar 313.6 21 797x15+180x25 angle bar 313.6 The ship hull structural has a problem of longitudi nal strength in waves, only two working conditions of bending moment at midship (sagging and hoggong) Constraint, z = 2100 mm end face, using multi-point restraint function (MPC), the bending moment is load- 235.2 The ultimate strength of ship hull has been calculat ed by using the finite-element software (Abaqus soft ware) When using Abaqus software for nonlinear finite element calculation, the influence of material nonlin earity and geometric nonlinearity is taken into account; the Riks/Ramm arc length method is used to track the instability path and the Newton-Raphson method is used to solve the nonlinear equation system The model includes 1524 plate elements and 1737 nodes The material properties are Yield stress of the material: Ơ = 313.6 N/mm2; Young’s modulus: E = 2.1 e5N/mm2; Poisson’s ratio Y= 0.3 Tạp chí Nghiên cứu khoa học, Trường Đại học Sao Đỏ, số (77) 2022 I 51 NGHIÊN CỨU KHOA HỌC ed on the main node and gradually increases with time; the bending moment value on the main node is 2x1012N.mm 2.2.2 Analysis of calculation results The Abaqus software was used for ultimate strength alanysis of bulk carrier structure The calculation results of each working condition are shown in Fig It shows the Von/Mises stress diagram of the calculated mod el at the ultimate bending moment (sag condition) It can be seen from Figure that the loading factor of the ultimate bending moment in the mid-sag condition is 0.3157 The ultimate bending moment value in the sag ging condition: = 2x1012x0,3157x2=1,2628X105 t.m Figure Calculated model load-deformation curve (middle arch condition) 2.3 Material Finite Element Model Analysis Figure Von/Mises stress contour of the initial model at the ultimate bending moment (sag condition) From Figure and Figure that the Von-Mises stress of the inner bottom and the bottom of the ship is very large under the action of the ultimate bending mo ment of the hull girder Therefore, on the basis of the initial calculation model, the material properties of the inner bottom plate were changed from Q235 steel to Q355 steel and the material properties of the ship bottom plate were changed from Q315 steel to Q355 steel Analysis of the variable material finite element model to improve the ultimate strength of the river-tosea ships 2.3.1 Analysis of the calculation results of the inner bo ttom plate (sag condition) Figure is the Von/Mises stress cloud diagram of the calculation model at the ultimate bending moment (the middle arch condition) It can De seen from Figure that the loading coefficient of the ultimate bending moment under the middle arch condition is 0.3018, then the mid dle arch ultimate bending moment value under working condition: = 0,3018 x2x1012x2=1,2070x106 t.m Figure Von/Mises stress cloud diagram of the initial model at the ultimate bending moment (middle arch condition) 52 Figure shows the Von/Mises stress cloud diagram of the inner bottom plate variable material calculation model at the limit bending moment (sagging condition) It can be seen from Figure that the load factor of the ultimate bending moment under the sag condition is 0.3251 The ultimate bending moment value under the sag condition = the bending moment value on the main node X the ultimate bending moment loading factor X = 0.3251 x2x1012x2=1 ,3004x105 t.m The percentage increase of ultimate bending moment = (1,2628x10® -1,2628x1 o5)/1,2628x o5 = 2,978% Figure Von/Mises stress cloud diagram of the calculation model at the ultimate bending moment (sag condition) Tạp chí Nghiên cứu khoa học, Trường Đại học Sao Đỏ, Sơ' (77) 2022 LIÊN NGÀNH KHÍ - ĐỘNG Lực As can be seen from Figure 11, the loading factor of the ultimate bending moment in the mid-sag condition is 0.3271 The ultimate bending moment value under the sagging condition = the bending moment value on the main node X the ultimate bending moment loading factor X = 0.3271 x2x1012x2= 1.3084X105 t.m 100% increase in ultimate bending moment = (1.3084x10s-1.2628x105)/1.2628x1 o5 = 3.611% Figure Calculated model load-deformation curve (sag condition) Figure shows the Von/Mises stress cloud diagram of the inner bottom plate variable material calcula tion model at the limit bending moment (center arch working condition) It can be seen from Figure that the load factor of the ultimate bending moment un der the middle arch condition is 0.3089 The ultimate bending moment value under the middle arch condi tion = the value of the bending moment on the main node X the ultimate bending moment load factor X = 0.3089x2x1012x2 = 1.2356X105 t.m Figure 10 Vbn/Mises stress cloud diagram of the calculation model at the ultimate bending moment (sag condition) The percentage increase of ultimate bending moment = (1,2356x10s-1,2070x105)/1.20 70X105 =2.353% Figure 11 Calculated model load-deformation curve (sag condition) Figure Von/Mises stress cloud diagram of the calculation model at the ultimate bending moment (middle arch condition) Figure 12 is the Von/Mises stress cloud diagram of the variable material calculation model of the ship bottom plate at the ultimate bending moment (in the middle arch condition) As can be seen from Figure 13, the loading coefficient of the ultimate bending moment un der the middle arch condition is 0.3095, then the ul timate bending moment value under the middle arch condition = the bending moment value on the main node X the ultimate bending moment loading coeffi cient X = 0.3095x2x10’2 = 1.238x10s t.m 100% increase in ultimate bending moment = (1.238x10s- 1.2070x105)/1.2070x10s = 2.551% Figure Calculated model load-deformation curve (middle arch condition) 2.3.2 Analysis of calculation results of bottom plate Figure 10 is the Von/Mises stress cloud diagram of the variable material calculation model of the bottom of the ship at the ultimate bending moment (sag condition) The calculation results of the variable material finite el ement model and the initial model are shown in Table By changing the material properties of the bottom and inner bottom of the ship, the ultimate strength of the river-to-sea ship can be improved without sacri ficing the weight of the ship Therefore, changing the plates in the high-stress area of the ship structure un der the ultimate load to high-strength steel is an im- Tạp chí Nghiên cứu khoa học, Trường Đại học Sao Đỏ, Sõ (77) 2022 53 NGHIÊN CỨU KHOA HỌC portant means to improve the ultimate strength of the river-to-sea direct ship 2.4 Influence of partition coefficient on ultimate strength Since the mid-section structure is the most important structure of the hull, and the dimensions of its mem bers usually extend at least 0.2 times the length of the ship to the bow and stern, it can best represent the final structural weight and cost of the ship (for exam ple, the mid-section structure accounts for about the entire ship 70% of the structure), due to the reasonable design of the mid-section of the ship, it is always an im portant issue in the structural design The design of the mid-section can be roughly divided into two steps: first, calculate the thickness of the structure that meets the requirements of the overall longitudinal strength, that is, to solve the problem of the optimal configuration of materials in the entire section Then, according to the obtained considerable thickness, the size of the plate and the longitudinal frame is determined according to the local strength and local stability requirements, that is, the problem of reasonable distribution of materials between the plate and the frame is solved Figure 12 The Von/Mises stress cloud diagram of the calculation model at the ultimate bending moment Generally, after two similar calculations, the consider able thickness of the midship section can be obtained The next problem is how to reasonably distribute the materials to the frames and how to determine the spac ing between the frames For the purpose of simplifying the discussion in this chapter, it is assumed that the The spacing of the timber remains unchanged, and only the distribution coefficient between the aggregate and the plate is changed (the proportion of the aggre gate in a considerable thickness) Taking the bottom frame of the ship as an example, a series of calcu lations are carried out to discuss the influence of the distribution coefficient on the ultimate strength of the ship The bottom structure is shown in Figure 14 The calculation results of each model are shown in Table Figure 13 Calculated model load-deformation curve (sag condition) Table Calculation results of variable material finite element model (unit: t.m) Sagging ulti mate bending moment Inner bot tom plate Hogging Raise per Raise ultimate centage percentage bending (sag) (sag) moment 1.3004x10s 1.2356x10s 2.978% Bottom plate 1.3084x10s Initial model 1.2628x10s 1.2070x10s 1.238x10s 2.353% 3.611% 2.551% 0 Table Model calculation results Plate Plate (mm) (mm) Dimension (mm) Aggregate Partition Coefficient % change in mass Variation of ultimate bending Variation of ultimate sag moment of middle arch bending moment 15 14 HP120X6 6.615% 0.1137% -2.501% 0.063% 14.5 13.5 HP140X8 9.823% 0.0320% -1.51% 0.095% 14 13 HP160X9 12.702% -0.4334% -0.232% -0.032% 13.5 12.5 HP180X10 16.024% -0.4068% -0.265% -0.032% 13 12 HP200X11 19.653% 0 12.5 11.5 HP240X10 23.052% 0.1457% -0.348% -0.0348% 12 11 HP26ŨX12 26.424% 0.27% -1.21% -0.0317% 11.5 10.5 HP300X11 29.299% 0.1599% -2.145% -0.475% From the calculation results in Table 3, it can be seen that changing the distribution coefficient of the frame has no obvious effect on the ultimate strength of the ship under the sagging condition The reason is that 54 the bottom plate is subjected to tensile stress, and its possible failure form is yield failure; The distribution coefficient of the frame has an obvious influence on the ultimate strength of the ship under the middle arch Tạp chí Nghiên cứu khoa học, Trường Đại học Sao Đỏ, Sô (77) 2022 LIÊN NGÀNH KHÍ - ĐỘNG Lực condition The reason may be that the bottom plate bears compressive stress and the excessive distribu tion coefficient leads to the excessive height of the bot tom longitudinals and the longitudinals are prone to roll instability, the too low distribution coefficient results in the undersize of the bottom longitudinals, which can not support the bottom of the ship, and the longitudi nals are unstable together with the plates to which they are connected ship On the contrary, if the thickening position is not appropriate, the ultimate strength may decrease For the river-to-sea ship, it is more effective to increase the deck thickness under the two conditions of sag and mid-arch (3) The distribution coefficient of the aggregate has a great influence on the ultimate strength It should be noted that in the compression area, it is necessary to avoid the rolling instability of the aggregate caused by the too high distribution coefficient and the instability of the longitudinal frame and the plate caused by the too low distribution coefficient Figure 14 Bottom structure REFERENCES CONCLUSION Based on the sufficient proof of the effectiveness of the nonlinear finite element calculation of ultimate strength in this paper chapter has carried out a series of lim it tests by changing the material properties and plate thickness of the key areas of the 12400t river-to-sea ship and changing the distribution coefficient of the bottom plate Intensity calculation, the following con clusions are obtained: (1) By changing the material properties of the bottom plate and the inner bottom plate, the ultimate strength of the river-sea direct ship can be improved without increasing the weight of the ship structure Therefore, it is an important means to improve the ultimate strength of the ship directly to the sea by changing the plate in the high stress area of the ship structure under the ac tion of the ultimate load to high-strength steel (2) At the same time, increasing the thickness of the plate at an appropriate position can effectively improve the ultimate bending moment value of the river-to-sea [1], Owen F Hughes (2020), A Pioneer of Comput er-Aided Ship Structural Design, Ships and Off shore Structures, Vol.16, No.1, pp.1-4 [2], Paik, J.K and Seo, J.K (2009), Nonlinear finite ele ment method models for ultimate strength analysis of steel stiffened-plate structures under combined biaxial compression and lateral pressure actions - Part I: Plate elements, Thin-Walled Structures, Vol.47, pp.1008-1017 [3], Paik, J K„ Kim B, J and Seo J K (2008), Methods for ultimate limit state assessment of ships and ship-shaped offshore structures, Part II stiffened panels Science Direct, Vol.35, pp 271-280 [4], Paik, J K (2008), Methods for ultimate limit state assessment of ships and ship-shaped offshore structures, Part III hull girders, Science Direct, Vol.35, pp.281 286 [5] Liu B and Wu W.G (2013), standardized nonlinear finite element analysys of the ultimate strength of bulk carriers, Journal of Wuhan university of Tech nology Transportation Science, Vol.37, pp.716-719 AUTHORS INFORMATION Vu Van Tan - 2015: Graduated with Doctor’s degree program in Naval Architecture and Ocean Engineering - Current job summary: Lecturer, Faculty of Mechanical Engineering; Head of deparment of training management, Sao Do university - Areas of interest: Ship structural analysis and design, Mechanics of material ( -Phone:0911422658 Email: vutannnn@gmail.com Tạp chí Nghiên cứu khoa học, Trường Đại học Sao Đỏ, Số (77) 2022 55