Ultimate Limit State Assessments of Steel Plates for Spar-Type Floating Offshore Wind Turbines 1. Sajad Rahmdel 1) 2. Hyerin Kwon 2) 3. Seonghun Park 3) 1), 2), 3) School of Mechanical Engineering, Pusan National University, Busan, Republic of Korea Corresponding Author E-mail: paks@pusan.ac.kr Abstract Corrosion can significantly reduce the ultimate strength of offshore structures. In this study, a comprehensive ultimate limit state assessments of these structures are made. The goal of this study is to statistically evaluate the ultimate limit state (ULS) performance of Spar-type Floating Offshore Wind Turbines (FOWTs) by considering the effects of pit corrosions. 17 plates with different configurations are selected and using ANSYS finite element analysis, the ultimate strength of these models are calculated. The amount of reduction in ultimate strength of the structure for various ages of the structure is then found using distribution fitting method. It is concluded that the results of the current study can provide important design guidelines of ultimate limit state assessment of spar-type floating offshore wind turbines. Keywords: ultimate limit state; floating offshore wind turbine; ultimate strength; 1. Introduction It is well known that the ultimate limit state (ULS) is a better approach for design and strength assessment of various types of structures than the conventional allowable working stress approach. The reason is that by determining the limit states of the structures, it is possible to find the true margin of structural safety. While the offshore industry has previously applied the limit state approach, the floating offshore wind turbine (FOWT) is a new concept and further studies are needed before limit state approach could be used for strength assessments of FOWTs. Also, in maritime industry, it is mandatory to compute the ultimate strength of structural components based on ULS method [1-4]. Paik et al. [5] did a thorough comparison between three different methods, namely ANSYS nonlinear finite element analysis (FEA), DNV PULS and ALPS to calculate the ultimate strength of the ships and ship-shaped offshore structures. Unstiffened panels, stiffened panels and hull girders were considered as models to evaluate which method is better. Different types of boundary conditions (i.e., simply supported, partially rotational restrained supported and clamped supported) were used. It was concluded that ANSYS nonlinear 1), 2) Graduate Student 3) Professor Corresponding Author
finite element analysis (FEA) is the most accurate method, while, DNV PULS and ALPS had also acceptable results [5-7]. The hull of most offshore structures (spar platforms, ships, etc.) are built of steel plates and understanding the ultimate strength of these plates help finding the ULS of the whole structure. The aim of this paper is to statistically assess the ULS of stiffened plates. 2. The SPAR-type FOWT and its structural characteristics For the present study, a hypothetical spar-type FOWT with a typical stiffened plate structure is considered. Table 1 shows mechanical properties of these plates, while dimensions and boundary conditions are illustrated in Figure 1. Figure 1: stiffened plate s (a) dimensions (b) boundary conditions Table 1: mechanical properties of the stiffened plates Mechanical Property Value Yield stress ( ) (MPa) 250 Elastic modulus ( ) (GPa) 200 Bulk modulus (GPa) 166.67 Modulus of rigidity (GPa) 76.923 Poisson's ratio 0.3 Table 2: properties of the stiffened plates Parameter Value (mm) Plate length ( ) 10790 Plate breadth ( ) 4950 Stiffener spacing ( ) 830 Stiffener height ( ) 463 Stiffener breadth length ( ) 172 Stiffener web thickness ( ) 8 Stiffener breadth thickness ( ) 17 The spar-type FOWT plates are made of structural steel with yield stress of 250 MPa, Young s modulus of 200 GPa, Poisson s Ratio of 0.3, Bulk Modulus of 166.67 GPa, and Shear Modulus of 76.923 GPa. The welding-induced initial deflections of plating and stiffener webs are considered by, where is the maximum plate deflection and is the breadth of the plating as shown in Figure 1.
In the present study, the ULS assessments are made for the stiffened plates of the hull of a hypothetical classic spar platform. The stiffened plates are assumed to have simply supported edges and are assumed to be under combined biaxial compression (Figure 2). The length and the breadth of the plate are and, while the slenderness ratio is ( ). In this study, the plates are considered to have regular distribution of pit corrosions, however, in reality the distribution of pit corrosions are random. As an example, two of the plates used in the simulation are shown in Figure 2. 3. The ultimate strength of plates Using ANSYS finite element analysis, the ultimate strength of all models under different biaxial compression loadings, density of pit corrosions (DOP) and corrosion depths were calculated. The results of these analyses are shown in Table 3. Table 3: ultimate strength of plates under compressive X-Y-direction loading by considering different pit depth Case DOP (%) Loading Ratio Pit Depth (mm) US (MPa) Case DOP (%) Loading Ratio Pit Depth (mm) US (MPa) 35 0% 1:1 0 87.65 36 17.87% 1:1 0.5 81.905 44 30.4% 1:1 0.5 86.155 37 17.87% 1:1 1 73.835 45 30.4% 1:1 1 76.795 38 17.87% 1:1 1.5 69.875 46 30.4% 1:1 1.5 71.495 39 17.87% 1:1 2 71.02 47 30.4% 1:1 2 69.015 40 17.87% 1:1 2.5 68.32 48 30.4% 1:1 2.5 68.045 41 17.87% 1:1 3 66.565 49 30.4% 1:1 3 62.87 42 17.87% 1:1 3.5 64.845 50 30.4% 1:1 3.5 62.445 43 17.87% 1:1 4 62.11 51 30.4% 1:1 4 57.58 Figure 2: ultimate strength of (a) case #45 (b) case #51 Using the results of cases #44-51, which are shown in Table 3, the relationship
between different pit depths and different ultimate strength of plates are calculated (Table 4). Table 4: percent reduction in ultimate strength (case 44-51) Pit Depth (mm) 0 0.5 1 1.5 2 2.5 3 3.5 4 Ultimate Strength (MPa) 87.65 86.155 76.795 71.495 69.015 68.045 62.87 62.445 57.58 Percent Reduction (%) 0 1.7 12.38 18.4 20.7 21.8 27.6 28.7 35 The relationship between pit depths of plates with age is experimentally collected in [8], these results are used to find the relationship between age and reduction of ultimate strength (Table 5). Table 5: age vs. reduction of ultimate strength (Experimental results from [8] Copied with permission) Age (years) 0% to 1.7% 1.7% to 12.38% Reduction of ultimate strength (%) 12.38% to 18.4% 18.4% to 20.7% 20.7% to 21.8% 21.8% to 27.6% 27.6% to 28.7% 28.7% to 35% 11-12 20 5 0 0 0 0 0 0 12-13 29 5 9 0 0 0 0 0 13-14 25 28 30 2 0 0 0 0 14-15 4 5 0 0 0 0 0 0 15-16 31 14 10 3 2 0 0 0 16-17 17 8 5 2 1 1 0 0 17-18 103 2 2 4 0 0 0 0 18-19 35 26 39 9 4 3 0 0 19-20 137 20 12 8 9 2 0 1 20-21 179 62 22 13 17 2 0 0 21-22 114 116 28 26 7 6 0 0 22-23 52 57 5 12 7 5 3 0 23-24 75 49 12 5 3 5 0 0 24-25 59 42 10 2 0 0 0 0 25-26 40 50 49 59 40 2 2 3 26-27 8 15 2 0 0 0 0 0 Using Matlab Distribution Fitting Tools, the relationship between ultimate strength reduction of plates and the age of structure is found and illustrated in Figure 3.
Figure 3: change in ultimate strength reduction percentage for different age of the plate
5. Conclusions In this study, the ultimate strength of diverse steel plates with different loading ratios, DOPs, and pit depths were obtained by using numerical analysis. Using the obtained ultimate strength, the relationship between the plate s age and the ultimate strength reduction percentage was found. By considering the evaluation results, some design guidelines for ultimate limit state evaluation of steel plates were made. Acknowledgement This work was supported by the Human Resources Development program (No. 20113020020010-11-1-000) of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea government Ministry of Trade, Industry and Energy and by Leading Foreign Research Institute Recruitment Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (No.2013044133). References [1] IACS. (2006), Common structural rules for double hull oil tankers. [2] IACS, C. (2006), Common Structural Rules for Bulk Carriers. [3] ISO, I. (2006a), CD 18072-2: Ships and marine technology-ship Structures-part 2: Requirements for their Ultimate Limit State Assessment International Organization for Standardization, Geneva. [4] ISO, I. (2006b), FDIS 18072-1 Ships and marine technology-ship Structures-part 1: general requirements for their limit state assessment International Organization for Standardization, Geneva. [5] Paik, J. K., Kim, B. J., & Seo, J. K. (2008a), Methods for ultimate limit state assessment of ships and ship-shaped offshore structures: Part I Unstiffened plates Ocean Engineering, 35(2), 261-270. [6] Paik, J. K., Kim, B. J., & Seo, J. K. (2008b), Methods for ultimate limit state assessment of ships and ship-shaped offshore structures: Part II stiffened panels Ocean Engineering, 35(2), 271-280. [7] Paik, J. K., Kim, B. J., & Seo, J. K. (2008c), Methods for ultimate limit state assessment of ships and ship-shaped offshore structures: Part III hull girders. Ocean Engineering, 35(2), 281-286. [8] Paik, Jeom Kee, and Do Kyun Kim. "Advanced method for the development of an empirical model to predict time-dependent corrosion wastage." Corrosion Science 63 (2012): 51-58.