Structural analysis of a steel double hull underwater tank, intended for oil recovery from shipwrecks

Transcription

1 76 Int. J. Computer Aided Engineering and Technology, Vol. 5, No. 1, 2013 Structural analysis of a steel double hull underwater tank, intended for oil recovery from shipwrecks D.E. Mazarakos, D.E. Vlachos and V. Kostopoulos* Applied Mechanics Laboratory, Department of Mechanical Engineering & Aeronautics, University of Patras, Patras University Campus, GR Patras, Greece dmazarak@mech.upatras.gr vlahos@mech.upatras.gr kostopoulos@mech.upatras.gr *Corresponding author Abstract: In the present work, the survivability of a submerged structure against loads, imposed by the operational environment, such as hydrostatic pressure is presented. The structure under consideration is a component (buffer bell) of a system called DIFIS that recovers fuel from shipwrecks. It consists of two parts: the reservoir and the floater. The floater is the part that produces the buoyancy force that holds the whole system in place and therefore its structural integrity is crucial for the safety of the structure. The floater is designed as a double hull structure made of steel plates and stiffeners. The task of the structural analysis is to ensure that the floaters double hulls are able to withstand the hydrostatic pressure due to the depth and maintain the needed buoyancy forces. In the present analysis, the strength of the hulls is evaluated for three different scenarios (operational, worst case and accident scenarios). Keywords: FEM; double hull; subsea; HY100 steel; DIFIS Project. Reference to this paper should be made as follows: Mazarakos, D.E., Vlachos, D.E. and Kostopoulos, V. (2013) Structural analysis of a steel double hull underwater tank, intended for oil recovery from shipwrecks, Int. J. Computer Aided Engineering and Technology, Vol. 5, No. 1, pp Biographical notes: D.E. Mazarakos is an Aeronautical Engineer working in AML as an R&D Engineer. He has received his PhD degree from the Mechanical and Aeronautics Engineering Department in the field of Subsea Structures Design. He is the author of two journal publications and eight conference presentations. D.E. Vlachos is a Mechanical Engineer working in AML as a Senior Researcher. He has received his PhD degree from the Mechanical and Aeronautics Engineering Department in the field of Ceramic Composites for High Temperature Applications. He is the author of eight journal publications and more than ten conference presentations. Copyright 2013 Inderscience Enterprises Ltd.

2 Structural analysis of a steel double hull underwater tank 77 V. Kostopoulos is the Director of the Applied Mechanics Laboratory (AML) in the University of Patras. He has an extensive experience in the field of composite materials and structural dynamics. He is the author of 75 journal publications, more than 100 conference presentations and three books in the field of composites. He holds five patents. 1 Introduction The analysis of underwater structures using the finite element (FE) approach is a methodology applied in ship design, offshore and submarine engineering during the last decades. The structural analysis of ship, naval and submarine structures is investigated by researchers such as McKay (Mackay et al., 2011; Radha and Rajagopalan, 2006; Mouritz et al., 2001; Reynolds et al., 1973; Graham, 1995). The hydrostatic and the dynamic pressure due to submersion depth is the main load that the hull of a submerged structure must withstand. In addition, the sea environment is corrosive (salinity) and in the case of the present study, the underwater tank contains oil (leakage from the shipwreck), which is both toxic and corrosive. All these factors could affect the structural integrity of the hull. The main challenge of the present work was to develop a submerged structure, that its component have to meet many contradicting requirements such as predefined general dimensions, limited maximum weight in water, produce adequate buoyancy forces to hold the whole DIFIS system in place, corrosive operational environment due to salt water and oil, need of high safety level during operations together with the low risk of any possible failure (DIFIS, 2006). Thus, the methodology followed for the analysis includes preliminary simplified analytical calculations, FE analysis of sub-models (for parts and components) and finally the FE analysis of the complete buffer bell system. During the preliminary analysis phase, materials and material behaviour models were selected, and the main dimensions were calculated based on stiffness and strength requirements. Then, FE analysis of the system components was performed and the basic structural characteristics were concluded. These results were input to the full scale FE model in order to validate the smooth stress distribution over the several parts of the structure, to perform all the necessary corrective actions and the optimisation with respect to the thickness of the plates and the manufacturing process and finally verify that the double hulls can safely carry the imposed loads. During the worst case scenario, the hull structure has to withstand the extreme operational loads keeping the appropriate safety margin against failure. Plasticity effects nave been considered for this case. 2 Description of the DIFIS system The DIFIS system consists of seven parts and is anchored on the seabed for oil recovery from shipwrecks (DIFIS, 2006, 2007, 2008). A schematic representation of the system is given in Figure 1. These parts are:

3 78 D.E. Mazarakos et al. 1 the buffer bell (BB): an underwater tank for the temporary storing of recovered oil 2 the dome (DM): a conical shaped structure made of a fabric material which covers the shipwreck and drives the collected oil through the riser tube 3 the riser tube (RT): an almost vertical pipe for the connection of the BB to the DM that covers the shipwreck 4 the dome interface unit (DIU): a conical substructure serving as a connection interphase between the RT and the DM structure 5 the mooring lines (ML): cables which support the RT and the DM, and are anchored to the seabed 6 the stiffening rings (SR): disks that connect each part of the RT with the ML 7 the anchoring system (AS): deadweight cement anchors, holding the overall structure to the seabed. Figure 1 The underwater structure (DIFIS system), BB RT, SR, and ML (c) DIU (d) DM and AS (see online version for colours) (c) (d) During the operation phase, the BB is the substructure that produces the upwards force (buoyant force) that keeps the structure in place and prevents it from sinking. This tensioning force keeps the RT almost straight and supports the whole system by means of the ML that run from the BB all the way down to the anchors. The RT is connected to the

4 Structural analysis of a steel double hull underwater tank 79 BB by the ML which run across the whole length of the tube through the SR, until they reach the. In this manner the upward force is not transmitted to the RT as it consists of a number of pipe parts simply stacked and held together due to their own weight. At this point, the DIU is secured between the DM and the RT. The ML run in periphery of the DM and finally attach to the deadweight anchors. In contrast to common offshore structures, this new design for oil recovery is not affected by weather conditions at the sea surface such as waves, storm conditions etc., because it is fully submerged. As a result the structure needs to withstand only the hydrodynamic loads from sea currents and the high hydrostatic pressure due to the operational depth. This is an advantage as the system may need to remain submerged for long periods of time until oil recovery is completed. 3 Description of BB 3.1 BB dimensions The BB is the main element of this underwater structure (DIFIS, 2007), composed of two main parts: the upper and the lower. A schematic configuration of the BB is shown in Figure 2. The upper part is a cylindrical structure with a spherical cup and it is called capacitor (A). The capacitor is actually a tank for the temporary storage of the recovered oil. The lower part, the floater, is a steel structure that consists of parallelepiped (B) and pyramid (C) substructures, of a double hull configuration that held together with connector plates (D). The floater is connected with the capacitor by means of steel tubes (E). The floater transfers the tensioning (upward) force through the steel rods (F) to the first stiffening ring where the ML are anchored (G). Figure 2 The BB parts (see online version for colours)

5 80 D.E. Mazarakos et al. The production of net upward force is the difference between the buoyancy and the weight of the structure. The preliminary calculations and weight estimations (DIFIS, 2006, 2007, 2008) determined that the BB should produce 2000 tons buoyancy in order to retain the whole structure under tension (DIFIS, 2007). Since the heaviest part of the system is the BB and especially the floater, the design challenge was to develop a structure able to withstand the operation loads while keeping the weight limited under a maximum value. The basic external dimensions of the buffer were dictated by its oil storage capacity (based on the functional specifications of the system). The main dimensions are presented in Table 1. Table 1 BB main dimensions BB s part Dimension Capacitor Diameter (mm) 16,000 Cylinder height (mm) 22,000 Cup sphere radius (mm) 8,000 Capacity (m 3 ) 5,000 Estimated weight (tons) 20 Floater External diameter (mm) 26,000 Internal diameter (mm) 16,000 Hull length (mm) 5,000 Hull height (mm) 6,000 Number of pyramid hulls 6 Number of parallelepiped hulls 12 Estimated weight in air (tons) Floater double hull The floater part is essentially an assembly of a number of parallelepiped and pyramid double hull sub-structures. The double hull design was selected because it can be more efficient in terms of weight than the single hull, as far as the stiffness concerns. It also provides increased safety in the case of damage e.g. impact with a mini-sub and is easier to repair. Each hull must be able to withstand the hydrostatic pressure and its weight should not exceed a nominal value. In this work the structural analysis of the hulls is presented for the case of the operational and maximum hydrostatic pressure, in order to investigate the survivability of the structure. The functional specifications for the double hulls of the floater are presented in Table 2.

6 Structural analysis of a steel double hull underwater tank 81 Table 2 Double hull s functional specifications Functional specification Hydrostatic pressure Safety factor n = 1.5 Corrosion environment Value Operational depth 50 m, 0.5 MPa Maximum depth 70 m, 0.7 MPa Sea salinity 35 ppt Withstand the crude oil corrosion Seawater temperature 15 C Extreme loading requirements Withstand the maximum hydrostatic pressure without rupture The pyramid hull is formed of three parts a rectangular and two triangular. In contrast, the parallelepiped hull is consisted of rectangular parts only. Each of these parts is a double hull structure which is connected with the other two. The double hull design is based on a structure, which consists of the outer/inner plates (1), longitudinal stiffeners (girders) (2), transverse stiffeners (3) and stringers (4) attached to the outer and internal plates. The basic dimensions of the double hull are presented in Table 3. Table 3 Dimension Double hull s main dimensions Rectangular part Value Triangular part Overall length (L) (mm) 5,000 5,000 Overall width (W) (mm) 5,000 5,000 Overall height (H) (mm) 6,000 6,000 Vertical distance between hulls (H2) (mm) 1,000 1,000 Girder height (H3) (mm) 1,000 1,000 Transverse height (mm) 1,000 1,000 Stringer minimum height (H4) (mm) Horizontal distance between girders and transverse (L2) (mm) 1,000 1,000 The manufacturing of the double hull structures can me made with typical processes used in ship-building. An effective building sequence is to first weld together the girders and transverse stiffeners and create a rigid frame (Figure 4). The outer plates can then be welded onto the frame (Figure 5). The distances between the various steel plates that make up the structure are properly selected to maintain enough space for the assembly and welding processes (Eyres, 2001).

7 82 D.E. Mazarakos et al. Figure 3 Double hull basic elements, pyramid hull with rectangular part (A) and triangular parts (B) pyramid hull s girders and transverse (c) pyramid Hull s plates and stringers (d) parallelepiped hull with rectangular pats (A) (e) double hull s girders and trans (f) pyramid hull s plates and stringers (see online version for colours) (c) (d) (e) (f) Figure 4 The rigid frame of double hull (see online version for colours) Figure 5 The outer plates, stiffened plate unstiffened triangular plates (see online version for colours)

8 Structural analysis of a steel double hull underwater tank 83 4 Material selection The functional requirements for the BB component have led to the selection of HY100 steel for the double hull construction material. This quenched and tempered grade of low-carbon steel alloy is used in pressure vessels, heavy construction equipment, submarine hulls and large steel structures. It has high tensile strength (yield and ultimate), good ductility, notch toughness, atmospheric and seawater corrosion resistance and very good welding ability. The typical properties of HY100 are presented in Table 4. Table 4 HY100 steel typical properties Property Value Density (kgr/m 3 ) 7,870 Yield strength (MPa) 689 Elasticity modulus (GPa) 205 Poisson ratio ν 0.28 Shear modulus (GPa) 80 However, since this steel grade is used in corrosive and low temperature environment, the material properties for the current analysis are adopted from military standards (US Navy, 1992), making the choice more conservative. The strength properties of HY100 according to the military standards are presented in Table 5. Table 5 HY100 steel strength properties coming from military standards Property Value Military standard specification Yield strength (MPa) 552 MIL-S (plate) Tensile strength (MPa) 793 MIL-S (shapes) 5 Structural design and FE sub-models The design of a structure such as the double hull presented above is not an easy task as there are a number of structural members to be determined. As a first step, structural calculations were made in order to estimate the thickness of the plates, girders, transverse and longitudinal stiffeners considering specific parts of the structure under simplified loading conditions. These simplified conditions allowed the use of analytical calculations that provided an estimation of minimum thickness of the various components. The analytical calculations were also used to calibrate FE sub-models, prior to the full scale FE analysis of the overall double hull structure. The calculations were carried out for the two basic structures the parallelepiped and the pyramid hull. For each component the maximum thickness between the results of the two analyses was adopted for the design. For the preliminary calculations four (4) simplified load cases were considered:

9 84 D.E. Mazarakos et al. 1 The rectangular panel that comprises the side of the parallelepiped hull with the largest dimensions (L = 6,000 mm, L y = 5,000 mm) and the triangular part (a = 5,000 mm, equilateral triangle) are assumed to be homogenous equivalent plates with thickness h (mm) having the same stiffness as the real part. The equivalent plates are considered clamped at the edges in order to simulate realistic boundary conditions (the connection between the hulls). The load is the hydrostatic pressure P at the top surface of the plate. The calculations determine the equivalent moment of inertia required in order to withstand the pressure load. All these steps are presented in Figure 6. For the rectangular part The maximum stress is (Pilkey, 2005) given by σ 2 P* Ly max = 6 L 2 y 2* h * 0.623* + 1 L (1) while, the maximum displacement is given by y * P* Ly max = 5 L 3 y E* h * 1.056* + 1 L (2) For the triangular part The maximum displacement is given (Pilkey, 2005) by y max * P* a = (3) E* h The inertia of the equivalent plate area is given by 3 L* h I equiv = (4) 12 The analysis showed that the loading of the rectangular part is more demanding than the triangular, therefore further calculations are going to be based on the equivalent stiffness obtained for the rectangular part.

10 Structural analysis of a steel double hull underwater tank 85 Figure 6 Double hull design, double hull s rectangular part equivalent plate s boundary conditions and pressure load (see online version for colours) Figure 7 Double hull design, double hull s triangular part equivalent plate s boundary conditions and pressure load (see online version for colours) Table 6 Equivalent plate s inertia and stiffness Value Rectangular part Triangular part Material HY100 steel Maximum hydrostatic pressure (MPa) 0.7 Modulus of elasticity (GPa) 210 Equivalent s plate thickness h (mm) Maximum displacement (mm) Equivalent moment of inertia I equiv (mm 4 ) 5.324E Equivalent stiffness EI equivalent (kn*mm 2 ) 1.1E E+13 2 The equivalent moment of inertia can then be used to design the double hull. The side panel with the largest length (6,000 mm) is selected for the analysis. It is assumed that only the transverse stiffeners carry the imposed load so the thickness of the transverse members is calculated in order to obtain the required moment of inertia. The maximum inertia of each transverse is 3 t* h I max = (5) 12

11 86 D.E. Mazarakos et al. The minimum inertia of each transverse is 3 h* t I min = (6) 12 The total maximum inertia of the transverse in order to withstand the hydrostatic pressure is I tot 7 = I (7) i= 1 max Table 7 The total moment of inertia obtained, exceeds the equivalent value calculated in Step 1. Due to the connection between the pyramid and parallelepiped parts, the girders/transverse have the same thickness on both parts. The thickness of girders and transverse members are compared with the analysis of Step 3 and the largest value is retained. Rectangular part s transverse member dimensions and inertia properties Dimension Value Transverse thickness (mm) t 10 Transverse height (mm) H 1000 Horizontal distance between the transverse (mm) 1000 Minimum inertia of each transverse I (mm 4 ) 8.34E+04 Maximum inertia of each transverse I (mm 4 ) 8.33E+08 Total inertia (mm 4 ) 5.831E+09 Figure 8 The double hull s transverse, location boundary conditions and pressure load for the analysis (see online version for colours) 3 The hull can be considered to follow a cellular configuration. The hydrostatic pressure is applied on the external face of each cell and it is transferred to the girders and transverse members. One may consider that each cell consists of four plates, and assuming each of these plates stands on its own, can check for buckling under the compressive load applied. The critical buckling load of the

12 Structural analysis of a steel double hull underwater tank 87 girder/transverse plates must be greater than the pressure force per plate to accept a safe design. The area of the parallelepiped part is A1 = L* L y (8) The area of the triangular part is ( L Y) A2 = 2* 0.5* * (9) where, Y is the height of triangular part. The pressure force in parallelepiped part is F = P* A (10) P1 1 The pressure force in triangular part is F = P* A (11) P2 2 In each part, there is different number of cells, so the pressure force per cell is given by F = F / n (12) pc P where, n is the number of cell structures. The pressure force per plate is Fpcp = F pc /4 (13) The elastic buckling load for a simply supported plate is given by (Timoshenko and Krieger, 1959) N cr where, π 2 * D = K* b 3 E* t D = 12* 1 2 ( v ) is the plate rigidity and (14) (15) 2 n* b a K = + (16) a n* b with n = number of buckle-waves (buckling mode). The minimum elastic buckling load is calculated for n =1. The buckling calculations indicated that the thickness of girders and transverse elements must be increased following the results of Step 2, therefore a thickness of 12 mm was adopted. According to the analysis a safety factor near 2.5 against buckling is obtained.

13 88 D.E. Mazarakos et al. Table 8 Double hull s buckling analysis Part Rectangular Triangular Hydrostatic Pressure P (MPa) Area A (mm 2 ) 3E E+07 Pressure force Fp (kn) 2.1E E+04 Number of cells n Pressure force per cell Fpc (kn) 700 1,380 Pressure force per plate Fpcp (kn) Modulus of elasticity (GPa) Plate height a (mm) 1,000 1,000 Plate length b (mm) 1,000 1,000 Plate thickness t (mm) Buckling critical load (Ncr) (kn) Buckling safety factor The last elements of the double hull that have to be analysed are the outer and inner skins. More specifically, considering the cellular configuration, the outer faces of the cells. These parts consist of rectangular stiffened plates in the case of both hulls and un-stiffened triangular plates in the case of the pyramid hull. These plates must withstand the hydrostatic pressure locally and transfer the reactions to the girders/ transverse plates. It is assumed that they are fixed at four edges. The maximum stress due to the pressure load is calculated. The evaluation of the stress field is based on analytical calculations and FE sub-models. For unstiffened (Pilkey, 2005) rectangular plate, the maximum stress is located at the centre and it is given by the expression: σ 0.75* P* b = h *1.61* + 1 L max 3 2 b 2 For a stiffened plate (the cell structure is assumed to be undeformed) the maximum stress at the centre of plate is given by (US Navy, 1992): (17) σ max 2 P* b * ra = * (18) i b The triangular plates are presented only in the triangular part, in specific locations wherever it is necessary to accomplish the structure configuration. Due to the fact that these plates remain unstiffened, their thickness is checked with a FE sub-model in order to check the maximum stress they sustain. For unstiffened simply supported triangular plate the maximum stress is located at the centre. The stress and displacement contours are presented in Figure 9.

14 Structural analysis of a steel double hull underwater tank 89 The thickness of the triangular plate considered to be same as the stiffened plates. From the results concluded, the maximum stress in triangular plates is 370 MPa and the maximum displacement is 3.50 mm, values that are fully accepted. Figure 9 The cell like structure, location on pyramid hull location on parallelepiped hull (c) pressure force per plate on cellated structure (d) buckling analysis of plate (force and boundary conditions) (see online version for colours) (c) (d) Figure 10 The double hull s stiffened plate boundary conditions and pressure load (see online version for colours)

15 90 D.E. Mazarakos et al. Figure 11 Pyramid hull s triangular unstiffened plates, location boundary conditions and pressure load (see online version for colours) Figure 12 Triangular unstiffened plate contours stresses in Pa displacements in m (see online version for colours) 6 Full scale FE model The double hull floater of the BB structure was modelled and analysed in Patran/Nastran commercially available FEM code. Due to the fact that the thickness to length ratio of all members is not less than 1/20, shell elements were used for all the components (plates, girders, transverse elements, and stringers) (Kilroy, 1996). A safety factor of 1.5 was adopted for the operational phase analysis as it is common for subsea structures. In current analysis the survivability at the operational and maximum depth was investigated, so the maximum yield stress must not be exceeded. The thickness of each component used in the FE model is presented in Table 9. The FE model of double hall is presented in Figure 13. A total number of 200,000 4-node (quad) elements were used for the parallelepiped structure and 100,000 4-node (quad) elements were used for the pyramid hull. Due to the height of the plate stringer a minimum of three elements per width were used for the accurate calculation of stress field. The double hull is clamped at the eight surfaces (where one hull is attached to the other with the connector plate). The hydrostatic

16 Structural analysis of a steel double hull underwater tank 91 pressure is applied as a uniform load on the element faces. The material is modelled as linear elastic and the analysis is linear static. The Nastran solver was used for the calculations. Table 9 Components dimensions for FEM analysis Parameter Value (mm) Thickness of plate (external hull) 10 Thickness of plate (internal hull) 10 Thickness of girders 12 Thickness of transverse 12 Thickness of stiffeners 8 Figure 13 Double hull mesh, parallilepiped hull mesh the number of elements at the width in parallelepiped hull (c) pyramid hull mesh (d) the number of elements at the width in pyramid hull (see online version for colours) (c) (d) 7 FE model (accident scenario) The accident scenario is an extreme operation condition, during which the double hull must withstand the hydrostatic pressure in the case an external plate is damaged. This could happen during the deployment phase of the system or when the BB is in operational depth and a part of the deployment equipment impacts and damages the hull,

17 92 D.E. Mazarakos et al. (for example, the collision of a ROV with the hull structure). In such a situation, the hydrostatic pressure is acting on the internal components. The survivability of the hull structure is critical in such a case, since further damage due to hydrostatic pressure could jeopardise the operation of the system as the buoyancy can be gradually decreased as compartments are flooded. To analyse this scenario, only one quarter (one side panel) of the double hull was considered. A total amount of 50,000 elements were used in this model. The model is clamped at four edges and a plate of the external hull is missing in order to model the structure after the accident conditions have occurred. The pressure load is applied on the surface of the external hull and at the internal surfaces of the cell under the damaged plate. For this case the material is modelled as non-linear elastic with plasticity and the analysis applied is non-linear quasi-static. The model and the non-linear mechanical properties are presented in Figure 14 and Table 10 respectively. Figure 14 The finite element model of 1/4 double hull (see online version for colours) Table 10 HY-100 steel mechanical properties for non-linear analysis Parameter Value Modulus elasticity E (GPa) 205 Tangent modulus Ey (GPa) 2.02 Yield strength (MPa) 552 Rupture strength (MPa) Results The results presented in the next are based on the analysis of the three different scenarios (operational, worst and accident). 8.1 Operational scenario (applied pressure 0.5 MPa) The stress and displacement distribution for both basic structural components of the BB, namely parallelepiped hull and pyramid hull, made out of HY100 steel are presented in Figures 15 and 16 respectively.

18 Structural analysis of a steel double hull underwater tank 93 Figure 15 Operation scenario: results for the parallelepiped hull structural part maximum Von-Misses stress in (Pa) and displacements in (m) (see online version for colours) Figure 16 Operation scenario: results for the pyramid hull structural part maximum Von-Misses stress in (Pa) and displacements in (m) (see online version for colours) Figure 17 Operation scenario: results for the parallelepiped hull structural part at middle plane, maximum Von-Misses stress in (Pa) and displacements in (m) (see online version for colours)

19 94 D.E. Mazarakos et al. Figure 18 Operation scenario: results for the pyramid hull structural part at middle plane maximum Von-Misses stress in (Pa) and displacements in (m) (see online version for colours) In order to have a more detailed view of the developed maximum Von-Misses stresses and displacements, the above results have been plotted again for the middle plane of the analysed structural components. These results are presented in Figures 17 and 18. As it can be seen the maximum stress is at the level of 350 MPa for the parallelepiped and 404 MPa for pyramid hull. The respective maximum displacement is 2.41 mm for parallelepiped hull and 2.19 mm for pyramid hull. 8.2 Worst case scenario (applied pressure 0.7 MPa) The stress and displacement distribution for both basic structural components of the BB, namely parallelepiped hull and pyramid hull, made out of HY100 steel, in the worst case scenario are presented in Figures 19 and 20 respectively. Again, in order to better visualise the developed maximum Von-Misses stresses and displacements, the above results have been plotted again for the middle plane of the analysed structural components. These results are presented in Figures 21 and 22. Figure 19 Worst case scenario: results for the parallelepiped hull structural part maximum Von-Misses Stress in (Pa) and displacements in (m) (see online version for colours)

20 Structural analysis of a steel double hull underwater tank 95 Figure 20 Worst case scenario: results for the pyramid hull structural part maximum Von- Misses Stress in (Pa) and displacements in (m) (see online version for colours) Figure 21 Worst case scenario: results for the parallelepiped hull structural part at middle plane, maximum Von-Misses Stress in (Pa) and displacements in (m) (see online version for colours) Figure 22 Worst case scenario: results for the pyramid hull structural part at middle plane maximum Von-Misses Stress in (Pa) and displacements in (m) (see online version for colours)

21 96 D.E. Mazarakos et al. As it can be seen by the results presented above, in the case of worst case scenario the maximum stress is close to 510 MPa for the parallelepiped and pyramid hull, still away from the conservative value (MIL-S-16216) selected, which gives yield stress of 552 MPa. In both cases a safety factor of 1.5 has been used. The maximum displacement in this case is 5.50 mm, and appears for the pyramid hull. Finally, the total weight of the parallelepiped hull is 41 tons and the respective total weight of the pyramid hull is 20 tons, values which are accepted according to the functional specifications given. 8.3 Accident scenario As mention earlier, in this extreme loading case the assumption that the material may pass to the non-linear elastoplastic region has been made, and due to the large displacements developed in this scenario, a non-linear static analysis has been used. The results of this scenario are based on the maximum stresses that appear in the region of the damage section. Closed to the damaged area the maximum stress could exceed the yield stress, and then the materials would plastically deform. The critical parts are the girders and the transverse parts that form the cellular structure. In the case this substructure collapses, then the sea water will pass to the neighbouring cell substructures. This could lead to the catastrophic failure of the double hull and the final loss of the tensioning force. Based on the analysis, the hull is overstressed near the connection between the rectangular parts. Additional overstressed zones are the unstiffened plates of the pyramid hull. The dimensions of these plates were adopted from the preliminary analysis, so they are not changed by the FE analysis. The results of the non-linear elastoplastic analysis are presented in Figure 23. Figure 23 Accident scenario results, maximum Von-Misses stress in (Pa) and plastic strains of the HY100 steel hull (see online version for colours) The maximum von-misses stresses in this case reach 525 MPa for the operational hystostatic pressure. There is no plastic deformation for the steel and rupture does not occur. The accident scenario changes the stress field around the damage area. The girders and the transverse parts are overstressed in order to withstand the high hydrostatic

22 Structural analysis of a steel double hull underwater tank 97 pressure. The difference between the stresses during the operational and accident scenario is presented in Figure 24. Figure 24 Comparison results, maximum Von-Misses stress in (Pa) for operational scenario and maximum Von-Misses stress in (Pa) for accident scenario (see online version for colours) For the operational scenario, the maximum stress reaches 80 MPa in the middle of the rectangular part of the hull. In contrast, in the case of accident scenario, closed to the damage area the respective maximum stress increases to 400 MPa. This stress value presents at the transverse parts. Since, the transverse member is loaded locally; there is a large difference between the stress field distributions for these two scenarios. 9 Conclusions In this work, structural calculations for the estimation of the main dimensions (thicknesses) were performed and a FE model was built up to predict the stress distribution over the critical zones of a double hull BB structure. The results showed that for all the operational, worst case and accident scenarios, the double hull can withstand the hydrostatic pressure. The maximum weight of the steel hull does not exceed the maximum limit according to the functional specifications, so the required tensioning force is obtained. Future work includes the redesign of the hull from aluminium or composite material such as glass fibre reinforced plastic (GFP) in order to increase the strength to weight ratio. Acknowledgements The authors wish to acknowledge the role of Dr. F. Andritsos, Dr. Juan Catret and Dr. Daniel Grosset (JRC) as co-inventors of the DIFIS patent. The authors also wish to acknowledge the work of the MARIN, IFREMER, SENER, CEA, CYBERNETIX, ISI, SIREHNA and CONSULTRANS that formed the DIFIS consortium. Special thanks to Dr. J.L. Cozijn, Senior Researcher of MARIN and coordinator of DIFIS project.

23 98 D.E. Mazarakos et al. References DIFIS Project FP (2006) Report on Requirements Specification. DIFIS Project FP (2007) Report on Deployment Recovery Procedure. DIFIS Project FP (2008) Early Design of Elements. Eyres, D.J. (2001) Ship Construction, Butterworth and Heinemann, UK. Graham, D. (1995) Composite pressure hulls for deep ocean submersible, Journal of Composite and Structures, Vol. 32, No. 1, pp Kilroy, K. (1996) Nastran/Patran Quick Reference Guide, version 70. MacKay, J.R., Van Keulen, F. and Smith, M.J. (2011) Quantifying the accuracy of numerical collapse predictions for the design of submarine pressure hulls, Journal of Thin-Walled Structures, Vol. 49, No. 1, pp Mouritz, A.P., Gellert, E., Burchill, P. and Challis, K. (2001) Review of advanced composites structures for naval ships and Submarines, Journal of Composite Structures, Vol. 53, No. 1, pp Pilkey, W.D. (2005) Formulas for Stress, Strain and Structural Matrices, John Wiley and Sons, New Jersey, USA. Radha, P. and Rajagopalan, K. (2006) Ultimate strength of submarine marine hulls with failure governed by inelastic buckling, Journal of Thin-Walled Structures, Vol. 44, No. 3, pp Reynolds, T., Lomacky, O. and Krenzke, M. (1973) Design and analysis of small submersible pressure hulls, Journal of Computers and Structures, Vol. 3, No. 5, pp Timoshenko, S. and Woinowsky-Krieger, S. (1959) Theory of Plates and Shells, Mc Graw Hill, New York, USA. US Navy (1992) Salvage Engineer s Handbook, Vol. 1.