LOCAL AND GLOBAL ANALYSIS OF LARGE MOTORYACHT SUPERSTRUCTURE. D. Boote, G. Vergassola, University of Genoa, Italy

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1 LOCAL AND GLOBAL ANALYSIS OF LARGE MOTORYACHT SUPERSTRUCTURE D. Boote, G. Vergassola, University of Genoa, Italy SUMMARY The superyacht manufacturing industry is currently facing big challenges, mainly related to the present economic crisis. Manufacturers are then competing on the ground of better and more aesthetic external and interior designs. This trend often leads to structural strength related issues, which can compromise the static or dynamic stability of superyacht hull. In several instances, the aforementioned fact is met, as in large openings and docks to recover tenders, the enlargement of windows to allow for better lighting of internal living spaces. So, for what the hull is concerned, large windows replaced small portholes on the yacht sides at mid length, rising non trivial problems about longitudinal strength. The same trend appeared on superstructures sides where traditional windows have been enlarged till to became glass doors extended from deck to deck which allow passengers to enjoy full sea landscapes. Despite the positive effect on the general design performance, this nice innovation implies serious structural problems. In fact in side areas where these doors are fitted the only structural elements are represented by very slender vertical stiffeners. The combined action of bending and compressive loads, together with the fact that superstructures are usually made by aluminium light alloy, can be the cause of buckling phenomena with severe consequences on structure and glass integrity. In this paper the contribution to steel hull strength of light alloy superstructures with large openings is studied by the finite element approach. A deep investigation of local strength of the superstructure has been assessed as well. NOMENCLATURE A i: Area of i-th part of a section [mm 2 ] D: Ship s construction height [m] E: Young s Modulus [N mm -2 ] G: Shear Modulus [N mm -2 ] H sl: Permissible wave height [m] I: Momentum of inertia [mm 4 ] L: Ship s length [m] v: Ship s velocity [m s -1 ] y : Distance between centre of gravity of i-th part of section and global neutral axis [mm] y gi: Distance between centre of gravity of i-th part of a section and a fixed axis [mm] ν: Poisson s Ratio ρ: Density [t/m 3 ] σ u: Ultimate tensile strength [N mm -2 ] σ a: Allowable strength [N mm -2 ] η xs: Bending efficiency in term of stresses η xd: Bending efficiency in term of displacements 1 INTRODUCTION The role of superstructures in superyacht strength has become more and more relevant in last years because of their large extension; even if they are usually constructed in aluminium light alloy, in order to reduce the global displacement, their contribution to the hull strength cannot be neglected. 1

2 The response of upper decks to longitudinal and torsional stresses can be summarized in two typical behaviour types: if superstructure role is neglected, stresses acting on hull became greater, unloading higher decks, which commonly have lower ultimate strengths. On the other hand, considering a fully effective superstructure, global strain are reduced due to the greater momentum of inertia; in this case, stresses acting on the higher deck are very relevant, and can cause several failure phenomena, i.e. yielding, buckling, vibrations, etc. There are several papers in literature dealing with hull superstructure interaction, like those by Caldwell (1957), Johnson (1957), Chapman (1957) and Albertoni (2000). Caldwell (1957) presented a formula for the direct calculation of bending efficiency of superstructures, comparing stresses on large deckhouse to the classic beam theory. Nevertheless, as stated by Zanic (2005), classic beam theory cannot be fully implemented for these purposes, even because transversal frames of modern yachts is, as already pointed out, composed by different materials. Moreover, the necessity of large opening on upper decks, in order to guarantee wide external view and bring natural light inside the vessel, reduces scantling to the minimum imposed by regulations. In addition, the scantling of plates and beams according to classification society rules is not as simple as for the hull: the presence of doors and windows make the calculation of beam s span and effective breadth more complicate. In the paper herein presented, the bending efficiency has been analysed by using finite element analysis (FEA) on a modern 45 meter long megayacht, with a steel hull and an aluminium light alloy superstructure. The structural response to local loads of megayacht s superstructure has been deepened as well 2 THEORETICAL APPROACH TO THE BENDING EFFICIENCY OF SUPERSTRUCTURE 2.1 Hull Superstructures interaction The role of superstructure in the structural response to global bending moment, as stated by Caldwell (1957), strictly depends on the superstructure s length compared to the hull. As shown in Fig. 1.a, if superstructures have a similar length to the hull, the longitudinal stress pattern on the entire structure can be easily compared to the classic beam theory behaviour; that is to say that longitudinal stress depends, linearly, on the distance to the neutral axis. Figure 1: Longitudinal stress distribution in case of a superstructure s length comparable to hull 2

3 Fig. 2 clarifies the longitudinal stress distribution of a superstructure with reduced length; in this case, the pattern is no more globally linear with the distance to the bending neutral axis. The new stresses distribution highlights an opposite in sign response to bending load between hull and superstructure. Figure 2: Longitudinal stress distribution in case of a superstructure s reduced length compared to hull This behaviour, as already pointed out by Okumoto (2009) and reported in Fig. 3, is due to the shear forces T and vertical reactive forces q, generated by the primary response to global load, which tend to deform hull and superstructure with opposite curvature. This phenomenon does not affect extended deckhouse. Figure 3: Hull-superstructure interaction forces 2.2 Non-linear effects in the hull-superstructures interaction All the aforementioned aspects of hull-superstructure interaction have been deduced by the use of classic hull girder theory, which, by the way, have some restrictive hypothesis, that cannot be neglected. The most important limitation is that longitudinal stresses depend only to the vertical distance with the neutral axis; even if this aspect, as stated by Roy et al. (2008), are generally true for hull structures, the structural behaviour of superstructure does not accomplish this hypothesis for different reasons, as follows: - shear leg effect: as reported in Fig. 4, superstructures extremities are not affected by longitudinal stresses. This aspect afflicts all frame in proximity of free ends, in which stresses are lower than theoretical ones. It can be easily deducted that in this zone, superstructures do not fully cooperate with hull to global bending moment. 3

4 Figure 4: Shear leg effect on longitudinal stress - main deck flexibility: shear and vertical forces, already defined in the previous section of this paper, cause main deck vertical deformation (Fig. 5), that afflicts superstructures sides. Figure 5: Main deck flexibility - structural connection between hull and superstructures: in modern mega and super yacht design, the actual trend for what concerns construction material is to use steel for hulls and aluminium light alloy for superstructures, in order to reduce the global weight of vessels. Different mechanic properties of materials (Tab. I) cause non linear distribution of stresses and deformation in the connection s area in main decks. Table I Materials mechanical characteristics AlMg 5083 Fe430 steel Aluminium light alloy E [N/mm2] υ 0,3 0,33 G [N/mm2] γ [t/m3] 7,8 2,7 σ u [N/mm2] σ a [N/mm2] (welded) 4

5 2.3 Theoretical formulation of banding efficiency In literature, different formulations for bending efficiency have been developed and assessed. Caldwell (1957) analysed the contribution of superstructure to the hull primary response to global loads, developing a formulation based on the reduction of longitudinal stress due to deckhouse cooperation: η xs = F x0 F x F x0 F x1 (1) where F x0 is the maximum stress on the hull at the main deck without superstructure, F x is the max stress on the hull at the main deck with superstructure and F x1 is the max stress on the hull calculated at the main deck using the beam theory with a full effective superstructure. In terms of structural displacement, Mackney (1999) has defined the efficiency η xd: η xd = w 0 w s (2) where w 0 is the maximum displacement of the plain hull (without superstructures) and w s is the maximum displacement of section with superstructure. 3 NUMERICAL APPROACH TO THE BENDING EFFICIENCY OF SUPERSTRUCTURES 3.1 Creation of numerical model The problem of the bending efficiency calculation, due to the non-linear effect aforementioned, can be achieved only by a numerical approach, as also stated by Albertoni (2000) and Zanic (2005). For the aim of this work, a 45 meter long megayacht has been assumed as study case and studied using Finite Element Analysis. The main characteristics of the vessel has been reported in Tab. II and the main frame has been reported in Fig 6. Table II: Main characteristics of the vessel Length overall [m] Breadth Overall 9.10 [m] Waterline Length [m] Depth [m] 4.45 Draught [m] 2.40 Design Speed [kn] Displacement [ton] 445 5

6 Figure 6: Main transversal section (frame 17) Starting from a 3D model, a complete finite element model of the vessel up to the first order of superstructures has been realised (Fig. 7). Figure 7: Finite element model of the vessel Plates and primary stiffeners has been modelled using 2D shell elements (Fig. 8), secondary stiffeners has been created by associating the characteristics of the transversal section to the 1D beam element (Fig. 9). Figure 8: 2D shell element with colorful thickness view Figure 9: 1D beam element 6

7 The global model created for this work is composed by up to elements and nodes. 3.2 Loading and boundary conditions In order to apply the formulation of bending efficiency developed by Caldwell (1957) and Mackney (1999), it is necessary to create pure bending moment loading scenario on the structures, as already stated by Albertoni(2000). For these reasons, a 24 meter slice of the model has been chosen, with enough distance to the main frame in order to avoid integrations error due to free ends effect (Fig ). Figure 10: Bending efficiency calculation s numerical model Figure 11: FE model used for bending efficiency calculation In order to prevent rigid body motion to the structures, which causes finite Element Analysis to fail, two nodes on the neutral axis of the free end section has been constrained to the translation in the X, Y and Z direction and two nodes in the final section has been constrained at the translation in the Z direction. All nodes in the extremity sections are connected to the bending neutral axis using MPC RBE2, as stated by MSC Software Company (2014) elements; this type of constraints allows the distribution of the bending moment applied on one node placed on the neutral axis to all nodes of the section. The complete boundary scenario of the two free end section has been reported in Fig 12 Figure 12: Boundary conditions scenario 7

8 The model has been loaded by pure bending moment, applied on the master nodes of RBE2 element. Its intensity has been calculated from R.I.Na rules (2013), in sagging condition, giving the values of knm. 4 COMPOSITE BEAM THEORY For what concerns bending efficiency, the reliability of FE results needs an accurate calculation of the vertical position of the flexional neutral axis, in order to create a pure bended loading condition. The neutral axis computation, that is very simple for structures made by a single material, has to be improved in order to be useful when beams and complex structures are composed by two different material; for this purpose, the composite beam theory must be used. N.A. Figure 13. Composite beam theory: center of gravity calculation and neutral axis position. The position of the neutral axis h can be determined by recalling that the stress distribution on the cross composite section must fulfil the following equilibrium condition: F x = 0 = A σ b da = A 1 σ b 1 da + A 2 σ b 2 da (3) Remembering that bending stresses are strictly linked to the beam s curvature, eq. (3) can be rearranged: 0 = A 1 E 1 y 1 ρ da + A 2 E 2 y 2 ρ da (4) Being beam s curvature constant in each cross section, eq. (5) can be deducted: 0 = E 1 (y 1 A 1 ) + E 2 (y 2 A 2 ) (5) By some geometrical consideration on the cross section, the vertical position h of the neutral axis can be deducted form eq. (5) and directly calculated from eq. (6): h = E 1 y g1 A 1 +E 2 y g2 A 2 E 1 A 1 +E 2 A 2 (6) where y g1 and y g2 are the distances from the lower side of the section and the gravity center of part 1 and 2 respectively, as shown in Fig. 13. For the vessel under investigation, the vertical position of the neutral axis is 3214 mm above the construction line. 8

9 Longitudinal stress [Mpa] 24 th International HISWA Symposium on Yacht Design and Yacht Construction As a common practice in naval and nautical structural architecture, the calculation of cross section momentum of inertia and, as a consequence, of the neutral axis has to consider only beams, whose extension is up to 90% of the vessel s length. 5 BENDING EFFICIENCY CALCULATION The bending efficiency numerical evaluation has been carried out by linear static analysis on the numerical model aforementioned in Section. 3. In Fig. 14, the stress fringe has been reported. Figure 14: Stress fringe on vessel s structure Because of the significant variation of the momentum of inertia in each transversal frame, the calculation of the bending efficiency has been accomplished in each cross section. This investigation allowed authors to better understand the contribution of glazing surface in a subsequent stage of this work. In Fig. 15, the variation of F x and F x0, as defined in Section 2.3, is reported Figure 15: Variation of stresses values with or without superstructure As it can be deducted from Fig. 15, the cooperation of superstructure reduces the level of stress on the vessel s structure. The presence of humps in correspondence of frames 23 and 28 is due to main deck s recesses. In Fig. 16, bending efficiency η xs values have been reported. 50 Frames Fx Fx0 9

10 0,8 0,7 0,6 0,5 η xs 0,4 0,3 0,2 0, Frames Figure 16: Bending efficiency η xs evaluation. From Fig. 16, it can be deduced that the superstructure s cooperation is included between 55% and 70%; these results are in compliance with what affirmed by Zanic (2005), for what concerns bending efficiency of a cruise ship, which, by the way, is the typology of vessels that can be considered more similar to a megayacht because of their large opening in deckhouses sides. The mean η xs value can be easily calculated by the mean values theorem; η xsm = L1 L0 η xs (x)dx L 1 L 0 = 0.62 (7) A similar evaluation has been made in order to calculate the bending efficiency η xd by Mackney s (1999) theory and results have been reported in Fig. 17 2,5 2 1,5 η xd 1 0, Frames Figure 17: Bending efficiency η xd evaluation It must be noted that Mackney s theory defines the bending efficiency η xd as the reduction of displacement between the plain hull without superstructure and the complete structure, so η xd values have to be grater then one. 10

11 6 LOCAL LOAD CASES 24 th International HISWA Symposium on Yacht Design and Yacht Construction In order to verify the local strength of a motoryacht s superstructure, a deep Finite Element Analysis must be accomplished as well. For this particular study, loading conditions are defined by Classification Societies Rules and Regulations (2013). In this study cases,6 different load cases have been identified (Tab. III). In order to simulate as well as possible the real connection between hull and superstructures, all nodes of superstructures welded to the main deck and hull (such as side plates, pillars, bulkheads, trunks as well as some webs and flanges) have been considered clamped. Table III: Loading conditions Dynamic Analysis Static analysis a CG a T Item (Value) Load Case 1 2 3a 3b 4 5 Static weight x x x x Pressure Deck (0,62 MPa) x Pressure Side (0,98 MPa) x Distributed Outfitting (350 kg/m 2 ) x x x x Sun deck (200 kn) x x x x 20 people stern zone x x 20 people saloon x x 20 people dining area aft exterior x 20 people seating area bow x 6 people stern zone x 6 people saloon x The weight of onboard people has been assumed as 980 N per person. Load cases 3a and 3b are different each other only for the position of people on board; in the first case they are located in the stern and saloon area, while in the second one they are distributed in the bow zone. Since the sun deck has not been included in the model (Fig. 10), it was decided to take into account its total weight by converting it into a distributed force along the perimeter on which the sun deck is welded onto the upper deck. The total weight of the sun deck is equal to 20.2 tons. 11

12 Load case 4 corresponds to a dynamic condition where all loads, including the sun deck weight, had to be multiplied by the vertical acceleration a CG in the XZ vertical plane (expressed in g), according to R.I.Na Rules (2013): a CG = 0,65 C F V L (8) where C F is: C F = [ 0.6 ] 0 (9) Racking load (Fig. 18), i.e. load case 5, has been obtained by applying a transversal acceleration in the YZ plane (again expressed in g) to the static load, as referred in Table III: a t = 2.5 H sl L V L [1 + 5 (1 + V 2 L ) 6 r L ] (10) where r is the distance of the calculation point from 0,5 D and H sl is the permissible wave height. Figure 18: Racking effect in a generic transversal section 7 LOCAL STRENGTH CALCULATION The aforementioned model has been tested, as described in Section I, by using a static linear analysis, being it the most appropriate one for this type of loading scenario, as stated by MSC Software Company (2014). In fact, non linear incremental analysis would have increased computational times and costs without any appreciable results, because materials are linear elastic and isotropic and the loading conditions are not time dependent. 7.1 Stress analysis The first parameter which has been considered in the local strength structural analysis is the stress level acting on plates and stiffeners. The results obtained by FEM analysis were compared with limit values imposed by R.I.Na. (2013), i.e. 110 MPa for aluminum light alloy type 5083 and 220 MPa for type 6082, in terms of Von Mises equivalent stresses. In Tab. IV the results of the comparison are synthetically presented, highlighting maximum Von Mises stresses for each critical element of the superstructure for each loading condition. 12

13 Table IV: Maximum Von Mises equivalent stresses [MPa] Load Case Rule s Member 1 2 3a 3b 4 5 Limits Aft double box beam Aft Trunk Stiffener Bulkhead stringer Saloon Bulkhead Aft Trunk shell Bulkhead shell As it is clearly shown in the previous table, the most critical load case is the first one, i.e. that coming from R.I.Na Rules Deck Pressure loading condition (Load Case 1). Nevertheless it is important to note that this condition does not correspond to a real scenario, since the value of the applied pressure on plates is calculated by using the formulation proposed by Classification Society Rules (2013), and it may not correspond to a realistic condition. Figure 4 shows the Von Mises stresses plot: for what stiffeners are concerned, the stress peak is located where the transverse supporting beam rests onto the pillar. However, the high peak is due to the fact that the load is concentrated into one node, rather than being distributed along the pillar plates and, since the stress reduces very quickly within one element, this peak results to be overestimated (see Fig.19-20). 13

14 (a) (b) Figure 19: Plots of Von Mises equivalent stresses in load case 1: (a) plates and (b) stiffeners. Figure 20: Peak stress located in aft double box beam. 14

15 7.2 Displacement Analysis In the second phase of the result analysis attention has been devoted to the global deformation evaluation. For what displacements are concerned, Classification Society Rules do not propose any limit values, contrary to what generally done for stresses. In this case the structural engineer s experience is needed to select an appropriate safety limit. In this paper, for load cases 1 and 2, i.e. those dealing with loads proposed by R.I.Na., the allowable deformation has been fixed to 1% of the shortest width of the corresponding plate. Load case 3a, 3b, 4 and 5, corresponding to more realistic loads, have a different limitation, namely 0,75% instead of 1%. From the Finite Element Analysis it can be noted that deformations caused only by R.I.Na. side pressure can be considered negligible; this is due to the fact that the glass windows have not been included in the model. By this approach, considering that the ratio of glass/side shell is more or less one half, one half of the pressure on these side structure has been neglected. Even though glazing gluing systems used in yacht manufactures does not guarantee a correct stress transfer between metallic structures and glasses, not considering them could lead to higher values of deformation and stress. By the way, the unique critical zone, i.e. the trunk side door (Fig. 21), highlights that plates in that zone are not enough stiffened. Figure 21: Side displacement plot referred to load case 2. The overall results has been reported in Tab. V, highlighting the displacement, in millimetres, for each critical element of the superstructure, in each loading condition, barring load case 2. Table V: Maximum displacements (mm) Areas Load Case 1 3a 3b Max Limit Max Limit Max Limit Max Limit Max Limit Saloon interior Exterior Deck Dining Exterior Deck Aft Exterior Deck Bow Bulwark Side Plating

16 The two values that are above the 0.75 % (Load Case 3a Exterior Deck Aft and Load Case 4 Exterior Deck Aft) can be considered admissible because the relative deformation between the pillars and the extreme deck has been investigated in the RINA deck pressure case. Table V also highlights the significant role of the racking load in the superstructure strength analysis. In this special case the deformation occurs along the y-axis, contrary to the previous ones where it occurred in the longitudinal direction, as shown in Fig. 22. (a) (b) Figure 22: Racking deformation: (a) global and (b) transversal section. 16

17 The resulting maximum local deformation due to racking of the superstructure s side is about 5mm over a shell height of 750 mm. Although the weight of the sun deck was accounted for in the analysis, it is expected that this deformation will increase once the actual meshed model of the second tier (sun deck) is added, as the vertical centre of gravity of the entire structures will move upward, generating higher transversal bending moment, increasing the global stress on the superstructure s sides. 7.3 Preliminary buckling verification In addition to the usual stress and displacement analysis, a preliminary buckling verification on the side s vertical struts must be carried out as well. The actual trend of super and megayacht is to enlarge glass windows in order to bring natural light inside the vessel and to allow passenger to take advantage of large sea landscapes. This trend leads to a reduction of structural scantling to the minimum imposed by Classification Societies, reducing significantly any safety factor during the structural layout design. On megayacht superstructures sides, structural components are simply vertical slender struts, sometimes reinforced by transversal stiffeners, as shown in Fig. 23. (a) (b) Figure 23: Vertical slender struts on superstructure s sides: (a) global view and (b) strut s structural design. These structural components have to withstand vertical compressive stresses which can lead to buckling failures. It must be noted that the buckling critical stress for slender structures can be significantly lower than material s yielding limit and so structural instability verification becomes mandatory. For a preliminary buckling approach during early design stage, it must be verified that: σ CR σ (11) 17

18 The value of buckling critical stress can be calculated by using the Timoshenko s plates theory (1940): σ CR = k π2 P b 2 t (12) where b is the slender span, t is the plate s thickness, k is a parameter depending on the aspect ratio and the boundary condition of the plate and P is the plate s stiffness defined as: P = E 1 ν 2 t3 12 (13) The study case megayacht does not highlights buckling criticisms in none of the considered load cases; this verification has been performed for the strut shown in Fig. 23, that is the one with the lowest critical load. 8 CONCLUSION The actual trend of yacht design, for what openings are concerned, is a paramount challenge for structural engineers. Reduction of costs involves smaller safety coefficient so that plates and beam are reduced to the minimum according to classification societies. In this scenario, superstructure must be considered as a part of the hull in order to contribute as much as possible to global bending moment. This trend has to be carefully treated because of buckling and yielding phenomena that can occur by using small safety coefficients together with materials such as aluminium light alloy. In this paper, a strength analysis of superstructures in terms of bending efficiency to primary loads has been analysed by using FEM technique, suitable for this kind of investigation. The cooperation of windows has been achieved as well, highlighting the role of adhesive material, which, even though they are considered as structural, cannot assure a complete stress transfer between superstructure and glass, forestalling the collapse of glazing structures, which have low mechanical characteristics. At present, this research is under course by studying the interaction between hull and superstructure made by different material, with particular attention to GRP materials, and developing a non-linear model of laminated glasses and gluing systems. 9 ACKNOWLEDGMENTS The authors wish to acknowledge the personnel of Azimut Benetti Research and Development Centre in Varazze, Italy, and in particular Mr. Carlo Ighina, for their kind availability and assistance in the development of this research. 18

19 REFERENCES 24 th International HISWA Symposium on Yacht Design and Yacht Construction Caldwell J.B., The effect of superstructures on the longitudinal strength of ships, trans. R.I.N.A., Johnson A.J., Stresses in deckhouse and superstructure, trans. R.I.N.A., Chapman J.C., The interaction between a ship hull and a long superstructures, trans. R.I.N.A., Albertoni F., Barbato A., Ivaldi A., Hull superstructure interaction. A naval ship case study, Fincantieri internal paper, Zanic V., Andric J., Preberg P., Superstructure deck effectiveness of the generic ship types a concept design methodology, Maritime Transportation and Exploration of Ocean and Coast Resources, Okumoto Y., Takenda Y., Mano M., Okada, T., Design of ship hull structures, Springer, Roy J., Munro B., Walley S., Meredith A., Longitudinal versus Transversely Framed Structures for Large Displacement Motor Yachts, 20th International HISWA Symposium on Yacht Design and Yacht Construction, Amsterdam, The Netherlands, Mackney M. D. A., Foss C.T.F., Superstructure effectiveness in the preliminary assessment of the hull behavior, Marine Technology, Vol 36, n 1, January R.I.Na., Rules for the classification of yachts designed for commercial use, Genoa, Msc Software Company, Nastran User Guide, Newport Beach, CA, USA, Verbaas S., van der Werff T., Structural design and loads on large yachts, 17th International HISWA Symposium on Yacht Design and Yacht Construction, Amsterdam, The Netherlands, 2002 Timoshenko S., Woinowsky-Krieger S., Theory of plates and shell, McGraw Hill,