1
STRUCTURAL DESIGN OF S/Y DREAM SYMPHONY: THE LARGEST WOODEN
SHIP EVER BUILT
A. Shimell, SP-High Modulus, United Kingdom T. Tison, SP-High Modulus, United Kingdom
H.P. ten Have, Dykstra Naval Architects, the Netherlands ABSTRACT
The Dream Symphony project is a 4- mast staysail schooner which blends classical styling with contemporary design. With a length of 141 meter (463 feet), she will not only be the largest private sailing yacht ever
constructed, but will also be of an all glued laminated wood (GLT) construction, incorporating some composite materials and steel. Initiated by Mr. Valeriy Stepanenko of Dream Ship Victory yachts, the design is a
collaboration between Ken Freivokh Design, Dykstra Naval Architects with SP High Modulus providing vital support on the structural analysis. The yacht is currently under construction at the DSV shipyard in Bozburun, Turkey.
The requirement to use laminated wood as the main building material for a yacht of this size posed several challenges. However, first aim was making sure the structural arrangement provided sufficient strength and stiffness to withstand the forces imposed by hydrodynamic and rigging loads. Due to the unique nature of this project most calculations were done using first principles. Working with RINA, specific requirements were defined, some of which based on non-marine regulations. An extensive material testing program was also conducted to determine the material design properties and account for the very specific nature and variability of wood. After an initial design using a two-dimensional approach by Dykstra Naval Architects, SP-High Modulus was contracted to carry out a full finite element analysis of the boat.
By presenting the design methodology, specific aspects of the laminated wood construction and key findings of the finite element analysis conducted, this paper will illustrate how modern design methods and tools can be applied to design such a unique yacht.
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Table of contents
Abstract ... 1
1.
General project information ... 3
1.1
Project background ... 3
1.2
Large wooden ships: A brief history ... 4
1.3
Environmental impact of glued laminated timber ... 4
2.
Material properties ... 4
2.1
Specific aspects of structural timber ... 4
2.2
Experimental material testing ... 5
2.3
Characteristic timber properties ... 5
2.4
Glued laminated timber ... 5
3.
Global scantling design ... 7
3.1
Main section design ... 7
3.2
Design loads ... 7
3.3
Reserve Factors ... 7
4.
2-d longitudinal strength analysis ... 8
4.1
Bending stress analysis ... 8
4.2
Bending deflection analysis ... 8
4.3
Preliminary longitudinal strength results ... 9
5.
Finite element analysis ... 10
5.1
Introduction ... 10
5.2
Introduction global analysis ... 10
5.3
Mesh ... 10
5.4
Loads & restrains ... 11
5.5
Shell structural analysis ... 12
3 1. GENERAL PROJECT INFORMATION
1.1 Project background
Mid 2007, Dykstra Naval Architects (DNA) was approached by the Dream Symphony shipyard (DSV) to provide design services for the 64,5 meter ‘Michael S. Vorontsov’ (MSV) project. Taking his passion for traditional sailing ships and timber as a construction material, the DSV shipyard was founded in 2005 by Mr. Valeriy Stepanenko. The MSV project was the largest of three hulls being built at that time at the yards facilities in Bozburun, south-west Turkey. With the hull nearing completion as DNA joined the project, design work was performed on the sailplan and deckplan, parallel to calculations on strength and stability to fulfill RINA class requirements.
In 2010, Mr. Stepanenko once again approached DNA with an idea for a ground breaking project: To build the largest sailing yacht in the world, and the largest wooden ship ever built. In collaboration with Ken Freivokh design, a preliminary design of the vessel was prepared and approved by the owner.
Fig.1: Sailplan of the Dream Symphony.
The resulting design consisted of a 4-masted staysail schooner with sleek, contemporary hull lines and a single superstructure. Below, the main particulars are summarized:
Length over all Loa 141 [m]
Beam max. B 18 [m]
Draft (DWL): T 8.0 [m]
Displacement (approx) 4500 [tons]
Sail Area: SA 5000 [m2]
Class, Flag state: RINA, Marshall Islands Table 1: Main particulars
This paper outlines the design considerations and calculation steps that have resulted in the structural arrangement of the yacht. As at the moment of writing of this paper the design process is still very much in progress, all mentioned results and values should be regarded as preliminary and for reference only.
4 1.2 Large wooden ships: A brief history
In the late 1800’s and early 1900’s the largest wooden ships to date were constructed. Used for both trade and navy purposes, 6 ships over 100 meters were built. However, the size of these vessels proved too large for practical operation, and they either sunk due to structural failure or were scrapped due to their limited seaworthiness. [6]
The main reason for these problems lies in the traditional carvel-planking building method of these ships. As their size increased, the thickness of their members also grew. However, being limited to pin or nail connections, the stresses around the joints and connections became very high. This caused the wood to crack and give way around the connections of members and seams of the shell, resulting in large deflections and ultimately structural failure. Another factor could be found in the higher probability of defects in the increasingly larger required pieces of timber, causing weakspots in key members as keelsons, stemposts etc.
To improve the longitudinal and torsional stiffness, steel reinforcing structure was commonly used. A good example of this was the 103 meter ‘USS Pretoria’, built in 1987, that was fitted with steel keelson plates, knees, and cross bracing. But even with these reinforcements, the lack of rigidity was never fully solved.
1.3 Environmental impact of glued laminated timber
Especially in recent history, the use of hardwood has been subject of discussion. In essence, wood can be regarded as a renewable and sustainable construction material when grown and harvested in a controlled way. Before committing to the project, DNA on behalf of DSV commissioned the Dutch technology institute TNO to perform an environmental impact analysis to qualify the impact of the construction and lifespan of the Dream Symphony project. [5]
In order to provide a frame of reference, this study was performed for a timber, steel, glassfibre epoxy (GRE) and aluminum hull. To see the specific effects of the timber, the impact of the production phase was analyzed for multiple wood types (softwood, hardwood) and harvesting methods (plantation, managed forest, rainforest). The managed forests hardwood showed to have an impact very much comparable to that of an aluminum yacht. Based on this study, DSV will solely use certified Iroko timber from managed forests (large areas of rainforest where a limited number of trees are harvested over a period of time).
2. MATERIAL PROPERTIES
2.1 Specific aspects of structural timber
Although the MSV project provided valuable experience in the field of wooden yachts, the structural calculations on this project were mainly performed using RINA scantling formulas from the guidelines for wooden charter yachts. As the size of the Dream Symphony project prevented the use of these formulas, a direct calculation approach was agreed with RINA. This called for a specific approach to deal with the some of the key aspects of wood:
Wood is anisotropic, meaning it has (significantly) different properties in relation to the grain direction.
Wood has different values for tensile and compressive and bending strength..
The strength of wood can show large variations within the supplied material, depending on moisture content, internal defects and density.
Load duration: Care is to be taken to limit the amount of sustained loading of timber, as the strength of the material can decrease over the years.
In the absence of dedicated class guidelines for the quantification of these aspects, the EN-338 standard was applied [2]. The EN standards are widely used in civil engineering, where timber is more commonly used as a construction material. The EN-338 regulations are based on a system of strength classes, where the wood is assigned to a specific class based on its bending strength, density and elasticity modulus. All other mechanical properties can then be derived as a function of these properties. As the EN formulas are based on very large amounts of strength experiments, this reduced the number of properties that needed to be tested for the project.
5 2.2 Experimental material testing
In order to study the strength of the Iroko timber acquired by the shipyard, a large set of material testing
experiments have been conducted at TNO in the Netherlands and Messina University on Sicily, Italy. Main goals of these tests were to determine the strength and stiffness properties for further application in the EN strength class formulas and to study the relation between the strength of the solid timber and the glued laminated timber. Testing samples consisted therefore of solid wood, uni-directional laminated wood and multi-directional laminated wood. The samples were tested under bending and tension loads, providing values for tensile/bending strength and elasticity/shear moduli. The tests also provided more insight in the behavior of the wood under load, showing for instance the strain curves.
As the strength and application properties of the resins and adhesives are also of great importance for the strength of the finished laminate, these products were also subject to laboratory testing. According to EN guidelines, the inter-laminar shear strength and permissible assembly time were tested by resin supplier Duratek under supervision of RINA.
2.3 Characteristic timber properties
As the properties of timber can show large variation, the EN regulations require that material properties that resulting from strength experiments are to be corrected to ‘characteristic values’. This process involves the following steps [3]:
Calculate the 5-percentile value: This value represents the 5th weakest sample in a set of 100 samples.
Correction for dimensions of the tested samples, in reference to the standardized sample dimensions
Correction for the amount of tested samples to take into account statistical variation.
After these corrections, the characteristics can be used in the formulations listed in the EN 338 standard to calculate the characteristic values of non-tested properties. (shear, compression, etc.)
2.4 Glued laminated timber
Compared to solid wood, GLT offers a number of key advantages:
Wood can be orientated within the laminate to align with the local load direction, using the strength of the timber in an optimal way.
The large number of thinner layers reduces the risk and effect of any defects in the wood. This is commonly referred to as the dispersion effect.
The effect of joints between individual laminations is less critical, as the surrounding laminations will reinforce the locally weakened layer.
The strength of GLT compared to solid wood is illustrated in the graph below. When testing a large set of samples with identical cross sections, the GLT will have approximately the same ultimate strength as the solid timber it is constructed of. However, the number of samples with a higher strength value within the set of samples will be much higher. Because of this phenomenon, often described as the lamination effect, the EN reserve factors applied for GLT are slightly lower than those being applied in solid wood construction.
Fig.2: Performance of glued laminated timber compared to solid wood.[1] Strength F re quenc y Glued Laminated Timber Solid Timber Difference in mean value Difference in 5th percentile
6 Using the characteristic strength and stiffness properties of the individual layers, the combined properties of the multi-directional laminate had to be calculated. These properties, as a function of the angle between the load and grain direction, are found using a relationship know as the Hankinson formula [1]:
For strength properties:
(eq.1)
For stiffness properties:
(eq.2)
As can be seen, the amount of both strength and stiffness decreases very rapidly as soon as the angle between load and grain direction increases. The last step is formed by applying the resulting properties for each individual ply to determine the combined properties of the shell laminate using classical laminate theory. For this, the maximum strain for each layer is found by dividing the tensile and compression strength by the E-modulus:
(eq.3)
Then, the equivalent E-modulus of the laminate (Es) is found by calculating the weighed average of the individual E-moduli by layer area (A) within a strip of laminate:
∑ ∑
(eq.4)
As the strength of the lamimate will be limited by the layer with the lowest permissable strain (‘first ply failure’), the lowest value within the laminate is multiplied with the equivalent E-modulus:
(eq.5)
The resulting design values are presented in the table below:
Characteristic wood properties:
Bending stength f m,k,l 46.9 [Mpa] *
Tensile strength f t,k,l 28.1 [Mpa] **
Tensile strength perp. f t,90,k 4.0 [Mpa] *
Compressive strength f c,k,l 28.2 [Mpa] **
Compressive strength perp. f c,90,k 8.3 [Mpa] **
E modulus mean E 0,mean 13.0 [Gpa] *
Characteristic Values:
E modulus long. E 0,05 10.9 GPa **
E modulus perp. E 90,mean 0.9 GPa **
* Based on tests ** Derived using EN 338
Characteristic laminate properties (longitudinal):
Bending stength f m,k,l 25.1 [Mpa]
Tensile strength f t,k,l 16.1 [Mpa]
Compressive strength f c,k,l 16.2 [Mpa]
E modulus long. tensile / compr. E 0,05 6.3 [Gpa]
E modulus long. bending E 0,05 9.8 [Gpa]
7 3. GLOBAL SCANTLING DESIGN
Using the design properties of the glued laminated timber, the longitudinal bending moment and the required reserve factors, a first estimate of the global scantlings could be made and checked for stresses and deflections.
3.1 Main section design
The scantling design started with the development of a main frame section. The primary considerations for this stage are summarized below:
Create continuous members at the outer fibers (maindeck planking & girders, beamshelf and keelson) of the section to take the longitudinal bending moment. As tensile and compression will be the major contributors to the stress in these parts, they are therefore constructed solely of longitudinal orientated laminations.
Design the shell to create enough sectional area to account for sufficient longitudinal stiffness. As the shell will also be subject to shear and torsional forces, approximately 50% of the thickness is formed by laminations running in 45 and -45 degrees direction to the longitudinal axis. In order to withstand the higher hydrostatic and hydrodynamic forces, the lower part of the shell has a thickness of
approximately 1,6 times that of the upper part.
To avoid hard spots at the end connections of frames, large radiused knees are placed at maindeck and tweendeck level and laminated keelfloors are positioned over de keelson and bottom ends of the frames.
To protect the wood laminate, an outer sheeting of glass fibre laminate with a thickness of approximately 8mm will be applied.
3.2 Design loads
In order to quantify the longitudinal bending moment, the following design loads were calculated:
Still water bending moment, based on preliminary weight studies and buoyancy distribution.
Rule wave bending moment, as calculated using the RINA regulations.
Operational or design wave bending moment, calculated by the buoyancy distribution of a actual wave shape. For this scenario, a wave length equal to the waterline length is taken, and the height calculated using a formula from the RINA regulation for charter yachts. This results in a wave height of 6.3 meter for a wavelength of 141 meter.
Rigging loads for several operational sailing conditions, calculated using an in-house developed method for determining rigging loads.
3.3 Reserve Factors
To account for the effects of load duration, the EN Eurocode 5 regulations have been applied [4]. These rules give a reserve factor, based on duration type of the load. Therefore, a number of loadcases have been defined, consisting of combination of the design loads mentioned above:
Duration: Loadcase: Reserve factor:
Permanent Still water bending moment (light ship) 2.3
Long term Still water bending moment (Full load) + Static rigging forces 1.9 Short term Design wave bending moment + working rigging forces 1.8 Instantanious Rule wave bending moment + Max rigging forces 1.4 Table 3: EN Eurocode 5 reserve factors based on loadcases and durations.
8 4. 2-D LONGITUDINAL STRENGTH ANALYSIS
4.1 Bending stress analysis
In order to perform a first check on the mainframe scantlings, a 2-dimensional approach was applied to study the bending stresses in the longitudinal structure. Due to the 45/-45 degree laminations within the shell laminate, the mechanical properties of the shell and deck planking are different to those of the longitudinal members (keelson, stringers, beamshelf, girders). To account for this, the properties of the cross sections of both types of structure are combined into an equivalent main section:
Fig.3: Main section showing combined neutral axis position for multiple E-modulus laminates. The position of neutral axis of combined section can be written as:
(eq.6)
In which Es and Em are the specific E-moduli of the uni- and multi directional laminates. The corrected moments of inertia for combined neutral axis position are then calculated by:
(eq.7,8)
Taking the EI of combined cross section by using:
(eq.9)
the resulting stresses at any position in the section can then be found by:
(eq.10,11)
4.2 Bending deflection analysis
As deflections are of great interest, a simplified deflection calculation was also made. This was performed by dividing the vessel in beam segments of 3 meter length and calculating their individual deflection by the radius of deflection. Using the calculated bending moments and geometric properties along the length of the hull, a calculation of the deflection could be made.
Using the local bending moment and stiffness (E x I) of each segment, the radius of curvature (ρ) can be calculated:
(eq.12)
The angular deflection (ϕ) is derived from the segment length (s) and the radius of curvature:
(eq.13)
Am As
9 The angular deflection at the end of the section is than found by:
, in which ais the angular deflection at the end of the previous section.
(eq.14)
The actual vertical displacement is calculated using:
(eq.15)
in which U1 is the vertical deflection at the end of the previous section.
Fig. 4: Schematic representation of the radius of curvature parameters 4.3 Preliminary longitudinal strength results
Below, the compressive and tensile stress values and the attained reserve factors for the design wave bending loadcase are shown. Please note that the attained reserve factors are shown for shell laminate in compression at the lowest vertical position, as this produces the lowest factors.
Frame #: s deck s bottom Att. reserve factor Req. reserve factor
[-] [Mpa] [Mpa] [-] [-] 14 3.72 -3.39 4.66 1.80 28 5.87 -5.20 3.04 1.80 42 8.52 -7.65 2.06 1.80 56 8.19 -7.11 2.22 1.80 70 4.84 -5.23 3.02 1.80
Table 3: Bending stress results for a 6.31m. design wave + rigging loads for RM30
For the same loadcase, the simplified deflection calculation results in the longitudinal deflection curve below:
Fig. 5: Longitudinal deflection curve for a 6.13m. design wave + rigging loads for RM30 0,00 0,20 0,40 0,60 0,80 1,00 1,20 0 20 40 60 80 100 120 140 160 D ef el ct io n [ m] Length [m] >
10 5. FINITE ELEMENT ANALYSIS
5.1 Introduction
SP-High Modulus, the marine business of Gurit, was contracted to support DNA in designing the yacht’s structure. As well as finite element analysis (FEA), SP-HM will also provide detailed engineering support and advice regarding marine wood structures. Two critical aspects were identified: the global behaviour of the yacht, and the definition of the hull shell structure to resist slamming loads. Both subjects will be treated independently and in the following chapters.
5.2 Introduction global analysis
The global analysis is aimed at studying the behavior of the boat when sailing. Typically, this analysis is carried out to look at the stresses and deflection when the boat is sailing in realistic steady state conditions. The loads applied are: rig tension, accelerations and buoyancy. Such an analysis is carried out for large yachts and ships and is therefore well documented [7]. Three main questions are of interest: is the hull strong enough to take the global loads? Is the hull stiff enough in bending and torsion? Are the hull and deck stable enough to resist the bending compressive stresses?
5.3 Mesh
Being a leading structural engineering consultancy in the marine industry for composite structures, SP High Modulus is used to dealing with highly orthotropic and complex structures. In many respects, wood behaves in a similar way as a ply of unidirectional composite fibre. Given the level of complexity of the design, it was deemed necessary to conduct the global analysis using FEA. FEA allows us to calculate the stiffness of the structure accurately and to calculate the strains in every ply at any location. FEA is now widely used and proven to be a reliable tool when used appropriately.
A model of the yacht’s structure was built using shell, solid and rigid elements. The relevant wood laminates were then applied in relation to a global orientation vector to represent the actual grain direction of the wood. A draping effect simulation could have been conducted to account for the actual grain direction of the hull planks. At this stage, the problem was simplified and classical laminate theory was used to look at the influence of the planks alignment on material properties. Most marine structures can be treated as thin walled structures and therefore modeled using shell elements. In this case though, a number of parts required special attention due to their proportions and the variation of their section along the length of the boat: the keelson, main deck beam shelf and stem. For these, it was decided to use solid elements. While the frames could have been modeled with beam elements, or shell elements normal to the hull surface, it was decided to treat them simply as a thicker part of the hull laminate. This greatly simplified the process of orienting the material properties which would have had to be defined for all frames while representing their stiffness correctly. A simple hull extrusion was built to validate the modeling method. In building the global model, the global ply method of defining laminates has also been used, which helps generate properties when different laminate areas overlap each other during the meshing process.
For the boat to be in equilibrium, representing the yacht’s mass distribution in the FE model is also paramount: the mass distribution, longitudinal centre of gravity and vertical centre of gravity must be replicated accurately. Part of the yacht’s displacement is already integrated in the properties applied via the density of wood (structural components). A non-structural mass in ton/m2 can also be added when necessary to replicate fairing, insulation, etc. Local point masses were added for the rigs, engines and heavy equipment. Finally, masses were applied at each hull frame to replicate the mass of the remaining components and their lengthwise distribution. Some simplification here can be made without altering the results drastically, it was decided to apply all added mass at the vertical centre of gravity required to obtain the required yacht global centre of gravity.
Introducing the rig loads in the structure is another key area. At this stage of the design process, chainplates were still being worked on and therefore rigid elements were used to introduce point loads. The model can be further
11 refined later on if required, or local models extracted for more analysis. The following figures show an overall view of the global model (with main shells removed to show stiffening members) and a typical close up view (hull shell hidden). In both cases, element thickness is not represented.
Fig. 6: Overall view of global FEA model
Notice that modern computers and powerful meshing tools such as Hypermesh, make it now more efficient overall to model a relatively detailed global model rather than to rely on too many idealizations. For information, element size on figures shown is 200mm.
5.4 Loads & restrains
Several load cases were defined: they cover different sail sets and wave profiles corresponding to matching sailing conditions. These loads were defined by DNA in relation with RINA. Loads were applied as point loads, pressure (for the buoyancy) and gravity. Specific tools have been developed to deal with the scale of such a large
12 project, mainly to make repeatable tasks automatic, or to simplify the set-up of the model. The following picture shows the pressure contour on the hull bottom at 30 degrees of heel in flat water.
Fig. 7: Buoyancy distribution on the shell at 30 degree heeling angle.
Provided the loads applied are in equilibrium, restraining the model can be done efficiently at rig points [8]. At the time of writing the paper, much of the global analysis remains to be done however a first case has been run and showed good agreement with hand calculations. The FEA analysis allows picking up details such as how effective the long keel is in stiffening the hull globally.
5.5 Shell structural analysis
Generally, a yacht’s hull shell structure is designed to resist the hydrostatic pressure and slamming impact of waves. Such a phenomenon is a complex fluid-structure interaction problem. SP High Modulus is conducting research in this area and has developed numerical tools which allow modeling the hydro-elastic response of hull shell panels subject to slamming loads [9]. At this stage, there is no plan to use such tools. DNA is working with RINA in developing design pressures for the analysis of this boat. Requirements of classification societies are based on a simplified approach where the influence of structural stiffness on the design pressure is neglected, the non linearity of material properties is neglected, the peak slamming pressure is spread and assumed to be uniform and simple assumptions are made about the boundary conditions of panels and stiffeners. This methodology works provided a chain of loads, factors of safety, and method of analysis are adhered to. More importantly, this methodology, while scientific in its structure, is very much based on proven experience. Given the unique nature of this yacht, such a methodology was therefore not applicable. It was also found that wooden structures, when treated by classification societies, are dealt with even more empirically. For instance, scantlings (frame spacing, frame section area, hull thickness, etc…) in Lloyds Register “Wood Rule” [10]
are just scaled up based on boat length, displacement and overall draft only, there is no mention of any factor of safety or timber bending strength.
SP-HM conducted an initial assessment of DNA’s hull frames and hull shell laminates using analytical methods. It showed that more detailed analysis would be beneficial to the project. Part of the global FE model was then extracted, refined (for instance to represent knees at the frames, a detail not necessary in global bending) to be able to deal more accurately with the design of the hull shell structure. The figure below is a contour plot of failure index of the hull shell and structure at an early phase of the design. A failure index below 1 indicates sufficient strength remains. Ultimate water pressure, and the deflection of frames were reported back to DNA.
13 Fig. 8: Shell structure model.
6. CONCLUSION & DISCUSSION
Direct calculations methods, material testing and international standards have been applied to create a
preliminary structural arrangement. Preliminary results from this design stage show that the resulting structure complies to the global longitudinal loads.
The FEA analysis carried out so far has proven useful in assessing the yacht’s structure and in determining the areas of the boat that require further research or analysis. More work will be required in the future to optimize the hull shell laminate and finalize the global analysis.
After finalizing the global analysis, design work continue on detailed structural engineering. Main aspects currently foreseen in this stage will be deflections and stresses around shell openings and the design and analysis of steel reinforcements and fittings as rigging attachments and rudder structure.
14
Nomenclature:
DNA Dykstra Naval Architects
DSV Dream Ship Victory Ltd
SP-HM SP-High Modulus
GLT Glued Laminated Timber
FEA Finite Element Analysis
Symbols:
f Strength property
s Stress property
a Angle to grain direction
E Elasticity modulus Subscripts: k Characteristic value l Property of lamination t Tensile c Compressive m Bending 90 Perpendicular to grain 0 Parallel to grain References:
(1) “Timber engineering”, Edited by Sven Thelanderson & Hans J. Larsen, John Wiley & sons Ltd, 2003. (2) “EN 338 Structural Timber – Strength classes”, European committee for standardization, 2009. (3) “EN 384 Structural timber – Determination of characteristic values of mechanical properties and
density”, European committee for standardization, 2010.
(4) “ EN 1995-1-1 Eurocode 5: Design of timber structures”, European committee for standardization,
2009.
(5) “Environmental impact comparison of yacht hull materials” , TNO, René van Gijlswijk & Bart Jansen,
2010.
(6) http://en.wikipedia.org/wiki/List_of_world's_largest_wooden_ships
(7) “Structural optimization of an AC90 racing yacht for the 34th America’s Cup with K-Challenge: the
influence of longitudinal hull stiffness on upwind performance.” Tison, T. and Stocking, P., The Second
International Conference on Innovation in High Performance Sailing Yachts, Lorient, 2010.
(8) “Challenges associated with design and build of composite sailing superyachts”, Meunier, M., Fogg, R., Design, Construction and Operation of Superyachts and Megayachts conference, 2009
(9) “A simplified Slamming Analysis Model for curved composite panels” Manganelli, P. and Louarn, F., 21st International HISWA Symposium on Yacht Design and Yacht Construction, Amsterdam, 2010
(10) “Lloyd’s Register of Shipping Rules and Regulations for the Classification of Yachts and Small Crafts”, 1979
Figures:
(1) Dykstra Naval Architects / Ken Freivokh design (2) Reproduced from [1]
(3) Dykstra Naval Architects (4) Dykstra Naval Architects (5) Dykstra Naval Architects (6) SP/High Modulus (7) SP/High Modulus (8) SP/High Modulus
