Structural analysis of HSC hull design
for JFD swimmer delivery system
Filip S
ÖDERLINGStructural analysis of HSC hull design for JFD
swimmer delivery system
by Filip SÖDERLING
Degree project in Navala Architecture Second level, 30.0 HEC
Stockholm, Sweden 2017
Abstract
ii
Strukturanalys av HSC skrov för JFD
transportsystem för dykare
Filip SÖDERLING
Examensarbete i Marina System Avancerad nivå, 30 hp Stockholm, Sverige 2017
Sammanfattning
Acknowledgements
The author would like to take the opportunity to show his gratitude to JFD Sweden for the collaboration regarding this thesis. The work behind this thesis has been supervised by Johan Pettersson, who shall have a special thanks. Also a thanks goes to Anders Magnerfelt, Karl Hagman and Gustav Larsson at JFD which all made this thesis work possible.
The time at JFD has contributed to developed engineering skills and also been instructive as well as fun and exciting. I have learned a lot and I know that the teachings will contribute in my future work.
Of course, I would also like to thank my examiner PhD Ivan Stenius for his guidance and encouragement. Also, thank you Anna and Carl-Anders, my follow class mates who have supported with both important and unimportant discussions.
iv
Contents
Abstract i Sammanfattning ii Acknowledgements iii 1 Introduction 2 1.1 Background . . . 2 1.2 Purpose . . . 3 1.3 Method . . . 3 2 Rule-based design 4 2.1 Limitations . . . 4 2.2 Pressure calculations . . . 4 2.3 Elasto-mechanical properties . . . 6 2.4 Structural response . . . 7 2.5 Design rules . . . 93 Verification of present hull 10 3.1 Assumptions and conditions . . . 10
3.1.1 General . . . 10
3.1.2 Material . . . 11
3.1.3 Hull . . . 12
3.2 Seal Carrier hull bottom structural arrangement . . . 12
3.2.1 Structural arrangement . . . 12
3.2.2 Structural hierarchy . . . 14
3.3 Seal Carrier hull bottom laminate plan . . . 15
3.4 Material . . . 16
3.5 Design criteria . . . 17
3.6 Results . . . 18
3.7 Evaluation and discussion . . . 20
3.7.1 Panel fields . . . 20
3.7.2 Beams . . . 21
3.7.3 General . . . 21
3.8 Longitudinal hull girder global strength . . . 21
3.8.1 Result global strength . . . 22
3.8.2 Discussion global strength . . . 22
4 Differences in rules for classification 23 4.1 Design loads . . . 23
4.2 Hull structural design . . . 24
4.3 Design criteria . . . 25
5 Discussion and conclusion 29 5.1 Discussion . . . 29 5.1.1 Panel fields . . . 29 5.1.2 Longitudinal beams . . . 30 5.1.3 General . . . 30 5.1.4 Rule changes . . . 30 5.1.5 Certification . . . 30 5.2 Conclusions . . . 31 5.2.1 Structural . . . 31 5.2.2 Input data . . . 31
5.2.3 Rule set changes . . . 31
5.3 Further work . . . 31
A Code structure 32 A.1 Main code structure . . . 32
A.2 Hull and pressure . . . 32
A.3 Elasto-mechanical properties . . . 32
A.4 Reactions forces and moments . . . 32
A.5 Structural response . . . 33
A.6 Stability and buckling . . . 33
A.7 Design rules . . . 33
B Classical laminate theory 35 B.1 The lamina . . . 35
B.2 The laminate . . . 35
B.3 Stress and strain . . . 36
C Results of verification of present hull result 37 C.1 Utilization graphs panel fields . . . 37
C.2 Utilization graphs beams . . . 39
D Effects of input data variation 43 D.1 Lamina layer thickness . . . 43
D.2 Volume fraction . . . 43
D.3 Poisson’s ratio and Young’s modulus transverse fibre direction . . . 44
D.4 Load carrying width shift coefficient . . . 45
D.4.1 Summary load shift . . . 48
vi
List of Figures
1.1 SEAL Carrier, swimmer delivery system . . . 2
3.1 Hull bottom specimen used to determine lamina thickness, marked with red dots at measuring point . . . 11
3.2 Definition of local coordinate system relative fiber direction . . . 11
3.3 SEAL Carrier hull bottom structural arrangement . . . 12
3.4 SEAL Carrier hull bottom load carrying area . . . 13
3.5 Hull bottom structural arrangement in section 2,3,4 and 5, y-distances as in sec-tion 4 . . . 13
3.6 Hull bottom structural arrangement in section 1, y-distances as in section 1 . . . 13
3.7 Cross section view of port side hull. Assumed distribution of load carrying width between beams . . . 15
3.8 Hull bottom layup sequences . . . 15
3.9 To the left is crest landing and to the right is hollow landing Courtesy of DNV-GL 21 3.10 Cross section view of hull bottom used for analysis identified as section number 4 22 4.1 Slamming pressure rule formula for 2011 DNV and 2016 DNV-GL . . . 24
4.2 Percentage difference between 2011 DNV and 2016 DNV-GL rule formula for slamming pressure . . . 24
4.3 Stress difference described as edition 2015 over 2011 . . . 25
4.4 Calculated lateral deflection differences in percentage relative 2015 edition . . . . 26
4.5 Percentage difference in lateral deflection criteria edition 2015 compared to 2011, panel 5 excluded due to differences >500% . . . 27
4.6 Difference in [mm] between criteria - deflection difference between the edition 2015 and 2011 . . . 27
A.1 Code structure flow chart . . . 34
C.1 Utilization panel 1 all sections . . . 37
C.2 Utilization panel 2 all sections . . . 38
C.3 Utilization panel 3 all sections . . . 38
C.4 Utilization panel 4 all sections . . . 39
C.5 Utilization panel 5 all sections . . . 39
C.6 Utilization shear web beam 1 all sections . . . 40
C.7 Utilization top hat beam 1 all sections . . . 40
C.8 Utilization shear web beam 2 all sections . . . 41
C.9 Utilization top hat beam 2 all sections . . . 41
C.10 Utilization shear web beam 3 all sections . . . 42
C.11 Utilization top hat beam 3 all sections . . . 42
D.2 Panel strain in top layer 1-direction and lateral deflection dependency of varied fibre volume fraction vf, normalized by vf = 0.60 . . . 44
D.3 Strain in 1-, 2- and 12-direction dependency of varied Young’s modulus trans-verse fibre direction . . . 45 D.4 Strain in 1-, 2- and 12-direction dependency of varied Poisson’s ratio of fibre . . . 45 D.5 Strain in 1-direction dependency of varied load distribution between outer and
middle beam . . . 46 D.6 Strain in 1-direction dependency of varied load distribution between middle and
inner beam . . . 47 D.7 Strain in 1–direction dependency of varied load distribution between inner beam
viii
List of Tables
1.1 SEAL Carrier main particulars . . . 3
2.1 DNV-GL mechanical reference value . . . 9
2.2 DNV-GL allowable deflections . . . 9
3.1 Hull structural arrangement . . . 14
3.2 Laminate plan SEAL Carrier . . . 16
3.3 Material properties used for verification of hull . . . 17
3.4 Calculated mechanical properties from equation 2.13 to 2.18 according to table 3.2 17 3.5 Design rules allowable values . . . 18
3.6 Panel failure . . . 18
3.7 Failure in panel lateral deflection . . . 18
3.8 Failure in strain compression 1-direction . . . 19
3.9 Failure in stress compression 1-direction . . . 19
3.10 Local stresses for global strength analysis with conservative assumptions . . . . 22
D.1 Comparison of beam bending stiffness, note that middle beam (2) do not exist in section 1 . . . 46
List of Abbreviations
HSC High-Speed CraftJFD James-Fisher Defence
DNV-GL Det Norske Veritas - Germanischer Lloyd
CLT Classic Laminate Theory
CAD Computer-Aided Design
CSM Chopped-Strand Mat
x
List of Symbols
Symbol Name Unit
psl slamming pressure kN m−2
acg design acceleration m s−2
∆ displacement ton
Aref reference area m2
Kred reduction factor
-Kl longitudinal distribution factor
-Kβ correction factor for deadrise angle
-Aref reference area m2
pR reference pressure kN m−2
T fully loaded draught in m at L/2 with the craft m floating at rest in calm water
pm peak pressure kN m−2
ppsl pitching slamming pressure kN m−2
βx deadrise angle at pressure point ◦
Cw wave coefficient
-TF P distance keel line to water line at fore perpendicular kN m−2
L hull length m
A load carrying area kN m−2
psea sea pressure kN m−2
h0 loading depth m
ks sea load distribution factor
-E1 young‘s modulus lamina in fibre direction MPa
ϕ volume fraction fibre kN m−2
Ef L young‘s modulus fibre in fibre direction kN m−2
Em young‘s modulus matrix kN m−2
E2 young‘s modulus lamina transverse fibre direction MPa
νm poisson‘s ratio matrix
-Ef T young‘s modulus fibre transverse fibre direction kN m−2
ν12 poisson‘s ratio matrix lamina action in 1 reaction in 2
-νf 12 poisson‘s ratio matrix fibre
-ν21 poisson‘s ratio matrix lamina action in 2 reaction in 1
-G12 shear modulus modulus lamina MPa
Gm shear modulus modulus matrix MPa
ExL young‘s modulus laminate in x-direction MPa
EyL young‘s modulus laminate in y-direction MPa
GxyL shear modulus modulus laminate MPa
νxyL poisson‘s ratio laminate action in x reaction in y
-EIx flexural stiffnes of laminate x-direction N m2
EIy flexural stiffnes of laminate y-direction N m2
I specific section modulus m4
ei distance from neutral bending plane to centre of element m
GA shear stiffness m4
t element thickness m
h height of web perpendicular to associated plating m MB−max maximum bending moment N
β boundary condition coefficient bending moment plate -Fq−max maximum shear force N m2
γ boundary condition coefficient shear force plate
-ω load width beam m
l length of beam between support m
rcb beam curvature coefficient
-cb boundary condition coefficient
-ˆ
σ maximum allowable stress MPa
ˆ
τ maximum allowable shear stress MPa
ˆ
ε maximum allowable strain MPa
ˆ
γ maximum allowable shear strain MPa
FR reference mechanical strength/resistance
-R reserve factor
-crm manufacturing coefficient
-εx/y lamina strain
-γxy shear strain in lamina
-εx/y0 middle plane strain
-γxy0 middle plane shear strain
-zi distance from middle plane to lamina i mm
κ warping mm−1
ω angular frequency rad
Def f effective flexural stiffness N mm
-Chapter 1
Introduction
The ability of traveling with high speed on water has for long been an aim of design work. The procedure to validate the performance of structures is not straight and simple. The struc-tures are geometrically complicated, the loads are not static nor evenly distributed and direct calculations are heavy. The classification societies have developed rules and guidelines to de-sign high-speed and light crafts which ensures the reliability of the structure with less effort. In this first chapter the background and purpose of this project is described and also a short description of the methodology used for carry out the project.
1.1
Background
Recently, the secretary of defence in Sweden announced that the Swedish military allocated 500 mil SEK extra this year to increase preparedness for incidents Holmström, (2017). This is a response to the security of the world around us, and all over the world the demand for military acquisition will keep on increasing. Gathering of information is always important from a military strategy point of view, and one source is divers with a capability to go further into the strategic area than surface vehicles or large submarines. To extend the endurance and range of divers a transportation system called SEAL Carrier by James Fisher Defence entered the market.
The SEAL Carrier is a hybrid craft, that on surface act as a HSC and submerged act as a so called wet submarine. This means that it has no pressure hull so that the ten operators travels wet and has to be supplied with air by the integrated system or by individual carried systems. The propulsion is divided into two systems, a diesel driven water jet at surface mode and a system of batteries powering two electric thrusters for submerged mode. See figure 1.1 for an overview image of the SEAL Carrier and table 1.1 for its main particulars.
The craft is build out of carbon fibre single skin plating and sandwich beams and is build upon a rule-based design that has been developed over time.
The SEAL Carrier system is under constant development and to ensure structural reliability of future generations of the system, the structure needs to be analyzed. The rules used for the design was the 2011 DNV rules, and since 2013 DNV and Germanischer Lloyd merged and
1.2. Purpose 3
TABLE1.1: SEAL Carrier main particulars
SEAL Carrier Parameter Value Unit
Length 10.45 m
Beam 2.21 m
Draught 0.5 m
W eight 4000 kg
became the newly formed DNV-GL Group. In 2016 they updated their rules for classification, which in this analysis will be used.
1.2
Purpose
The hull of the SEAL Carrier was designed in accordance with rules for classification but is not yet certified, and from the perspective of JFD it is a sales argument to have the craft certified by DNV-GL. The hull was originally designed upon the DNV rules for classification from 2011 and due to the changes in the rules 2016 and the update of the craft there is a need for an update of the structural analysis of the SEAL Carrier hull. This analysis discusses the input data and evaluates the hull bottom regarding the new rules for classification from 2016 by DNV-GL. It also addresses some of the differences between the two rule sets and proposes updates in the work to enable certification. The goal is to deliver a foundation of an update of the new hull in relation to the new DNV-GL rules with a Matlab tool for evaluate a design relative to the new rule set from 2016. This analysis can be used to verify appropriate changes for the new hull to fulfill the requirements and locate uncertainties in a future structural analysis.
1.3
Method
Chapter 2
Rule-based design
There are two main types of design procedures, direct calculation-based and rule-based design. Classification societies have developed rules based on standard mechanical formulas with ex-perience and understanding of sea loads and structural reactions and responses. Generally, the design principle is based on usage of a reserve factor R, which scales the ultimate strength to an acceptable and allowable strength. Working with the rules are rather simple, but it might fol-low with using standard reserve factors that the generated mass is larger due to over-designed structural members Misra, (2015).
The rule-based design in this analysis follows DNV-GL 2016 set of rules for classification. Within chapter 2 the used parts of the rule set is thoroughly described for the different main parts of the analysis. The procedure initiates with determining design load and the elasto-mechanical properties. It follows by determining the reactions from which the responses are determined. The responses are then compared to a set of criteria stated by the society. First of all some limitations in the procedure and analysis has to be stated.
2.1
Limitations
For the rule-based design there are some assumptions that’s needed to be made.
– equivalent uniform and static load over each structural member
this is to justify the usage of reaction calculations according to DNV-GL
– The full laminate is considered being one multi-ply
made to be able to calculate laminate stiffness properties from multi-ply data acc. DNV-GL
– Lateral deflection does not consider shear deflection
DNV-GL notes that the calculated deflections therefore might be under estimated which shall be accounted for
– maximum allowable compression stress is 60% of maximum allowable tension stress
compressive tests are more complex to carry out and this assumption do compensate for excluded test, compressive strength shall otherwise be tested for
– Kirchoff‘s hypothesis
"A line in the unloaded plate which is perpendicular to the middle plane remains plane and perpendicular to the middle plane even after the loads are applied"
2.2
Pressure calculations
2.2. Pressure calculations 5 well. Slamming pressure which is acting when the craft is moving through waves and the craft experience an acceleration when slamming into the water. Then there is the one called pitching-slamming which also is when the boat is slamming into the water, but generated by the rotation or pitching movement in the craft when subject to waves.
Slamming pressure is a high peak pressure moving from the keel outwards the chine, hence it only acts for a short period at each specific point. When the peak pressure hits the structural member, it starts to deflect. Since the load rapidly moves on, the structure does not reach the full deflection the load would have generated if it was constant. From this it also follows that the peak stress neither is generated see Koebel, (2000). From this, the assumptions of using equivalent uniform static load, and fixed boundary condition are justified.
To calculate the acting loads, DNV-GL Pt 3 Ch 1 Sc 3 is used. Slamming pressure is calcu-lated with respect to the design acceleration, geometrical aspects and loading conditions. The formula also includes reduction factors for dead-rise angle effects, longitudinal placement and reduction factor for design load area. Slamming pressure according to DNV-GL is calculated as,
psl=
acg· ∆
0.14 · Aref
· Kred· Kl· Kβ [kN/m2] (2.1)
expressed in kN/m2 or kP a. Here the central aspects are the design acceleration a
cg, and
dis-placement in tonnes ∆, which represents the total slamming force by Newton‘s second law. The equations origin has been discussed in Mikael Razola, (2014) and DNV-GL have added the dead-rise angle reduction. It is here stated that the total slamming force is translated to a reference pressure,
pR=
acg· ∆
Aref
[kN/m2] (2.2)
where the reference area Aref is defined as the area of the hull bottom that is subject to the
majority of the slamming load. The used definition of reference area is the one presented in Spencer, (1975) and transformed to SI-units is calculated as,
Aref = 0.7
∆
T [m
2]
(2.3) where parameter T is fully loaded draft in m at L/2 and rest in calm water. The peak pressure, which is the maximum pressure acting anywhere on the reference area, is defined as,
pm = pR 0.14 = acg· ∆ 0.14 · Aref [kN/m2] (2.4)
with the usage of equation 2.2. The design pressure is defined as Pd = Pm · Kred· Kl · Kβ.
These remaining coefficients are reduction factors that connects the total slamming force to the local design pressure. Kredreduces the pressure with a relationship between peak and design
pressure and is a function of the ratio AD
Aref where AD is the area of the structural member subject of the load. To compensate for the longitudinal position of the pressure calculation Kl
was introduced. The last coefficient Kβ, compensates for the local dead-rise angle of the hull.
For full definition of these reduction factors please refer to DNV-GL Pt 3 Ch 1 Sc 3. Pitching-slamming pressure shall also be designed for and is defined as,
ppsl = 21 tan(βx) kakbCW 1 −20TF P L 0.3 A 0.3 [kN/m2] (2.5)
psea= a 10h0+ ks− 1.5 h0 T CW [kN/m2] (2.6)
which is the static pressure acting on submerged body. The coefficient a is a load intensity factor and determined according to table 4 in DNV-GL Pt 3 Ch 1 Sc 3. For bottom hull structure, the sea pressure shall not be taken as less than 5.0 kN/m2 for the service area R3.
2.3
Elasto-mechanical properties
From the choice of materials, lay-up sequences and structural arrangement, the mechanical properties of each set of parameters has to be determined as in DNV-GL Pt 3 Ch 1 Sc 6. First is the single ply engineering constants calculated from raw material data of the fibre and matrix material. The longitudinal Young‘s modulus or elastic modulus in fibre direction for a single unidirectional ply is calculated as
E1= ϕ · Ef L+ (1 − ϕ) · Em [MPa] (2.7)
and the transverse Young‘s modulus or elastic modulus orthogonal to fibre direction is calcu-lated as E2= Em 1 − v2 m · 1 + 0.85 · ϕ 2 (1 − ϕ)1.25+ ϕ · Em Ef T·(1−v2m) [MPa] (2.8)
with the coefficients as in nomenclature. Poisson’s ratio for the two directions for the two materials are determined as
ν12= ϕ · νf 12+ (1 − ϕ) · νm [−] (2.9)
ν21= v12
E2
E1
[−] (2.10)
describing how the material tends to expand in direction perpendicular to the direction of compression.Shear modulus for the material combination is calculated as,
G12= Gm·
1 + 0.8 · ϕ0.8 (1 − ϕ)1.25+ Gm
Gf 12 · ϕ
[MPa] (2.11)
with Gmdefined as,
Gm=
Em
2 · (1 + vm)
[MPa] (2.12)
with Emand vmas earlier. Then the stiffness of each single ply and multi-ply is calculated using
Classic Laminate Theory (CLT) which is closer described in Appendix B. With the assumption that the full laminate is considered being one multi-ply, the laminate stiffness properties are determined from the extension matrix [A]L = [A]M. These are calculated according to DNV Pt
2.4. Structural response 7 GxyL = 1 tM · a33M [MPa] (2.15) νxyL = a12m a11M [−] (2.16)
and the notations follows from Appendix B. Flexural stiffness of a sandwich laminate is deter-mined by the bending stiffness matrix, with the assumption of the laminate considered as one multi-ply [D]L = [D]M. According to DNV-GL, the flexural stiffness can be calculated in the
following simple way,
EIx= D11 [Nm2] (2.17)
EIy = D22 [Nm2] (2.18)
as an alternative to the full matrices. Flexural stiffness for beams are determined as,
EI =XEi· (Ii+ Si· e2i) [Nm2] (2.19)
where the beam is considered to be a composition of five elements. These elements are the effective plate width, two times the shear web, the core and the flange. In equation 2.19 Ei is
the element Young‘s modulus 2.13/2.14, Ii is the specific moment of inertia of the element, Si
is the cross sectional area and ei is the distance from the beam neutral bending plane to the
centre of respectively element. Subscript i identifies the element of the five earlier mentioned. Equation 2.20 is used to determine the beam shear stiffness, for this it is only the shear web that is accounted for and is calculated as,
GA =XGi· ti· hi [N] (2.20)
where Gi is the in-plane shear modulus 2.15, ti is the element thickness and hi is the
perpen-dicular height associated to the plating.
In the same section, the reaction moments and forces of the structural members are calcu-lated using the design pressure and geometrical aspects. With stiffness properties and load case known for the structural member, the strain and stress are calculated in each ply according to CLT where the important parts are shortly described in appendix A.
2.4
Structural response
With known load and mechanical properties of the structural members, the reactions and re-sponses of the structure are calculated. The reactions are represented by bending moment and shear force for panels and beams respectively. These are all depending on the choice of bound-ary condition, but with a different approach. In the rules of DNV-GL, in order to determine which the maximum bending moment and shear force are for plates, the effective span Sef f
has to be determined. The effective span is either the span in x- or y-direction, depending on a geometric ratio between the two spans.
Starting with reactions for panels, the maximum bending moment is defined as in equation 2.21. The maximum bending moment occurs in different parts of the plate depending on the effective span and with different applied boundary condition defined by the designer. For shear force, which is defined by equation 2.22, the maximum value emerges in the middle of the panel edge adjacent to the effective span Sef f.
MB−max =
β · pd· Sef f2
Fq−max= γ · pd· Sef f [N/m] (2.22)
The two coefficients β and γ are the parameters that includes boundary condition effects scaled to the relation of geometric span ratio. These two, and a coefficient called α which will be introduced in relation to the lateral deflection for plates, are determined from table 2 DNV-GL Pt 3 Ch 4 section 6.
For beams, the procedure is similar to the one above. Maximum bending moment occur at different positions depending on boundary condition. For both ends clamped the maximum value occur at the ends, for simply supported it occur at the centre of the beam span. The maximum bending moment equation 2.23 and the maximum shear force equation 2.24, both depends on the boundary condition coefficient cb, which value is defined in DNV-GL Pt 3 Ch 4
Sc 6.4. So is also the curvature correction factor rcb, which includes the effects of beams which
follows curved plating.
MB−max= Pd· w · l2· rcb cb [Nm] (2.23) Fq−max = Pd· l · w · cb 2 [N] (2.24)
Equation 2.21 to 2.24 describes the reactions due to the loading and support conditions in the structure. With the combination of mechanical properties and reactions it is possible to determine the responses, such as strains, stress and deflections. The determination of middle axis strains in panel laminate follows in appendix B, from there the strain in each lamina is determined as, εx εy γxy = εx0 εy0 γxy0 + zi κx κy κxy [−] (2.25)
where ε subscript 0 indicates the middle plane strains. Variable κ indicates the warping, these are defined in appendix B. The variable zi defines the distance from the middle plane
to each lamina in the laminate, this is the expanded formulation of equation B.9. The lateral deflection for plates are calculated as in equation 2.26. It depends on the design pressure and effective span with the structural stiffness defined by the effective flexural stiffness Def f.
Co-efficient α scales the deflection in relation to the boundary condition in accordance with earlier mentioned method in DNV-GL.
zmax =
α · Pd· Sef f4
12 · Def f
[m] (2.26)
For beams the procedure is a bit different, first of all, each response is determined for the shear web and flange respectively. For shear web, two points are calculated, one above NA and one below NA to capture both tension and compression. Resulting bending strain is deter-mined as,
εi=
MB−max· ei
EI [−] (2.27)
where MB−maxand EI is beam specific and equal between shear web and flange. The
vari-able ei is the distance from the beam‘s neutral bending plane to centre of the shear web and
flange respectively, and therefore generates different strains as result. Same follows for in-plane shear strain, equation 2.28 where Fq−maxis the same for shear web and flange while GA is
2.5. Design rules 9 and loading that determines the maximum deflection, equation 2.29. In the determination of lateral deflection the coefficient s appears, which by DNV-GL is defined as stiffener spacing. The current structure do not have a even distribution of the beams and therefore also not a fixed value of distance between the beams, and for the usage within this analysis the value is assumed to the load carrying width described later in the report.
γs = Fq−max GA [−] (2.28) Zmax= pd· s · l4· cdp 384 · EI [m] (2.29)
Regarding stability and buckling, skin wrinkling of sandwich beam skins is considered. In equation 2.30 is the critical wrinkling strain for sandwich structures with solid and isotropic cores defined. εsw−crit= 0.5 · (Ebf · Ec· Gc) 1 3 Es [−] (2.30)
Coefficient Ebf is the skin laminate flexural modulus relevant to the direction of
compres-sion (calculated as in 2.19 without summation). Ecand Gcis Young’s and shear modulus for the
core material used in the beams. The strain in both web and top hat of each beam is compared to this critical value which shall not be exceeded.
2.5
Design rules
The main failure criteria is maximum strain in the fibre direction, but in this analysis also stress is considered. Except maximum stress and strain criteria, maximum deflection, core shear strength and minimum laminate reinforcement weight is also used as design rules. The calcu-lated values are compared to the allowable ones defined by DNV-GL Pt 3 Ch 1 Sc 7 and shown by equation 2.31.
ˆ
σ, ˆτ , ˆε, ˆγ = Fr R · crm
[−] (2.31)
Here Fr denotes reference mechanical strength and is chosen from table 5 in DNV-GL Pt
3 Ch 4 Sc 6.7 and Crm is equal to 0.95 for vacuum assisted production. The mechanical
refer-ence value are shown in table 2.1 and the reserve factor R is equal to 3.0. For deflections the maximum allowable value is chosen from table 8, DNV-GL Pt 3 Ch 4 Sc 6.7 here presented as table 2.2. The variable Sef f is the effective span, which the major bending and shear loads are
calculated from, and l is the beam span.
Then the margin, which the values has against the allowable values is defined as the per-centage of usage and is calculated by dividing the calculated value with the max/min allow-able. A good balance of this utilization will generate a good usage of material in relation to the rules and by these means new designs can be argued for and tested.
TABLE 2.1: DNV-GL mechanical reference value
Presumption Fr
HS Carbon, uni-axial strain 0.65 % HS Carbon, in-plane shear strain 1.15 %
Chapter 3
Verification of present hull
Within this chapter the analysis regarding DNV-GL rules of the future SEAL Carrier hull bot-tom structure is presented. First are assumptions and conditions regarding the boat structure and material discussed. Further, the hull structural parameters and hierarchy used in the cal-culations are described. The laminate plan and material parameters are presented in section 3.3 and 3.1.2. Last are the design criteria presented and this is followed by the results. In the end of this chapter an evaluation and discussion of the results an assumptions are made.
3.1
Assumptions and conditions
In section 2.1 the assumptions necessary within the design procedure by DNV-Gl is described. Those statements are defined by DNV-GL and limits the usage of the rules within those state-ments. In this section more specific assumptions made by the designer are described, which has varying influence on the result. The assumptions treats material and hull structure and also more general, and in section 3.7 the impact of some of the assumptions are also evaluated. The level of detail in the results, can only be so good as the input used in the analysis. This has led to a number of the below described assumptions.
3.1.1 General
In accordance with Zenkert, (2003), the transverse stresses, strains and deformations are ne-glected for single skin panel fields. When considering sandwich beams this is accounted for in the core material.
To be able to define the input as detailed as needed, the decision to only consider the part of hull aft of the forepart. This is due to the fore part consists of curved surfaces, inclined beams and several more difficulties that would decrease the level of detail in the result.
3.1. Assumptions and conditions 11 3.1.2 Material
One difficulty for this analysis has been the decision of material parameters, since some values needed for the rules has not been possible to gather from producers. The lamina thickness for example, which also has a large impact on the result had to be determined. For this analysis, the lamina thickness was assumed as 0.25mm for all lamina since the same material is used over the whole bottom structure. It was determined by measuring the thickness of a real part of the bottom panel laminate at 10 points and using the mean thickness, see figure 3.1. Then from the mean thickness 1mm was subtracted to compensate for coating and glass fiber CSM and divide it by the laminate layup. The method is attested from Advanced General Aviation Transport Experiments Tomblin, (2002) and the result is in accordance with values for thickness presented in the report and in Åström, (1997) for the manufacturing process.
The laminate properties depends on the amount of fibre in the mixture with matrix, and this is denoted as volume fraction of fibre/matrix. Volume fraction of fibre is in this analysis estimated from background knowledge and experience within JFD and it also corresponds to Åström, (1997) and used as vf = 0.6. Both lamina thickness and volume fraction is sensitive
variables, and is expected to have large impact on the outcome of the analysis.
Poisson‘s ratio of fiber and matrix which is a measure of reaction in the opposite direction of the load direction. Young‘s modulus orthogonal to the fibre direction is a measure of elasticity in the transverse direction relative fibre direction. These numbers haven‘t been possible to obtain from manufacturer and have therefore been taken as equal to the proposed ones in table 1 in DNV-GL, (2016)(a) Pt 3 Ch 4.6. These are generic constituent material properties proposed to be used without own material tests.
Another aspect that was not clear within the rules, was regarding design criteria orthogonal to the fiber direction, see figure 3.2 for definition of local coordinate system. In the rules it is stated that compression testing of the laminates may not be necessary if the compression strength used in the analysis does not exceeds 60% of the design tensile strength for carbon fibre DNV-GL, (2016)(a). From this then, the assumption of criteria in compression shall be 60% of the tension criteria for fiber direction, 1-direction. In the 2-direction the criteria is not stated, and from the material table 4.2 in Zenkert, (2003) another relation was seen for the 2-direction. From those relations, it was assumed that the compression strength is 4 times larger than tension in 2-direction.
FIGURE 3.1: Hull bottom specimen used to determine lamina thickness, marked with red dots at measuring
point
FIGURE3.2: Definition of lo-cal coordinate system
3.1.3 Hull
As mentioned in section 3.1.1 this analysis neglect the fore part of the hull. This is due to the level of detail in the analysis of the fore part of the hull, which has more difficult geometry. Another simplification regarding the geometry is that in the parts where the beams are angled relative the x-axis due to merging or division is considered as straight with a mean value po-sition in y-direction. The true length of the beam is still considered. The hull is divided into a finite number of sections, and the arrangement in each section is treated as constant based on a mean value of half the section length.
Since the beams are of different sizes, it has been assumed that their different properties affects the load carrying area. For beams with equal flexural rigidity the load carrying area is divided equally over the distances between the beams. Load carrying area for the middle beam is still shifted towards the inner one as an effect of the outer beam carrying a lot of the area outside of the middle beam. In section 3.2.2 the assumptions are in more detail explained.
3.2
Seal Carrier hull bottom structural arrangement
The SEAL Carrier, figure 3.3 is built upon a carbon fibre single skin plating with glass fibre reinforcement as outer protection and longitudinal sandwich beams. The glass fibre protection is not considered as essential in the structural strength and are in this analysis neglected. The hull structure has been divided into six compartments, from aft to stern. The bulkheads nat-urally divides the compartments which are marked as red lines in figure 3.3. Due to the need for detailed level of the structure, only the compartments 1 to 5 is analyzed. Since there are no transverse stiffening, this division defines the length of both the plate fields and beams. The panels are named 1 to 4 according to figure 3.3, and a fifth panel is added for the flat section called reverse chine next to the hard chine, marked as red in figure 3.4.
The structural arrangement for each compartment is defined with distance between keel and centre of beam, dead-rise angle and dimensions of the beams (height and width). From the structural arrangement in figure 3.3, the load carrying area can be determined. The load carrying area is the area on which the design pressure acts for the relevant structural member. For the different members, the load carrying area is graphically shown in figure 3.4. In the upper part of figure 3.4 the beam load carrying area is shown, the different colors illustrates each members load carrying area. Yellow defines the inner stiffener, blue the outer stiffener and green defines the girder. In the lower part of figure 3.4 the plate field load carrying area is shown, and the colors shows the different structural members.
3.2.1 Structural arrangement
As seen earlier, section 2 and 5 have angled beams relative the keel line which transforms the structure between two and 3 beams. The transformation in section 2 and 5 are calculated
3.2. Seal Carrier hull bottom structural arrangement 13
FIGURE3.4: SEAL Carrier hull bottom load carrying area
as mean values of the two end distances. Cross section views for section 1 and 4 structural arrangement are shown in figure 3.5 and 3.6. For the full structural arrangement considered, see table 3.1. Note that the distances in y-direction used in the analysis are as in table 3.1 and not as in the figures, the distances in the figures represents only section 1 and 4.
FIGURE 3.5: Hull bottom struc-tural arrangement in section 2,3,4 and 5, y-distances as in section 4
FIGURE 3.6: Hull bottom struc-tural arrangement in section 1,
TABLE3.1: Hull structural arrangement
Structural arrangement
Parameter values unit
Section 1 2 3 4 5
Length 2.7850 0.4370 0.5780 3.800 0.5000 m
Deadrise angle 15.3090 19.9320 19.9320 21.6379 27.5781 deg
Beam 1 Height 0.0770 0.1970 0.1970 0.1970 0.0770 m Width 0.0450 0.0170 0.0170 0.0170 0.0450 m y-distance 0.3925 0.2700 0.1615 0.1615 0.2300 m Beam 2 Height 0 0.1420 0.1420 0.1420 0.450 m Width 0 0.0450 0.0450 0.0450 0.0450 m y-distance 0 0.4575 0.5225 0.5225 0.3775 m Beam 3 Height 0.3600 0.3600 0.3600 0.3600 0.3600 m Width 0.0270 0.0270 0.0270 0.0270 0.0270 m y-distance 0.5635 0.6300 0.6965 0.6965 0.6300 m 3.2.2 Structural hierarchy
For the structural hierarchy in the bottom structure, the plate fields takes up the load from the design pressure and transfer it to the longitudinal beam which in their turn transfer the load onto the bulkheads. In this analysis the bulkheads are assumed to be fixed and does not transfer the load further.
For a bottom structure with both longitudinal and transverse stiffening, smaller beams as stiffeners transfer their load onto the transverse beams which in their turn transfer the load onto the stiffer longitudinal beams called girders. This example is a typical hierarchy which is not the case for this bottom structure.
Due to the large difference in mechanical properties between the outer beam relative the two other beams but the same longitudinal span, the outer beam is treated as higher in the hierarchy. Due to this assumed hierarchy, the distribution of load carrying width between the beams is shifted by scaling the percentage of load carrying width between the beams. Within this analysis the middle and inner beam have similar bending stiffness while the outer beam is ∼ 10 times stiffer in bending than the two other beams. In appendix D and section D.4 the relation between the beams are shown. It shows that with the shift coefficient, the strain in the beams can be distributed more like the true hierarchy. This effect has also been accounted for regarding the reverse chine. It has been assumed that the large stiffness in the outer beam makes it carry 100% of the load between the outer beam and the reverse chine to use conserva-tive measure.
3.3. Seal Carrier hull bottom laminate plan 15
FIGURE3.7: Cross section view of port side hull. Assumed distribution of load carrying width between beams
3.3
Seal Carrier hull bottom laminate plan
With the properties of fiber composites, it is possible to utilize the usage of fibre within different structural members. Different layups has been chosen for different members to fit the expected loads on the member. These different layups are shown with color code in figure 3.8 and are defined in table 3.2. In this analysis, the bottom panels are assumed to have the same layup sequence all over the length. Also the glass fiber reinforcement is neglected, since this is outer protection and not contributory to the structural strength.
TABLE3.2: Laminate plan SEAL Carrier
Laminate plan
Color code Layup Core
Red [07/45/ − 45] − Green [45/ − 45/0/90/45/ − 45/0/45/ − 45]s 20mm H250 Blue [45/ − 45/0/90/45/ − 45/0/45/ − 45]s 20mm H250 Purple [015/45/ − 45] − Pink [45/ − 45/0/90/45/ − 45/0/45/ − 45]s 12mm Brown [04/45/ − 45] − Light purple [015/45/ − 45] − Yellow [015/45/ − 45] − Light blue [015/45/ − 45] − Panel 1-4 [45/ − 45/0/90/45/ − 45/0/90/45/ − 45/0/90] − Panel 5 [45/ − 45/0/90/45/ − 45/0/90/45/ − 45/0/90/45/ − 45/0/90] −
3.4
Material
One important aspect in this analysis is all the material properties used as input for the calcu-lations. One problem is the fact that some data is impossible to get from the manufacturer and therefore are assumptions necessary. The purpose of this section is to define all material data used in the analysis, see table 3.3, where the assumed ones are described in section 3.1. Further more, the weight of fibre reinforcement per lamina has been taken from production specifica-tion defined by JFD. The weight is used in the unit g/m2and for single uni-directional fiber the
3.5. Design criteria 17
TABLE3.3: Material properties used for verification of hull
Material properties
Parameter Symbol Value Unit
lamina thickness t 0.30 mm
Volume fraction fibre vf 0.6 −
Young‘s modulus fibre direction Ef 1 240 000 M P a
Young‘s modulus ortho. fibre direction Ef 2 14 000 M P a
Density fiber ρf 1800 kg/m3
Poisson‘s ratio fiber νf 0.22 −
Young‘s modulus matrix material Em 3000 M P a
Shear modulus fiber Gf 23 000 M P a
Density matrix ρm 1096 kg/m3
Poisson‘s ratio matrix νm 0.316 −
Young‘s modulus core Ec 400 M P a
Shear modulus core Gc 97 M P a
Density core ρc 250 kg/m3
Poisson‘s ratio core νc 0.4 −
TABLE 3.4: Calculated mechanical properties from equation 2.13 to 2.18 accord-ing to table 3.2
Mechanical properties
Color code ExL[GP a] EyL[GP a] GxyL[GP a] νxy[−] EIx[kN m2] EIy[kN m2]
Red 117.92 16.64 12.24 0.57 98.97 23.08 Green 51.40 39.16 26.67 0.50 55.21 40.10 Blue 51.40 39.16 26.67 0.50 55.21 40.01 Purple 131.00 13.38 8.84 0.48 755.82 123.98 Pink 51.40 39.16 26.67 0.50 55.21 40.01 Brown 103.82 19.78 15.85 0.63 27.42 7.51 Light purple 131.00 13.38 8.84 0.48 755.82 123.98 Yellow 131.00 13.38 8.84 0.48 755.82 123.98 Light blue 131.00 13.38 8.84 0.48 755.82 123.98 panel 1-4 55.64 55.64 21.26 0.31 131.98 144.77 panel 5 55.64 55.64 21.26 0.31 318.47 336.53
3.5
Design criteria
TABLE3.5: Design rules allowable values
Allowable values
Parameter Symbol Value Unit
Strain 1-direction tension ε1t 0.0023 −
Strain 1-direction compression ε1c 0.0014 −
Strain 2-direction tension ε2t 0.0007 −
Strain 2-direction compression ε2t 0.0028 −
In-plane shear strain γ12 0.0040 −
Stress 1-direction tension σ1t 331.16 M P a
Stress 1-direction compression σ1c 198.70 M P a
Stress 2-direction tension σ2t 9.9399 M P a
Stress 2-direction compression σ2c 39.760 M P a
In-plane shear stress τ12 20.252 M P a
Deflection plate field Zmax/Sef f 0.0150 −
Deflection longitudinal beam Zmax/l 0.0050 −
Deflection longitudinal beam Zmax/l 0.0030 −
Engine foundation (section 1, beam 3)
Minimum reinforcement panel Wop 4200.0 g/m2
Minimum reinforcement beam Wob 1600.0 g/m2
3.6
Results
With the setup as above, the results are wide spread regarding design criteria. The strength criteria for panels is represented by stress in 1-, 2- and 12-direction, the stiffness criteria is rep-resented by lateral deflection. Minimum reinforcement is the last criteria for the plate fields. For beams the strength criteria is also represented by stress and divided into web and flange/hat, and stiffness is represented by lateral deflection. Shear strain is mainly taken care of by the shear webs in the beams, and therefore is the web strength representative for shear strain crite-ria. For beams, the minimum reinforcement is checked for web and flange separately.
The result shows only criteria not meet in panels and all beams fulfills the criteria. The panels which in one or more criteria do not fulfills the criteria are summarized in table 3.6. It shows that nearly 44% of the panel fields in one or more criteria does fail regarding to the design criteria. In more detail, it is possible to look at which criteria each member fails and also which lamina it is that fails. These results for panels are shown in table 3.7 to 3.9.
TABLE3.6: Panel failure
a a a a a aa SectionPanel 1 2 3 4 5 1 X X 2 X X 3 X X 4 X X 5 X X X
3.6. Results 19
TABLE 3.8: Failure in strain compression 1-direction
Failure panels
Section Panel Lamina Rotation[o]
1 1 1 45 1 1 12 90 1 4 1 45 1 4 2 -45 1 4 4 90 1 4 12 90 2 1 1 45 2 1 2 -45 2 1 12 90 2 4 1 45 2 4 2 -45 2 4 4 90 2 4 12 90 3 2 1 45 3 2 2 -45 3 2 4 90 3 2 12 90 3 4 1 45 3 4 2 -45 3 4 4 90 3 4 12 90 4 2 1 45 4 2 2 -45 4 2 12 90 4 4 12 90 5 1 1 45 5 1 12 90 5 3 1 45 5 3 12 90 5 4 1 45 5 4 12 90
TABLE 3.9: Failure in stress compression 1-direction
Failure panels
Section Panel Lamina Rotation[o]
3.7
Evaluation and discussion
Within this chapter the results and the effects of the earlier made assumptions are discussed. This section is divided into subsection each discussing different aspects of the result. The re-sults are also presented in relation to each criteria in polar diagrams called utilization plots. These plots are scaled in radius with the percentage used of the criteria. The appendix holds one graph for each structural member, however only the highest utilization of each criteria within each laminate is shown. This means that for a laminate with ten lamina, all lamina are controlled against all criteria, however only the largest utilization of all lamina is presented.
For structural response above the maximum allowed value 100% of the criteria, is marked with red. With the blue line outside the red marked area means that the design criteria is not meet. Appendix C holds the utilization plots of all structural members.
3.7.1 Panel fields
For all panels, the effective span is determined as the y-direction span, i.e the panel width. From this is follows that the maximum bending moment is the one in y-direction refereed to as My which generates a global strain in y-direction. For the studied structure, there seems
to be a problem with the arrangement of panel fields. From table 3.8 and 3.9 it shows that the panels do not meet the design criteria regarding to strength, compression strain and stress in 1-direction. One aspect of the result is that it is only fibres in 90 or 45/-45 orientation that fails which is an indication of stress in y-direction is ruling. This is an effect of the maximum bending moment being in the y-directions My. In appendix C, figure C.1 to C.4 it is seen that the
margin for strength criteria is large for some cases. The results shows values up to 100% above the minimum criteria for stress and it is implicitly that the there also is problems regarding to strain. Another aspect in the graphs and table 3.7 is the fact that the deflection is critical for seven panels. From equation 2.26 it is seen that it is an effect of lack in flexural rigidity or stiffness and it could be solved with smaller width of the panels generating lower bending moment.
The conclusion is that the panels lack both stiffness and strength properties. Since the pan-els are loaded on the outer side, it could be a way to reinforce the inner side of the laminate. In Professional Boat Builder Eliasson, (2007), he describes a method used in the production of Swedish Sea Rescue Society composite RIB, to reinforce the inner side of panels with extra bidi-rectional laminates. These bands are placed at the panel supports (i.e beams and bulkheads) which is to increase the strength at the places maximum bending moment occurs for the fixed boundary condition. Another way of increasing strength and stiffness would be to implement sandwich structure in the panels. From Zenkert, (2005) it is known that with a core structure that increases the distance of single skin halves with twice the original single skin thickness, the the flexural rigidity increases with 12 times and bending strength increases 6 times with almost the same mass. This is estimates from just adding a core without changing the skins, with a optimization of fibres the total mass could decrease.
Another aspect to consider is that the result may not be as bad as they initially might look, it is only a few lamina per laminate that fails and no full collapse occur. As seen in the figures of results in appendix C panels 1,2,3 and 4 does not meet the minimum reinforcement criteria. They lack 450g/m2, which can be solved with an extra 0/90 mat which also increase the strength
and stiffness in the problematic directions. The fact that it is Mygoverning, a 45/−45 mat could
3.8. Longitudinal hull girder global strength 21 3.7.2 Beams
According to the result, no beams fails in any of the criteria. In appendix C one can see that the margin to the criteria are fairly well balanced. The beams though, also influence the global strength which is more analyzed in this section 3.8.
3.7.3 General
It is important to highlight that the effects of the earlier mentioned assumptions are severe. Changing the variables described in section 3.1 have impact on the outcome of this analysis. In appendix D is an analysis of the effects of variation of the lamina thickness, volume fraction, Poisson’s ratio, transverse Young’s modulus and the load carrying width for beams. Further analysis of the results follows in chapter 5
3.8
Longitudinal hull girder global strength
Generally for small crafts, global strength is not an issue and therefore not considered Welli-come, (1993). DNV-GL enables determination of loads generated by bottom slamming where crest and hollow landing are two possible cases. The method assumes the whole bottom hull girder acts as a beam and the determination of loads are specified in DNV-GL Pt3 Ch1 Sc4. The loads are in this case specified as bending moments which bends the hull as shown in figure 3.9.
Since global hull girder strength is usually not an issue for small crafts like the SEAL Car-rier system a simplified version of the analysis has been carried out. The simplification implies that only slamming load is considered and not still water effects, also the structural member bending stiffness has a linear effect on global bending stiffness. Hence, the principle of super-position is used to determine global bending stiffness of the hull girder by adding EI for the beams only. This is due to the low impact of adding plate bending stiffness into the analysis. The neutral axis is calculated for the cross section shown in figure 3.10, and for the analysis the largest distance from NA is calculated for. In equation 3.1 is the global strain defined for the hull structure considered as one beam, with bending moment M as defined in DNV-GL Pt3 Ch1 Sc4 for crest and hollow landing. EI is the global bending stiffness and z defines the distance from NA to the analyzed area. Stress is defined as strain times stiffness which will be different for different fiber orientation. To include the orientation and stiffness into the deter-mination of local stress from the global strain, the stiffness of a fibre orientation is represented by Q from equation B.4 in appendix B shown by equation 3.2.
εx= M z EI (3.1) σ1 σ2 τ12 = T QlTt εx εy γxy (3.2)
FIGURE 3.10: Cross section view of hull bottom used for analysis identified as section number 4
3.8.1 Result global strength
The resulting stresses for the two specified cases are presented in 1- ,2- and 12-direction in table 3.10
3.8.2 Discussion global strength
Even with great conservative assumptions as mentioned before, the results shows large margin to the maximum allowable stresses in table 3.5. The maximum utilization is seen in the 12-direction for the 45 lamina where it reaches 0.3%. For the maximum stress, 1-12-direction for 0o
orientation in crest landing, the utilization is 0.15%. This analysis is not accurate enough to be able to say anything concrete about the the actual global strength, but from the result with conservative assumptions it is possible to draw the conclusion that a more detailed study is not necessary within this context of study.
TABLE3.10: Local stresses for global strength analysis with conservative assump-tions
Local stress [MPa]
landing crest hollow
orientation σ1 σ2 τ12 σ1 σ2 τ12
0o 0.5088 0.0102 0 0.4567 0.0086 0
90o 0.0354 0.0102 0 0.0297 0.0086 0
23
Chapter 4
Differences in rules for classification
In correspondence with representatives from DNV-GL it was stated that there are no docu-mented (published) effects of the changes in the rule equations. Since the SEAL Carrier hull was designed upon the DNV rules from 2011, and with the merge of DNV and GL and the update of the rules it is interesting to see what has happened regarding this hull structure. In section 4.1 slamming pressure between the two editions of rules are compared and the effects of the analyzed hull bottom structure. It is followed by section 4.2 which handles bending mo-ment, stress and deflection calculations together with the allowable values for criteria. It has been noticed that there are changes regarding the determination of design acceleration as well, since this analysis starts with an assumption of design acceleration, from earlier made analysis within JFD it has been neglected in this analysis.
4.1
Design loads
This section analyses the results of slamming pressure calculated in the rules for classification Pt 3 ch 1 for the two editions of DNV, (2011) and DNV-GL, (2016)(b). Design load according to DNV-GL 2016 is described in section 2.2, but for clarity slamming pressure (earlier equation 2.1) is rearranged and here stated in equation 4.1. In equation 4.2 is the slamming pressure according to DNV 2011 shown, and notice the similarities of the three last terms. As expected, there are a lot of similarities as, both methods using both depth at rest and loading area. Re-garding load area, it also hides the big difference together with the reduction factor Kred, which
connects the load area to the reference area. In section 2.2 the relationship between load area and reference area is described. The two expresions of slamming pressure are defined as,
psl2016 = ∆ · Kred 0.14 · Aref · Kl· Kβ· acg (4.1) psl2011 = 1.3 · T · ∆ A 0.3 · Kl· Kβ· acg (4.2)
where a description of the differences follows. The exact relationship between the formulas is hard to derive, but it is possible to see that is it the handling of load area and reference area in the 2016 rules that induces the largest difference. Another aspect that is handled differently between the two sets is the draught of the hull. For both sets, the draught is defined at L/2, but in DNV 2011 the hull is at normal operation at service speed while in DNV-GL 2016 the hull is at rest in calm water. From the definition of Aref in equation 2.3, the reader realize that
FIGURE4.1: Slamming pres-sure rule formula for 2011
DNV and 2016 DNV-GL
FIGURE 4.2: Percentage dif-ference between 2011 DNV and 2016 DNV-GL rule for-mula for slamming pressure
The result shows that the two different pressure formulas follows similar pattern but differ in order of kP a. The first finding was that the equation from 2011 4.2, generates larger pressure on the panel fields for all panels, see figure 4.1. To detect the relative difference, the result from 2011 is compared to the the result from 2015 and the outcome is presented in figure 4.2.
The range differs from 2 to 15% and for the longer sections as section number 1 and 4, the difference peaks. Between the panel 1 to 4 within each section, the difference do not differ significantly, while panel number 5 is not that affected by the difference in size of the sections. This might be an effect of the panel field being relatively small in all sections. The conclusion is that with more slender panel fields the pressure difference becomes larger, and with the rules from DNV-GL 2015 the pressure is lower.
4.2
Hull structural design
In the sections considering beams in the two editions, these defines bending moment equally as defined in equation 2.23. This means that the beam reactions and responses follows the pattern of the pressure calculation earlier discussed. For stress calculations in beams, it does not follow the same procedure. In edition from 2011 DNV defines effective section modulus as ruling and defines a minimum value for the beam. It is depending on the allowable design stress and therefore limits the generated stress. For edition 2015 DNV-GL defines the strain as dependent on the flexural stiffness which is dependent on the specific moment of inertia. The methods are similar but nut fully consistent. A more thorough analysis for beams has not been executed.
Considering panel fields the procedures differ once again. For 2011 DNV stress was cal-culated directly from design load and not via bending moment as it is in edition 2015. In this analysis the boundary condition is fixed at all sides to be consistent with the earlier analysis. For 2011 bending stress for panels are defined as,
σ = C3 · 1000 ·b
2
t2 · Pd (4.3)
4.3. Design criteria 25 the procedure to determine the bending stress is described in section 2.4. The SEAL Carrier structure is used to compare the results from these two methods and the percentage difference in favour for edition 2015 is shown in figure 4.3. A positive value shows that the stress in 2015 edition is larger than the one for 2011 even though the pressure is larger for the 2011 edition.
FIGURE4.3: Stress difference described as edition 2015 over 2011
4.3
Design criteria
For the rule set 2016 the design criteria follows the procedure described in section 2.5. Notice-able is that it does not consider the actual material properties but instead uses reference values if the laminates are not tested. In 2011 edition it takes the material properties in consideration, for both plate and beams it is specified as,
σn= 0.3σnu (4.4)
and the coefficient σnu is the tensile stress defined by the laminate, and for this analysis the
laminate considered is one layer of fiber with resin with values from Composites-Toray, (2016). With this setup and σnu = 1570 MPa, an allowable compressive stress of 471 Mpa is
as-signed. For edition 2015 the it follows section 2.5 and the usage of equation 2.7 to define one lamina strength modulus an allowable compressive strength of 331 Mpa is obtained. This states that the strength criteria (maximum stress) for 2011 is 42% larger than for the new 2015 edition. Further more, the definition of deflection has changed between the rule editions. In DNV 2011 lateral deflection for plates is defined as the thickness of the laminate times a deflection factor δ, which is shown in equation 4.5. Coefficient C1 is a boundary condition coefficient
FIGURE4.4: Calculated lateral deflection differences in percentage relative 2015 edition
With the procedure for determine lateral deflection for panels according to DNV-GL 2015 in section 2.4, the two methods for determine lateral deflection has been compared. In figure 4.4 are the results from the deflection from edition 2011 compared with edition 2015. The results shows that the in most cases the lateral deflection for edition 2015 is smaller than for edition 2011. Mostly it is in the range of 5 to 10% but for section 2 panel 4 it reaches 18%. This could be an effect of how the methods differ in the handling of geometrical and structural parameters. Edition 2011 consider width and thickness of the panels, while edition 2015 consider width and length. In the case of panel 4 in section 2 the span aspect ratio (mentioned in section 2.4) is close to 1 and therefor affects the boundary condition factor α in equation 2.26. This is an effect not seen in edition 2011.
Also found in the rules is that the criteria for lateral deflection differ between the two edi-tions. For edition 2015 the deflection criteria is described in section 2.5, where focus within this analysis is on the High strength carbon uni-axial strain and deflection for panels Zmax/Sef f. The
criteria for edition 2011 was stated above as 2 times the laminate thickness. With a comparison of the two criteria as a division between them it is seen, as presented in figure 4.5 that the dif-ferences are large. It shall also be noticed that panel number 5 is excluded due to ratios above 500%, which might be an effect of this panel being long and slender but with extra layers in the layup sequence. The results shows that the criteria defined by edition 2015 is smaller in mm and therefore more strictly than edition 2011. Even though the criteria and procedure differs remarkably, when applying 2011 procedure and criteria the outcome is that only one panel less do not fulfill the criteria with respect to deflection. However, the margins differ a lot.
4.3. Design criteria 27 advantageously regarding the lateral deflection criteria, and edition 2015 is more strict.
FIGURE4.5: Percentage difference in lateral deflection criteria edition 2015 com-pared to 2011, panel 5 excluded due to differences >500%
4.4
Discussion
The changes within the rule equations have had an noticeable impact on the result of the struc-tural capacity of the SEAL Carrier regarding the DNV-GL rules for classification. Pressure calculations now use the implementation of reference area described in section 2.2. The effect of this implementation seems for this hull structure arrangement be that the design pressure is lower than the earlier edition of the classification rules.
The effect of the decreasing design pressure, has a linear effect on the bending moment, since bending moment for beams is defined equally between the editions. For panels though, there is a considerable difference in methodology, edition 2011 calculates the bending stress directly from design pressure. The conclusion is that it follows that the stress calculated with DNV-GL rules 2015 is larger than the rules from 2011.
For design criteria for bending stress it was showed that the the 2011 edition included mate-rial properties that was not considered in edition 2015. This allows the choice of matemate-rial within the group of carbon fibre affect the design criteria, while in edition 2015 it is fixed for carbon fibre. For this setup where it was shown that the maximum allowable stress was 42% larger for edition 2011 than 2015. This makes the rules for classification edition 2015 more narrow than 2011 regarding stress.
For lateral deflection, only plates were considered. It was shown that in the edition 2011 lateral deflection affected by a relation of panel width and thickness, while in edition 2015 it is affected by panel width and length. The analysis shows that the lateral deflection considered in edition 2015 in the majority of the panel fields, is lower than the one calculated with edition 2011. However, it was also later shown that the criteria had changed with more narrow cri-teria for edition 2015. The cricri-teria fro 2011 considered the plate thickness as ruling and 2015 considered effective span. This led to a more varied criteria in the case of 2015 edition, and by comparing it in terms of absolute values [mm] it showed that the deflection criteria is a lot more strict for 2015 rules of classification than 2011.
29
Chapter 5
Discussion and conclusion
With the analyze setup as described, the results in chapter 3 shows that there are some criti-cal structural members related to the loading condition. Chapter 4 addresses the differences between the rule set by DNV in 2011 and DNV-GL in 2016. This chapter aims for summarize the results and conclusions from the whole analysis. It shall also be highlighted that a criteria not meet, do not necessary mean that a structure will fail, rather then that the society’s margin against failure is not meet.
5.1
Discussion
In chapter 2 are the fundamental theory defined by DNV-GL and CLT described which capture the essence of the equations used in the analysis. It does also specify some needed assumptions which limits the rule based design defined by DNV-GL together with the design rules which limits the reactions related to stiffness and strength. Then in chapter 3 it follows with definition of the calculated structure and some simplifications are presented and discussed along with appendix D. The results shows that 9 panels and 1 beam fails regarding to at least one of the criteria. In appendix C are the utilization regarding to the criteria for the worst ply for each lamina. In chapter 3.7 the results are discussed and some general propositions are presented. Chapter 4 follows up with an analysis of the differences in the rule sets which has induced the result of failure in the structure.
5.1.1 Panel fields
First of all do the panels lack 450g/m2 fiber reinforcement which of course helps the structure come closer to the criteria. However, some of the criteria is exceeded by 60% and therefore do the panel structure need more reinforcement. There are several ways of increasing the strength and stiffness in panels. One way is to rearrange the structural members to distribute the load better. Another way is to use sandwich structure by implementing a core element. In section 3.7.1, it was mentioned that implementing a core with the thickness of the single skin thickness increases the flexural rigidity 12 times and bending strength 6 times. With a short analysis it was seen that with using 2 times the bending stiffness for panels, the result showed only one ply failing the strain and stress criteria and now failure related to lateral deflection. By implementing a core element with thickness equal to the single skin thickness, the number of plies could be reduced and also therefore the total mass of the hull. It shall also be pointed out that minimum reinforcement requirement for a sandwich structure is 38% lower acc. DNV-GL which makes room for optimization.
increases with 100%. Since the method of determining the lamina thickness is not very pre-cise, it would be better to implement sandwich core and reduce the number of fiber layers to decrease the influence of this input and ensure stiffness and strength properties in the panels. 5.1.2 Longitudinal beams
As seen, the beams were much more suited for the loading condition relative the criteria. The two long span sections, 1 and 4 have higher utilization, but generally the beams are mainly governed by the required minimum reinforcements and the global loads.
In section 3.2.2 the author describes a procedure to implement hierarchy between the beams. The result are also affected by this procedure not corresponding to the actual relationship be-tween the beams. In section D.4 in appendix D is the effects of the procedure shown. The result is that the strain in the smaller beam is decreased while in the stronger beam the strain is increased which is the sought behaviour.
5.1.3 General
From the result and analysis made in appendix D it is shown, as expected, that lamina thickness is the most critical uncertainty in this analysis. It is seen that with even a small (0.02mm) decrease in thickness, the output strain in the analyzed panel increases with ∼ 20% and the lateral deflection increase with ∼ 35%.
The method to determine the thickness as described in 3.4, is assumed to well represent the real circumstances. However, the generated thickness of the panel laminates do differ 2mm compared to the real panel. A larger thickness would of course increase the strength and stiff-ness properties of the laminates. With a larger thickstiff-ness of the lamina though, it follows that the volume fraction decreases. The common effect of this variation is not analyzed, but in ap-pendix D these are analyzed one by one. From the graphs in figure D.1 and D.2 it can be seen that an increased lamina thickness has a stalled behaviour and a decreased value of volume fraction it has an escalating behaviour. Therefore, one could assume that the total effects of thicker lamina and lower volume fraction of fiber might have a negative outcome on strain and deflection.
5.1.4 Rule changes
This analysis shows that the established changes in the DNV-GL rule set has some significant effects on this hull structure. There has been changes in all steps of the rule-based design, from the loading to reactions and design criteria. The conclusion is that the 2016 DNV-GL rule set demands stronger structure which possibly could lead to heavier hull structure for the future SEAL Carrier.
5.1.5 Certification
