smeared shell modelling approach for structural analysis of heritage composite structures – an...

Computers and Structures 88 (2010) 649–663

Contents lists available at ScienceDirect

Computers and Structures

journal homepage: www.elsevier .com/locate /compstruc

Smeared shell modelling approach for structural analysis of heritage compositestructures – An application to the Cutty Sark conservation

Stoyan Stoyanov a,*, Peter Mason b, Chris Bailey a

a School of Computing and Mathematical Sciences, University of Greenwich, Old Royal Naval College, Park Row, Greenwich, London SE10 9LS, UKb Cutty Sark Trust, 2 Greenwich Church Street, Greenwich, London SE10 9BG, UK

a r t i c l e i n f o

Article history:Received 20 October 2009Accepted 8 February 2010Available online 5 March 2010

Keywords:Computer aided conservationComputational modellingShip modellingSmeared shell approachCutty SarkComposite structures

0045-7949/$ - see front matter � 2010 Elsevier Ltd. Adoi:10.1016/j.compstruc.2010.02.005

* Corresponding author. Tel.: +44 (0)20 8331 8520;E-mail address: [email protected] (S. Stoyanov

a b s t r a c t

This paper discusses the computational modelling used to simulate the structural behaviour of the his-toric ship Cutty Sark and her response to different load and new support conditions, various treatmentsand interventions as part of a major conservation programme. A novel modelling approach suitable toanalyse quickly and at a global level complex heritage structures with composite shell-like nature suchas the Cutty Sark is presented. This modelling approach is validated and applied to understand and ana-lyse a number of structural assessment problems relevant to the conservation programme includingplank removal procedures and the design of a new support structure.

� 2010 Elsevier Ltd. All rights reserved.

1. Introduction

Computational mechanics techniques, although not extensively,have been applied in the past to undertake structural analysis ofhistoric buildings, monuments and related structures [1]. Typicallyelastic or non-linear conventional finite element analysis is used inthe study of heritage architectural structures such as masonrywalls, bridges, and buildings of special shape. The main challengewhen modelling heritage structures is to accurately represent theaged state of the materials and to make reasonable assumptionsfor the structure, the load conditions and the interactions withthe surrounding world. Therefore, the modelling procedures andthe input information and data for the respective models in anysingle application could be very unique.

There is large number of historic ships that are in urgent need ofrestoration or conservation where computational mechanics canbe also used as a key tool to identify their structural state, to assessthe stress and strength of the aged materials and structural compo-nents, and to help put in place relevant conservation and repairprogrammes. Finite element analysis has been applied mainly inthe design of conventional monohull marine vehicles but also toother types of vessels and structures ranging from steel-basedthin-walled offshore structures to surface-effect marine vesselsto large military carriers and submarines [2]. These modern com-putational methods have been applied primarily for the purpose

ll rights reserved.

fax: +44 (0)20 8331 8665.).

of design of vessels built in the last few decades and looking intoissues related to structural strength and safety. However, in thepublic domain little can be found on the use of finite element anal-ysis, or similar computational techniques, for the conservation ofheritage marine structures.

The modelling and simulation studies and the associated analy-ses presented in this paper refer to the conservation of such a his-toric ship structure, the 140 year old last surviving clipper in theworld Cutty Sark. The key concept underpinning the modelling ap-proach is in the development of a global model of the ship whichrepresents the whole structure using shell elements with smearedproperties in order to provide the inclusion of key structural inter-actions at global level. This global model is then enhanced with anumber of explicitly represented structural components whichare of a specific interest and require detailed stress analysis assess-ment. These enhanced models are analysed using coupled smearedshell and beam structural finite elements. The methodology doesnot utilise the classical shell theory calculations but instead it ex-ploits the route of a direct formulation and input of the stiffnessmatrices of the smeared shell elements into the analysis program.

1.1. The history of Cutty Sark

Cutty Sark is the last surviving cargo clipper in the world, a typeof vessel that has marked the most advanced development in thedesign of the merchant sailing ships in the 19th century [3]. Theship was launched in 1869 and was the fastest ship in the worldat the time. During the first years of her life the ship was used in

http://dx.doi.org/10.1016/j.compstruc.2010.02.005

mailto:[email protected]

http://www.sciencedirect.com/science/journal/00457949

http://www.elsevier.com/locate/compstruc

650 S. Stoyanov et al. / Computers and Structures 88 (2010) 649–663

the China tea trade and later in the Australian wool trade. For al-most 30 years after that Cutty Sark sailed under Portuguese flagtramping cargoes, mainly between the Portuguese colonies. In1922 the ship was bought back and moored at Falmouth.

In 1954 Cutty Sark was towed to Greenwich London, restored toher original appearance and positioned to reside into a dry dock onthe river Thames. In 1957 the ship was opened as a tourist attrac-tion to the public. Since then, over 15 million people have visitedthis historic ship. Fig. 1 shows a photo of the vessel.

1.2. Composite design of the ship

Cutty Sark has a unique design which has marked the transitionfrom wooden to iron ships in the second half of the 19th century. It

Fig. 1. The Cutty Sark clipper ship.

Fig. 2. The composite design of Cutty Sark.

Fig. 3. The deterioration of

is a composite built vessel made of wrought iron frames skeletonto which wooden teak and rock elm planks are fastened. The fas-tenings were made of Muntz metal bolts (an alloy of copper andzinc is in an approximate ratio of 60:40). The two decks of the shipare hold by curved deck beams located every 1.37 m along the ship.The hull iron frames spacing is three times denser than the deckbeams, i.e. placed at every 0.42 m along the hull. A unique featureof the design is the presence of diagonal cross-bracing plates on thehull and on the lower deck. At present, 140 years after the ship wasbuilt, about 80–90% of her hull fabric is still dating from her origi-nal construction. Even after a devastating fire in 2007 which thestructure has suffered, fortunately very little of the fabric of theship was lost or damaged [4]. At that time the ship has alreadystarted the currently ongoing major conservation programmeand most of the ship has been dismantled and the fabric storedaway from the conservation site. The composite design of the CuttySark is illustrated in Fig. 2.

1.3. Cutty Sark – conservation programme and the future

Unfortunately, over the years the iron structure of the ship be-came corroded and immediate action was required to conserve theship. The degree of corrosion of the wrought iron in some placeswas quite severe. Some regions of the iron frames have corrodedaway completely and in others they have become very thin, espe-cially around the sides of the Muntz metal bolts as a result of thebi-metal corrosion. An examination of the structure undertakenfew years ago has shown also a major build-up of rust at the woodand iron interfaces. The impact of the environmental conditions onthe ship over the years has caused also a significant decay of thewooden planks. Fig. 3 shows examples of corroded and decayedmaterial of the ship’s fabric.

Despite the regular maintenance and partial repairs over theyears, the long-time deterioration of the wrought iron frameworkand timber planking was fact and major conservation was requiredif the ship is to survive. There was a real risk that the ship will dis-integrate if the deterioration process continues unchecked. In late2006 a major conservation programme has started. As part of theconservation, the ship is undergoing various interventions andtreatments to minimise the continuing corrosion. Raising the shiponto a new support structure and turning the entire dry dock siteinto a modern museum was the second key objective in theproject.

Some of the problems tackled in this ongoing programme are:

� Treating the ironwork with a combination of electrolysis andmechanical cleaning to preserve as much original fabric aspossible.

� Removal of the wooden planks and deck timber for treatment,then put them back to their original locations.

� Strengthening the weakened frames.� Replacing components that are beyond repair.� Raise the ship above ground; the new support system designed

in a way to give an even support to the hull.

the Cutty Sark’s fabric.

Fig. 4. Computer aided conservation framework for Cutty Sark.

S. Stoyanov et al. / Computers and Structures 88 (2010) 649–663 651

Computational mechanics is being undertaken to help under-stand the structural behaviour of the ship both in her current formand in the planned new support structure. The modelling frame-work is based on finite element analysis and is being utilised toaid the conservation program. The composite structure of the shipand the damage in the material poses a number of challenges forcomputational mechanics and finite element analysis; these havebeen addressed at all stages of the computational analysis, fromthe CAD model development to the actual structural analysis.The concepts behind this computer aided conservation as appliedto the Cutty Sark are outlined in Fig. 4.

2. Computational modelling

2.1. Development of a global model of Cutty Sark

A complete model capturing the whole length of the ship hasbeen developed. This model represents the ship as a shell structure.This has the advantage of being able to speed up the CAD modeldevelopment and to undertake the subsequent finite element sim-ulations quickly and more efficiently. This is because the analysisof a structural shell model is not as compute intensive as the anal-ysis of the detailed continuum finite element models. Using a com-puter model of the whole ship is important as it captures theresponse of the vessel to the analysed support and loading condi-

Fig. 5. Global CAD model o

tions at global level and can predict how different sections of thevessel interact.

Fig. 5 illustrates the CAD model of the Cutty Sark ship. The CADsoftware tool for non-uniform rational B-splines modelling Rhino[5] is used to model the complex curved shape of the ship. Themodel of the ship consists of surfaces that capture and representthe hull and the decks of the vessel. The advantage of having sucha model is in the ability to assign subsequently structural shellelements to the CAD model in a convenient and straightforwardmanner. The strategy of this CAD modelling is in line with thesmeared shell analysis approach detailed in the next section ofthe paper.

2.2. Smeared shell methodology

2.2.1. Basic classical shell theoryIn the classical thin shell theory, a structural shell obeys two

different types of behaviour [6,7]:

1. Membrane behaviour.2. Flexural behaviour (thin plate).

The shell behaviour is defined in the shell element local coordi-nate system where x and y are the notations for the shell in-planeaxes and z is the out-of-plane axis. For an isotropic linear elasticmaterial, the membrane (in-plane) rigidities relate the in-planeforces per unit length {N} to the strains {e} via the relationship

Nx

Ny

Nxy

8><>:

9>=>;¼

A1 A2 A4

A2 A3 A5

A4 A5 A6

264

375

ex

ey

exy

8><>:

9>=>;

ð1Þ

where [A] is the matrix of the shell stiffness (rigidly) in-plane coef-ficients. If the material has elastic modulus E and Poisson’s ratio mand if we denote the shell thickness with t, the membrane rigiditiescan be calculated as:

A1 ¼ A3 ¼Et

1� m2 ; A2 ¼mEt

1� m2 ;

A6 ¼Et

2ð1þ mÞ and A4 ¼ A5 ¼ 0 ð2Þ

The flexural behaviour (the case of thin shells) is representedthrough a relationship between the bending moments of the shellper unit length {M} and the curvatures {k}:

f the Cutty Sark ship.


Mx

My

Mxy

8><>:

9>=>;¼

D1 D2 D4

D2 D3 D5

D4 D5 D6

264

375

jx

jy

jxy

8><>:

9>=>;

ð3Þ

In the above relationship [D] is the matrix of the bending stiff-ness (rigidity) coefficients defined as

D1 ¼ D3 ¼Et3

12ð1� m2Þ ; D2 ¼mEt3

12ð1� m2Þ ;

D6 ¼Et3

24ð1þ mÞ and D4 ¼ D5 ¼ 0 ð4Þ

As evident from the definitions (2) and (4) of the shell stiffnesscoefficients, the in-plane and the bending rigidities are not inde-pendent; these coefficients are functions of the shell material prop-erties and the shell thickness. Unfortunately, the above classicalshell theory relations (1)–(4) cannot be used in this form for theanalysis of the Cutty Sark despite many similarities between theship’s structure and a typical shell structure. The reason for thisis the composite nature (iron and wood) of the Cutty Sark andsome of the unique features in the ships design.

To be able to analyse the ship based on a shell representation ofthe structure, in particular the hull and the decks of the ship, analternative modelling strategy that exploits the actual unique com-position of the ship has been developed, tested and applied. Themodelling approach, referred in this paper as a ‘‘smeared shell ap-proach” is outlined in the following section.

2.2.2. Smeared shell approachThe Cutty Sark vessel is a typical example of a historic structure

with composite nature. The wooden planks on the hull of the shipare orientated along the longitudinal direction of the vessel whilethe iron frame stiffeners are perpendicularly placed with respectto the planks (i.e. vertically orientated on the hull). Similarly, thedeck iron beams and the deck wooden planks attached to themare also perpendicularly placed to each other. In the direction of

Fig. 6. Composite iron–wood structure of ship (a) and mo

the hull iron frames, small gaps exist between the adjacent woo-den planks; therefore in vertical direction with respect to the ship’shull, the structural integrity of the wooden planks is a result oftheir fastening to the iron ribs only. Similarly, adjacent iron ribson the hull are connected primarily through the wooden planksalthough there are also some iron plate stringers which are longi-tudinally placed.

The lower and upper decks of the ship have the same uniquecomposition as the hull comprising of deck wooden planks anddeck iron beams. A unique feature of the design of the Cutty Sarkis the presence, both on the hull and on the upper deck, of diagonalcross plates. The main purpose of the diagonal cross plates is toprovide shear stiffness in the respective regions of the hull andthe main deck. The composition of the ship is illustrated in Fig. 6a.

The approach being developed is to use and exploit the abovedescribed nature of the Cutty Sark composite design in the struc-tural modelling and stress analysis of the clipper. Looking at theship at a global level and on the structure as a whole, it is clear thatthe stiffness in the ship’s longitudinal direction, along the hull, isprovided primarily through the wooden planks of the hull anddecks and a number of stringer plates. However, in the directionof the iron ribs (vertically) the contribution for stiffness comesmainly from the wrought iron frames and deck beams for the hulland the decks respectively. Shear stiffness is presented primarilythrough the diagonal cross plates on the hull and the upper deck.

Accounting for the above composite features in the design ofthe ship, we start to look at the ship as a shell structure. The under-lying concept utilised in this development is for the shell to repre-sent the composite wood–iron nature of the structure. The shellsobey behaviour that smears the stiffness contributions from theships wooden and iron components by taking into account thedirection of their orientation. This requires the calculation of therigidity coefficients associated with the stiffness of the smearedshell elements in an independent manner. The axial and shearin-plane and the bending stiffness of the smeared shells are inputsfor this type of analysis using finite elements. These values depend

delling it through shells with smeared properties (b).


on the location on the hull for each shell element and the localcoordinate directions (along the planks or along the iron frames).Note that the smeared shell definition still exploits the classicalshell theory relations (1) and (3). However, because we deal withcomposite shells with very different stiffness behaviour in the dif-ferent directions based on the composition, the stiffness coeffi-cients in the matrices [A] and [D] are independent and can notbe calculated anymore using Eqs. (2) and (4).

Let’s use the following notations for the smeared shellelements:

� In-plane (membrane) stiffness components: Ax, Ay and Axy.� Bending (plate) stiffness components: Dx, Dy and Dxy.

where x and y are the local element coordinate system axes.In the utilised smeared shell approach for modelling and analy-

sis of composites as those realised on the Cutty Sark, the six shellstiffness coefficients (Ax, Ay, Axy, Dx, Dy, and Dxy) are obtained usingthe following rules and equations (refer also to Fig. 6b):

� Hull axial stiffness (given in the shell element coordinate systemx–y axes)

(1) X-axis: Wooden planking(Ew, tw)

where

Ew is wood Young’s modulus,Ax = twEw tw is wooden plank thickness,

(2) Y-axis: Iron beams(y-oriented)

Ei is iron Young’s modulus,

(Ei, Ai) Ai is the frame cross-section area,Ay ¼ te

i Ei tei is iron equivalent thicknessðAi ¼ te

i � sÞ,(3) Shear X–Y stiffness if iron

diagonal platesGd is the equivalent shearmodulus of diagonal plates

Axy = tdGd (Axy = 0 otherwise) td is diagonal plates equivalentthickness.

� Hull bending stiffness (given in shell element coordinate systemx–y axes)

(1) X-axis: Wooden planking (Ew, tw) whereDx = (tw)3Ew/12 Ew is wood Young’s modulus,

(2) Y-axis: Iron beams (y-oriented)(Ei, I)

Gw is wood shear modulus,

Dy = IEi/s tw is wooden plank thickness,(3) Torsional stiffness Ei is iron Young’s modulus,

Dxy = (tw)3Gw/12 I is the beam moment ofinertia,s is distance between ironframes

The rules for shell stiffness determination account for the degree towhich any component of the structure contributes to the stiffness.The in-plane and bending stiffness coefficients are calculated inde-pendently; there is also no Poisson’s ratio effect associated withthe smeared shell elements. The analysis requires the input ofthese stiffness coefficients (the so called matrix input) whichreplaces the usual coefficients used in the shell theory. Based onthe actual location of the iron components and wooden planking,there are a number of areas that make up the hull and decks ofthe ship with different axial and bending stiffness.

The degree of corrosion of iron components is modelled byappropriately reducing the iron beams cross-sectional area andmoment of inertia based on the real degree of material lost as a re-sult of the corrosion damage. This consequently affects the valuesof the smeared shell stiffness coefficients.

2.2.3. Smeared shell approach: the case of Cutty SarkIn the global model of the Cutty Sark, the hull and decks part of

the structure is represented by shells to which the smeared ap-proach is applied. On the hull, six different regions are definedbased on the nature of the composition that they have. Some ofthe regions are composites of iron frames and wooden planks, oth-ers have in addition iron plates and/or iron cross-bracing. Dimen-sions of planks (thickness) and iron components cross-sectionalproperties also change from region to region. This division of thehull to regions aims to ensure more accurate representation ofthe structural behaviour of the hull at these locations. Followingsame principle, the lower deck of the ship is divided to three re-gions corresponding to:

(1) Composition of deck beams and wooden planks only.(2) As (1) above plus longitudinal iron plates.(3) As (1) above plus deck stringer plate.

Because the self weight of the structure itself is the key loadthat will be presented, it is important to accurately calculate theequivalent smeared shell density. This is straightforward and allthat is required are the volumetric dimensions of the woodenplanks and iron components that build-up the composition of aparticular region on the hull or deck. Based on the shell area, thefirst calculation is on the equivalent smeared shell thickness sothat the volume of the smeared shell is equal to the volume ofthe wood and iron in that area. Then using the rules of mixture,a smeared density for the shell is calculated as a sum of the densityof each material (wood and iron) multiplied by the correspondingvolumetric fraction for that material from the total compositionvolume. Having smeared shell thickness and smeared shell density,the analysis program can calculate the weight and apply this asload if required.

The shell stiffness for any region on the hull or deck iscalculated following the smeared shell approach rules for CuttySark. As a demonstration, detailed calculation of the shell stiffnesscoefficients in this section is given only for the following tworegions:

(1) Region R1 – Iron frames and wooden planks compositionstrengthen by iron sheerstrake (topmost part of the hull).

(2) Region R2 – Deck beam and deck wooden planks.

The structural properties of the components in Regions R1 andR2 are listed in Table 1.

Using these properties it can be calculated that the bendingstiffness of the iron frame with respect to YY axis of the cross-sec-tion is 1.6116E+06 N m2 (Iyy

* E). The iron frames on the hull are lo-cated every 0.457 m, along the ship, and therefore an equivalentshell bending stiffness per unit length (along the ship) is3.525E+06 N m2. Similarly, in Region R2 the deck beams are lo-cated every 1.376 m along the ship. Therefore, the deck beambending stiffness 7.915E+06 N m2 with respect YY cross-sectionalaxis is equivalent to a shell bending stiffness 5.77E+06 N m2.Applying the rules for calculation of the smeared shell stiffness,the coefficients reported in Table 2 are determined. Note that forRegion R1 the stiffness along iron frames (local y-direction forshell) is sum of the stiffness from both the iron frame and the ironsheerstrake. Similarly, the stiffness along the wooden planks (local

Table 1Structural and material properties of the components comprising the composite build-up in Regions R1 and R2 of the Cutty Sark.

Component Thickness t (m) Young’smodulus E (GPa)

Shear modulusE (GPa)

Wooden plank (Region R1) 0.12 9.0 0.9Wooden plank (Region R2) 0.0762 9.0 0.9Iron sheerstrake 0.016 204.0 82.0

Cross-section area A (m2) Moment of inertia I (m4)

Hull iron frameYY

ZZ

0.004777 Iyy = 0.790E�05Izz = 0.558E�05

204.0 82.0

Lower deck beam YYZZ

0.00595 Iyy = 0.388E�04Izz = 0.321E�05

204.0 82.0

Table 2Smeared shell stiffness coefficients for the direct matrix input for Regions 1 and 2.

Region Ax (N m) Ay (N m) Axy (N m) Dx (N m) Dy (N m) Dxy (N m)

Region R1 4.344E+09 4.859E+09 1.312E+09 1.366E+06 3.595E+06 1.296E+05Region R2 0.686E+09 0.8872E+09 0 0.3318E+06 5.77E+06 0.03318E+06


x-direction for shell) is sum of the respective stiffness from woodenplanks and the iron sheerstrake.

The in-plane smeared shell stiffness in direction of an ironframe or a deck beam (coefficient Ay) is calculated by estimatingan equivalent thickness for the iron component cross-section overa unit smeared shell area. For example, in the case of the compo-nents in Table 1, the iron frame equivalent thickness te

i over a unitarea of smeared shell is 0.00782 m and for the lower deck beam theequivalent thickness is 0.0043 m.

2.2.4. Smeared shell approach: the analysis outputThe structural shell analysis based on smeared shell approach

exploits the direct matrix input of the smeared shell stiffness coef-ficients and does not require any specification of material proper-ties of the shell element. The results from such an analysis includethe deformation of the structure (3 translations and 3 rotations ofeach mesh node), strain, shell in-plane forces per unit length andshell bending moments per unit length. In this study, the smearedshell approach calculations are carried out using element typeSHELL99 in ANSYS analysis software [8]. SHELL99 is the elementtype with an option to switch on and use a direct input of the stiff-ness matrix.

The forces and bending moments of the smeared shells must bepost-processed to the relevant stress quantities associated with theactual components that build-up the ship’s hull and decks. In thisstudy the interest is primarily on the stresses in the iron frames.Therefore only these secondary calculations will be outlined. Sim-ilar procedure can be used to predict stresses in the wooden planksand the other structural components.

Using the smeared shell model predictions for in-plane forcesand bending moments and the cross-sectional properties anddimensions of the iron frames, the actual axial and bending stres-ses associated with the iron frames can be computed. These post-processing calculations are performed in two steps:

(1) The smeared shell results for the in-plane forces in directionof iron ribs Fshell and the bending moments Mshell per unitlength are related to the axial force Firon and bendingmoment Miron of the iron frames based on the number of ribs

per unit length. If s is the distance between two adjacent ironframes (as illustrated in Fig. 6a) then the following relation-ships exist:

Firon ¼ s Fshell and Miron ¼ s Mshell ð5Þ

(2) The iron frames axial force and bending moment predictionsare used to calculate the axial and bending stresses in thesection in a conventional way. This requires the iron framecross-sectional properties and dimensions: the cross-sec-tional area A, moment of inertia Iyy, cross-section centroidlocation and the maximum distance from the centroid tothe external frame flange zmax. The stresses are calculatedas follows:

raxial ¼Firon

AðAxial stressÞ ð6Þ

rbend ¼Mironzmax

IyyðMaximum bending stressÞ ð7Þ

where raxial and rbend are the iron frame axial and bendingstresses, respectively.

3. Validation of smeared shell modelling approach

3.1. Computational validation

The modelling study presented in this section is intended as aform of validation of the smeared shell approach. The followingthree modelling strategies for static elastic analysis have beentested and the results compared:

� Model A: Full 3D (three-dimensional) model with continuumfinite elements.

� Model B: Model based on combined use of structural beam andshell elements.

� Model C: Structural shell model with smeared stiffness behav-iour (smeared shell approach).

Fixed UX, UY and UZ

Fixed UZ

Force F=1.5 KN in Z-direction applied at

top end of each frame

F F F

Fig. 7. Test case structure and the boundary/loading conditions.


The test case structure corresponds to a small section on thehull of the Cutty Sark ship. It is a panel that consists of a woodenshell with iron frames acting as the shell stiffeners. The test struc-

Fig. 8. Stress (Model A and B, in Pa) and bending moment per unit length

ture and the analysis boundary and loading conditions are illus-trated in Fig. 7.

The test structure consists of a wooden shell (comprised ofwooden planks) with three iron frames running from one end tothe other perpendicularly to the planks. The wooden planks arenot modelled explicitly; the fact that the wooden planks are orien-tated along the x-axis and will not provide stiffness in the otherdirection is modelled through the orthotropic properties for thematerial behaviour of the wooden shell.

The predictions for stress in iron ribs from the three modelsagree favourably. The location of stress concentration and thestress magnitude are well predicted with each of the three model-ling approaches. The 3D continuum finite element analysis is themost accurate but time consuming. On the other side, the smearedshell approach would involve a degree of approximation but theanalysis itself is very fast. The maximum stress predictions frommodel A (Von Mises stress), Model B (bending stress) and ModelC (bending stress) are 31–32 MPa, 27.5 MPa and 27.5 MPa, respec-tively. The contour plot of stresses is shown in Fig. 8. If we add theaxial stress of 2–3 MPa in iron frames predicted in models B and Cto the bending stress values and compare with Model A, the differ-ence in the stress results from the three models is in fact less than3%.

The test case results from the modelling validation clearly indi-cate that the smeared shell approach applied to a composite struc-ture is sufficiently accurate and can be exploited for the analysis ofthe Cutty Sark ship. In terms of computational cost, for identicalmesh density and number of nodes, the smeared shell Model C is

(Model C, in N) predictions and comparison of the three approaches.


4.5 times faster to run compared with the coupled structural shellsand beams Model B. Compared with the full 3D Model A that hasthe same surface mesh density but larger number of nodes dueto meshing across the domain in the third dimension, the smearedshell model is significantly faster, with a factor of almost 100.

To gain further confidence in the proposed modelling smearedshell modelling approach an experimental test to provide furthervalidation is carried out as discussed in the next section.

3.2. Experimental validation

Experimental tests have been also undertaken as part of the val-idation procedure. A real prototype panel that was representingthe composite nature of the ships hull was built. This prototype,with dimensions 2.50 � 2.88 m is shown in Fig. 9. The panel mim-ics a typical Cutty Sark composition of wooden planks and, in thiscase, steel frames. The steel components are slightly curved (curva-ture 0.11 m�1) in a similar manner as the iron frames on the hull ofCutty Sark. The wooden planks have length 2.50 m and cross-sec-tion area 0.016553 m2 (0.182 � 0.0913 m). The cross-sectional areaof the L-shape steel ribs is 0.001574 m2 and the second moment ofinertia Iyy = 0.211E�5 m4. The length of the eight steel frames usedto construct the panel is 2.88 m. The eight steel frames are locatedat distance 0.31 m from each other in the direction of woodenplanks.

An experimental test has been also designed to evaluate thematerial properties of the panel. The Young’s modulus of woodalong grain is estimated at 9 GPa and across grain is 1 GPa. Theshear modulus of wood is assumed 0.9 GPa. Young’s modulus ofsteel used to make the frames for the prototype panel is 210 GPa.

Eight strain gages, one on each steel component, are used tomonitor the strain and out-of-plane deformation of the panel. Eachstrain gage is located at the central point of the corresponding steelframe, i.e. half way along the length of the component. The testthat is conducted has the following set up (see Fig. 9):

Fig. 9. A panel prototype (a) CAD represe

Table 3Strain gage transducer readings for out-of-plane displacement (mm) at the centres of the

Load (KN) Strain gage transducer reading for out-of-plane displacement

Sgtd 1 Sgtd 2 Sgtd 3 Sgtd

0 0 0 0 0�0.52 0.1 0.1 0.13 0.11�1.04 0.21 0.24 0.3 0.24�1.56 0.32 0.35 0.43 0.41�2.08 0.45 0.49 0.57 0.57�2.52 0.56 0.62 0.71 0.71�3.04 0.67 0.73 0.82 0.88�3.56 0.77 0.9 1.01 1.07�4.08 0.88 1.01 1.09 1.23�4.52 0.96 1.09 1.23 1.37�5.04 1.07 1.23 1.37 1.54�5.47 1.15 1.36 1.48 1.67

(1) Panel is placed horizontally.(2) Vertical load is applied downwards at the panel central loca-

tion point of the panel (perpendicularly to the panel plane).The load is distributed over the centre points of the centraltwo steel frames.

(3) Support of the panel is at the four corners of the panel.

The maximum load applied in this test is 5.47 KN. This valuewas identified in the process of applying the load in steps, in anincremental manner, and by monitoring the readings from thestrain gage transducers at each load step. The reason for this ap-proach is to ensure we do not overload the test structure and wedo not cause any permanent deformation. The important aspectin this test is to gather sufficient and distinctive information aboutthe deformation of the frames and the panel as a whole. This data isthen used for validation of the smeared shell model and comparedagainst simulation results of the same experiment. Table 3 showsthe observed readings from the experiment in terms of displace-ment at the locations of the eight strain gauges (denoted by Sgtd1–Sgtd 8).

The graph in Fig. 10 shows the deformation of the panel at thepoints of the strain gauge locations, i.e. along a line across middleof the panel and perpendicular to the steel frames, at the maxi-mum applied load level 5.47 KN.

The composite test structure is now modelled as a shell andanalysed using the smeared shell approach. Boundary and loadconditions are applied as in the real test. In particular, the cornersof the shell representing the panel are restrained to move in verti-cal direction and the load of 5.47 KN is applied as a pressure oversmall patch at the centre of the shell defined by the centre pointsof the two central steel frames which take the load in the realexperiment. The stiffness coefficients of the smeared shell are cal-culated using the rules for the smeared shell rigidity definitionspresented earlier. The values of these stiffness coefficients are re-ported in Table 4.

ntation and (b) actual construction.

eight steel ribs.

(mm)

4 Sgtd 5 Sgtd 6 Sgtd 7 Sgtd 8

0 0 0 00.13 0.13 0.12 0.110.28 0.26 0.24 0.20.45 0.41 0.37 0.320.61 0.56 0.49 0.440.76 0.69 0.62 0.530.93 0.84 0.74 0.621.11 1 0.89 0.741.26 1.14 0.99 0.831.42 1.28 1.11 0.921.59 1.42 1.25 1.041.74 1.56 1.37 1.13

-2.00

-1.75

-1.50

-1.25

-1.00

-0.75

-0.50

-0.25

0.000 0.5 1 1.5 2 2.5

Distance along the panel (woodenpalnks dierction) [meters]

Out

-of-p

lane

def

orm

atio

n at

stra

in g

auge

loca

tions

[mm

]

Fig. 10. Out-of-plane displacement at centres of steel frames measured by of strain gauges at load 5.47 KN.

Table 4Smeared shell stiffness coefficients of the real testing prototype.

In plane (membrane) stiffness (N m) Bending (plate) stiffness (N m)

Ax Ay Axy Dx Dy Dxy

Stiffness valuea 1.0577e9 0.8217e9 0 1.4179e6 0.5708e6 0.05708e6

a x-direction corresponding to steel frame orientation; y-direction along wooden planks.


The deformed shape of the panel, with magnification factor 40,predicted by analysing the model using the smeared shell ap-proach is shown in Fig. 11. The contour levels represent the defor-mations in vertical (global Y) direction. The dotted white linecrossing the shell through the central line of the panel indicatesthe locations of the eight strain gauge transducers used in the realexperiment.

Fig. 11. Out-of-plane deformation of the sm

The out-of-plane displacement prediction from the model alongthe dotted line of interest is compared with the measured readingsfrom the strain gauges in the experiments. Fig. 12 shows how theexperimental measurement and the model predictions compare. Avery good agreement between both set of results is found. Thisfinding has confirmed the very good predictive capability of thesmeared shell approach and that only minor loss of accuracy is

eared shell model of the test panel (m).

-2.00

-1.75

-1.50

-1.25

-1.00

-0.75

-0.50

-0.25

0.000 0.5 1 1.5 2 2.5

Model Predictions

Experimental Measurements

Distance along the panel (woodenpalnks dierction) [meters]

Out

-of-p

lane

def

orm

atio

n at

stra

in g

auge

loca

tions

[mm

]

Fig. 12. Comparison of the out-of-plane displacement results at the centres of the steel frames obtained form the smeared shell model and the real experiment.


associated with this modelling strategy. The average relative errorbetween the model and the experiment for the displacement at thelocation of the eight strain gauges is 1.5%. The experimental valida-tion of the tested approach re-confirmed the conclusions from themodelling validation outlined earlier.

4. Cutty Sark modelling results

This section details a demonstration of the smeared shell ap-proach using a global shell model of Cutty Sark. The discussion isfollowed by two conservation programme studies on the plank re-moval trials and the structural response of the ship to loads ex-erted into the original fabric through a new steel support structure.

4.1. Smeared shell approach: an analysis demonstration on Cutty Sark

This section details the smeared shell analysis of the global shellmodel of the Cutty Sark. In her future state the ship will be liftedand reside above the ground level of the dry dock. This analysisinvestigates how the ship would respond if the support points onthe ships hull are at the level of lower deck. In this first studythe support structure is not modelled explicitly. Fig. 13 illustratesthe shell model and the applied boundary conditions for this typeof support system. It is a simple assumption for the ship structure

Fig. 13. Smeared shell regions and mod

only, with constraints of zero displacement in vertical Z directionimposed at the points where the new steel external beams shouldbe in contact with the hull. Same figure shows different regionswhere the smeared shell elements have different stiffness coeffi-cients. For this analysis twenty different stiffness regions on thehull and on the decks were defined. This analysis is based on a halfship model and assumes symmetry in the structure.

Finite element analysis of this shell structure using the smearedshell approach has been performed. The smeared shell results forforces and bending moments per unit length in direction of theiron ribs are given as contour plots in Figs. 14 and 15, respectively.Note that these smeared shell results are per unit length.

From these results we can see where high forces and bendingmoments develop. Using the smeared shell model results for thein-plane forces and bending moments, the dimensions of the ironribs and their cross-sectional properties and Eqs. (5)–(7), we cancalculate the actual axial and bending stresses in the ships ironframes in different locations on the hull. In Fig. 14 it can be seenclearly where the boundary conditions representing the twelvepoints of support on each side of the hull are applied. In these re-gions the highest axial forces on the iron frames can be found. Highbending moments develop in the mid section of the ship, withopposite signs with respect the approximate location of the bilgeplate. This is not surprising and it is a result of the sagging of theship under the support conditions assumed.

el boundary conditions for support.

Fig. 14. Contour plot of smeared shell in-plane forces per unit length (N/m) across the ships hull.

Fig. 15. Contour plot of smeared shell bending moments per unit length (N) across the ships hull.


For example, in the mid section of the ship the iron frames arelocated every 0.457 m and have a cross-sectional area0.004777 m2. If we focus on a particular section of the rib, e.g. Loca-tion A in Fig. 14, and by using Eq. (5) the axial force in the framecan be calculated. Using Eq. (6) we can then relate to axial stressvalues, in the case of Location A this is 4.5 MPa tensile stress. Sim-ilarly, by taking the simulation result for the smeared shell bendingmoments per unit length and by applying in sequence Eqs. (6) and(7), the maximum bending stress can be assessed. For example, forthe iron frame section in Location B in Fig. 15, maximum bendingstress of 27 MPa (absolute value) is estimated. The information forthe iron rib moment of inertia Iyy = 0.79 E�5 m4 and the maximumdistance from centroid to flange 0.061 m is used in the abovecalculation.

4.2. Modelling the Cutty Sark plank removal trials

Trial repairs on the Cutty Sark have been scheduled as part ofthe conservation plan to verify and test various activities in thisprocess. The planned activities involve the removal of severalplanks from the outer hull in two trial areas. The strategy is to re-move around 4 planks at the level of iron bilge plate and around 3planks from the area around the keel. The final decision on thenumber of planks to be removed will be taken once the trial areais exposed. The planks in the trial area are about 11 m long. Thetrial areas for plank removal are illustrated in Fig. 16.

The undertaken finite element analysis aims to answer the fol-lowing questions:

(1) What is the stress in iron ribs in the location of trial repairsbefore the planks are removed?

(2) Will the stress change when the planks are removed fromthe hull in the area of trial repairs?

This analysis is based on boundary conditions that correspondto the present state of support, i.e. a ship residing on the groundof the dry dock on her keel. The presence of a number of supportprobes on each side of the hull is also captured. First, analysis ofthe ship in her current state before plank removal is undertaken.Then the same analysis is undertaken but this time with the modelafter the planks have been removed. The planks removal is mod-elled by implementing the following modifications in the analysis:

� Full model of the ship is used (there is no symmetry after plankremoval).

� The stiffness of smeared shell elements in the areas of repair indirection of planks is zero.

� The weight from planks in the trial areas is taken away from theloading conditions in the model.

The magnitude of the axial in-plane forces in direction of ironribs across the hull before the planks removal is shown inFig. 17. The maximum axial force associated with a single ironrib in the trial area near the bilge plate is 16.7 KN. This force causesaxial stress with magnitude of 3.6 MPa. The predicted axial force iniron ribs in the other trial area near the keel is 24 KN and the axialstress is 2.3 MPa. Note that at the bottom areas of the ship the ribstransform into floors that gave tapered cross-section and the dis-tance from the centroid to the flange in the cross-section increases.The results show that for both areas the axial stress in iron ribs donot exceed 4 MPa.

The analysis of the same model after the plank removal showsalmost identical contour plot for the shell axial force as the onepresented in Fig. 17.

Fig. 18 shows the contour plot of the bending moments per unitlength in the smeared shell elements in direction of iron ribs acrossthe ships hull before the plank removal. From the analysis predic-tions, the maximum bending moment associated with a single iron

Fig. 16. Trial areas for plank removal strategies (bold line defined regions).

Fig. 17. In plane forces per unit length (N/m) in smeared shell elements.

Fig. 18. Bending moments per unit length (N) in smeared shell elements.


rib in the trial area near the bilge plate is 1.472 KN m. This wouldresult in a maximum bending stress in the flange of the iron rib ofalmost 12 MPa.

Similarly, the maximum bending moment in iron rib in the sec-ond trial area near the keel is 11 KN m. The maximum bendingstress in the flange of the reverse frame is just below 11 MPa.The predictions from the undertaken analysis indicate that thebending stresses in the two repair areas should be less than12 MPa.

The analysis of the same model after the plank removal showsalmost identical contour plot for the shell bending moments asthe one shown in Fig. 18.

The results from finite element analysis show that there is vir-tually no difference in the ships response and her structural statebefore and after the removal of planks in the trial areas. Therefore,removing the planks in the trial areas will not cause increase in thestress magnitude of iron frames in these locations and there is nodanger of failure (e.g. buckling) as a results of the potential loadre-distribution in this regions of the hull.

4.3. Structural analysis of Cutty Sark and the new steel supportstructure

The basic smeared shell model of the ship presented earlier hasundergone a number of modifications and enhancements. In par-ticular, a detailed and explicit inclusion in the model of the newsteel support structure is realised. The design of the support struc-

ture demonstrated here is an option that the structural engineeringteam for Cutty Sark has developed and considered. Under this newsupport, the ship resides above ground sitting onto a new steelstructure comprising of several cradles along the ship.

The design of the new support structure, as illustrated inFig. 19a, consists of twelve main and un-evenly distanced cradlesalong the ship. Each cradle has two external support beams, oneach side of the ship, which hold the ship at the level of the lowerdeck. The other end of the external beams is located at the topmoststep of the dry dock site. Internally, there is a curved horizontalstrut running just below the lower deck of the ship and an internalV-type ties that connect the points of the external support on thehull to the new steel keel that will be put in place. This triangulatedsystem prevents the ship from sagging when lifted and holds thevessel above ground with minimum deformation in the originalfabric. There is an external flat plate at the level of the lower deckwhich, on each side of the ship, which connects all cradles alongthe ship. The end of the keel on the stern side is held through spe-cially arranged ties connected to the last cradle of the supportstructure. In the model, given dimensions and cross-sectional sizesof the members of this new steel support structure are imple-mented and used in the subsequent analysis.

This analysis focuses on predicting the response of the lowerdeck beams to the forces exerted onto the structure through thenew steel supports. It is critical to capture the global effects andthe interactions between original ship and new steel support com-ponents. Therefore the global smeared shell model is used in this

Fig. 19. An illustration of the (a) proposed new steel support structure and (b) the fusion of the basic smeared shell model of the ship with the explicit structural model of thenew steel support structure.


study. However, the approach we have used here is different. Wenow model the components of interest explicitly using structuralbeam elements. The role of the global smeared shell model is toact as a ‘‘super imposed structure” that affects and impacts theloading on those components. The ship’s components includedexplicitly in the modified global model are the lower deck beamsand the stringer plates. These are represented using beam type ele-ments and explicit definitions of their sectional properties andcross-sectional orientation. As a result of this, the smeared shellstiffness coefficients in the regions of these components are mod-ified to take out the stiffness contribution from the componentswhich now explicitly exist. The global model has also few othermodifications such as the inclusion of new steel frames at the low-er part of the hull to strengthen the shear stiffness and also anreplacement of the old corroded diagonal plates on the hull withnew steel cross-bracing at exactly the same location. In addition,two asymmetric openings on the hull representing entrance andexit doors are included and represented in the model as patcheswith stiffness zero. Therefore, a full model of the ship is used in thisanalysis as no symmetry plane exists in this case. This updatedsmeared shell model of the ship which incorporates the changesabove and the new support structure is shown in Fig. 19b.

The loading for the structural analysis in this study includes:

(1) The self weight of the ship.(2) Weight from masts and rigging. This is approximately 140

tones.(3) Weight of new steel support structure.(4) Live load (people on decks). The load used is 4 KN/m2,

applied to the lower and upper decks.

The total weight of the ship and the new steel support structure,excluding the live load under (4) above, is approximately 790tones.

Finite element analysis is undertaken on the enhanced smearedshell model where a range of components are modelled explicitlyas discussed previously. Simulation results for the stress in thelower deck beams only are presented and discussed here but pre-dictions for the structural response of other components of interesthave been also obtained and analysed. Although the internal newsteel struts will take substantial load exerted into the structurethrough the external support beams, the actual lower deck beamsof the ship will be also exposed to compression loads. Understand-ing the nature and magnitude of these stresses is important tojudge the degree of suitability of the entire supports design.

Fig. 20 shows the predicted axial forces at the end of the lowerdeck wrought iron beams. There are 45 deck beams and the graphillustrates the magnitude in the axial force in the individual beams.The top part of the figure shows the predicted results for the axialforce in deck beams along the ship, from bow (left) to the stern(right). The bottom of the figure shows a schematic of the locationof deck beams and external support beams and relates this to thegraph bars above. It is evident that the beams adjacent to the loca-tions of the external new steel support beams carry out more loadscompared with beams away from the support points on the hull.The forces in the beams peak also close the masts locations. Finally,beams next to the last cradle at the stern side are also exposed tohigh forces as most of the stern weight is transferred to the supportstructure in this region. The maximum axial force in a deck beam,under the load conditions and the model assumptions, is predictedto be approximately 150 KN in compression. The maximum axial

Fig. 20. Simulation results for axial forces at the end points of the lower deck wrought iron beams.


stress, detected in the deck beam next to the middle mast of theship and also in the deck beams surrounding the last cradle atthe stern side, is approximately 25.8 MPa.

Bending stress in deck beams is also investigated. The maxi-mum bending stress component observed is the stress in ZZ-cross-sectional direction of the deck beam, at the bottom side(notation SBZB, stress bending in Z bottom; refer to Table 1, lowerdeck beam component). The simulation results are shown inFig. 21. The critical deck beams are those adjacent to the middlemast, and the most stressed location alongside the beams is atthe end points of the beam. The maximum bending stress valueof SBZB is 87 MPa. It should be noted that this reported value isactually on the pessimistic side because the model assumes a uni-form cross-sectional profile along the beam. In reality, the deck

Fig. 21. Simulation results for the bending stress in ZZ-cross-

beams at their very end points have tapered cross-section overlength of approximately 0.20–0.30 m, hence the true bendingstress in that part of the beam will be lower than what the modelpredicts.

Finally, an evaluation of the combined stresses (axial and bend-ing) is undertaken. It is found that the combined stress in the worstcase can be as high as 128 MPa. This stress must be taken in per-spective and compared with the stress limit of 200 MPa whichhas been identified as critical. Note that this stress is predictedassuming deck planks on the lower deck are presented.

Additional analyses not discusses in this paper but undertakenin a similar way have studied the impact of the new support struc-ture on other ship’s components such as the deck stringer plate,the need of new steel cross-bracing and other components on

sectional direction of the deck beam, at the bottom side.


the hull to strengthen the structural response of the ship, the trans-fer of loads from the stern through the last cradle design into thenew steel keel and from there into the original hull iron ribs, etc.

5. Conclusions

An efficient modelling strategy suitable to analyse historic com-posite shell-like structures has been developed, tested and used tohelp the conservation programme of the historic Cutty Sark ship.The key concept is to represent the large scale structure at globallevel as a shell with membrane and flexural rigidity coefficientscalculated independently and based on the actual nature of thecomposition. The stress predictions from the smeared shell modelshave compared favourably with the predictions obtained usingrespective detailed continuum finite element and coupled struc-tural shell and beam models. The smeared shell analysis approachhas been also experimentally validated. The benefit of applyingthis approach is in its great computational efficiency and majorreduction of the effort required to build global level CAD modelsas a computer representation especially in the case of large andcomplex structures.

In the case of Cutty Sark and the related conservation pro-gramme, and because of the heritage and unique nature of the ship,it is absolutely critical to evaluate the ship’s response priory to anystructural, loading or conservation related change the ship is aboutto experience. Therefore, having the ability to undertake fast sim-ulations on a large number of problems and over limited time toaid the decisions making and the detailed conservation planningwas seen as an essential capability that was required. Simulationsdriven by smeared shell finite element calculations have been usedextensively to predict the structural behaviour of Cutty Sark for arange of conservation problems and scenarios and under a numberof different load conditions. Stresses in iron frames on the hull andin the deck beams have been assessed and analysed. The results

have been used to understand critical structural regions of the shipand their interaction with the new steel support structure.

Future work on the presented developments will focus primar-ily on applying the techniques to other historic ships and compos-ite built heritage structures that are in need of conservation andmay also require structural assessment under current and futureload conditions. One particular area of interest is the inclusion ofthe developed global models of Cutty Sark within a predictivemaintenance and life-time Prognostics and Health Management(PHM) framework for the ship to be deployed and used in thepost-conservation future of Cutty Sark.

Acknowledgments

This work has been undertaken under Knowledge Transfer Part-nerships (KTP) programme between the University of Greenwich,London, UK and the Cutty Sark Trust, London, UK and was jointlyfunded by the Department of Trade and Industry (UK) and theCutty Sark Trust.

References

[1] Leftheris B, Stavroulaki ME, Sapounaki AC. Computational mechanics forheritage structures. WIT Press; 2006.

[2] Andrews D. Finite element analysis and the design of thin-walled shipstructures. In: Bull JW, editor. Finite Element Analysis of Thin-WalledStructures. Spon Press; 1990.

[3] Lubbock B. The Log of the Cutty Sark. Glasgow: Brown, Son & Ferguson Ltd.;2004.

[4] http://news.bbc.co.uk/1/hi/england/london/6675381.stm.[5] http://www.rhino3d.com/.[6] Kollar L, Springer G. Mechanics of Composite Structures. United

Kingdom: Cambridge University Press; 2003.[7] Case J, Chilver L, Ross C. Strength of Materials & Structures: With an

Introduction to Finite Element Methods. London, United Kingdom: EdwardArnold; 1993.

[8] ANSYS 11.0 Documentation, http://www.ansys.com.

http://news.bbc.co.uk/1/hi/england/london/6675381.stm

http://www.rhino3d.com/

http://www.ansys.com

smeared shell modelling approach for structural analysis of heritage composite structures – an...

Documents