Optimisation of the Filament Winding Approach Using a Newly Developed In-House Uncertainty Model

Article Optimisation of the Filament Winding Approach Using a Newly Developed In-House Uncertainty Model

Nada Aldoumani 1, Cinzia Giannetti 2, Zakaria Abdallah 3,*, Fawzi Belblidia 1, Hamed Haddad Khodaparast 1 , Michael I. Friswell 1 and Johann Sienz 1 1 The Advanced Sustainable Manufacturing Technologies (ASTUTE) Project, Faculty of Science and Engineering, Swansea University, Swansea SA1 8EN, UK; [email protected] (N.A.); [email protected] (F.B.); [email protected] (H.H.K.); [email protected] (M.I.F.); [email protected] (J.S.) 2 The Future Manufacturing Research Institute (FMRI), Faculty of Science and Engineering, Swansea University, Swansea SA1 8EN, UK; [email protected] 3 The Steel and Metals Institute (SaMI), Faculty of Science and Engineering, Swansea University, Swansea SA2 8PP, UK * Correspondence: [email protected]; Tel.: +44-1792-6043-95

Received: 15 September 2020; Accepted: 10 October 2020; Published: 13 October 2020

Abstract: The device under investigation in this paper consists of a float used to capture tidal energy, which is tethered by multiple flexible cables to a large barge-like reactor. The proposed float is made of a continuously wound glass-reinforced composite shell with stainless steel bolting plates integrated into the float walls to allow the connection of 5 stainless steel cables. Numerical computations are required to assess whether a delamination of the composite layers in the float is likely. The manufacturing of the device has various potential uncertainties that should be investigated, such as the number of the plies, the bond strength between the composite layers, and the fibre orientations of the composite material relative to the applied load. This paper provides a multi-level strategy to optimise the composite float system, which is manufactured from glass-reinforced plastic (GRP). In contrast to previous publications on the topic, the current work uses an efficient link between ANSYS Workbench and MATLAB through an in-house code that has been developed over 3 years. This allowed the whole process to be fully automated and to reduce the time and cost of the simulations. Previously, ANSYS APDL was linked to MATLAB, but limitations in terms of the geometry and boundary conditions made it impractical when compared to ANSYS Workbench for the simulation of complex features. This makes the current approach unique and rare when compared to the published work in the field. This approach allows the use of a huge number of trials and is able to reduce the number of parameters to be studied by selecting the most sensitive ones. Additionally, the developed tools may be used for the efficient, robust optimisation of the proposed structure. The current study has focused on exploring the effects of the fibre orientations and the optimum number of plies on the overall performance of the structure.

Keywords: robust design; ﬂoating systems; bond strength; composites; ﬁlament winding; uncertainty; ANSYS; MATLAB

1. Introduction

1.1. Background The device under investigation consists of a float that is tethered by multiple flexible cables to a large barge-like reactor to harvest tidal energy. The cables are attached to a hydraulic power take-off

Eng 2020, 1, 122–136; doi:10.3390/eng1020008 www.mdpi.com/journal/eng Eng 2020, 1, FOR PEER REVIEW 2 of 15

Eng 2020, 1 123 The device under investigation consists of a float that is tethered by multiple flexible cables to a large barge-like reactor to harvest tidal energy. The cables are attached to a hydraulic power take-off system that captures the energy from the relative movement between the float float and and the the reactor, reactor, which is then converted to electricity. The proposed device has the potentialpotential to compete favourably with other available renewable technologies, since since the the proposed device relies on sea waves waves,, which are more consistent consistent than than wind wind and and offer offer an an average average power power density density of 2 of–3 2–3 W/m W2/,m which2, which is superior is superior to that to ofthat wind of wind (0.5 (0.5W/m W2)/ mand2) and solar solar energy energy (0. (0.1–0.31–0.3 W W/m/m2) 2[1])[1 Although] Although several several experiments experiments have have been conducted on on the the system, system, computational computational modelling modelling of the of device the device immersed immersed in sea water in sea is water also required. is also required.The proposed The proposed float is made float of is a made continuously of a continuously wound glass-reinforced wound glass-reinforced composite composite shell with shell stainless with stainlesssteel bolting steel plates bolting integrated plates integrated into the floatinto the walls float to walls connect to connect the float the to afloat large to bargea large on barge the seabedon the seabedusing 5 using stainless 5 stainless steel cables, steel ascables, shown as inshown Figure in1 .Figure The barge 1. The hosts barge the hosts energy the harvesting energy harvesting devices devicesthat depend that ondepend the variation on the variation of the tension of the loads tension in the loads cables in the due cables to the due constrained to the constrained float movement. float Amovement. sub-modelling A sub technique-modelling is introduced technique with is introduced a layered (float) with a model layered and (float) a solid model (anchoring and system) a solid (anchoringmodel to fully system) explore model and to assess fully explore the stress and levels assess within the stress each oflevels the within winding each layers of the of thewinding float. layersThe integrity of the float. of the The bonding integrity between of the bonding the cable between connectors the cable and connectors the composite and layersthe composite under normal layers underoperation normal will operation also be investigated, will also be as investigated it represents, as a majorit represents potential a major weakness potential in the weakness integrity in of the integritystructure. of In the other structure. words, In the other existence words, of the high existence stress levels of high at stress the boundary levels at betweenthe boundary the anchoring between thesystem anchoring and the system float under and normalthe float operation under normal is one ofoperation the issues is that one might of the be issues encountered that might in the be encounteredstructure. In additionin the structure. to locally In altering addition the to design locally in altering these zones the design to improve in these the zones structural to improve response, the it structuralis necessary response, to perform it is furthernecessary computations to perform further to assess computations if a delamination to assess of theif a floatdelamination layers is of likely, the floattaking layers into is account likely, taking the variable into account wave loading, the variable i.e., thewave development loading, i.e., of the faults development due to fatigue, of faults which due tois beyond fatigue, the which scope is of beyond the current the paper. scope Theof the system current suff ers paper. from The various system uncertainties, suffers from such various as the uncertaintiesnumber of plies, such in theas the top number and bottom of plies shells, in the the top strength and bottom of the steel shells, cable, the thestrength bond of strength the steel between cable, the steelbond plates strength and between the composite the steel layers, plates the and bond the strength composite between layers, the the composite bond strength layers, between and the fibre the comporientationsosite layers, of the and composite the fibre material orientations relative of to the the composite applied load. material The current relative study to the will applied concentrate load. Theon exploring current study the eff willects concentrate of the fibre orientationson exploring and the the effects number of the of pliesfibre onorientations the overall and performance the number of ofthe plies structure. on the overall performance of the structure.

FiFiguregure 1. TheThe floating ﬂoating device in the energy harvesting system.

The filament filament winding winding process process consists consists of two of main two elements: main elements: a filament- a or filament tape-type- reinforcementor tape-type reinforcementand a matrix or and resin. a matrix The process or resin. wraps The a process band of wraps continuous a band resin-impregnated of continuous resin fibres-impregnated around a rotating mandrel, which is then cured at room temperature or in an oven under prescribed pressure 2 EngEng 2020,, 1, FOR PEER REVIEW 3 of124 15 fibres around a rotating mandrel, which is then cured at room temperature or in an oven under prescribedand temperature, pressure as shownand temperature, in Figure2. as The shown mechanical in Figure properties 2. The ofmechanical the final product properties depend of the on final the productmaterial, depend winding on angle, the material, fibre strength, winding resin angle, chemistry, fibre strength, and curing resin cycleschemistry [2]., The and filament curing cycles winding [2]. processThe filament has become winding very process popular has due become its the very attractive popular properties, due its the such attractive as its high properties stiffness-to-weight, such as its highratios. stiffness Such properties-to-weight have ratios. made Such this process properties widely have used made in many this applications, process widely such usedas in aerospace, in many applicationshydrospace,, andsuch military as in aerospace, applications. hydro Thespace reinforcement, and military and applications the matrix. canThe be reinforcement tailor-made inand order the matrixto satisfy can particular be tailor-made properties. in order The to windingsatisfy particular pattern isproperties. controlled The through winding the pattern rotational is controlled speed of throughthe mandrel the rotational and the movement speed of the of mandrel the fibre and feed the mechanism movement [3 of]. Thethe fibre mechanical feed mechanism properties [3] of. The the mechanicalfilament-wound properties component of the arefilament heavily-wound influenced component by the are mechanical heavily influenced properties by of the the mechanical fibres, the propertiessurface interaction of the fibres, of the the fibre surface and interaction resin (interface), of the thefibre amount and resin of fibres(interface), in the the composite, amount of and fibres the inorientation the composite of the, fibres.and the The orientation properties of of the the fibr compositees. The propertiesare highly direction-dependentof the composite are and highly the directionfibres may-dependent be laid in and the directionthe fibres ofmay the be expected laid in the significant direction loading of the expected to ensure significant high integrity loading of the to ensurestructure high [3]. integrity The helical of windingthe structure process [3]. (see The Figure helical2) winding lays down process the fibres (see at Figure angles 2 ranging) lays down from the 5 ◦ fibreto 85s◦ atrelative angles to ranging the longitudinal from 5° to axis 85° ofrelative the mandrel to the andlongitudinal lays the fibresaxis of in the alternating mandrel positiveand lays andthe fibresnegative in alternating orientations positive [4]. and negative orientations [4].

Figure 2. The working principle of the helical filament winding process. Figure 2. The working principle of the helical filament winding process. 1.2. The Winding Angle 1.2. The Winding Angle The winding angle is defined as the angle between the laid-down fibres and the longitudinal axis of theThe cylindrical winding mandrel.angle is defined Several as studies the angle have between been conducted the laid- indown order fibres to find and the the approach longitudinal that axisapproximates of the cylindrical and optimises mandrel. the Several best combination studies have of winding been conducted angles. Sulaiman in order etto al.find (2013) the approach utilised a thatset of approximates winding angle and combinations optimises ranging the best between combination 0 and 90 of win, i.e.,ding [00 , angles. 00 ]s, [15 Sulaiman, 15 ]s, et [30 al., (2013)30 ]s, ◦ ◦ ◦ ◦ ◦ − ◦ ◦ − ◦ utilised[45 , 45 a set]s, [55of winding, 55 ]s, angle [60 , combinations60 ]s, [75 , 75ranging]s, and between [90 , 90 0° ]sand orientations 90°, i.e., [0 (where0°, 00°]s,+ve [15 is°, denotes −15°]s, ◦ − ◦ ◦ − ◦ ◦ − ◦ ◦ − ◦ ◦ − ◦ [3an0° anti-clockwise, −30°]s, [45°, − angle45°]s, and[55°, –ve −55 indicates°]s, [60°, −6 a clockwise0°]s, [75°, −7 angle).5°]s, and In their [90°, study, −90°]s the orientations exact solutions (where along +ve withis denotes the Tsai–Wu an anti maximum-clockwise stress angle failure and –ve criterion indicates were a clockwise employed angle). for data In analysis. their study, The optimum the exact windingsolutions angle along obtained with the wasTsai approximately–Wu maximum 55 stress◦, which failure was criterion in agreement were employed with the experimental for data analysis. work Thein the optimum same study. winding In a similarangle obtained investigation was approximately by Onder et al. 5 [55°],, which the ply was orientation in agree behaviourment with was the experimentalexplored to identify work in thethe optimal-anglesame study. In a ply similar orientations investigation of symmetric by Onder and et al. anti-symmetric [5], the ply orientation [θ/ θ]s − behaviourshells. The wasTsai–Wu explored failure to criterion identify was the employed optimal-angle for structures ply orientations that were of built symmetric of glass-reinforced and anti- plasticsymmetric (GRP) [θ/− usingθ]s shells. the filament The Tsai winding–Wu failure process. criterion The was study employed investigated for structures several plythat orientation were built ofarrangements, glass-reinforced i.e., p [45lastic/ 45(GRP)]s, [55using/ 55the]s, filament [60 / 60winding]s, [75 process./ 75 ]s, The and study [88 /investigated88 ]s orientations. several ◦ − ◦ ◦ − ◦ ◦ − ◦ ◦ − ◦ ◦ − ◦ plyBéakou orientation and Mohamed arrangements, (2001) examined i.e., [45°/−45°]s, the optimal [55°/−55°]s, design based [60°/−60°]s, on the [75°/−75°]s ply orientation, and of [88°/−88°]s the fibres, orientations.and the optimal Béakou angle and for Mohamed the best design (2001) wasexamined determined the optimal as 55◦ design, which based is in agreementon the ply orientation with other ofstudies the fibres, [6]. The and authors the optimal utilised angle the for analysis the best approach design was of a determined [ α]n filament-wound as 55°, which composite, is in agree wherement ± withthe optimum other studies fibre winding[6]. The angle authors significantly utilised the varied analysis with the approach scattering of ofa [±α]n some design filament variables.-wound Thecomposite stresses, where were analysed the optimum using fibre classical winding laminated angle membrane significantly theory varied and with the Tsai–Wuthe scattering failure of criteria. some Thedesign analysis variables. showed The thatstresses the Young’swere analysed modulus using of the classical matrix laminated and the transverse membrane ply theory strength and tharee Tsaithe two–Wu main failure parameters criteria. influencingThe analysis the showed design. that The the aforementioned Young’s modulus studies of share the matrix several and aspects the transversein terms of ply identifying strength the are optimum the two main ply orientation parameters and influencing all employed the thedesign. Tsai–Wu The aforementioned analysis, which providedstudies share reliable several results aspects in terms in terms of the of safety identifying of the structuresthe optimum relative ply orientation to the build-up and anglesall employed during thefilament Tsai– winding.Wu analysis The, which same approachprovided willreliable be utilised results inin theterms current of the case safety study of the in orderstructure to determines relative tothe the optimal build- designup angle parameterss during filament and ply orientationswinding. The for same the filament-wound approach will be structure. utilised in the current

3 Eng 2020, 1, FOR PEER REVIEW 4 of 15

Engcase2020 study, 1 in order to determine the optimal design parameters and ply orientations for the filament125- wound structure.

2. The Modelling Procedure and Assumptions

2.1. Geodesic Path Principle The startingstarting point in identifyingidentifying the optimumoptimum winding angle is the use ofof certaincertain mathematicalmathematical tools,tools, suchsuch asas thethe geodesicgeodesic pathpath principle,principle, whichwhich is oneone ofof thethe mainmain principlesprinciples employedemployed inin filamentfilament winding.winding. A A line segment (the shortest distance between two points) wrapped onto a a right-angle right-angle cylindercylinder is a a geodesic geodesic arc, arc, i.e. i.e.,, the the shortest shortest path path around around a cylinder a cylinder (see (seeFigure Figure 3). This3). is This true is no true matter no matterhow tightly how tightlythe cylinder the cylinder is rolled is (decreasing rolled (decreasing the radius the radiusr). The rprofile). The of profile a geodesic of a geodesic arc on a arc right on 1 acircular right circular cylinder cylinder is a function is a function of arcsine, of i.e. arcsine,, sin−1, i.e.,which sin −is ,a whichpart of is a acircular part of helix. a circular This definition helix. This is definitionuseful in filament is useful winding in filament, since winding, the fibres since will the fibresfollow will the followshortest the path shortest on the path mandrel on the mandrelsurfaces surfacesbetween betweenany given any two given points. two Logically, points. Logically, the geodesic the geodesic arc is a arc stable is a stablepath, as path, the asfibres the fibreswould would have haveto stretch to stretch to deviate to deviate from the from set the pat seth. On path. a cylinder, On a cylinder, the geodesic the geodesic arc is a helical arc is apath helical with path a constant with a constantwinding windingangle, α. angle, This meansα. This that means in order that in to order wind to the wind end the points end pointsof a cylinder, of a cylinder, the geodesic the geodesic path pathcannot cannot be followed be followed completely. completely. A change A changein the winding in the winding direction direction is required is requiredto generate to generatea complete a completelayer, where layer, this where deviation this deviation from the fromgeodesic thegeodesic path ensures path that ensures the fibres that the stay fibres in place stay inthrough place through friction friction[7]. [7].

Figure 3.3. An illustration of the geodesic path on a cylindrical surface.

When the the geodesic geodesic principle principle is utilised, is utilised, any anypoint point on the on geodesic the geodesic arc of an arc axisymmetric of an axisymmetric mandrel satisfiesmandrel [ 8satisfies]: [8]: r sin(α) = constant (1) r sin(α) = constant (1) where r is the radius of the cylinder and α is the winding angle, which represents the orientation of Where r is the radius of the cylinder and α is the winding angle, which represents the orientation of the fibre with respect to the axial direction of the cylinder. When helical winding is used, as in the the fibre with respect to the axial direction of the cylinder. When helical winding is used, as in the current study, the winding angle varies between 5 and 85 . Depending on this angle, the mandrel current study, the winding angle varies between 5◦° and 85◦°. Depending on this angle, the mandrel might rotate several times before the fibres have traversed the whole circumference of the mandrel might rotate several times before the fibres have traversed the whole circumference of the mandrel and start laying adjacent to the previous winding. This provides a pattern of alternating positive and and start laying adjacent to the previous winding. This provides a pattern of alternating positive and negative winding angles, with each layer forming a two-ply layup of [α/ α]. negative winding angles, with each layer forming a two-ply layup of [α/−−α]. 2.2. Material and Boundary Conditions 2.2. Material and Boundary Conditions The various mechanical properties of the utilised glass fibre composite material in the current studyThe are v summarisedarious mechanical in Table properties1. These of properties the utilised were glass measured fibre composite through material mechanical in the testing current at Swanseastudy are University summarised during in Table the course1. These of properties the current were project. measured As would through be expected, mechanical the testing Young’s at modulusSwansea inUniversity the X direction during (longitudinal)the course of isthe higher current than project. that in As the would Y and b Ze directionsexpected, (transverse).the Young’s Thismodulus also appliesin the X to direction the other (longitudinal) mechanical properties is higher suchthan asthat the in shear the Y modulus, and Z directions tensile strength, (transverse). and Poisson’sThis also applies ratio, as to shown the other in the mechanical table. properties such as the shear modulus, tensile strength, and Poisson’s ratio, as shown in the table.

4 Eng 2020, 1, FOR PEER REVIEW 5 of 15 Eng 2020, 1 126 Table 1. The experimental properties of the glass fibre material (Swansea University).

Table 1. The experimentalMaterial properties Properties of the glass ﬁbre materialValue (Swansea University). Young’s Modulus X direction 28,000 MPa Material Properties Value Young’s Modulus Y direction 6900 MPa Young’sYoung’s Modulus Modulus X direction Z direction 28,0006900 MPa MPa Young’s ModulusPoisson’s Y Ratio direction XY 69000.3 MPa Young’s Modulus Z direction 6900 MPa Poisson’sPoisson’s Ratio Ratio XY YZ 0.19 0.3 Poisson’sPoisson’s Ratio Ratio YZ XZ 0.190.19 Poisson’sShear Ratio Modulus XZ XY 11,100 0.19 MPa ShearShear Modulus Modulus XY YZ 11,1002980 MPa MPa ShearShear Modulus Modulus YZ XZ 2980 MPaMPa TensileShear Modulus Strength XZ X direction 29801100 MPaMPa Tensile Strength X direction 1100 MPa TensileTensile Strength Strength Y direction Y direction 35 MPaMPa TensileTensile Strength Strength Z direction Z direction 35 MPaMPa

A sub-structure modelling technique was utilised to allow the analysis of the (float) model and the solidA sub-structure (anchoring system) modelling model technique to assess was the utilised stress levels to allow in the the laminate analysis that of the wa (float)s built modelutilising and thethe solidfilament (anchoring winding system) approach. model The plate to assess of the the sup stressport,levels which in is theconnected laminate to a that stainless was built steel utilisingcable, thewa filaments embedded winding between approach. the plies The of the plate top of and the bottom support, shells. which The is contact connected boundary to a stainless condition steel of cable,the wasplate embedded with the top between and bottom the plies shells of thewas top assumed and bottom to be frictionless shells. The in contact order boundaryto reduce the condition number of of the plateuncertain with theparameters top and, bottomas well as shells to minimise was assumed the modelling to be frictionless time and in cost. order The to “ reduceribs” that the surround number of uncertainthe float were parameters, assumed as to well be circumferential as to minimise thearound modelling the body time ofand the float cost. system. The “ribs” The that cables surround utilised the floatin the were model assumed were assumed to be circumferential to be made of around stainless the steel body, w ofith the fixed float supports system. Theassumed cables at utilised the end in of the modelthe cables. were In assumed order to to simplify be made the of analysis stainless of steel, the geometry, with fixed one supports quarter assumed of the float at the was end modelled of the cables. by Inapplying order to symmetric simplify the axis analysis boundary of theconditions. geometry, These one conditions quarter of theassume float that was as modelled long as the by applyingfloat is symmetricsymmetric axisalong boundary the three conditions. employed axes, These one conditions-quarter is assume sufficient that to as simplify long as the the problem float is symmetric, as well alongas to thegeneralise three employed the solution. axes, This one-quarter makes the is suanalysisfficient significantly to simplify the more problem, efficient as welland asapplicable to generalise to thethe solution. whole geometry. This makes the analysis significantly more efficient and applicable to the whole geometry.

2.3.2.3. Multi-LevelMulti-Level Optimisation Strategy OneOne of the the major major aims aims of the of current the current study study is to determine is to determine the optimum the optimum thickness of thickness the filament of thefilament-woundwound composite composite top and bottom top and shells bottom that support shells that the supportstainlessthe steel stainless plate, as steel shown plate, in Figure as shown 4. inMoreover, Figure4. the Moreover, sequence the for sequence the filament for thewinding filament angle winding orientations angle of orientations the plies is of also the required plies is alsoto requiredensure that to ensure the highest that the possible highest strength possible of strength the structure of the is structure attained. is This attained. requires This the requires optimum the optimumcombined combined solution for solution the thickness for the and thickness filament and winding filament angle winding orientations angle that orientations provide the that highest provide thesupportive highest supportivestrength to strengththe float system. to the float system.

FigureFigure 4.4. The stainless steel support support with with the the top top and and bottom bottom plies plies of of the the filament filament-wound-wound composite. composite. Thus, the design variables of the system consist of the stacking sequence in terms of angle Thus, the design variables of the system consist of the stacking sequence in terms of angle orientations,orientations, asas wellwell as the number of of plies plies in in the the top top and and bottom bottom shells shells used used to tosupport support the the structure. structure. The optimisation process of the float system can be divided into three successive phases that involve 5 Eng 2020, 1, FOR PEER REVIEW 6 of 15 Eng 2020, 1 127 The optimisation process of the float system can be divided into three successive phases that involve the thickness of the top and bottom shells, as well as the stacking sequence of the plies, as shown in the thickness of the top and bottom shells, as well as the stacking sequence of the plies, as shown in the the flow diagram of Figure 5. flow diagram of Figure5.

FigureFigure 5. 5. TheThe m multi-levelulti-level o optimisationptimisation s strategy.trategy.

In this analysis, the Tsai–Wu failure theory is applied to the composite material structures to In this analysis, the Tsai–Wu failure theory is applied to the composite material structures to estimate the remaining life of the material under various loading conditions [9]. The Tsai–Wu failure estimate the remaining life of the material under various loading conditions [9]. The Tsai–Wu failure criterion with a high safety limit is widely applied to composite materials. This approach allows the criterion with a high safety limit is widely applied to composite materials. This approach allows the sensitivity of each shell to be investigated and for the inverse reverse factor (IRF) to be studied, which sensitivity of each shell to be investigated and for the inverse reverse factor (IRF) to be studied, which is given by [9,10]: is given by [9,10]: Ultimate applied load IFR = Ultimate applied load (2) 퐼푅퐹 = Ultimate strength (2) Ultimate strength where the ultimate applied load is the maximum allowable load imposed on the structure, whereas the whereultimate the strength ultimate is applied the maximum load is load the thatmaximum the material allowable can withstandload imposed prior on to the fracture. structure If the, whereas value of theIRF ultimateis below strength 1, then the is the applied maximum load is load below that the the ultimate material strength can withstand of the material, prior to which fracture. indicates If the valuethat the of structureIRF is below is safe. 1, then Whereas the applied when theload value is below of IRF theis ultimate above 1, strength the applied of the load material is beyond, which the indicatesmaterial’s that strength, the structure which means is safe. that Whereas the structure when isthe unsafe, value i.e.,of IRF failure is above is likely. 1, the The applied various load phases is beyondfor the analysisthe material’s are: strength, which means that the structure is unsafe, i.e., failure is likely. The various phases for the analysis are:

Phase 1. The minimum number of plies for the top and bottom shells Phase 1. The minimum number of plies for the top and bottom shells This phase starts by assuming that the fibre orientation for all plies is 90◦. This assumption will provide the best option to hold the stainless steel supports in place. This stems from the fact that This phase starts by assuming that the fibre orientation for all plies is 90°. This assumption will when the stainless steel cables are under tension, they will try to pull the stainless steel support that provide the best option to hold the stainless steel supports in place. This stems from the fact that resides within the plies. This action will result in pure tension in the uni-directional orientation of the when the stainless steel cables are under tension, they will try to pull the stainless steel support that fibres, which are assumed to be 90 filament-wound. This will provide a coherent and strong design resides within the plies. This action◦ will result in pure tension in the uni-directional orientation of the for the float, with the minimum number of plies used to start the process and simplify the solution. fibres, which are assumed to be 90° filament-wound. This will provide a coherent and strong design The Tsai–Wu failure criterion is employed at this stage and solutions with IRF < 1.0 are considered for for the float, with the minimum number of plies used to start the process and simplify the solution. the next phase. The Tsai–Wu failure criterion is employed at this stage and solutions with IRF < 1.0 are considered forPhase the 2.nextThe phase. optimum stacking sequence, i.e., fibre orientations

PhaseAt 2. this The stage, optimum the thickness stacking ofsequence, the top and i.e., bottomfibre orientations plies is kept constant while varying the stacking sequence of the fibres during filament winding. The angles start with [5 /85 ] and [ 5 / 85 ] stacking ◦ ◦ − ◦ − ◦ sequences,At this whichstage, the means thickness that the of optimumthe top and solution bottom is plies within is kept this constant range of while angles. varying The reason the stacking for this sequenceselection isof thatthe fibres angles during between filament 0 and winding.5 result The in angles “planar” start winding with [5°/85°] rather thanand [ “helical”−5°/ −85°] winding,stacking ◦ ± ◦ sequencewhich ares, bestwhich suited means to supportthat the optimum the heads, solution domes, is or within caps and this arerange beyond of angles. the scope The reason of the currentfor this selectionstudy. Additionally, is that angles angles between above 0° and 85◦ ±5°are result closer in to “ “hoop”planar” winding,winding rather which than is been “helical explored” winding, in the whichcurrent are study, best since suited the to “helical” support design the heads, is the domes major focus, or caps of the an presentd are beyond investigation, the scope as recommendedof the current study.by Marine Additionally Power Systems, angles (MPS). above The 85° Tsai–Wu are closer criterion to “hoop is again” winding employed, which and is fibrebeen orientations explored in with the currentIRF < 1.0 study are considered, since the for “helical the final” stagedesign of isthe the optimisation major focus process. of the present investigation, as

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Phase 3. The optimum combination of plies vs. stacking sequence In this phase, a 3D surface response is created in order to evaluate the combined eﬀects of the stacking sequence and the ply thickness. The optimum solutions for phases 1 and 2 with the minimum IRF values are combined at this stage. Again, the Tsai–Wu failure criterion is employed to ﬁnd the minimum combined IRF value of the stacking sequence alongside the ply thickness, which ensures the highest level of safety in the structure.

2.4. Uncertainty and Robust Design Procedure The probability distribution of the possible solutions was obtained from the fact that there are 16 possible angles in the (+) direction and 16 possible angles in the (-) direction, given that the angles are within the range of 5◦ to 85◦ (with 5◦ increments). This gives a total 256 combined possible solutions 2 for the stacking angles (16 = 256 solutions). The reason for the 5◦ increments is that in real-world situations, filament winding processes are restricted to winding the fibres at angles of 0◦, 5◦, 10◦, 15◦, 20◦, ...... , 90◦. These input values of the stacking sequence were manually input into the innovative model that was developed at Swansea University. Through this, ANSYS Workbench was linked via MATLAB utilising the developed and in-house written code. The code automatically operates ANSYS, runs the model, retrieves the results, and continues to obtain the remaining sets of results. This reduces the effort, time, and number of trials used to choose the optimum design parameters for any given design. The framework for robust design proposed and employed by the authors has recently been published elsewhere, although for carbon fibre composite materials bonded via aluminium joints [11]. For the optimum and robust design, the blind kriging approach [12], a typical meta-model process, was utilised in the analysis. This approach provided outstanding results with a minimal amount of variation. This facilitated the construction of the response surfaces for each stage in the analysis, from which the optimum and robust design parameters were determined. The strategy used to optimise the uncertain parameters and the robust design starts by assuming that a certain number of plies are oriented at 90◦ to provide the maximum possible strength while optimising the number of plies, which is the first phase. This reduces the risk of failure of the glass fibre material. The optimum number of plies will then be taken into the second phase to obtain the best angle combinations of the filament-wound fibres. At this stage, the number of plies is kept unchanged while optimising the fibre orientation so that the likelihood of failure is eliminated. The third phase optimises the number of plies and the fibre orientations in order to obtain the best performance, i.e., maximum strength and no failure. This exercise provides a procedure that can be applied to any engineering application that involves more than a single variable through the employment of 3D response surfaces that are able to define the safest operational region.

2.5. Meta-Model Design Optimisation In industrial practice, the optimisation of complex engineering problems is becoming increasingly popular utilising meta-model based approaches. This is due to the fact such methods reduce the burden of computationally expensive simulations. The meta-model-based optimisation relies on building a surrogate model, i.e., a meta-model, based on a reduced number of simulations, after which the model is used for optimisation purposes [13]. An approximate relationship is developed by the meta-model between the design variables and the output variable, e.g., y = f (x1, x2 ... , xn), where y is the output variable and x1, x2 ... , xn are the input variables. This process can provide an optimised solution more quickly when the surrogate model is utilised and is less expensive to execute compared to the corresponding deterministic simulations. The “response surface” is commonly used to present the results, with a linear model being the simplest form, where the functional relationship f (x1, x2 ... , xn) is approximated by a linear function of the design variables. On the other hand, higher order response surfaces (e.g., polynomial models) can be employed, in which the response surface is a polynomial function of the design variables. The linear or polynomial response functions are Eng 2020, 1 129 developed by minimising the sum of the squared distances from the response surface for given set of data points, i.e., the ordinary least squares approach. In this respect, the surrogate modelling approach assumes that all errors obtained from the ordinary least squared approach are normally distributed with a deﬁned mean and variance. This assumption is often only approximate in real-world problems. The most widely used meta-model approach is known as the “kriging” or the “Gaussian interpolation” method. The surrogate model is assumed to be capable of approximating the deterministic noise-free data and is used for high level optimisation, design space exploration, sensitivity analyses, visualization, and prototyping [14]. The additional advantage of using the kriging approach compared to the conventional least squares method is that the model goes through each data point. This allows the model to describe the uncertainty of the interpolation outside the given range of data points [15]. The kriging method is favourable compared to other techniques due to the fact that it is able to approximate complex response functions with less restrictive assumptions on the distribution of residual errors [16].

2.6. The Ordinary Kriging Model The kriging approach is normally pre-ﬁxed with various names, depending on the form of the function utilised in the regression analysis. In this context, the simple kriging method assumes a constant function, i.e., f (x) = 0. However, the ordinary kriging method assumes aconstant function, f (x) = 0. For more complex processes, the trend functions can be linear or quadratic, with the universal kriging model utilising a multi-variate polynomial of the form:

Xp f (x) = αibi(x) (3) i=1 where b1(x), b2(x), ... , bp(x), are the basis functions (i.e., the basis polynomials) and αi = (α1, α2, ... , αp) denote the coeﬃcients. In this approach, the regression function reproduces the general trend in the data (i.e., the largest variance), after which a Gaussian process is used to interpolate the residuals.

2.7. The Blind Kriging Model In contrast, the blind kriging approach assumes a trend function f (x) that is unknown and difficult to determine for a given problem. This offers the possibility of identifying the most reasonable interactions within the data points [12]. This method determines the most efficient functions or features that capture the most observed variance in the sample. In an ideal scenario, the data is represented fully by a chosen trend function. The main idea is to choose new features in addition to the existing features that can be included in the kriging regression function to improve the results. The linear model that incorporates a whole set of candidate functions is:

Xp Xt g(x) = αibi(x) + βici(x) (4) i=1 i=1 where t is the number of candidate functions. The ﬁrst term in this equation is the kriging regression function, where the values of the coeﬃcient are determined independently relative to βi = (β1, β2, ... , βt). The second term involves the parameters that are estimated based on the relevance of the candidate features. The estimation of the parameters, i.e., the least-squared solution, is a straightforward approach that can help to rank the features.

2.8. The Co-Kriging Model The co-kriging approach is considered a special case of the multi-output or multi-task Gaussian process. This method exploits the correlation between coarse and fine model data to improve the predictiveEng 2020, 1 capability and accuracy [17]. The co-kriging model can be interpreted as the sequential130 construction of two kriging models—the first Kriging model is related to the coarse data and the secondconstruction Kriging of modeltwo kriging is related models—the to the residuals first Kriging of the model coarse is data.related In to other the coarse words, data this and model the employssecond Kriging a small modelset of short is related-term to characte the residualsristics ofin theorder coarse to predict data. Inthe other long- words,term characteristics. this model employs This, ina smallturn, reduces set of short-term the time and characteristics cost associated in order with to generating predict the such long-term long-term characteristics. characteristics This, and in turn,can providereduces predictions the time and both cost within associated and outside with generating the assumed such range long-term of characteristics. characteristics and can provide predictionsIn the current both within study, and the outsideordinary, the b assumedlind, and rangeco-kriging of characteristics. approaches were employed in order to determineIn the the current optimum study, regions the ordinary, of the blind,bond strength and co-kriging in the current approaches case werestudy. employed The study in aims order to to validatedetermine existing the optimum data, as well regions as provide of the bondinformation strength on in the the optimum current and case robust study. design The study parameters. aims to Invalidate essence, existing these models data, as attempt well as provideto find the information surrogate on model the optimum that simulates and robust the problem designparameters. using less strictIn essence, assumptions these models about the attempt residual to finderrors the [1 surrogate8]. model that simulates the problem using less strict assumptions about the residual errors [18]. 3. Results and Discussion 3. Results and Discussion 3.1. Phase 1 Results (Number of Plies of Top and Bottom Shells) 3.1. Phase 1 Results (Number of Plies of Top and Bottom Shells) The obtained results from the blind kriging approach for phase 1 analysis are summarised in FigureThe 6. The obtained mean s resultsquared from error the of the blind leave kriging-out cross approach-validation for phase was chosen 1 analysis to evaluate are summarised the quality in ofFigure the fit6., Theas well mean as squaredthe predictive error ofcapabilit the leave-outy of the cross-validation technique. The wasblind chosen kriging to evaluateresults in the Figure quality 6a showof the a fit,very as good well asfit thecapability predictive for the capability data through of the the technique. response The surface blind, with kriging data results showing in Figure low IRF6a valuesshow a(below very good 1.0), fitwhich capability is desired for the to dataensure through the safety the response of the structure. surface, withThe major data showing outcome low is theIRF combinedvalues (below optimisation 1.0), which of the is desired number to of ensure plies for the the safety top of and the bottom structure. shells The, as major shown outcome by the isdata the havingcombined IRF optimisationvalues < 1.0. The of the contour number plot of in plies Figure for 6b the more top clearly and bottom shows shells, the safety as shown regions by with the dataIRF

(a) (b) (c)

FigureFigure 6. 6. PhasePhase 1: 1: Optimising Optimising the the number number of of plies plies:: (a (a) )the the b blindlind k krigingriging response response surface surface;; (b (b) )t thehe contourcontour plot plot;; ( (cc)) t thehe variance variance plot. plot.

TheThe results results in in the the acceptable acceptable range, range, i.e. i.e.,, IRFIRF << 1.0,1.0, are are summarised summarised in in Table Table 2.2. Additionally Additionally,, the IRFIRF valuesvalues are are much much more more sensitive sensitive to to the the number number of of bottom bottom plies plies when when compared compared to to the the top top plies. plies. InIn this this table, table, smaller smaller IRFIRF valuesvalues result result in in a a better better optimisation optimisation of of the the structure. structure. It It can can be be seen seen that that by by increasingincreasing the the plies plies of of both both the the top top and and bottom bottom shells, shells, a better a better and and safer safer design design of ofthe the float ﬂoat system system is obtained.is obtained. This This is logical is logical,, since since the the thicker thicker the the shell shell,, the the higher higher the the resistance resistance against against deforma deformationtion under the applied loading conditions. The minimum acceptable number of plies is 10 plies for the 9 top shell and 23 plies for the bottom shell, which shows the more severe loading on the bottom shell when compared to the top shell. Additionally, the IRF values are much more sensitive to the number of bottom plies when compared to the top plies. Eng 2020, 1 131

Table 2. A summary of the inverse reverse factor (IRF) values obtained for the shell optimization *.

Top Plies # Bottom Plies # IRF Values 30 31 0.6160867 26 30 0.6853152 22 31 0.6944406 28 29 0.6949207 29 28 0.7232109 24 29 0.7396711 20 30 0.7493208 18 30 0.790386 31 26 0.7919314 25 27 0.8047401 21 28 0.8076068 27 26 0.8297545 14 31 0.844326 30 25 0.8538816 23 26 0.8634863 16 29 0.8730014 19 27 0.8788239 22 25 0.914228 17 27 0.9276962 26 24 0.9404642 28 23 0.984838 12 29 0.9925366 13 28 0.9995041 Note: * When the value of IRF < 1, this means the structure is safe, whereas when IRF > 1 the structure will fail.

This variation in the number of plies for the top and bottom shells is due to the fact that the type of loading on the bottom shell is compressive, while it is mostly tensile on the top shell when the stainless steel cable is trying to pull the supports away from the body of the float. Since composite laminates have a significantly lower compressive strength than tensile laminates [19], the bottom shell under compression must have more plies than the top shell under tension. This means that the bottom layers will suffer more than the top layers under such loading conditions. However, choosing the highest number of plies for the top and bottom shells is impractical from cost and weight perspectives. This has to be optimised in the following stages of the optimisation process. The next phase will optimise the stacking sequence, i.e., fibre orientations, based on the minimum acceptable number of plies (10 for the top and 23 for the bottom). This number of plies will remain unchanged during the winding angle optimisation process (i.e., phase 2) to ensure that the filament winding angle is optimised while keeping the number of plies constant.

3.2. Phase 2 Results (The Fibre Stacking Sequence)

At this stage of the analysis, the stacking sequence has a fixed set of angles ranging between 5◦ and 85 (in the + and directions), which gives 256 possible solutions. The top shell was assumed to ◦ − have a thickness of 4.3 mm (10 plies @ 0.43 mm ply thickness, as given by the supplier), whereas the bottom shell was assumed to have a thickness of 10.08 mm (23 plies @ 0.43 mm ply thickness). In the analysis, the Tsai–Wu criterion approach along with the blind kriging fitting method were employed in order to obtain the optimum stacking sequence for the fibres. The obtained results of this phase are shown in Figure7. It can clearly be seen from the blind kriging results in Figure7a that this fitting approach had very good representation capability for the data, as shown by the surface response. The plot shows the minimum IRF value (i.e., below 1.0), characterised by its “valley” shape, which contains the optimum design solution to the problem. The optimum solution can be viewed more clearly in Figure7b, i.e., the contour plot, where the optimum solution lies somewhere between +50◦ Eng 2020, 1, FOR PEER REVIEW 11 of 15 are shown in Figure 7. It can clearly be seen from the blind kriging results in Figure 7a that this fitting approach had very good representation capability for the data, as shown by the surface response. The plot shows the minimum IRF value (i.e., below 1.0), characterised by its “valley” shape, which contains the optimum design solution to the problem. The optimum solution can be viewed more Eng 2020, 1 132 clearly in Figure 7b, i.e., the contour plot, where the optimum solution lies somewhere between +50° to +85° (value of α) and −60° (value of β), with IRF values < 1.0. The variance plot in Figure 7c shows veryto + 85good(value quality of α fitting) and , as60 shown(value by of theβ), withminimalIRF valuesamount< of1.0. variation The variance for most plot regions. in Figure 7c shows ◦ − ◦ very good quality fitting, as shown by the minimal amount of variation for most regions.

(a)

(b)

(c)

FigureFigure 7. Phase 2: 2: Optimising Optimising the the ply ply orientation: orientation (a:) the(a) blindthe blind kriging kriging response response surface; surface (b) the; ( contourb) the

contourplot; (c) plot the; variance (c) the variance plot. Note: plot. All Note: angles All areangles in degrees are in degrees (◦). (°).

The obtained results in Figure7 are summarised in Table3 to find the best combination of filament winding angles with the lowest possible IRF value. It can be clearly seen that the +60◦/ 60◦ combination11 − is the optimum solution to the problem. In order to find a possible explanation to this stacking sequence, a simple structural analysis of the load and the floating system was performed. Based on the geometry and specifications from the Eng 2020, 1, FOR PEER REVIEW 12 of 15

The obtained results in Figure 7 are summarised in Table 3 to find the best combination of filament winding angles with the lowest possible IRF value. It can be clearly seen that the +60°/−60° combination is the optimum solution to the problem. In order to find a possible explanation to this stacking sequence, a simple structural analysis of the load and the floating system was performed. Based on the geometry and specifications from the manufacturingEng 2020, 1 company, the angle between the load and the float system was specified as 60°. 133In other words, the tensile load in the stainless steel cable will be resisted by the filament-wound fibres that are aligned in the same direction as the tensile load, as shown in Figure 8. This explains the manufacturing company, the angle between the load and the float system was specified as 60◦. In other words,optimised the tensilesolution load obtained in the stainless in the analysis steel cable, which will bewas resisted the +60°/−60° by the filament-wound combination. However, fibres that theare anglealigned of inthe the (+) same orientation direction might as the vary tensile between load, +50° as shownand +85° in due Figure to 8the. This actual explains motion the of optimisedthe waves in reality. In other words, the stainless steel cable might be inclined at 60° on a certain occasion and solution obtained in the analysis, which was the +60◦/ 60◦ combination. However, the angle of the (+) then at 80° at another time. This variability explains the− previous results shown in Figure 8, wherein orientation might vary between +50◦ and +85◦ due to the actual motion of the waves in reality. In the value of the (+) fibre orientation showed acceptable IRF results in the range of +50° to +85°. other words, the stainless steel cable might be inclined at 60◦ on a certain occasion and then at 80◦ at another time. This variability explains the previous results shown in Figure8, wherein the value of the Table 3. A summary of the IRF values obtained for the stacking sequence optimisation* (the first (+) fibre orientation showed acceptable IRF results in the range of +50◦ to +85◦. column of angles is α, whereas the second column is β).

Table 3. A summary of the IRFAnglevalues 1obtained Angle for2 theIRF stacking Values sequence optimisation* (the ﬁrst column of angles is α, whereas the second60 column−60 is β).0.936464153 Angle 165 Angle−60 2 0.936740126IRF Values 55 −60 0.937034556 60 60 0.936464153 − 65 75 −6060 0.937040329 0.936740126 − 55 70 −6060 0.937175776 0.937034556 − 75 80 −6060 0.937716612 0.937040329 − 70 60 0.937175776 85 −−60 0.938415852 80 60 0.937716612 50 −−60 0.940729225 85 60 0.938415852 − 50 70 −6065 0.982900049 0.940729225 − 70 55 −6565 0.982931364 0.982900049 − 55 65 0.982931364 60 −−65 0.983015988 60 65 0.983015988 65 −−65 0.983230577 65 65 0.983230577 75 −−65 0.983428191 75 65 0.983428191 − 50 50 −6565 0.983641761 0.983641761 − 80 80 −6565 0.984033312 0.984033312 − 85 65 0.984664912 85 −−65 0.984664912 50 55 0.999807636 50 −−55 0.999807636 55 66 0.999854478 55 −−66 0.999854478 Note: * When the value of IRF < 1, this means the structure is safe, whereas when IRF > 1 the structure will fail. All Note:angles * are W inhen degrees the value (◦). of IRF < 1, this means the structure is safe, whereas when IRF > 1 the structure will fail. All angles are in degrees (°).

Figure 8. A simple structural analysis explaining the optimum +60◦/ 60◦ combination of the optimum − 12 stacking sequence. Note: All angles are in degrees (◦). 3.3. Phase 3 Results (Number of Plies vs. the Stacking Sequence) According to the Tsai–Wu failure criterion and the IRF values for phases 1 and 2, the analysis has shown that the bottom shell is more sensitive to the applied load than the top shell of the ﬂoat Eng 2020, 1, FOR PEER REVIEW 13 of 15

Figure 8. A simple structural analysis explaining the optimum +60°/−60° combination of the optimum stacking sequence. Note: All angles are in degrees (°).

3.3. Phase 3 Results (Number of Plies vs. the Stacking Sequence) Eng 2020, 1 134 According to the Tsai–Wu failure criterion and the IRF values for phases 1 and 2, the analysis has shown that the bottom shell is more sensitive to the applied load than the top shell of the float system.system. Moreover, Moreover, phase phase 2 2has has shown shown that that the the optimum optimum combination combination of angles of angles lies liesbetween between +60° +and60◦ −and60°. At60 this. At st thisage, stage,the combined the combined solution solution of phase ofs phases 1 and 2 1 for and an 2 optimum for an optimum design is design shown is in shown Figure in − ◦ 9.Figure In this9. Infigure, this figure,the combined the combined angle– angle–plyply thickness thickness optimum optimum solution solution can be can defined be defined (for the (for ±6 the0° winding60 winding angles). angles). Moreover, Moreover, the vertical the vertical axis presents axis presents the combined the combined thickness thickness (i.e., the (i.e., bottom the bottom plus ± ◦ theplus top the shell). topshell). From this From total this thickness total thickness of the float, of the the float, individual the individual thickness thicknesseses of the top of and the topbottom and shellsbottom can shells be determined. can be determined. For instance, For instance, if the circled if the point circled is pointtaken is as taken an example, as an example, the thickness the thickness of the floatof the at float this atpoint this is point 14.3 is8 m 14.38m. This mm. represents This represents the minimum the minimum acceptable acceptable thickness thickness of the of wall the wallof the of float,the float, i.e., i.e.,the thetop top and and bottom bottom shells shells together. together. As As discussed discussed earlier earlier in in Section Section 3 3.2.2, , the the minimum minimum acceptableacceptable thickness thickness of of the the bottom bottom shell shell is is 10.0 10.088 m mm,m, whereas whereas that that of of the the top top shell shell should should be be at at least least 4.4.33 m mm.m. The The summation of thethe twotwo thicknessesthicknesses gives gives the the thickness thickness of of the the circled circled point point in Figurein Figure9, i.e., 9, i.e.14.38, 14.3 mm,8 m whichm, which is the is the worst worst case case scenario. scenario. At thisAt this particular particular point, point, the the optimum optimum thickness thickness and and ply plyangle angle orientation orientation are obtained,are obtained giving, giving a reduced a reducedIRF value IRF ofvalue 0.89 of (an 0.89 improvement (an improvement of 10% inof terms10% in of termssafety of when safety compared when compared to the original to the or caseiginal of phasecase of 1). phase This 1). is This applicable is applicable to any to point any onpoint this on graph, this graphwhich, which allows allows the designer the designer to choose to choose the number the number of plies of plies for the for top the and top bottomand bottom shells, shells taking, taking into intoconsideration consideration the minimumthe minimum allowable allowable number number of plies of forplies each forshell. each Thisshell. solution This solution to the floatto the system float systemproblem problem is comprehensive is comprehensive and applicable and applicable to the investigatedto the investigated design design for an optimumfor an optimum solution solution for the fornumber the number of plies of and plies filament and filament winding winding angles. angles.

Figure 9. The combined solution for the thickness of the float (the top and bottom shells) at the optimum Figure 9. The combined solution for the thickness of the float (the top and bottom shells) at the filament winding angle of 60 . optimum filament winding± angle◦ of ±60°. 4. Conclusions 4. Conclusions This study has provided a full-scale investigation of the proposed MPS float system, which is to be manufacturedThis study has from provided glass-reinforced a full-scale plastic investigation (GRP). This of the case proposed study has MPS allowed float system the implementation, which is to beof the manufactured developed code from at Swansea glass-reinforced University plastic to link (GRP).ANSYS Workbench This case through study has MATLAB allowed in order the implementationto generate a set of of the data developed that can becode studied at Swansea using uncertaintyUniversity to models. link ANSYS The study Workbench has revealed through the MATLABoptimum filamentin order to winding generate angle, a set as of well data as that the can optimum be studied thicknesses using uncertainty of the top and models. bottom The shells study of hasthe revealed float system the inoptimum terms of filament the number winding of plies angle from, as which well as each the shelloptimum is constructed. thicknesses The of optimumthe top and set bottom shells of the float system in terms of the number of plies from which each shell is constructed. of filament winding angles is 60◦, which is in agreement with the applied load in the cable, which The optimum set of filament winding± angles is ±60°, which is in agreement with the applied load in was specified by the manufacturer to be inclined at 60◦ relative to the float system. Furthermore, the theoptimum cable, which number was of specified plies that by provided the manufacturer a safe structure to be underinclined the at applied 60° relative loads to was the alsofloat obtained. system. Furthermore,The combined the solution optimum provides number a setof plies of thickness that provided values a from safe whichstructure the under designer the canapplied choose loads the wasoptimum also obtained. thickness The for combined a certain solution geometry, provide takings intoa set accountof thickness the weightvalues from and costwhich of construction.the designer This analysis is a useful exercise that can be applied to any engineering structure that involves more13 than a single uncertain parameter in the final design. This reduces the modelling time and the involved costs when the optimum range of properties is defined. This also provides the starting point for the design and manufacture of components for any engineering application. A new innovative technique Eng 2020, 1 135 that is not available in ANSYS was employed so that the number of layers and the fibre orientation could be simulated simultaneously while providing the optimum design requirements.

Author Contributions: Investigation, Validation and Writing, N.A.; Methodology and Software, C.G.; Writing—Review and Editing, Z.A.; Resources and Supervision, F.B.; Supervision and Conceptualisation, H.H.K.; Writing—Review and Editing, M.I.F.; Funding Acquisition, J.S. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the Advanced Sustainable Manufacturing Technologies (ASTUTE 2020) project based at Swansea University. The ASTUTE 2020 project is funded by the European Regional Development Fund through the Welsh Government and the Welsh European Funding Office (WEFO). Furthermore, Dr Cinzia Giannetti acknowledges the support of the UK Engineering and Physical Sciences Research Council (EPSRC) project EP/S001387/1 towards the publication of this paper. Conflicts of Interest: The authors declare no conflict of interest. Replication of Results: This is possible utilising the published data in the current article. However, the MATLAB code is owned by Swansea University under copy right protection and cannot be made available. However, open calls to the research community to collaborate on various projects by providing data to Swansea University for a joint publication are more than welcome. Please get in touch with the corresponding author for future collaborative projects.

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