A Structural Design Concept for a Multi-Shell Blended Wing Body with Laminar Flow Control

energies

Article A Structural Design Concept for a Multi-Shell Blended Wing Body with Laminar Flow Control

Majeed Bishara 1,*, Peter Horst 2, Hinesh Madhusoodanan 3, Martin Brod 3, Benedikt Daum 3 ID and Raimund Rolfes 3 ID 1 Aeronautics Research Center Niedersachsen (NFL), TU Braunschweig, Hermann-Blenk-Straße 42, 38108 Braunschweig, Germany 2 Institute of Aircraft Design and Lightweight Structures, TU Braunschweig, Hermann-Blenk-Straße 35, 38108 Braunschweig, Germany; [email protected] 3 Institute of Structural Analysis, Leibniz University of Hannover, Appelstraße 9A, 30167 Hannover, Germany; [email protected] (H.M.); [email protected] (M.B.); [email protected] (B.D.); [email protected] (R.R.) * Correspondence: [email protected]; Tel.: +49-531-391-66663

Received: 15 December 2017; Accepted: 3 February 2018; Published: 7 February 2018

Abstract: Static and fatigue analyses are presented for a new blended wing body (BWB) fuselage concept considering laminar flow control (LFC) by boundary layer suction in order to reduce the aerodynamic drag. BWB aircraft design concepts profit from a structurally beneficial distribution of lift and weight and allow a better utilization of interior space over conventional layouts. A structurally efficient design concept for the pressurized BWB cabin is a vaulted layout that is, however, aerodynamically disadvantageous. A suitable remedy is a multi-shell design concept with a separate outer skin. The synergetic combination of such a multi-shell BWB fuselage with a LFC via perforation of the outer skin to attain a drag reduction appears promising. In this work, two relevant structural design aspects are considered. First, a numerical model for a ribbed double-shell design of a fuselage segment is analyzed. Second, fatigue aspects of the perforation in the outer skin are investigated. A design making use of controlled fiber orientation is proposed for the perforated skin. The fatigue behavior is compared to perforation methods with conventional fiber topologies and to configurations without perforations.

Keywords: blended wing body; multi-bubble fuselage; structural analysis; controlled ﬁber placement; ﬁber-reinforced plastics; fatigue; degradation; damage model

1. Introduction The research project “Energy System Transformation in Aviation (EWL)” has been initiated by the Aeronautics Research Centre Niedersachsen (NFL) in Germany with the aim of reducing CO2 emissions by developing new aircraft concepts and evaluation of new technologies. As a result of the project, the blended wing body (BWB) design concepts were identified as a promising technology path. BWB aircraft are a concept promising advantages in aerodynamic performance and a reduction of fuel consumption. Preliminary research shows the potential of unconventional aircraft with respect to environmental concerns and noise pollution [1]. Liebeck et al. [2] developed an efficient structural concept abandoning the constraint of a cylindrical pressure vessel of a conventional aircraft. The advantage of the new configuration is a reduction of the maximal bending stress due to the better distribution of the aerodynamic loads compared to a conventional tube and wing aircraft. A higher passenger acceptance of BWB cabins was also identified in [3] as an advantage. The structural layout of non-cylindrical fuselages is an aspect of aircraft design that remains under research. Alternative designs featuring multiple intersecting partial cylinders for the pressure

Energies 2018, 11, 383; doi:10.3390/en11020383 www.mdpi.com/journal/energies Energies 2018, 11, 383 2 of 21 skin are referred to as “multi-bubble” designs. Mukhopadhyay [2,3] and Mukhopadhyay et al. [4] presented structural analysis of different concepts of non-conventional cross sections. They performed preliminaryEnergies studies 2018, 11 on, x FOR multi-bubble PEER REVIEW fuselages with two different design approaches: vaulted2 of 21 sandwich shell and flat sandwich shell. These studies found that the multi-bubble vaulted approach leads to a skin are referred to as “multi-bubble” designs. Mukhopadhyay [2,3] and Mukhopadhyay et al. [4] membranepresented stress dominated structural loadanalysis state of and,different therefore, concepts a lightof non-conventional weight design. cross However, sections. the They multi-bubble design is notperformed suitable preliminary for forming studies the aerodynamicon multi-bubble profile fuselages of with the BWB-designtwo different design and a doubleapproaches: shell concept with an aerodynamicvaulted sandwich outer shell shell and isflat required. sandwich shell. For thisThese reason studies a found double that shellthe multi-bubble design is envisagedvaulted here. approach leads to a membrane stress dominated load state and, therefore, a light weight design. Research on laminar flow control (LFC) began in the 1930s and became more important during the However, the multi-bubble design is not suitable for forming the aerodynamic profile of the BWB-design energy crisisand ina double the 1970s shell concept because with of an the aerodynamic potential outer aerodynamic shell is required. performance For this reason benefits a double for shell commercial aircraft [5].design The is boundary envisaged here. layer flow on today’s large aircraft is turbulent at almost the entire wetted surface. ThisResearch results inon laminar viscous flow drag control five (LFC) to ten began times in the larger 1930s and than became that more of laminar important boundary during layers. the energy crisis in the 1970s because of the potential aerodynamic performance benefits for While for unswept wings at low Reynolds numbers, laminar flow can be achieved by a properly commercial aircraft [5]. The boundary layer flow on today’s large aircraft is turbulent at almost the designed pressureentire wetted distribution, surface. This high results Reynolds in viscous numbers, drag five especiallyto ten timesin larger combination than that of with laminar swept wings, require activeboundary flow layers. control While to for keep unswept the wings boundary at low Reynolds layer laminar. numbers, Suckinglaminar flow the can part be achieved of the boundary layer nearby the a properly wall through designed pressure the porous distribution, skin into high Reynolds the wing numbers, dampens especially aerodynamic in combination instabilities with and swept wings, require active flow control to keep the boundary layer laminar. Sucking the part of the prevents transition from laminar to turbulent flow. Figure1 from [ 6] presents the concepts of natural boundary layer near the wall through the porous skin into the wing dampens aerodynamic laminar flowinstabilities (NLF), and full-chord prevents transition laminar from flow laminar control to turbulent (LFC) and flow. hybrid Figure laminar1 from [6] flowpresents (HLFC), the which integratesconcepts the two of previous natural laminar concepts. flow (NLF), The diagramfull-chord showslaminar aflow schematic control (LFC) of the and three hybrid concepts laminar with the flow (HLFC), which integrates the two previous concepts. The diagram shows a schematic of the corresponding surface pressure coefficient (CP) versus chordwise extent (x/c). three concepts with the corresponding surface pressure coefficient () versus chordwise extent (x/c).

x/c

Figure 1. Schematic of natural laminar flow (NLF), laminar flow control (LFC) and hybrid laminar Figure 1. Schematicflow (HLFC) of approaches natural laminarfor wing from flow [6]. (NLF), laminar flow control (LFC) and hybrid laminar flow (HLFC) approaches for wing from [6]. In most studies, the effect of LFC on aircraft wings was investigated. Since for BWB design the wetted surface of the fuselage is substantial, the utility of Fuselage-LFC was investigated in the EWL In mostproject. studies, Results the show effect that offor LFC a conventional on aircraft tube wings and wing was design investigated. drag could Sincebe reduced for BWB to one design the wetted surfacefourth ofcompared the fuselage to the fully is substantial, turbulent fuselage the utilityby using of suction Fuselage-LFC from near the was nose investigated to the beginning in the EWL project. Resultsof the showtailcone that [7]. for For a conventionalthe BWB design tube under and consideration wing design here, drag the could Fuselage-LFC be reduced can tobeone fourth advantageously integrated into the double shell concept. The inner skin contains the interior compared to the fully turbulent fuselage by using suction from near the nose to the beginning of the pressure, while LFC occurs via the perforated outer skin. The plenum between the inner and outer tailcone [7skin]. For can the house BWB ductwork design to divert under the consideration ingested air to the here, propulsion the Fuselage-LFC system. can be advantageously integrated intoIn thethe EWL double project, shell new concept. technologies The were inner evaluated skin containsand combined the interiorin order to pressure, reduce fuel while LFC occurs viaconsumption the perforated and outerCO2 emission skin. Theof aircraft. plenum A new between long-range the innerBWB design and outer concept skin was can developed house ductwork considering the impacts of different technologies together, see [8]. The developed design in the EWL to divert the ingested air to the propulsion system.

In the EWL project, new technologies were evaluated and combined in order to reduce fuel consumption and CO2 emission of aircraft. A new long-range BWB design concept was developed considering the impacts of different technologies together, see [8]. The developed design in the EWL Energies 2018, 11, 383 3 of 21 project forms the basis for the structural analysis presented here. A summary of the speciﬁcations is listed in Table1.

Table 1. Summary of the parameters and best technologies according to [8] for the long range BWB-design under consideration in the present work.

Long Range Blended Wing Body (BWB) Aircraft Passengers 300–400 Maximum takeoff weight MTOW (t) 132 Operating empty weight OWE (t) 78 Outer wing area (m2) 133 Outer wingspan (m) 53.3 Energy conversion Intercooled recuperated gas turbine, synchronized electric motor Energy storage Synthetic fuel

The first part of this paper presents a structural analysis of a composite multi-bubble fuselage segment for a BWB aircraft. Since only a preliminary design study is intended here, only a partial model truncated in longitudinal direction is considered. Section forces in longitudinal direction are neglected and aerodynamic loads are represented in a simplified manner. Based on the suggested cabin geometry from [4,5], a multi-bubble double skin hull segment was created using Python scripting for Abaqus/CAE® (Dassault Systèmes HQ, 78140 Vélizy-Villacoublay, France) to allow automatic model generation. The developed tool provides the possibility to parameterize the geometrical and stiffness properties of the BWB fuselage section under consideration here. Different structural configurations and laminate layups are investigated. In the second part of the work the different fiber topologies in conjunction with the perforation hole are investigated for their on fatigue behavior. Three fiber topologies for the outer skin are taken into account: perforation with controlled fiber placement (CFP), perforated unidirectional and unperforated. CFP refers to a fiber topology were uninterrupted fibers are directed around the perforation [9]. On the contrary, perforated unidirectional refers to a topology obtained, for example, by drilling the perforation holes. The effect of CFP on orientation, fiber volume content, effective strength and effective stiffness is considered. The analysis is performed on micromodels loaded in such a manner that it is consistent with results obtained from the fuselage-model in critical a location. The load amplitude spectrum is a simplified version of the Transport WIng STandard (TWIST) spectrum [10]. A recently developed fatigue damage model (FDM) [11,12] is utilized for the analysis and load sequence effects are taken into account. Although the exact load sequence is unknown, the sequence dependence is exploited by exemplary studies of assumed increasing (Low–High) and decreasing (High–Low) load amplitudes from the spectrum.

2. Fuselage Segment Model For the intended purpose of this work, that is, a preliminary design study, the fuselage is represented by a segment of a longitudinal length of 5 m and a lateral width of 15 m. No particular boundary conditions are applied at the front and back section plane of the segment, thus neglecting any section forces transmitted in longitudinal direction.

2.1. Structural Components Based on the multi-bubble concepts taken from [13,14], a ﬁrst shell is generated with seven bubbles corresponding to the BWB overall design with seven engines presented in [8]. The middle three bubbles are identical with a diameter of 3.7 m. The diameter of the two outer cylinders is decreased in order to adjust the aerodynamic shape of the wing. Figure2 shows the geometry of the cross section in the generated multi-bubble cabin. The proposed layout is able to include 20 to 24 seats in on row, see [4,5]. The generated 3D cabin-skin is presented in Figure3a. Energies 2018, 11, 383 4 of 21 Energies 2018, 11, x FOR PEER REVIEW 4 of 21

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Figure 2. Multi-bubble cross section of the inner shell with floor. Figure 2. Multi-bubble cross section of the inner shell with ﬂoor. Figure 2. Multi-bubble cross section of the inner shell with floor.

(a) (b) (a) (b)

(e) (f)

(g)

Figure 3. Structural components of the multi-bubble fuselage comprising of (a) generated 3D cabin Figure 3. Structuralskin, (b) separate components outer skin, (c of) cross the ribbed multi-bubble design for the fuselage inner and comprising outer skin, (d of) interrupted (a) generated walls, 3D cabin skin, (b) separate(e) floor connected outer skin, to (wallsc) cross and ribbedcabin skin design and (f for) stringers the inner in the and curved outer cabin skin, skin. (d) Here, interrupted (g) walls, (e) ﬂoor connectedrepresents tothe walls division and of the cabin fuse skinlage in and the (chordf) stringers wise direction. in the curved cabin skin. Here, (g) represents the division of the fuselage in the chord wise direction. (g) The vaulted shape of the inner skin is dictated by the requirement to withstand the cabin pressure. It is,Figure however, 3. Structural not optimal components for the aerodynamic of the multi-bubble purposes fuselage and, comprising thus, requires of (a a) generated separate outer3D cabin skin see skin, (b) separate outer skin, (c) cross ribbed design for the inner and outer skin, (d) interrupted walls, (e) floor connected to walls and cabin skin and (f) stringers in the curved cabin skin. Here, (g) represents the division of the fuselage in the chord wise direction.

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Energies 2018, 11, 383 5 of 21 The vaulted shape of the inner skin is dictated by the requirement to withstand the cabin pressure. It is, however, not optimal for the aerodynamic purposes and, thus, requires a separate outer skin see Figure3 3b.b. TheThe outerouter skinskin contributescontributes toto thethe stiffnessstiffness withwith respectrespect toto thethe bendingbending momentmoment exertedexerted byby the wing forces and experiencesexperiences according stress.stress. BucklingBuckling instability in the outer- and cabin-skin is prevented byby stiffeningstiffening thethe thinthin skinskin withwith frames,frames, stringers,stringers, chord-chord- andand span-ribs.span-ribs. A cross ribbedribbed designdesign waswas adoptedadopted toto join join the the inner inner and and outer outer skin, skin, see see Figure Figure3c. 3c. Compared Compared to to a honeycomba honeycomb core, core, the the crossed crossed ribbed ribbed structure structure is is lighter lighter [ 6[6]] and and itsits geometrygeometry andand laminatelaminate layup can be optimized. The number of the ribs and their separation distances are parameterized in the model generator tool. High stress concentrations concentrations are are ex expectedpected at at the the seams seams of ofthe the bubbles bubbles [15]. [15 Structural]. Structural elements elements are arerequired required in order in order to tojoin join the the lower lower and and upper upper sides sides to to the the cabin-skin. cabin-skin. At At the the intersection intersection of two cylindrical bubble sections they are joined to verticalvertical wallswalls inin thethe cabin.cabin. The vertical walls can be designed in a closeclose oror openopen configuration.configuration. From From a structural point of view, closed bubbles with continuous walls will have a smoother stress distri distributionbution between the sections. However, However, interrupted walls, see Figure3 3d,d, allowallow forfor interiorinterior flexibility,flexibility, passengerpassenger freedomfreedom ofof movementmovement andand fastfast evacuation.evacuation. The floorfloor is spurted on the walls and the cabin-skin as shown in Figure 3 3e.e. SandwichSandwich floorfloor panelspanels with honeycomb core are considered in the finitefinite element model. A reasonable stiffening concept for the inner skin employs I-, Z- oror omega-sectionomega-section stringers.stringers. In this work, the stringers are simplifiedsimplified to blades perpendicular to the curved cabin-skin. The stringers are distributed on the curved curved cabin-skin, cabin-skin, see Figure3 3f.f. CurvedCurved compositecomposite framesframes onon thethe innerinner skinskin areare modelledmodelled inin orderorder toto dividedivide thethe fuselagefuselage into multiple parts in chordwise direction, seesee FigureFigure3 3g.g. AA highhigh bendingbending momentmoment isis expectedexpected inin thethe span wise direction due to the wide form of thethe BWB fuselage.fuselage. Therefore it appears pertinent to use the frames to support this load. The The frames frames are are repr representedesented in simplified simplified form by blades perpendicular to the curved cabin-skin.

2.2. Material An advantage of composite material based structural designs is the ability to affect the stiffness and strength of thethe ﬁber-reinforcedfiber-reinforced laminatelaminate byby thethe stackingstacking sequence.sequence. In this work, all plies are ® assumed to be IM7-8552 carbon-epoxy. For ﬂoorfloor andand interior walls corecore honeycombhoneycomb HexWebHexWeb® CRIII (Hexcel(Hexcel Corporation,Corporation, Stamford,Stamford, CT,CT, USA)USA) isis assumed.assumed. The mechanical properties of the materials are taken from [[16,17].16,17].

2.3. Loads and Boundary Conditions for the Static Analysis The static stress analysis considers four types of loadings on the fuselage section. A 2.5 g (where g is the acceleration due to gravity) maneuver at maximum take-off weight is considered as bending moment fromfrom thethe wingswings asas wellwell asas the the lift lift load load on on the the upper upper part part of of the the outer outer skin. skin. Internal Internal pressure pressure is appliedis applied on on the the cabin cabin skin skin and and mid-deck mid-deck ﬂoor floor loading loading at at 2.5 2.5 g g is is taken takeninto into account.account. TheThe loadsloads were multiplied by a safety factor of 1.51.5 toto generategenerate thethe designdesign loadsloads (ultimate(ultimate loads).loads). According to the 2 works [[6,13],6,13], an internal pressurepressure ofof 0.1280.128 N/mmN/mm2 isis assumed assumed including including all safety factors. The internal pressure loads are applied on the interior surface of cabins as a uniform pressure as represented in Figure4 4.. TheThe applied applied ﬂoor floor pressure pressure includes includes the the weight weight of of passengers, passengers, cargo, cargo, systems systems and and fuel fuel and and it 2 isit is assumed assumed to to be be 0.00431 0.00431 N/mm N/mm2at at the the loading loading case case 2.5 2.5 g g maneuver maneuver according according to to [6 [6,13].,13].

Figure 4. Cross section of the fuselage with applied loads, reference points and constraints. Figure 4. Cross section of the fuselage with applied loads, reference points and constraints.

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The aerodynamic loads for the long range considered BWB aircraft are estimated based on different design results corresponding toto different technologytechnology scenarios.scenarios. The results of the load cases are calculated using the methods developed in [[8].8]. The loads are provided for 80 sections along the span-wise axis of the aircraft. The forces related to wings (areas which are outside the fuselage) are multiplied with their distance to the fuselage edge in order to calculate their bending moments at the fuselage edge. The resultant moments are assumed to be distributeddistributed uniformlyuniformly along thethe fuselagefuselage edges. The equivalent moments for the 5-m segmentsegment are determined and applied on two reference points (RF1(RF1 and RF2)RF2) as shown in Figure 44.. TheThe referencereference nodesnodes areare locatedlocated onon thethe cabincabin sidessides andand coupled to the nodes nodes of of the the outer outer skin skin using using kinema kinematictic coupling coupling constraints. constraints. The The aerodynamic aerodynamic lift lift at atthe the outer outer skin skin is isconsidered considered as as uniform uniform pressure pressure at at the the outer outer surface surface and and included included in in the the analysis. Fixed boundary conditions in the vertical directio directionn were assumed at both reference points where one of thethe referencereference pointspoints was was also also ﬁxed fixed in in the the horizontal horizontal direction. direction. Section Section forces forces acting acting on theon frontthe front and backand back section section planes planes are neglected are neglected in the in analysis. the analysis.

2.4.2.4. Static Failure Criterion ® The Hashin failure criterion of Abaqus® (Dassault(Dassault Systèmes Systèmes HQ, HQ, 78140 78140 Vélizy-Villacoublay, Vélizy-Villacoublay, France) is used toto assessassess failurefailure initiationinitiation forfor fiber-reinforcedfiber-reinforced compositecomposite shells,shells, seesee [[18].18]. Hashin’sHashin’s theory [[19,20]19,20] distinguishesdistinguishes betweenbetween fourfour differentdifferent failurefailure initiationinitiation modes:modes: fiberfiber tension;tension; fiberfiber compression; matrix tension, and; matrix compression. Four Four output variables are provided by the simulation to indicate the failure index for each damagedamage mode. An index of less than 1 indicates that the criterion is not satisfiedsatisfied andand nono damagedamage isis initiatedinitiated inin thethe material.material. The safety margin is ensured by 50% excess excess load load imposed imposed on on the the model. model. Therefore, Therefore, a value a value of 1 ofor 1higher or higher indicates indicates that at that this at point this pointthe safety thesafety margin margin is not isrespected. not respected. The stress The stressanalysis analysis on the on fuselage the fuselage model model does not does consider not consider stress stressconcentrations concentrations due to due the to perforat the perforationion in the in theouter outer skin. skin. Thus, Thus, failur failuree in inthe the outer outer skin skin cannot cannot be detected in this model.

3. Micro Model for the Perforated Outer Skin 3. Micro Model for the Perforated Outer Skin One aspect of the analysis of the effect of fatigue loading on the perforated holes is the controlled One aspect of the analysis of the effect of fatigue loading on the perforated holes is the controlled fiber placement of the fibers around the holes. Results from [21] show that the effective properties of fiber placement of the fibers around the holes. Results from [21] show that the effective properties of the plates with the hole are generally improved when the fibers are curved around the hole, rather the plates with the hole are generally improved when the fibers are curved around the hole, rather than interrupted by the hole. CFP can substantially mitigate the weakening effect of the hole, both than interrupted by the hole. CFP can substantially mitigate the weakening effect of the hole, both with respect to strength and and stiffness. stiffness. However, However, in in cases cases with with high high compressive compressive loading loading situations, situations, it ithas has been been seen seen that that the the CFP CFP did did not not bring bring about about any any improvements improvements and and also also reduced reduced the the compressive compressive strengths [[21,22].21,22]. Figure Figure 55 representsrepresents thethe CFPCFP forfor perforatedperforated holesholes forfor aa rectangularrectangular patternpattern basedbased perforations. In Figure5 5,, thethe basicbasic geometrygeometry perforatedperforated skinskin isis shown.shown. Here,Here, thethe diameterdiameter ofof thethe holehole is 0.24 mm and the spacingspacing betweenbetween thethe perforationsperforations amountsamounts toto 1.001.00 mmmm inin bothboth directions.directions.

Figure 5. Controlled fiber placements for a rectangular based perforation arrangement in a [0/90]s Figure 5. Controlled ﬁber placements for a rectangular based perforation arrangement in a [0/90]s composite laminate. composite laminate.

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Energies 2018, 11, x FOR PEER REVIEW 7 of 21 3.1. Fiber Placement 3.1. Fiber Placement Fibers are assumed to follow a cosine function in the vicinity of the hole, such that a greater Fibers are assumed to follow a cosine function in the vicinity of the hole, such that a greater curvature is seen near the hole and fibers further away from the perforation remain straight. The fiber curvature is seen near the hole and fibers further away from the perforation remain straight. The fiber orientation due to CFP is described by Equation (1). The total fiber volume content of any given orientation due to CFP is described by Equation (1). The total fiber volume content of any given x = const. section plane is constant at 60% with respect to the interval from y = 0 to y = 0.5 mm. = const. section plane is constant at 60% with respect to the interval from =0 to = 0.5 mm. The x/y-plane is split into a compressed and undisturbed segment. The vertical extend of the The /-plane is split into a compressed and undisturbed segment. The vertical extend of the compressed segment is defined so that the maximum geometrically possible fiber volume is attained at compressed segment is defined so that the maximum geometrically possible fiber volume is attained the left edge, see Figure6. This is based on the presumption that in manufacturing the CFP would be at the left edge, see Figure 6. This is based on the presumption that in manufacturing the CFP would implemented via a displacement of the fibers by, for example, pins or similar implements. The topmost be implemented via a displacement of the fibers by, for example, pins or similar implements. The segment of the 0◦-ply, and the right most segment of the 90◦-ply, is filled by undisturbed fibers. The topmost segment of the 0°-ply, and the right most segment of the 90°-ply, is filled by undisturbed unshaded fish-eye region in Figure6a, is filled by a pure matrix region in the model. The fiber angle, fibers. The unshaded fish-eye region in Figure 6a, is filled by a pure matrix region in the model. The Equation (2), was obtained by differentiating Equation (1). There, the symbols x and y refer to the fiber angle, Equation (2), was obtained by differentiating Equation (1). There, the symbols and horizontal and vertical position with respect to the origin at the hole center. The symbol y denotes the refer to the horizontal and vertical position with respect to the origin at the hole center.0 The symbol vertical position of a particular fiber at x = 0.50. denotes the vertical position of a particular fiber at =0.50.

y [mm]

[mm] (a) (b)

Figure 6. Controlled fiber placement (CFP) in the micro model: (a) fiber orientation defined by Figure 6. Controlled fiber placement (CFP) in the micro model: (a) fiber orientation defined by Equation (1) (b) variation in volume fraction within the micro-mechanical model. Equation (1) (b) variation in volume fraction within the micro-mechanical model. , = + 0.25 (1− )(1 + cos ) (1) h π x i f [x, y ] = y + 0.25 (1 − y )(1 + cos )2 (1) 0 0 0 2 1.57081.5708 ( (−1−1 + +1 1y) )sin sin π x 2 2 ,α[ x, y=−] = − (2).(2) −3−3 ++ 11 cos[1.57081.5708x] As depicted in Figure6, a quarter model with appropriate symmetry constraints is employed for As depicted in Figure 6, a quarter model with appropriate symmetry constraints is employed the micro-mechanical model. Because thickness and perforation spacing are of comparable magnitude, for the micro-mechanical model. Because thickness and perforation spacing are of comparable a 3D-solid discretization by eight-node fully integrated solid elements is used for the micro model as magnitude, a 3D-solid discretization by eight-node fully integrated solid elements is used for the shown in Figure7a. It has to be noted that the chosen fiber orientation results in a pure-matrix region micro model as shown in Figure 7a. It has to be noted that the chosen fiber orientation results in a as shown in Figure6a. To facilitate the model generation, the small pure-matrix pockets indicated by pure-matrix region as shown in Figure 6a. To facilitate the model generation, the small pure-matrix blue region in Figure7b, were omitted. The stiffness in those pockets is very low in comparison to the pockets indicated by blue region in Figure 7b, were omitted. The stiffness in those pockets is very low reinforced regions. in comparison to the reinforced regions.

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(a) (b)

Figure 7. Here (a) represents the 3D micro model comprising of [0/90]s laminate and (b) represents Figure 7. Here (a) represents the 3D micro model comprising of [0/90]s laminate and (b) represents thethe front front view view of of the the 3D 3D model, model, indicating indicating the the orientations orientations as as well well as as the the matrix matrix pocket, pocket, fish-eye ﬁsh-eye and and reinforcedreinforced region. region.

3.2. Variation in Material Properties 3.2. Variation in Material Properties As apparent from Figure 6b the change in fiber volume content , is substantial and strength As apparent from Figure6b the change in fiber volume content ϕ, is substantial and strength and stiffness parameters cannot be considered constant. The volume fraction along the left edge of and stiffness parameters cannot be considered constant. The volume fraction along the left edge of the micro model approaches the maximum fiber volume content that is geometrically permissible in the micro model approaches the maximum fiber volume content that is geometrically permissible a square based packing of fibers in a composite, i.e., =0.91. On the right edge the fiber volume in a square based packing of fibers in a composite, i.e., ϕmax = 0.91. On the right edge the fiber content is taken to be 0.6 (default volume fraction of IM7 [16]). This causes the stiffness as well as the volume content is taken to be 0.6 (default volume fraction of IM7 [16]). This causes the stiffness as consequent strength parameters to be different in the model. Therefore, the stiffnesses in the well as the consequent strength parameters to be different in the model. Therefore, the stiffnesses longitudinal and transverse directions are approximated by the Chamis mixture theory [23]. A similar in the longitudinal and transverse directions are approximated by the Chamis mixture theory [23]. method of approximation was also used in determine the Poisson’s ratio,  . However,  , the A similar method of approximation was also used in determine the Poisson’s ratio, ν . However, out-of-plane Poisson’s ratio is set to the Poisson’s ratio of the matrix, which in this case 12set to be 0.4. ν , the out-of-plane Poisson’s ratio is set to the Poisson’s ratio of the matrix, which in this case set to As23 transverse isotropy is assumed, the out-of-plane modulus, can be calculated using the be 0.4. As transverse isotropy is assumed, the out-of-plane modulus, E can be calculated using the following equation: 23 following equation: E E = 22 (3) 23= 2(1 + ν ) (3). 2(1+23) SinceSince only only a apreliminary preliminary study study is intended is intended here, here, a linear a linear rule ruleof mixture of mixture for the for strength the strength in fiber in directionfiber direction was assumed was assumed with withrespect respect to to. Inϕ. Intransverse transverse direction direction the the strengths strengths were were assumed assumed constantconstant as as shown shown in in Figure Figure 8.8. It can be seen thatthat the homogenization of longitudinal strength was carriedcarried out out based based on on the the known known strengths strengths for for =0.6 ϕ = 0.6andand the the fiber fiber strength strength (solid (solid line), line), rather rather than than interpolatinginterpolating to to zero zero (dashed line)line) asas shownshown in in Figure Figure8 a.8a. In In the the direction direction transverse transverse to theto the fiber fiber and and for forthe the shear shear strength strength no dependenceno dependence on ϕ onwas considered,was considered, as represented as represented in Figure in Figure8b. The 8b. blue The shaded blue shadedregion marksregion themarks range the of rangeϕ in the of model. in the As model. indicated As in indicated Figure8, thein Figure parameters 8, theX parameterst(ϕ)/Xc(ϕ) , indicate the corresponding tensile/compressive strengths in fiber direction. Similarly, the parameters ()/(), indicate the corresponding tensile/compressive strengths in fiber direction. Similarly, Yt(ϕ)/Yc(ϕ), indicate the corresponding strength parameters in transverse direction and S(ϕ) denotes the parameters ()/(), indicate the corresponding strength parameters in transverse direction andthe shear() strengths. denotes the shear strengths. Energies 2018, 11, 383 9 of 21 Energies 2018, 11, x FOR PEER REVIEW 9 of 21

(a) (b)

Figure 8. Approximation of consequent strengths due to varying volume fractions in: (a) longitudinal Figure 8. Approximation of consequent strengths due to varying volume fractions in: (a) longitudinal and (b) transverse to fiber and shear directions. and (b) transverse to fiber and shear directions. 3.3. Simplified Layup and Consequent Extensional Stiffness Matrix 3.3. Simplified Layup and Consequent Extensional Stiffness Matrix With the approximation procedures defined in Sections 3.1 and 3.1 the representation of the CFP Within the the micromodel approximation proved procedures to be complicated defined for in the Sections [45/0/-45/90/45/90/-45/90]s 3.1 and 3.2 the representation laminate layup of the used CFP in the micromodelin the global proved model of to the be fuselage complicated section. for As the a su [45/0/bstitute,−45/90/45/90/ a layup of equivalent−45/90]s diagonal laminate coefficients layup used in theA global11 and A model22 in the of extensional the fuselage stiffness section. of the As laminate a substitute, was adevised layup for of equivalentthe micro-mechanical diagonal coefficientsmodel used in the fatigue calculations. The simplified layup comprises 0° and 90° plies. In this simplification A11 and A22 in the extensional stiffness of the laminate was devised for the micro-mechanical model approach, the individual thickness t, for 0° and 90° plies were determined◦ ◦ so that the A11 and A22 usedentries in the fatiguein the extensional calculations. stiffness The simplifiedmatrix for the layup complex comprises layup used 0 and in the 90 globalplies. fuselage In this simplification laminate ◦ ◦ approach,model theand individualthe simplified thickness laminatet configur, for 0 ationand 90in theplies micromodel were determined are the same. so that the A11 and A22 entries inFor the determining extensional the stiffness individual matrix thicknesses for the complexfor all the layupthree cases, used finite in the element global method fuselage (FEM) laminate modelbased and stress the simplified analyses were laminate performed configuration on the individual in the micromodel plies (oriented are in the0° and same. 90°) of unit length. ForThe determiningreaction forces the in both individual the plies thicknesses were comput fored and allthe later three correlated cases, to finite the whole element laminate method using (FEM) basedthe stress extensional analyses matrix were and performed resultant reaction on the individualforces. This pliesleads (orientedto two sets inof 0linear◦ and equations, 90◦) of unit when length. The reactionsolved provided forces in boththe thickness the plies werevalues computed required andto match later correlatedthe A11 and to theA22 wholeentries laminatein the global using the extensionalextensional matrix matrix and A resultant. Based on reaction the above forces. procedure, This leadsthe newly to two calculated sets of linearthickness equations, for all the when 3 cases solved of micro model in comparison to the global fuselage configuration are shown in Table 2. provided the thickness values required to match the A11 and A22 entries in the global extensional matrix A. Based onTable the above 2. Thickness procedure, approximation the newly for the calculated simplified laminate thickness configuration. for all the 3 cases of micro model in comparison to the global fuselage configuration are shown in Table2. Type Laminate Configuration/Thickness [mm] Total Thickness [mm] Global fuselageTable 2.laminateThickness approximation[45/0/-45/90/45/90/-45/90]s/(0.125 for the simplified laminate) configuration.2 Simplified micro model Without perforation [0/90]s/(0.27/0.52) 1.58 Type Laminate Configuration/Thickness [mm] Total Thickness [mm] With perforation, no CFP [0/90]s/(0.29/0.61) 1.81 GlobalWith perforations, fuselage laminate with CFP [45/0/−45/90/45/90/[0/90]s/(0.27/0.57−45/90]s/(0.125)) 1.68 2 Simplified micro model Without perforation [0/90]s/(0.27/0.52) 1.58 As shown in Table 2, the global fuselage laminate has a constant thickness of 0.125 mm for all With perforation, no CFP [0/90]s/(0.29/0.61) 1.81 the plies, whereas the simplified micro model has different thickness for the 0° and 90° plies. It can With perforations, with CFP [0/90]s/(0.27/0.57) 1.68 be seen that the perforated micro model with the CFP, required a reduced thickness, particularly for the 90° plies, to attain the same stiffness that of the global model when compared to the same laminate Asconfiguration shown in Tablewithout2, theCFP global and is fuselage more comparable laminate hasto the a constant micro model thickness without of 0.125perforation mm for [21]. all the plies,In whereas comparison the to simplified the globalmicro fuselage model laminate has conf differentiguration, thickness due to the for particular the 0◦ and stacking 90◦ plies. sequence It can be seen thatin the the simplified perforated laminate micro configuration, model with not the all CFP, entries required in the extensional a reduced stiffness thickness, and particularlybending matrix for the 90◦ plies,could to be attain matched. the This same shortcoming stiffness that seems of acceptab the globalle for model the purpose when comparedof a preliminary to the design same study laminate configurationin the present without work, CFPhowever, and it is is more intended comparable to be properly to the addressed micro modelin future without works. perforation [21]. In comparison to the global fuselage laminate configuration, due to the particular stacking sequence in the simplified laminate configuration, not all entries in the extensional stiffness and bending matrix could be matched. This shortcoming seems acceptable for the purpose of a preliminary design study in the present work, however, it is intended to be properly addressed in future works. EnergiesEnergies 2018, 11, 383x FOR PEER REVIEW 1010 ofof 2121

4. Static Analysis 4. Static Analysis In this section, strength and buckling analyses are performed for the previously described fuselageIn this segment section, strengthmodel. andDifferent buckling configurations analyses are performedare evaluated for the by previously stress analysis described under fuselage the segmentpreliminary model. flight Different loads. In configurations the first analysis are evaluatedstep, two different by stress configurations analysis under are the considered preliminary for flight the loads.ribbed In double-skin the first analysis fuselage. step, The two first different configuration configurations contains are 34 consideredchord-ribs, forfive the span-ribs, ribbed double-skin five frames fuselage.and six walls The between first configuration each two adja containscent bubbles. 34 chord-ribs, Whereas, five in the span-ribs, second configuration, five frames and the sixdistances walls betweenbetween eachthe span-ribs two adjacent and bubbles.distances Whereas,between the in theframes second are configuration,decreased from the 1 distancesm to 0.5 m between which theincreases span-ribs the andnumber distances of each between of them the framesfrom five are decreasedto 10. Stress from analyses 1 m to 0.5 are m performed which increases for both the numberconfigurations of each ofapplying them from the five load to 10.case Stress 2.5 analysesg maneuver are performed at maximum for both takeoff configurations weight. applyingFigure 9 therepresents load case the 2.5 stress g maneuver distributions at maximum in the takeoffspan wise weight. direction Figure and9 represents the deflections the stress for distributions the fuselage insection the span under wise the direction critical ultimate and the deflectionsloads. for the fuselage section under the critical ultimate loads.

(a)

(b)

(c)

(d)

Figure 9. Stress distributions and the deflections for the two different fuselage configurations. Figure 9. Stress distributions and the deflections for the two different fuselage configurations. (a,c) correspond to configuration 1, (b,d) correspond to configuration 2. (a,c) correspond to configuration 1, (b,d) correspond to configuration 2.

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Figure9 9a,ba,b show show aa decreasedecrease in in thethe maximalmaximal stressstress of of 36%36% byby increasingincreasing thethe numbernumber ofof thethe framesframes and spanEnergies ribs 2018 from, 11, x FOR 5 to PEER 10 ininREVIEW thethe secondsecond configuration.configuration. The deflectiondeflection in the center of the 11 fuselage of 21 is decreased fromfrom 421421 mm mm in in configuration configuration 1 1 to to 257 257 mm mm in in configuration configuration 2. 2. Due Due to to the the internal internal pressure pressure on theon the cabin-skin, cabin-skin,Figure high-stress 9a,b high-stress show a concentrationsdecrease concentrations in the maximal can can be observed bestress observed of 36% in the by in junctionincreasingthe junction between the between number walls of walls the and frames and cabin-skin. cabin- Figureskin. andFigure 10 span represents 10 ribs represents from the 5 to failed 10 the in elements.thefailed second elements. Matrixconfiguratio failureMatrixn. The underfailure deflection compression under in thecompression center and tensionof the and fuselage are tension observed is are decreased from 421 mm in configuration 1 to 257 mm in configuration 2. Due to the internal pressure there.observed A redesignthere. A redesign is required is required for these for local these areas. local However, areas. However, considering considering the main the objective main objective of the on the cabin-skin, high-stress concentrations can be observed in the junction between walls and cabin- present work is the definition of a basic structural concept rather than the individual component design of theskin. present Figure work 10 representsis the definition the failed of a elements.basic structural Matrix conceptfailure under rather compression than the individual and tension component are of fuselage, the required redesign process is not addressed here. designobserved of fuselage, there. Athe redesign required is required redesign for process these lo iscal not areas. addressed However, here. considering the main objective of the present work is the definition of a basic structural concept rather than the individual component design of fuselage, the required redesign process is not addressed here.

Figure 10. Damaged elements for matrix failure criteria under compression in conﬁgurationconfiguration 1.1. Figure 10. Damaged elements for matrix failure criteria under compression in configuration 1. Buckling analysis is an important aspect in the design of thinthin walledwalled structures.structures. In addition to strength andBuckling stiffness analysis requirements is an important thethe thinthinaspect compositecomposit in the designe structuresstructures of thin mustwalledmust bebe structures. structurallystructurally In addition stable.stable. to Due to strength and stiffness requirements the thin composite structures must be structurally stable. Due to the preliminarypreliminary charactercharacter ofof the the structural structural design design under under consideration consideration here here buckling buckling is investigatedis investigated in the preliminary character of the structural design under consideration here buckling is investigated thisin this work work by by linear linear buckling buckling analysis analysis in this work by linear buckling analysis For theFor the linearthe linear linear buckling buckling buckling problem problemproblem the the the firstfirst ﬁrst four four eigenvalueseigenvalues eigenvalues and and eigenshapes and eigenshapes eigenshapes are arepresented. presented. are presented. The The lowest eigenvalue is associated with buckling, if the buckling load is: F =F= and <1< The lowestlowest eigenvalue is is associated associated with with buckling, buckling, if the if the buckling buckling load load is: is:FFbuck=Fλ andFref and<1λ 1 buckling,buckling, while while λ>1> >11 safe.safe. safe. The The The buckling bucklingbuckling modesmodes areare are presentedpresented presented in in inFigures Figures Figures 11 and1111 and 12, where1212,, where local locallocal bucklingbuckling shapes shapes can can be be observed observed at at the the twotwo sidessides of of the the outer outer skin skin (load (load introduction introduction areas) areas) and and betweenbetween the ripsthe rips at the at the upper upper pressurepressure pressure sideside side where wherewhere bucklingbuckling is isis expected. expected.expected.

FigureFigure 11. Four 11. Four bucking bucking modes modes of of the the linear linear buckling anal analysisysis for for configuration configuration 1 with 1 with five span-ribs, five span-ribs, five frames.five frames. Figure 11. Four bucking modes of the linear buckling analysis for configuration 1 with five span-ribs,

five frames.

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Figure 12. Four bucking modes of the linear buckling anal analysisysis for configuration conﬁguration 2 with 10 span-ribs, 10 frames.

Therefore, at these smaller areas in Figure 11 locallocal stiffeningstiffening isis needed,needed, whichwhich increasesincreases thethe buckling strength and has nono substantialsubstantial impactimpact onon thethe weight.weight. Another approach is a generally narrower stiffening scheme,scheme, asas inin FigureFigure 1212,, whichwhich showsshows nono bucklingbuckling problems.problems. The fuselage weight per unitunit floorfloor areaarea isis determineddetermined forfor bothboth configurations.configurations. The estimatedestimated weight forfor thethe first first configuration configuration is is 34.63 34.63 kg/m kg/m2 with2 with five five span-ribs span-ribs and and five five frames. frames. When When doubling doubling the numberthe number of span-ribs of span-ribs and and frames frames in thein the second second configuration, configuration, the the weight weight was was increased increased to to 38.68 38.68 kg/m kg/m2.. Table3 3 presents presents the the comparison comparison between between the the two two configurations. configurations.

Table 3. Comparison between conﬁgurationsconfigurations 11 andand 2.2. Numerical Results Conf. 1 Conf. 2 Numerical Results Conf. 1 Conf. 2 Max. stress (MPa) 1646 1049 Max. stress (MPa) 1646 1049 Max. deflection (mm) 421 257 Max. deﬂection (mm) 421 257 FirstFirst four four eigenvalues λ λ 0.82, 0.82, 0.87, 0.87, 0.89, 0.89, 0.93 0.93 1.26, 1.26, 1.31, 1.31, 1.33, 1.33, 1.36 1.36 Weight (kg/m (kg/m2)2) 34.6334.63 38.68 38.68 WeightWeight of of damaged damaged elements to to segment segment weight weight MatrixMatrix compression 1.26% 1.26% 0.58% 0.58% MatrixMatrix tensiontension 0.28% 0.28% 0.03% 0.03% FiberFiber compression 0.00% 0.00% 0.00% 0.00% Fiber tension 0.00% 0.00% Fiber tension 0.00% 0.00%

The maximal bending stress in a BWB aircraft is expectedexpected to occur in the span wise direction, the influenceinfluence of otherother structuralstructural components is studied in thethe secondsecond stepstep ofof thisthis section.section. AA parameterparameter study isis carriedcarried out out for for different different thicknesses thicknesses of span-ribsof span-ribs and and two two different different laminate laminate layups layups of the of outer the skin.outer Theskin. first The configuration first configuration with five with frames five isframes chosen is forchosen these for studies. these Instudies. the first In study, the first the study, span-ribs’ the thicknessspan-ribs’ isthickness increased is fromincreased 2 mm from to 5 mm.2 mm The to 5 resulting mm. The weight, resulting max. weight, deflection, max. deflection, max. stress max. and criticalstress and areas critical are presented areas are in presented Table4. The in Table analysis 4. The results analysis show aresults stress show reduction a stress of 19% reduction by increasing of 19% 2 theby increasing thickness fromthe thickness 2 mm to 5from mm. 2 Wheremm to the5 mm. weight Wher pere the unit weight floor area per increasesunit floor from area 33.91increases kg/m fromto 2 36.0633.91 kg/m2 to. Compared 36.06 kg/m to2. Compared the first analysis to the offirst configurations analysis of configurations 1 and 2, the increasing 1 and 2, the of theincreasing span-ribs’ of the span-ribs’ thickness reduced the main deflection in the span wise direction of 8.20% by increasing

Energies 2018, 11, 383 13 of 21 thickness reduced the main deflection in the span wise direction of 8.20% by increasing of 6.34% of the weight. On the other hand, the increasing of the number of the frames reduced the main deflection of 38.95% with a weight increasing of 11.70%. The second parameter analysis presents the influence of laminate layups for the outer skin on the strength analysis. For this purpose, three different layups are introduced for the outer skin, where the first layup [45/0/−45/90/45/90/−45/90]s is assumed in configuration 1. The calculated stress, deflection and weight are presented in Table5.

Table 4. Parameter study for the laminate thickness of the span-ribs.

Numerical Results t = 2 mm t = 3 mm t = 4 mm t = 5 mm Max. stress (MPa) 1811 1646 1542 1472 Max. deﬂection (mm) 439 421 410 403 Weight (kg/m2) 33.91 34.63 35.35 36.06 Weight of damaged elements to segment weight Matrix compression 1.50% 1.26% 1.05% 0.97% Matrix tension 0.39% 0.28% 0.20% 0.15% Fiber compression 0.00% 0.00% 0.00% 0.00% Fiber tension 0.00% 0.00% 0.00% 0.00%

Table 5. Parameter study for the laminate layups of the outer skin.

[45/0/−45/90/ [45/90/−45/0/ [45/−45/45/−45/ Numerical Results 45/90/−45/90]s 45/0/−45/0]s 45/−45/45/−45]s Max. stress (MPa) 1646 1672 1663 Max. deﬂection (mm) 421 423 422 Weight (kg/m2) 34.63 34.63 34.63 Weight of damaged elements to segment weight Matrix compression 1.26% 1.27% 1.27% Matrix tension 0.28% 0.29% 0.28% Fiber compression 0.00% 0.00% 0.00% Fiber tension 0.00% 0.00% 0.00%

5. Fatigue Analysis Based on the static results for the load factor n = 1 g a point on the centerline of the outer skin was chosen for the fatigue analysis. This point was deemed representative, because in a large area around it similarly high strain occurs. Regions of even higher, but very localized, strain near joints were not considered, since in a practical design those regions would not be weakened by perforation. The representative points (indicated by highlighted regions in red in Figure 13) are seen to have a high ◦ −4 value of the strain component in 0 direction, ε11 = 2.96 × 10 , but negligible strain ε22. The strain component ε11 obtained from the fuselage model manifests itself on the micromodel as the average strain [24], that is: 1 Z µ ε11 = µ ε11(x, y, z) ·dV. (4) V Vµ µ In Equation (4), ε11 is the (homogenized) macroscopic strain observed in the fuselage model, ε11 is the locally inhomogeneous strain in the micro model and Vµ is the Volume of the micro model. Loading conditions for the micro model that are equivalent to the global strain component ε11 can be obtained by displacing the appropriate boundary in the micromodel by the value speciﬁed in Equation (5). There, U1 is the displacement in span wise-direction and L is the length of the micro model.

U1 = ε11·L. (5)

A corresponding expression exists for U2, however, in the present case ε22 is negligible in the critical point and, therefore U2 = 0. Energies 2018, 11, x FOR PEER REVIEW 14 of 21 Energies 2018, 11, 383 14 of 21

Location for the fatigue analyses

Figure 13. StrainStrain distribution distribution in in the outer skin.

5.1. Fatigue Damage Model (FDM) 5.1. Fatigue Damage Model (FDM) In case of high performance applications such as rotor blades for wind turbines and aircraft, In case of high performance applications such as rotor blades for wind turbines and aircraft, fiber-reinforced plastics (FRPs) based components are not only subjected to just static loads but also fiber-reinforced plastics (FRPs) based components are not only subjected to just static loads but to stochastic cyclic loads during their life time. Therefore, effective fatigue predictions in these also to stochastic cyclic loads during their life time. Therefore, effective fatigue predictions in these components have become a matter of priority and in the last decade different modelling techniques components have become a matter of priority and in the last decade different modelling techniques have been investigated. Depending on the accuracy of the damage prediction and the physical form have been investigated. Depending on the accuracy of the damage prediction and the physical form of of damage, these fatigue models can be classified into three groups: fatigue life models, damage, these fatigue models can be classified into three groups: fatigue life models, phenomenological phenomenological models and progressive damage models [25]. A physically based fatigue damage models and progressive damage models [25]. A physically based fatigue damage model recently model recently developed [11,12] addresses several disadvantages of many of the models currently developed [11,12] addresses several disadvantages of many of the models currently used for composite used for composite materials. The model (denoted in the following as FDM) is capable to consider materials. The model (denoted in the following as FDM) is capable to consider stress redistributions stress redistributions and load sequence effects and is used as the basis for the fatigue studies in this and load sequence effects and is used as the basis for the fatigue studies in this paper. Furthermore paper. Furthermore the FDM is able to accumulate redistributions and load sequence effects, and is the FDM is able to accumulate redistributions and load sequence effects, and is able to describe the able to describe the nonlinear fatigue damage accumulation [26], which is typical for FRPs [27]. The nonlinear fatigue damage accumulation [26], which is typical for FRPs [27]. The original model as original model as described in [11,12] is based on the classical laminate theory (CLT), such that it is described in [11,12] is based on the classical laminate theory (CLT), such that it is capable to analyze capable to analyze damage states ply-wise and also works on the basis of fracture-mode depended damage states ply-wise and also works on the basis of fracture-mode depended theory of Puck [28,29]. theory of Puck [28,29]. Based on the material orientation (longitudinal and transverse to fiber Based on the material orientation (longitudinal and transverse to fiber direction) and the applied direction) and the applied load (e.g., tension, compression and shear) degradation factors are load (e.g., tension, compression and shear) degradation factors are introduced for both strength and introduced for both strength and stiffness degradations. Figure 14 represents the layout of the FDM stiffness degradations. Figure 14 represents the layout of the FDM and as depicted, it comprises two and as depicted, it comprises two parts, a continuous and a discontinuous part. In the discontinuous parts, a continuous and a discontinuous part. In the discontinuous part, the material degradation is part, the material degradation is calculated under static loading using Puck’s criterion for static calculated under static loading using Puck’s criterion for static failure. Once the quasi-static analysis is failure. Once the quasi-static analysis is done, the continuous part is initiated, calculating the material done, the continuous part is initiated, calculating the material degradation as a result of cyclic loading. degradation as a result of cyclic loading. The main feature of the FDM is the energy-based hypothesis by Pfanner [30], which was originally developed for reinforced concrete. This hypothesis equalizes the energy dissipated during fatigue loading to that of the energy in the quasi-static loading and that the damage state due to degradation in mechanical properties such as stiffness and strength not only depend on the amount of energy dissipated but also on the duration and amplitude of loading in the structure. Due to this energy-based approach it is possible to consider block loadings in the analysis. In particular highly dynamic stressed structures can thereby be calculated in an efficient manner. The method was partially validated with the results from the OptiDAT-Data bank [31].

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Figure 14. Flowchart of the fatigue damage model (FDM) with discontinuous and continuous method Figure 14. Flowchart of the fatigue damage model (FDM) with discontinuous and continuous method of degradation [11]. of degradation [11]. The main feature of the FDM is the energy-based hypothesis by Pfanner [30], which was originallyHowever developed analysis for of reinforced more complicated concrete. situations This hypothesis involving equalizes three-dimensional the energy dissipated (3D) stress during states, thefatigue CLT loading based FDM to that is no of longer the energy applicable in the and quasi- stressesstatic in all loading directions and have that tothe be damage considered. state Recently, due to Madhusoodanandegradation in mechanical et al. [26] extended properties the such FDM as [ 11sti,12ffness] to takeand intostrength account not the only stresses depend and on degradations the amount forof energy 3D. In thedissipated present but work, also the on FDM the duration based on and the 3Damplitude framework of loading is employed. in the structure. Due to this energy-based approach it is possible to consider block loadings in the analysis. In particular highly 5.2. Load Spectrum and Load Ratios dynamic stressed structures can thereby be calculated in an efficient manner. The method was partiallySeveral validated suggestions with the forresults the from appropriate the OptiDAT-Data load spectra bank for[31]. aircraft can be found from literatureHowever[10,32 analysis–34]. By of definition,more complicated a spectrum situations is ordered involving by frequency, three-dimensional and the (3D) sequence stress ofstates, the amplitudethe CLT based cannot FDM be restored is no longer from it.applicable In the present and st caseresses the loadin all sequence directions is ofhave importance, to be considered. however, sinceRecently, the employedMadhusoodanan fatigue modelet al. [26] considers extended sequence the FDM effects. [11,12] As to a take consequence, into account a precise the stresses prediction and regardingdegradations the for fatigue 3D. In life the requires present flight work, by the flight FDM load based block on the definitions 3D framework and cannot is employed. be made based on a spectrum alone. However, due to the large computational effort required for the flight by flight5.2. Load analysis, Spectrum this and method Load Ratios is not used in the present work. Instead, some approximate results are obtained from an assumed load sequence, that is, sorting the load blocks obtained from the spectrum Several suggestions for the appropriate load spectra for aircraft can be found from literature in ascending (Low to High or Lo–Hi) or descending (High to Low or Hi–Lo) order. Among the three [10,32–34]. By definition, a spectrum is ordered by frequency, and the sequence of the amplitude load spectrums [10,32–34], the fatigue predictions using simplified flight-simulations are found to cannot be restored from it. In the present case the load sequence is of importance, however, since the yield good results for residual crack growth in aircraft components [33]. As an alternative, the fatigue employed fatigue model considers sequence effects. As a consequence, a precise prediction regarding based strength degradation in the outer skin is analyzed by using a separate Hi-Lo and Lo-Hi simple the fatigue life requires flight by flight load block definitions and cannot be made based on a spectrum block loading spectrums. alone. However, due to the large computational effort required for the flight by flight analysis, this A realistic fatigue loading sequence is not readily available for conceptual BWB aircraft. In the method is not used in the present work. Instead, some approximate results are obtained from an fatigue analyses using the FDM, load sequences as used in experimental testing of aircraft are applied assumed load sequence, that is, sorting the load blocks obtained from the spectrum in ascending as(Low virtual to High tests. Theor Lo–Hi) load spectrum or descending defined for(High the soto calledLow TWISTor Hi–Lo) [10] isorder. considered Among to bethe appropriate, three load however,spectrums only [10,32–34], a reduced the fatigue version predictions of the TWIST using sequence simplified shown flight-simulations in Figure 15 is are used found for to fatigue yield calculation.good results Thefor residual corresponding crack grow fatigueth indata aircraft for components each load block [33]. can As an be alternative, found in Table the 6fatigue. Only based load R R ratios,strength =degradation 0 and above in the= 0.63outer are skin considered is analyzed for by the using present a separate work. ThisHi-Lo is and due Lo-Hi to the simple fact that block the R employedloading spectrums. FDM has not been properly validated for the reversible loading ratios, < 0. A realistic fatigue loading sequence is not readily available for conceptual BWB aircraft. In the fatigue analyses using the FDM, load sequences as used in experimental testing of aircraft are applied as virtual tests. The load spectrum defined for the so called TWIST [10] is considered to be appropriate, however, only a reduced version of the TWIST sequence shown in Figure 15 is used for fatigue calculation. The corresponding fatigue data for each load block can be found in Table 6. Only load ratios, R = 0 and above R = 0.63 are considered for the present work. This is due to the fact that the employed FDM has not been properly validated for the reversible loading ratios, R < 0.

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FigureFigure 15. Simpliﬁed15. Simplified load load spectrum based based on TWIST on TWIST [10]. [10].

Table 6. Fatigue data for each load block for the simplified load spectrum based on TWIST [10]. Table 6. Fatigue data for each load block for the simplified load spectrum based on TWIST [10]. Load Block V VI VII VIII IX X 0 0.09 0.19 0.31 0.45 0.63 Load Block V 5.2 × 10 VI1.52 × 10 8×10 VII4.17 × 10 VIII3.48 × 10 3.59 IX × 10 X R 0Figure 0.09 15. Simplified load 0.19 spectrum based on 0.31 TWIST [10]. 0.45 0.63 5.3. Determination of Appropriate S-N Curves n 5.2 × 102 1.52 × 103 8 × 103 4.17 × 104 3.48 × 105 3.59 × 106 The keyTable components 6. Fatigue data required for each for load the block assessment for the simplified under fatigue load spectrum failure are based the onS-N TWIST curves. [10]. These curves relate the number of load cycles to failure to a given applied maximum stress. Furthermore, Load Block V VI VII VIII IX X 5.3. Determinationthey also serve of Appropriate as the abort criterion S-N Curves for the FDM. The characteristic of these curves depend strongly 0 0.09 0.19 0.31 0.45 0.63 on the fiber orientations and the applied stress ratio [35]. Experimental methods to determine the The key components required5.2 × 10 for 1.52 the ×assessment 10 8×10 under4.17 ×fatigue 10 3.48 failure × 10 are3.59 the × S-N 10 curves. These individual S-N curves are cumbersome and not cost-effective. As a result, numerical methods are curves relateusually5.3. the Determination employed number for of the Appropriate load effective cycles S-Nprediction toCurves failure of the to different a given S-N applied curves. One maximum appropriate stress. method Furthermore, of they also servenumerical as theapproximation abort criterion is the Modified for the Fatigue FDM. TheStrength characteristic Ratio by Kawai of [36]. these It is curves able to dependpredict strongly The key components required for the assessment under fatigue failure are the S-N curves. These on the fiberfurther orientations S-N curves based and theon virtual applied test results stress for ratio the same [35]. failure Experimental mode. This methodsmethodology to of determine the the approximationcurves relate isthe explained number inof theload following cycles to steps. failure Firstly, to a given a so called applied fatigue maximum strength stress. ratio, Furthermore, can be individual S-N curves are cumbersome and not cost-effective. As a result, numerical methods are definedthey also as: serve as the abort criterion for the FDM. The characteristic of these curves depend strongly on the fiber orientations and the applied stress ratio [35]. Experimental methods to determine the usually employed for the effective prediction of the different+ S-N curves. One appropriate method of individual S-N curves are cumbersome= and not= cost-effective.. As a result, numerical methods(6) are numerical approximation is the Modified Fatigue Strength Ratio by Kawai [36]. It is able to predict usually employed for the effective prediction of the different S-N curves. One appropriate method of further S-Nnumerical curvesIn Equation basedapproximation (6), on the virtual parameters, is the test Modified results, Fatigue, for, theStrength are same the Ratio corresponding failure by Kawai mode. [36]. fatigue This It is strength,able methodology to predict the of the approximationstaticfurther strength, is S-N explained curves the stress based in amplitude the on followingvirtual and test the resultssteps. mean forstress. Firstly, the sameFigure a sofailure 16 called describes mode. fatigue Thisthe characteristics methodology strength ratio, ofof athe ψ can be defined as:typicalapproximation fatigue loading is explained and also in the the relationships following steps. among Firstly, these avalues. so called It should fatigue be strength noted that ratio, for =1 can, be the material is considered to have failed. σ σ + σ defined as: = max = a m ψ t t . (6) R R+ = = . (6) t In Equation (6), the parameters, σmax, R , σa, σ m are the corresponding fatigue strength, the static strength, the stressIn Equation amplitude (6), the and parameters, the mean stress., , Figure, are 16 the describes corresponding the characteristicsfatigue strength, the of a typical static strength, the stress amplitude and the mean stress. Figure 16 describes the characteristics of a fatigue loading and also the relationships among these values. It should be noted that for ψ = 1, typical fatigue loading and also the relationships among these values. It should be noted that for =1, the materialthe is material considered is consi todered have to failed.have failed.

Stress [MPa] [MPa] Stress 0

Time [s]

Stress [MPa] [MPa] Stress 0

Time [s]

Figure 16. Characterization of fatigue loading and relationship between the parameters in Equation (6). Energies 2018, 11, 383 17 of 21

Based on the fatigue strength ratio, ψ the modiﬁed fatigue strength ratio, Ψ can be represented using Equation (7). In Equation (7), the parameter R, corresponds to the stress ratio and be expressed in Equation (8).

σ 0.5·σ ·(1 − R) = a = max Ψ t t , (7) R − σm R − 0.5·σmax·(1 + R) σ σ − σ R = min = a m . (8) σmax σa + σm For the case of a fully tension-compression based reversible loading condition (R = −1), Ψ will be equal to ψ. In order to describe a similar mean stress variation as in the Goodman diagram [37], a non-dimensional scalar, Ψ has been introduced. With the help of Equations (6)–(8), it is possible to estimate any S-N curves based on the respective failure mode. Using the Kawai model, the S/N curve mapping procedure can be said to comprise of three main steps, as stated in [36]. Some complication arises from the circumstance that no S-N curves are readily available for IM7-8552. Hussain et al. [38] reports a constant amplitude fatigue tests to determine S-N curves for unidirectional carbon FRP (CFRP)-plies of various fiber orientations and stress ratios. The material properties of CFRP used in [38] was found to be similar to the one used in the present work and as a result the basis S-N curves were adopted from the same reference. With the help of Basquin’s law [39], the experimental data were fitted using Equation (9). Here, the parameter Nf corresponds to the number of load cycles to failure, n, for a corresponding maximum stress, σmax(Rexp). The fitting values 0 σf and b depend on the fiber angle and the applied stress ratio. For this work experimental S-N curves ◦ ◦ with a stress ratio of Rexp = 0.1 is chosen for the 0 and 90 plies.

b = 0 σmax(Rexp) σf Nf . (9) Based on [36,40], the second step involves the derivation of a master modiﬁed fatigue strength ratio, Ψ∗ based on Equation (7). This relation depends on the number of load cycles and is directly related to the experimental parameters. This can be expressed as 0.5·σmax(R )(n)· 1 − Rexp Ψ∗(n) = exp . (10) t − · ( )· + R 0.5 σmax(Rexp) n 1 Rexp

In the last step, the approximated S-N curves are obtained by further combining the Equations (7) and (11). This relation is expressed in Equation (11). Based on the simplified TWIST load spectrum indicated in Figure 14, the mapping procedure has been used to determine S-N curves for both 0◦ and 90◦ plies in the simplified micro model. These curves are generated for several load ratios ranging from R = 0 to R = 0.63 as well as for different loading conditions, such as tension and compression, both in the longitudinal and transverse to fiber directions. Figure 17 represents the approximated S-N curves for the simplified TWIST spectrum for the 90◦ plies in the simplified micro model.

t ∗ ∗ 2·R ·Ψ σmax(Rnew, n) = ∗ . (11) (1 − Rnew) + (1 + Rnew)·Ψ In none of the micro models degradation in fiber direction of either strength or stiffness due to fatigue was observed. The longitudinal stress is well below the tensile strength of the composite and were found not lead to fatigue. A varying degree of fatigue degradation was observed in the transverse fiber direction in both of the perforated micro models, see Figure 18. However, no degradation occurred in the unperforated micro model. The fiber topology without CFP leads to a higher longitudinal stress concentration near the hole, but showed only a very minor degree of transversal degradation. For the fiber topology with CFP the concentration of longitudinal stress near the hole was reduced. In fact, for this configuration the stress maximum occurred near the transition from the compacted to the undisturbed fibers, Energies 2018, 11, x FOR PEER REVIEW 18 of 21

Energies 2018, 11, 383 18 of 21 ca. at y = 0.45 mm in Figure 18b. The diversion of the longitudinal stress induced somewhat higher transversal stress. In turn, this caused the CFP micro model to accumulate more transversal Energies 2018, 11, x FOR PEER REVIEW 18 of 21 degradationFigure than 17. the Approximated one without S-N-curves CFP. for the simplified TWIST load spectrum for the 90° plies in the micro model.

In none of the micro models degradation in fiber direction of either strength or stiffness due to fatigue was observed. The longitudinal stress is well below the tensile strength of the composite and were found not lead to fatigue. A varying degree of fatigue degradation was observed in the transverse fiber direction in both of the perforated micro models, see Figure 18. However, no degradation occurred in the unperforated micro model. The fiber topology without CFP leads to a higher longitudinal stress concentration near the hole, but showed only a very minor degree of transversal degradation. For the fiber topology with CFP the concentration of longitudinal stress near the hole was reduced. In fact, for this configuration the stress maximum occurred near the transition from the compacted to the undisturbed fibers, ca. at = 0.45 mm in Figure 18b. The diversion of the longitudinal stress induced somewhat higher transversal stress. In turn, this caused the CFP micro model to accumulate more transversal degradation than the one without CFP. As is apparent from Figure 18 the load sequence has little effect on the distribution of the transverse degradation. In both sequences, the load block with the highest amplitude (Load block V in Figure 15)

caused essentially all degradation. Figure 17. Approximated S-N-curves for the simplified TWIST load spectrum for the 90° plies in the Substantial degradation was observed for the shear strength and stiffness. However, the◦ lack of Figure 17. Approximatedmicro model. S-N-curves for the simpliﬁed TWIST load spectrum for the 90 plies in the calibration data prevented the generation of R-ratio dependent shear S-N curves, limiting the accuracy micro model. of the predictedIn none shear of the degradation. micro models degradation in fiber direction of either strength or stiffness due to fatigue was observed. The longitudinal stress is well below the tensile strength of the composite and were found not Highlead to to fatigue. low Low to high A varying degree of fatigue degradation was observed in the transverse fiber direction in both of the perforated micro models, see Figure 18. However, no degradation occurred in the unperforated micro model. The fiber topology without CFP leads to a higher longitudinal stress concentration near the hole, but showed only a very minor degree of transversal degradation. For the fiber topology with CFP the concentration of longitudinal stress near the hole was reduced. In fact, for this configuration the stress maximum occurred near the transition from the compacted to the undisturbed fibers, ca. at = 0.45 mm in Figure 18b. The diversion of the longitudinal stress induced somewhat higher transversal stress. In turn, this caused the CFP micro model to accumulate more transversal degradation than the one without CFP. Energies 2018As, 11 is, x apparent FOR PEER from REVIEW(a) Figure 18 the load sequence has little effect on the distribution(b) of the transverse19 of 21 degradation. In both sequences, the load block with the highest amplitude (Load block V in Figure 15) caused essentially all degradation. Substantial degradation was observed for the shear strength and stiffness. However, the lack of calibration data prevented the generation of R-ratio dependent shear S-N curves, limiting the accuracy

of the predicted shear degradation.

High to low Low to high

(a) (b)

(e) (f)

Figure 18. Strength degradation in transverse direction for all three micro models: (a,b) perforated Figurewith 18. CFP,Strength (c,d) perforated degradation without in transverse CFP, (e,f) unperforated. direction for Left all column three load micro sequence models: high (a to,b low,) perforated with CFP,right( columnc,d) perforated load sequence without low to CFP, high. (e,f) unperforated. Left column load sequence high to low, right column load sequence low to high. 6. Results and Conclusions In this paper, a new structural design concept for a multi shell BWB fuselage with LFC has been developed in order to gain insight into the structural performance at the conceptual aircraft design stage. For this purpose, a new double shell design concept was modelled using a parametric Python tool. Different laminate thicknesses, layups and geometries were studied for their influence on the strength and buckling loads. Furthermore, the effect of different number of frames, span rib thicknesses and outer skin layups were considered. Weight, maximal stress, maximal deflection and failed areas are obtained and compared between the considered configurations. It was found that while the changes in the skin layups do not have a major impact (under 2%) on the maximum stress, the change in frame and rib distances from 1 m to 0.5 m has reduced the maximal stress to 36%. Furthermore the first eigenvalue in the linear buckling analysis is increased from 0.82 to 1.26. In the sensitivity study for the laminate thickness of the span-ribs, it was found that the maximal stress is decreased to 19% by increasing to thickness from 2 mm to 5 mm. Three micromodels of equivalent membrane stiffness where investigated for their fatigue behavior. The respective micro models were for a perforation with CFP, a conventional perforation without CFP and an unperforated topology. The fatigue analysis used a simplified variant of the TWIST spectrum. In the fatigue model employed in the analysis sequence effects are taken in to account. Since the actual amplitude sequence is unknown, the TWIST amplitudes were applied in an assumed order: sorted by increasing and decreasing amplitude. The fatigue investigations did not indicate a clear advantage of a CFP micro-topology over a conventional interrupted fiber microstructure for the considered load situations. This is likely due to the particular loading scenario. Loads were insufficient to trigger fiber failure, a failure mode where the larger amount of uninterrupted fibers in the CFP microstructure would be advantageous. Only a single normal strain component was imposed on the micromodel and, thus, the applied strains were perfectly aligned with the rectangular grid pattern of the perforation. This circumstance might have further contributed to the favorable performance of the interrupted fiber micromodel by essentially unloading the interrupted fibers, negating any shear-lag load transfer from interrupted to continuous fibers. The CFP topology, on the other hand, suffers from degradation induced by shear due to the fiber axes being at an angle to the load axis.

Energies 2018, 11, 383 19 of 21

As is apparent from Figure 18 the load sequence has little effect on the distribution of the transverse degradation. In both sequences, the load block with the highest amplitude (Load block V in Figure 15) caused essentially all degradation. Substantial degradation was observed for the shear strength and stiffness. However, the lack of calibration data prevented the generation of R-ratio dependent shear S-N curves, limiting the accuracy of the predicted shear degradation.

6. Results and Conclusions In this paper, a new structural design concept for a multi shell BWB fuselage with LFC has been developed in order to gain insight into the structural performance at the conceptual aircraft design stage. For this purpose, a new double shell design concept was modelled using a parametric Python tool. Different laminate thicknesses, layups and geometries were studied for their influence on the strength and buckling loads. Furthermore, the effect of different number of frames, span rib thicknesses and outer skin layups were considered. Weight, maximal stress, maximal deflection and failed areas are obtained and compared between the considered configurations. It was found that while the changes in the skin layups do not have a major impact (under 2%) on the maximum stress, the change in frame and rib distances from 1 m to 0.5 m has reduced the maximal stress to 36%. Furthermore the first eigenvalue in the linear buckling analysis is increased from 0.82 to 1.26. In the sensitivity study for the laminate thickness of the span-ribs, it was found that the maximal stress is decreased to 19% by increasing to thickness from 2 mm to 5 mm. Three micromodels of equivalent membrane stiffness where investigated for their fatigue behavior. The respective micro models were for a perforation with CFP, a conventional perforation without CFP and an unperforated topology. The fatigue analysis used a simplified variant of the TWIST spectrum. In the fatigue model employed in the analysis sequence effects are taken in to account. Since the actual amplitude sequence is unknown, the TWIST amplitudes were applied in an assumed order: sorted by increasing and decreasing amplitude. The fatigue investigations did not indicate a clear advantage of a CFP micro-topology over a conventional interrupted fiber microstructure for the considered load situations. This is likely due to the particular loading scenario. Loads were insufficient to trigger fiber failure, a failure mode where the larger amount of uninterrupted fibers in the CFP microstructure would be advantageous. Only a single normal strain component was imposed on the micromodel and, thus, the applied strains were perfectly aligned with the rectangular grid pattern of the perforation. This circumstance might have further contributed to the favorable performance of the interrupted fiber micromodel by essentially unloading the interrupted fibers, negating any shear-lag load transfer from interrupted to continuous fibers. The CFP topology, on the other hand, suffers from degradation induced by shear due to the fiber axes being at an angle to the load axis.

Acknowledgments: The authors would like to acknowledge the support of ir. Eelco Jansen and would like to express their gratitude for his comments. The authors would also like to acknowledge the support of the Ministry for Science and Culture of Lower Saxony (Grant No. VWZN3177) for funding the research project “Energy System Transformation in Aviation” in the initiative “Niedersächsisches Vorab”. Author Contributions: Majeed Bishara designed the new concept of the multi-bubble fuselage, coded the python tool to create the different configurations of the fuselage segments, carried out the FE-analyses on the global models, analyzed the results, and wrote the main part in Sections1,2,4 and6. Peter Horst initiated and coordinated the work, gave valuable guidance, and reviewed the complete paper. Hinesh Madhusoodanan conducted the literature research on the fatigue topic, contributed to the development of the micro model for perforated outer skin (Section3) and provided the extension of the FDM to the 3D framework used in the fatigue analysis (Section5). The majority of the text in the development of micro model (Section3) and certain parts of the text in the fatigue analysis (Section5) were also edited and modified by him. Martin Brod carried out the fatigue analysis, contributed to the literature research, provided fatigue material parameters and S/N curves required for the load spectrum (Section5). The majority of the text in the fatigue analysis (Section5) were also edited and modified by him. Benedikt Daum developed the micro model for the perforated skin (Section3), provided technical supervision and number of key suggestions in the work. Raimund Rolfes initiated the work, coordinated between the institutes and supervised the paper. Conflicts of Interest: The authors declare no conflict of interest. Energies 2018, 11, 383 20 of 21

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