Structural mass prediction in conceptual design of blended-wing-body aircraft

Wensheng ZHU, Zhouwei FAN, Xiongqing YU

College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

KEYWORDS

Abstract The Blended-Wing-Body(BWB)is an unconventional configuration of aircraft and considered as a potential configuration for future commercial aircraft.One of the difficulties in conceptual design of a BWB aircraft is structural mass prediction due to its unique structural feature.This paper presents a structural mass prediction method for conceptual design of BWB aircraft using a structure analysis and optimization method combined with empirical calibrations. The total BWB structural mass is divided into the ideal load-carrying structural mass, non-ideal mass, and secondary structural mass. Structural finite element analysis and optimization are used to predict the ideal primary structural mass,while the non-ideal mass and secondary structural mass are estimated by empirical methods. A BWB commercial aircraft is used to demonstrate the procedure of the BWB structural mass prediction method. The predicted mass of structural components of the BWB aircraft is presented,and the ratios of the structural component mass to the Maximum Take-Off Mass(MTOM)are discussed. It is found that the ratio of the fuselage mass to the MTOM for the BWB aircraft is much higher than that for a conventional commercial aircraft,and the ratio of the wing mass to the MTOM for the BWB aircraft is slightly lower than that for a conventional aircraft.

1. Introduction

Over the past decades,there has been great interest in improving the performances of transport aircraft. Unconventional aircraft configurations, such as Blended-Wing-Body (BWB),are supposed to contribute to a significant improvement of efficiency in civil air transport.The BWB concept proposed based on earlier flying wing designs is a tailless design that integrates a wing and a fuselage.1The BWB-type aircraft as compared to conventional aircraft has many advantages such as larger internal volume, lower wetted-area aspect ratio, higher liftto-drag ratio, and noise reduction.2Consequently, the BWB aircraft has large potential fuel savings and offers superior operating economics.3-5

Mass prediction is an essential part in aircraft conceptual design, and it affects cost as well as performance characteristics. Two kinds of methods (i.e., empirical methods and physics-based methods)are commonly used to estimate the aircraft structural mass in aircraft conceptual design. Empirical methods estimate the mass of the main component group of an aircraft using analytic equations that are expressed by aircraft geometric parameters, load factor, and statisticallyderived coefficients.6On the contrary, physics-based methods compute the structural mass by physical principles (for instances,the beam method or finite element modeling),which require more detailed design information such as the geometric shape, loads, structural layout, and material properties.Although empirical methods need much less computational expenses compared to that of physics-based methods, their applications are usually limited to conventional aircraft for the reason that empirical methods are based on historical data of existing conventional aircraft. In contrast, physics-based methods usually have higher flexibility, which can be used to estimate the structural mass of either a conventional or unconventional aircraft,but their applications are more complicated and require much more computational expenses.

A significant difficulty in BWB aircraft conceptual design is the lack of a reliable method for BWB structural mass prediction due to its unique structural feature and no historical data for the structural mass.Several studies have been attempted to solve this difficulty. Howe7proposed a method called empirically weighted theoretical approach by which the BWB aircraft planform is idealized into inner and outer wings.Their masses can be calculated primarily as a wing, and then penalties are applied for them. Bradley8used finite element analysis to develop a mass estimation equation which relates the BWB fuselage structural mass to the takeoff gross mass and the payload cabin area. The mass of the aft fuselage is estimated by treating it as a horizontal tail and modifying the tail mass equation to include a factor for the number of engines supported by the fuselage. The total mass of the fuselage of a BWB aircraft can be calculated by the sum of the two components masses. Laughlin et al.9developed a physics-based multidisciplinary analysis and mass optimization environment for structural mass estimation of a BWB aircraft. Then, the mass was calibrated by the calibration factor from a Boeing Hybrid Wing Body (HWB) sizing study for the total structural mass.

However,the above mass prediction methods for BWB aircraft still have several limitations. In Howe’s method,7BWB structures are highly simplified, and structural design features are not reflected sufficiently, which may lead to inaccuracy in mass computation. In Bradley’s method,8a triangular lift distribution is assumed in computation of aerodynamic loading.This assumption is corrected for some specific BWB configurations, but might be not appropriate for all BWB configurations. In Laughlin’s method,9a calibration factor for total structural mass prediction is needed,but how to obtain the calibration factor is not presented in detail in their paper.

In this paper, we attempt to develop a more accurate and universal method for structural mass prediction in BWB aircraft conceptual design. Our work follows Howe’s idea, in which the structural mass consists of the ideal load-carrying structural mass, mass penalty for non-ideal structural considerations, and the secondary structural mass. The proposed method combines physics-based methods (finite element analysis and optimization) with empirical methods. Finite element analysis and optimization are used to predict the mass of the ideal load-carrying structure of a BWB aircraft, which can model the unique features of the BWB structure. Empirical methods are applied to calculate the non-ideal structural mass and used for calibration of the ideal load-carrying structural mass.For consideration of computational expense in BWB aircraft conceptual design, the secondary structural mass is also predicted by empirical methods.

2. General description of method

One of the key tasks in an aircraft conceptual design stage is structural mass prediction for a selected baseline design concept. A practical way for structural mass prediction usually follows four steps7,10: (A) computing the ideal load-carrying structural mass; (B) adding penalty factors to the ideal structural mass for non-ideal considerations;(C)computing the secondary structural mass; (D) calculating the total structural mass by the sum of the ideal load-carrying structural mass,the non-ideal structural mass, and the secondary structural mass.

An ideal load-carrying structure accommodates aerodynamic,inertia,and ground loads acting on an aircraft and collects loads from secondary structures as well as fuselagemounted items such as landing gear, engines, nacelles, and pylons. It can be divided into fuselage and wing sections,and its main elements are upper and lower stiffened skin panels,multi spars,frames,ribs,floors,and floor beams.The nonideal mass must be considered for the reason that the ideal load-carrying structure is required to comply with principles of fail-safety, damage tolerance, manufacturing, and operational and maintenance considerations. Secondary structures consist of components located at the fore of the front spar and the back of the rear spar, such as leading and trailing high-lift devices, flight control devices, etc.

The main difference of structural mass prediction between BWB and conventional aircraft is how to calculate the ideal load-carrying structural mass.In this study,the ideal structural mass is computed by structural analysis and optimization.The BWB structural mass prediction procedure is illustrated in Fig.1.

Fig.1 Procedure of a mass prediction method for BWB structures.

The baseline design concept is to define the cabin layout,external configuration, structural layout, and so on. It is the starting point for aircraft structural mass prediction in aircraft conceptual design.

After the structural layout and geometric model are defined, a Finite Element (FE) model of the BWB structure can be generated, which features the structural elements of the fuselage and the wing including stiffened panels, frames,ribs, spars, floors, and bulkheads.

Structure optimization of BWB aircraft is performed to determine the sizes of structural elements of the ideal loadcarrying structure under constraints of displacement, stress,strain, and buckling. Once the sizes of structural elements are determined, the mass of the ideal load-carrying structure can be computed.

Since there is no detailed information on the non-ideal structure in a conceptual design stage, a physical method has difficulty to estimate non-ideal mass factors. For a BWB aircraft,its most unique structural feature is the pressurized fuselage with a non-circular cross-section and cabin structural walls, but its non-ideal mass factors such as joints, fasteners,and inspection hatches are similar to those of conventional aircraft. Therefore, the non-ideal mass factors of the BWB aircraft can be calculated using empirical methods.

Modeling and analysis for secondary structures by a physical method would lead to a large amount of computational burden, which might not be suitable for aircraft conceptual design. On the other hand, secondary structures such as high-lift devices and flight control devices are similar to those of conventional aircraft. For the above considerations, the mass of secondary structures is also estimated by empirical methods, which are based on statistical data using basic geometric and functional parameters as inputs.7,10

Finally,the total BWB structural mass is computed by adding non-ideal mass penalties and the secondary structural mass to the ideal structural mass.

The remainder of the paper is organized as follows. Section 3 briefly introduces the baseline design concept of a BWB aircraft. The BWB structural analysis method is presented in Section 4. Optimization for the ideal structural mass is described in Section 5. The procedure for computing the total BWB structural mass is given in Section 6. Predicted results of the BWB structural mass are presented and discussed in Section 7, followed by conclusions in Section 8.

3. Baseline design concept of a BWB aircraft

A baseline BWB aircraft with 219 seats of passengers based primarily on Boeing’s BWB-009A configuration11is used as an example for a structural mass prediction study in this paper.The cabin layout and external configuration of the BWB aircraft are illustrated in Figs. 211and 3, respectively. The primary parameters for the BWB aircraft are presented in Table 1.

As shown in Fig.3, the BWB aircraft can be broken down into three main sections,i.e.,a pressurized fuselage,an inboard wing, and an outer wing. The leading-edge sweep angles are swept back 57° for the fuselage and 37° for the outer wing,respectively. The average value of thickness-to-chord ratios of the fuselage is around 17%. The average value of thickness-to-chord ratios of the outer wing is around 9%.The inboard wing blends the thick fuselage with the thin outer wing. The baseline structural layout is illustrated in Fig.4.

Fig.2 Cabin layout of a baseline BWB aircraft.11

Fig.3 BWB aircraft external configuration.

Table 1 Primary parameters of BWB aircraft.

In general, the fuselage of the BWB aircraft has a large width considering the constraint of comfort and evacuation.Large internal walls are used to divide cabin bays and decrease the span distance. By decreasing the span distance, this additional support decreases the bending moments induced from resisting the internal pressure. The cabin floor is positioned based on the desired cabin height,and the rear spar in the fuselage is specified as bulkheads.The main frames are attached to multiple spars,12and the pressure loads are carried by a bending resistant structure (i.e., normal frames). The frames are more densely arranged in the center areas of the fuselage to resist buckling and more sparsely arranged in the fore of the fuselage.

Fig.4 Structural layout of a baseline BWB aircraft.

The inboard wing structure blends the fuselage with the outer wing, and consists of multiple spars, ribs, and stiffened skin panels. Front and rear spars provide a continuous load path from the outer wing to the fuselage cabin. Intermediate spars connect the front spar of the outer wing to the sidewall of the fuselage. All ribs in this section are oriented in the streamwise direction.

The structural layout of the outer wing is similar to that of a conventional aircraft wing, which consists of a front spar, a rear spar, upper and lower stiffened wing panels, and evenlyspaced ribs. In this layout, the ribs are perpendicular to the rear spar, thus the rib length is shorter, and its mass can be reduced.13

4. Structural analysis method

4.1. Finite element modeling

For the BWB aircraft, the fuselage and wing are blended, and there is strong integration between the wing and fuselage structures. Its finite element model including the fuselage and wing structures has to be created as whole in the structural analysis of the BWB aircraft.

In the structural finite element model, spar webs, rib webs,frame webs, floors, and skin panels are mainly modeled by using quadrilateral elements with shell properties, while triangular elements are used in transition areas.Axial rod elements are used to represent spar, frames, and rib caps, while floor beams are represented by beam elements.The stringers of stiffened panels are not modeled, but their stiffness properties will be represented by an equivalent shell element.Fig.5 shows the overall structural FE model. Finite element analysis is conducted by MSC Nastran software.

4.2. Panel analysis model

Equivalent panels can simplify the stiffened panels(skins) and significantly decrease the scale of the FE model. Without the complex shapes of stringers, equivalent panels can efficiently simulate global buckling modes. Fig.6 shows a detailed stiffened panel model and its corresponding equivalent panel model.

The stiffness of an equivalent panel can be described as the superposition of a skin’s stiffness and stringers’stiffness.Thus,an equivalent matrix of the entire panel can be obtained by assembling the stiffness matrices of the skin and stringers,which can be calculated by14,15

where Ask,Bsk,and Dskare the in-plane,coupling,and bending stiffness coefficient matrices of a skin, respectively, and Astr,Bstr, and Dstrare the in-plane, coupling, and bending stiffness coefficient matrices of a stringer, respectively.

Generally, aerodynamic loads generate bending and twist moments on the load-carrying structure,and cause upper panels to bear in-plane compression and shearing loads.Based on this load case,the edge boundary condition of a stiffened panel is assumed to be simply supported and carry combined inplane uniform loads including axial compressive Nxand shearing Nxy.Thus,the buckling load(Nxcritunder compression and Nxycritunder shear)under a boundary case of simply support is given by

where m represent the number of half waves, and AR is the aspect ratio(AR=a/b,a and b represent the length and width of the panel, respectively). Dijis the bending stiffness coefficient, and the ‘‘±” sign indicates that buckling can be caused by either positive or negative shear loads.

Stringers are usually cemented or co-cured with a skin in composite panels, and the skin among two adjacent stringers might be under a boundary case of simple support.Therefore,local buckling of a skin can also use formulas described above.

The static allowable axial load Nxstaticand allowable shear load Nxystaticof a panel are

Fig.5 Finite element model of BWB structure.

Fig.6 Detailed stiffened panel and its equivalent panel model.

where εxallowand εxyallowrepresent the allowable strain under axial and shear loads, respectively. Aeqis the equivalent axial tensile stiffness of the panel,and A66is the shear stiffness coefficient of the panel. The buckling load is not the failure load,but the stiffened panel can withstand a higher load than the buckling load before being damaged.

For a combined-load case, interaction curves can be obtained by substituting the global buckling, local buckling,and static failure loads into the following equation:

Interaction curves16provide a means to determine: (A) if a panel fails under combined loads Nxand Nxy, or(B) the maximum allowable in one direction (compression or shear) given the applied load in the other. Load combinations inside an interaction curve imply that a panel does not buckle. Load combinations corresponding to points outside an interaction curve correspond to a panel that has buckled already.

Fig.7 Interaction curve for global buckling and local buckling under combined compression and shear.

Fig.8 Interaction curve for static failure under combined compression and shear.

4.3. Material properties

The BWB aircraft is designed with advanced composite materials for both primary and secondary structures, which has resulted in significant mass reduction and performance enhancement.11,17Carbon-epoxy T800 is applied for the load-carrying structure, and the aft fuselage and floor structures are made from metal material. Material properties used in this study are shown in Tables 2 and 3. Parameters E1,E2,G12,ν12and ρ are the longitudinal Young’s modulus,transverse Young’s modulus, shear modulus, Poisson’s ratio and density of the composite laminate. Parameters E, G and νare the elastic modulus, shear modulus and Poisson’s ratio of the metal material.

Table 2 Composite material properties.

Table 3 Metal material properties.

4.4. Loads

Loads considered in this study include the aerodynamic load,internal cabin pressure, and inertia loads from mass distributions. Concentrated loads from landing gears and engines are not considered,instead the mass penalty for mounting engines and landing gears will be estimated by an empirical method.

Fig.9 Surface pressure coefficient distributions at cruise condition.

Fig.10 Locations of the passenger cabin and fuel tanks.

The load case includes the flight maneuver and cabin pressure with a safety factor of 1.5.The aerodynamic load is computed by an in-house code18which is developed based on the potential flow method. Pressure coefficient (Cp) distributions on the upper surface of the BWB aircraft at the cruise condition are shown in Fig.9. The cabin pressure is assumed to be an ultimate cabin pressure of 1264 mbar(1 mbar=100 Pa).19,20Distributed masses that are considered in structure analysis include passenger payloads and fuels.Payloads are located in the fuselage, and fuel tanks are located in the wing sections, as depicted in Fig.10.

5. Ideal structural mass computation using optimization

Component sizes of the ideal load-carrying structure for the BWB aircraft are determined by optimization.Once those sizes are determined, the mass of the ideal load-carrying structure can be computed straightforward.

5.1. Optimization strategy

To determine the sizes of the structural components of the BWB aircraft efficiently, an integrated global-local optimization strategy21,22is used, and its flowchart is illustrated in Fig.11.

In the integrated global-local optimization strategy, the procedure of optimization is divided into two parts: (A)FEM (Finite Element Method)-based global sizing optimization that optimizes the dimensions of spars, ribs, frames, and floors to minimize the structural mass, and (B) local panel optimization which optimizes the design variables of local panels bordered by spars and ribs to minimize the mass of local stiffened panels.

Global optimization is performed under the given finite element model, loads, boundary conditions, and design constraints. When FEM-based global sizing optimization is completed,the in-plane axial load and the shear load of panels from global optimization results are extracted for local panel analysis and optimization.14Then, local panel analysis and optimization are performed using the method presented in detail in Section 4.2.

After a round of global-local iteration, results need to be checked whether to satisfy the deformation constraint for the reason that local optimization does not consider the deformation constraint. If the deformation constraint is not satisfied,the global FE model will be updated by using the results of these optimal design variables of local panels. Then, an additional global-local iteration needs to be conducted. To simplify the computational process and reduce the computational expense in aircraft conceptual design,the aerodynamic load is not changed during integrated global-local optimization.

Over several rounds of iterations,the convergence criterion is satisfied,which means that the optimal structure of the BWB aircraft satisfies the stress, strain, displacement, and buckling constraints, and has the minimum mass.23After the convergence, the ideal primary structural mass is extracted from the integrated global-local optimization results.

The following two subsections will present details on the global and local optimization formulations.

5.2. Global optimization formulation

The task of global optimization is to find the dimensions of structural elements with the minimum main load-carrying structural mass under the constraints of the material’s allowable stress and strain, buckling, and structural deformation.The global optimization problem is formulated as in Table 4.

Fig.11 Integrated global-local optimization strategy.

Several attempts using Sequential Linear Programming(SLP), Sequential Quadratic Programming (SQP), and the Modified Method of Feasible Directions(MMFD)respectively provided by MSC Nastran software show that the MMFD solver has the fastest convergence than those of other solvers.Therefore,the MMFD solver is adopted to solve the structural optimization problem. After optimization, the sizes of the structural components (excluding the upper and lower panels)over the main load-carrying structure are obtained.

5.3. Local optimization formulation

Local optimization is to find the minimal mass of each local stiffened panel without any strength or buckle failure. Local optimization is defined as in Table 5. In local optimization,SQP is used to determine the sizes of the panels.

Fig.12 Distributions of thickness of skins and areas of stringers.

Table 4 Global optimization problem.

Table 5 Local optimization problem.

5.4. Optimization results

When global-local iterations have converged, integrated global-local optimization is completed. Usually, the number of the entire global-local iterations is around 4.

After optimization, the distributions of the thickness of skins and the areas of stringers are illustrated in Fig.12. The thickness of skins and the areas of stringers increase rapidly along the spanwise direction and up to the peak around the kink(the interface of the inboard and outer wings).Then,they both decrease from the outer wing root to the wingtip.Results show that the upper skin is thicker than the lower skin for the reason that the bending loads which cause compression on the upper surface are generally somewhat higher than those causing compression on the lower surface.

6. Total BWB structural mass calculation

The total BWB structural mass consists of the fuselage structural mass and the wing structural mass, which can be further partitioned into a number of mass items,as depicted in Fig.13.The following subsections will present calculations of the fuselage structural mass and the wing structural mass.

6.1. Fuselage structural mass

The fuselage structural mass can be partitioned into the primary structural mass and the secondary structural mass,7where the secondary structural mass is composed of the nose fuselage mass and the trailing-edge structural mass as classified in Fig.13.

6.1.1. Primary structural mass

Structural optimization in Section 5 can only predict the mass of the ideal load-carrying structure of the fuselage,as the pure FE model does not fully represent the total mass. As a matter of fact, cutouts in structures unavoidably exist, which lead to mass increasing, because the structure adjacent to a cutout must be reinforced to redistribute the load. In a practical design, allowances are made for non-ideal features such as entry and freight doors, emergency exits, windows, general access hatches, and cutouts for the main landing gear.

Therefore, the primary structural mass of the fuselage consists of the ideal load-carrying structural mass of the fuselage,mass penalty of apertures for entry and freight doors, windows, emergency exits and manholes, and mass penalty of powerplants and the main landing gear attachment. Those mass penalties can be predicted by empirical formulae derived from relevant constructional details of existing aircraft.Howe7presented detailed formulas for those mass penalties.

6.1.2. Nose fuselage mass

The nose fuselage is defined as being the structure in front of the front spar at the fuselage, as shown in Fig.4, which includes the pressurized outer shell, fuselage leading-edge fairings,the nose landing gear attachment,windscreen,crew floor,and allowance for doors. The masses for those items can be calculated by empirical formulas presented in detail in Ref.7.

6.1.3. Trailing-edge structural mass

Unlike conventional aircraft, the fuselage of the BWB aircraft features large control surface geometries due to high control power demands, and consists of trailing-edge flaps and spoilers/airbrakes. The masses of those secondary structures are statistically related to the maximum takeoff mass, and have been formulated in Ref.7.

Fig.13 Mass items of BWB structure.

6.2. Wing structural mass

The wing structural mass can be partitioned into the wing box mass, the secondary structural mass, and miscellaneous items,10as depicted in Fig.13.

To compute non-ideal mass penalties and the secondary structural mass using the method in Ref.10, it is necessary to employ an equivalent tapered wing as shown in Fig.14,which has the same areas as those of the inboard and outer wings.Then, the BWB aircraft configuration is divided into sections of the fuselage and the equivalent wing. The equivalent wing is used to calculate the structural span(bst)defined as the total length of the structural box measured along the elastic axis.

6.2.1. Wing box mass

Wing box mass prediction is based on the ideal wing box mass that contains the mass of upper and lower stiffened skin panels, spars, and ribs, and is obtained from the results of optimization in Section 5. Then, the ideal wing box mass is calibrated by a variety of mass penalty factors for considerations of non-ideal features.

Mass penalties for non-ideal features include non-tapered skins, joints, fasteners, and inspection hatches in the lower box cover plates, as well as a fail-safe and damage tolerant.However, those mass penalties cannot be calculated analytically. In practice, mass penalties for non-ideal features are derived from relevant constructional details of existing aircraft, and have been presented in detail in Ref.10. The total wing box mass is computed by adding non-ideal mass penalties to the ideal wing box mass.

6.2.2. Secondary structural mass

Wing secondary structures are all the wing structures that do not belong to the wing box, and comprise the fixed leadingedge, leading-edge high-lift devices, fixed trailing-edge,trailing-edge flaps, and flight control devices.

Masses of those secondary structures can be predicted by empirical equations derived from historic data.10The usage of composites for secondary structures such as leading- and trailing-edges, flaps, control surfaces, and fairings results in mass reduction.Typical achievable secondary mass reductions with composites relative to Al-alloy structures are shown in Table 6.10

Table 6 Typical achievable secondary mass reductions with composites.

6.2.3. Miscellaneous items

Typical miscellaneous items are paint,fuel tank sealant,rivets,nuts, bolts, and wing tips. A total miscellaneous mass can be approximately predicted by increasing the secondary mass of the wing by 10%.10

7. Results and discussion

The structural mass of the baseline BWB aircraft(see Section 3)was predicted using the above method. The structural mass breakdown of the BWB and values for the ratios of the structural mass to the MTOM are listed in Table 7.

From Table 7, we can see that the fuselage structural mass is 1.6 times of the wing structural mass.The primary structure of the fuselage has the largest mass among all mass items.The nose fuselage and trailing-edge structure of the fuselage have a relatively small amount of mass, around 8% of the fuselage structural mass. The wing box has the second largest mass among all mass items. The secondary structural mass of the wing has a considerable proportion (around 25%)in the wing structural mass.

It is interesting to compare structural mass proportions of the BWB aircraft with those of a conventional wide-body commercial aircraft. For a conventional commercial aircraft, typical values for the ratio of the fuselage mass to the MTOM range from 7% to 12%,24,25and typical values for the ratio of the wing mass to the MTOM range from 10% to 12%.24,25From Table 7, we can see that the ratio of the fuselage mass to the MTOM is 16.15%, and the ratio of the wing mass to the MTOM is 9.91% for the baseline BWB aircraft.This comparison reveals that the fuselage mass of the BWB aircraft is much larger than that of a conventional commercial aircraft,and the wing mass of the BWB aircraft is slightly less than that of a conventional commercial aircraft.

Table 7 Mass breakdown of BWB structure.

The following reasons lead to a large fuselage mass for the BWB aircraft.

(1) The fuselage structure of the BWB aircraft has cabin structural walls, leading-edge fairings, and trailing-edge high-lift devices, which do not exist in a conventional aircraft.

(2) The frames in the non-cylindrical fuselage of the BWB aircraft need to be strengthened to resist highly nonlinear bending stress and large deformation. Consequently, the frame mass of the BWB aircraft is much heavier than that of a conventional aircraft.

(3) Mass penalties such as attachments of engines and main landing gear units in the fuselage also increase the fuselage mass.

For a conventional aircraft, aerodynamic loads are mainly carried by its wings. The wings are highly loaded by bending and usually heavier than the fuselage.26However, for the BWB aircraft, its fuselage carries a considerable proportion of the total aerodynamic force,and its wing carries lower aerodynamic loads than those of the wings of a conventional commercial aircraft. Thus, the wing size of the BWB aircraft is relatively smaller than that of a conventional commercial aircraft, which leads to a lower ratio of the wing mass to the MTOM for the BWB aircraft.

8. Conclusions

Due to the unique structural feature of BWB aircraft, the empirical methods of mass prediction for conventional aircraft are not suitable for structural mass prediction of BWB aircraft.This paper presents a structural mass prediction method for BWB aircraft conceptual design. The BWB structural mass is divided into the ideal load-carrying structural mass, mass penalties for non-ideal considerations, and the secondary structural mass.

The ideal load-carrying structural mass is estimated by structural finite element analysis and optimization. Finite element modeling is defined by taking into account primary structural components (i.e., ribs, spars, panels, frames, floors, and floor beams). To improve the computational efficiency in structural analysis, the stiffened panels of the BWB structure are simplified into equivalent panels,and the scale of the structural FE model decreases significantly. By applying a globallocal optimization strategy, each sub-optimization can be solved with much less computing expense,and the overall optimization problem can be solved effectively and efficiently.

The mass penalties for non-ideal considerations and the secondary structural mass are predicted by empirical methods,which are difficult to be included in the finite element analysis and optimization method in aircraft conceptual design.

Predicted results of the structural mass for the baseline BWB aircraft reveal that the fuselage structural mass has a large proportion of the structural mass and might lead to a‘‘weakness” of the BWB aircraft. To make the BWB aircraft concept more competitive, there is a need for further research on fuselage structural mass reduction by using innovative design. For example, one way for fuselage mass reduction is to reduce the area of flat pressure panels as much as possible.Design concepts such as an efficient Multi-Bubble Fuselage(MBF) or a Y-braced box-type fuselage can be developed to reduce the area of flat pressure panels. Since the ideal loadcarrying structure of the BWB aircraft is analyzed by the finite element method in the proposed method, the design concepts of an MBF and a Y-braced box-type fuselage can be simulated and analyzed using this method.In our future study,the influence of a decrease in the area of flat pressure panels on the whole structural mass will be investigated using the proposed method.

Ideally, the proposed method should be validated by data resulting from a detailed design or manufactured BWB aircraft, but the absence of such data prevents a full validation.Nevertheless,a combination of structural finite element analysis optimization with empirical methods is quite logical for structural mass prediction in conceptual design of BWB aircraft. This method is expected to be suitable for structural mass prediction in conceptual design of BWB aircraft.

Acknowledgement

This study was supported by the National Natural Science Foundation of China (No. 11432007).