Optimum alternate material selection methodology for an aircraft skin

Freed AHMAD, Mohmmed Al AWADH, Shr NOOR

a Industrial Engineering Department, University of Engineering and Technology, Peshawar 25000, Pakistan

b Department of Industrial Engineering, College of Engineering, King Khalid University, Abha 62529, Saudi Arabia

KEYWORDS Aircraft skin;Carbon Fibre Reinforced Plastic (CFRP);Material index;Material selection methodology;Optimum material

Abstract Weight penalty has been a challenge for design engineers of aerospace vehicles.Today’s high-efficiency combat aircraft undergoes intense stress and strain during flying missions, which require stronger and stiffer materials to retain structural integrity.Though metallic materials have been successfully used for the construction of aircraft structures and components,metals still have a low strength-to-weight ratio.This paper aims to develop an alternate optimised material selection methodology to replace the metallic skin of a medium-sized military aircraft.The search for the optimum material will result in reduced aircraft weight which will be benefitted by extra payload on the aircraft.The selection methodology is comprised of finding design pressure limits on the aircraft skin, and comparison of properties (strength, elastic modulus, shear modulus, etc.) and performance (safety factor, deflection, and stress) of the existing metallic skin with alternate optimised material.The comparison was made under aerodynamic pressure, bending force, and twisting moment.Carbon Fibre Reinforced Polymer/Epoxy(CFRP)Uni-Directional(UD)prepreg(elastic modolus is 209 GPa) was selected as an alternate optimum material to replace the aluminium alloy skin of the aircraft studied.The selected alternate optimum material resulted in the reduction of aircraft skin weight by 30%.

1.Introduction

Light weightiness is a fundamental requirement alongside other mechanical and physical properties for all aerospace vehicles.Engineers have been struggling to reduce the weight penalty of aircraft by selecting lighter materials and developing new materials with a high strength-to-weight ratio.In a medium-sized military aircraft, more than 40% of the total weight is contributed by its structure.The design of a semimonocoque structure is also an effort to reduce the overall weight penalty of the aircraft structure.The use of optimum materials for the structure of an aircraft is an efficient way to reduce the weight of an aircraft.For this purpose,optimization techniques are utilized during modelling phase.1Composite materials have been used for aerospace applications as optimum materials due to extraordinary directional strength,2stiffness-to-density ratios,3,4higher corrosion resistance5,6and improved fatigue performance.6–9The partial replacement of metallic material by composites has resulted in reduced fuel consumption,10lesser emissivity,3,11payload gain, improved aircraft performance, enhanced manoeuvrability, and reduced environmental pollution which are the important design aspects for all types of aircraft.12–15Prepreg Carbon Fibre Reinforced Polymer/Epoxy (CFRP) is the most popular composite material for aircraft due to its availability in a wide range of properties, suitability for aircraft, and superior quality of the finished product.16,17Though there are certain disadvantages of using composites, the advantages have outnumbered those limitations.18–20

The selection of optimum material for any application involves the derivation of objective functions, which mostly depend upon conflicting parameters,17e.g.,strength/toughness vs weight/cost.Due to this reason, there is no unique solution to the problem,21and in the end,a set of non-dominated solutions is obtained.The set of the objective functions of these non-dominated decision vectors is called the Pareto front.22Various methodologies have been used by researchers for the selection of optimum materials for aerospace applications.Aceves et al.described a simple methodology in their paper for material selection to optimise composite structures.They used finite element analysis to identify the mechanical response of a range of proposed designs.23Kalanchiam carried out a comparative study on the skin of a crown panel assembly of a commercial aircraft fuselage.The skin panel margin of safety was compared by using two candidate materials i.e., 2024-T3 and CFRP.24In another study, Ashby’s multiple constraints methodology was used for the selection of an aircraft skin panel.Minimization of the skin mass was the objective function and the coupling constant was used to identify the candidate materials.25

This research paper deals with the replacement of the existing aluminium alloy skin of a medium-sized combat aircraft with an Alternate Optimum Material(AOM)lighter in weight but compatible in performance and properties.Thus, the AOM will result in reduced aircraft weight.The reduction in the weight of aircraft will be used for either taking extra payload or enhancing the aircraft endurance.Section 2 describes an overview of the aircraft skin and the distribution of aerodynamic forces on various parts of the skin.Section 3 describes the existing Multi-Criterion Decision Making (MCDM) techniques, generally used by researchers.In Section 4, novelty of the research is highlighted.Section 5 presents the summary of the methodology used to achieve the objective,the pressure limit is estimated on selected skin units by applying the reverse engineering concept.In Section 6, stress and deflection of the existing skin are determined computationally and validated analytically.Section 7 deals with the development of objective function for minimization of skin mass and selection of AOM for the skin of the aircraft studied, and the results are validated.In Section 8, the AOM is used for modelling skin subjected to aerodynamic pressure, bending forces, and twisting moments,and its performance is compared with that of metallic skin.

Aerodynamic parameters estimation is a vital tool in aerospace research leading to aircraft characterization.Various techniques have been employed by researchers such as wind tunnel test, numerical simulation,26maximum likelihood and filter error method,27and response surface method.28Malik and Tevatia carried out CFD analysis for the characterization of F16 and F22 aircraft.29Toor et al.carried out a similar CFD analysis on transport aircraft.30Bergmann et al.used wind tunnel test for the characterization of small-scale aircraft models.31Determination of the maximum aerodynamic pressure on the skin of the aircraft is significant.But the referred simulation or experimental techniques are time-consuming and expensive.This paper introduces a simple and fast methodology to determine Design Pressure Limit (DPL) on the skin of the aircraft under study through reverse engineering.The DPL is used for the selection of AOM for the skin of the aircraft.

2.Aircraft skin

The aircraft skin is designed to provide a smooth aerodynamic shape to reduce drag, produce lift, and transfer aerodynamic pressure to a load-bearing structure.To reduce the overall weight, the skin is conventionally made of a thin metal sheet,supported by stiffeners (Fig.1, which shows stiffeners spacing for the rectangular, circular, and miscellaneous shapes of skin units).Smaller skin units are used at high-pressure zones of aircraft surfaces.The entire skin of the understudy aircraft(fuselage, wings, and empennage) is fabricated from a large cold-rolled metal sheet.However,the skin is divided into smaller structural units by providing stiffeners under the skin.These skin units are of various sizes and shapes which facilitate to reduce deflection, stress, bending and twisting of the entire skin.The space between stiffeners is comparatively small(small skin unit) in those portions of the skin subjected to higher aerodynamic pressure such as wings and vertical/horizontal stabilizers.Thirty-three skin units of various shapes and sizes are used in the fabrication of the aircraft’s fuselage,wings, vertical and horizontal stabilizers skin (Fig.2, which was taken from the right wing-fuselage joint of the deskinned aircraft under study.The requirement of smooth contour and aerodynamic shape of the location demands a triangular skin unit at the wing-fuselage joint).The non-rectangular skin units are designed for smooth contours and the aerodynamic shape of the aircraft (Fig.2).

Each skin unit is supported by underneath stiffeners(Figs.1 and 2) and can be considered as a thin plate constrained at four edges, subjected to aerodynamic pressure.The aerodynamic pressure develops deflection and bending stresses,whereas elastic deformation of spares, stringers and stiffeners develops bending and twisting in the skin of the aircraft during flight (Fig.3).The pressure distribution on aircraft skin is unsteady and spatially nonuniform.

3.Existing methodologies

Fig.1 Photograph taken from deskinned fuselage of medium format combat aircraft.

Fig.2 Photograph showing stiffener designs for supporting rectangular and triangular skin units.

Fig.3 Pictorial representation of bending (Mx and My) and stretching (Nx and Ny) produced in aircraft skin unit by aerodynamic pressure during flight.

Selection of application-specific optimum material has a significant role in design and operation of the application.Selection of an improper material for any application may lead to early failure of the component causing loss of time and money.32This arises requirement of utmost care while selecting a material for any application.33Researchers have used various methodologies for selection of alternate optimum materials for different applications.The commonly used technique for selection of optimum material is the MCDM technique.32,34,35MCDM techniques are further divided into Multi-Objective Decision Making (MODM) and Multi-Attribute Decision Making (MADM) techniques.36Ashby approach is classified as a MODM technique, based upon optimization of alternate material keeping in view prioritized objectives, whereas Technique for Order Preference by Similarity to Ideal Solution(TOPSIS)and Vise Kriterijumska Optimizacija Kompromisno Resenja (VIKOR) are classified as MADM techniques, based upon ranking and selection of optimum alternate keeping in view prioritized attributes.Investigators and researchers have justified the utility of MCDM in multiple case studies and applications.36–40Despite the suitability of TOPSIS and VIKOR, Ashby approach is regarded as a robust technique for screening and ranking the optimum candidate material for an engineering application.38,39Ashby technique is a systematic procedure for selecting both material and processes.The structure of Ashby technique provides rapid access to data bank and permits the user greater freedom in exploring the potential of choice.This approach emphasizes design with material, rather than only science of materials.The technique integrates material selection with the design, optimization,and mechanics of materials.41It is demand of this research work to link selection of material with processing of the material i.e., the material could be fabricated as plate.Therefore,one of the most popular, simple and direct MCDM techniques42i.e., Ashby approach, has been used.

4.Novelty of research

The skin of an aircraft is subjected to aerodynamic pressure,twisting, and bending moment during a flight.For the purpose, estimation of the maximum aerodynamic pressure on the skin of the aircraft is significant.There are various techniques for the estimation of maximum pressure on the skin.CFD simulation and experimental techniques are such two techniques, but these are time-consuming and expensive.A fast, simple, and novel procedure to determine DPL on the skin of aircraft through reverse engineering was introduced.The DPL was used for the selection of alternate optimum materials for the skin of the aircraft.

Two objective functions, specific to the aircraft skin studied, were derived as a requirement of MCDM/MODM for minimization of skin mass.

5.Applied methodology

A new approach has been opted to formulate the methodology and achieve the objective.The methodology is elaborated by implementing it on a medium-sized combat aircraft skin, as depicted in Fig.4.

The aerodynamic pressure was analytically estimated on various sizes of skin units.The capability of the aircraft skin to sustain maximum aerodynamic pressure, without permanent deformation, is termed as DPL and the corresponding skin units were selected as Reference Skin Units (RSUs).An objective function (for minimization of mass) and equation for Material Index (MI) were derived for the selection of AOMs with minimum skin mass.The objective function, MI and three filters were used to screen the Cambridge Engineering Selector (CES) software aerospace materials database.A scalar multi-objective function was used to find out a set of non-dominated optimum materials.The non-dominated materials’MI were compared and the material with the highest MI was selected as AOM.The properties of AOM were compared with those of the existing metallic skin.The selected AOM was used to model composite skin units in ANSYS software.Safety factors, deflection, and stress of AOM skin units were compared with RSU under aerodynamic pressure, bending force and twisting moment to check their performance.Finally,the safety factor of the composite skin units was analysed to determine their suitability for aircraft skin.The dimensions of the AOM units and existing skin units were considered the constraints of the optimisation problem.Therefore, the stress,deflection, bending and twisting of skin-supporting structures(longerons, stringers, spars, ribs, stiffeners, Fig.2) would remain the same under aerodynamic and inertia forces.This eliminates the requirement of stress analysis of the skin supporting structure of the aircraft.

Fig.4 Flowchart of methodology applied on a medium-sized combat aircraft.

The investigated aircraft is a supersonic, medium-sized,lightweight,combat aircraft.The structure of the aircraft contributes to 43% of the aircraft’s total weight.The aircraft has been used for more than a decade for various types of flying missions.Not a single event of skin failure under aerodynamic pressure has been recorded yet.This indicates that the skin strength is safely higher than the stress produced by the highest aerodynamic pressure, during all types of flying missions.The estimation of DPL was a fundamental necessity for computational and analytical analysis of the aircraft skin.The DPL as a function of yield strength and dimensions of a thin rectangular skin unit constrained from all four edges is expressed by43,44

where DPL is design pressure limit on the skin unit,MPa;styis yield strength in transverse to the rolling direction, for LY12CZ (Chinese grade of aluminium alloy equivalent to 2024-T4), sty=265 MPa; t is thickness of the skin unit, mm;β is dimensional coefficient to be determined from Fig.5,where the length/width ratio for selected RSUs varies between 2.00 and 2.67,and β=0.5 for the selected RSUs;b is the short dimension of the skin unit, mm.

Approximately 65%–70% of the skin is made from seventeen recurrent sizes of rectangular skin units.Eq.(1) was used to determine the DPL of these seventeen recurring skin units of the fuselage, wings, horizontal and vertical stabilizers.One skin unit under the DPL was selected from each of the aircraft sections.The selected skin units were termed RSUs 1,2 and 3.The skin unit under the highest DPL from wings(No.14)and horizontal stabilizer (No.15) are identical in dimensions,therefore a total of three skin units were selected.The summary of the calculated DPL on the seventeen recurrent skin units is presented in Table 1, where the seventeen recurrent rectangular skin unit sizes are selected from the four main aircraft sections i.e., fuselage, wings, horizontal and vertical stabilizers.RSU 2 on the wings and horizontal stabilizers were found to be under maximum DPL.

Fig.5 Relationship between dimensional coefficient β and length/width ratio of skin unit.

These RSUs are critical for the selection of optimum material due to maximum aerodynamic pressure during aircraft flight.All these RSUs are made of 2.5 mm thick metallic sheet.These RSUs were used for deflection and stress analysis of the optimum material.The detailed view of the smallest skin unit(RSU 2)under maximum DPL is shown in Fig.6,which shows the position and size of the rivet holes in the smallest skin unit of the wings/horizontal stabilizers.

The material used for manufacturing the aircraft skin is aluminium alloy LY12CZ, the most commonly used material for aircraft structure, equivalent to 2024-T4.45The properties of LY12CZ are presented in Table 2.45–47

6.Aluminium alloy skin deflection and stress

The estimated DPL(Table 1)and LY12CZ properties(Table 2)were used to determine the maximum deflection and stress of the three RSUs in ANSYS software.The RSUs are riveted at the four edges with underneath stiffeners (Fig.6).A total of 66 elements and 84 nodes were used to create a mesh for the analysis.The computational deflection of the RSU 2 is shown in Fig.7.A deflection of 0.30 mm was observed at mid-point of RSU 2 (160 mm×60 mm).The deflection logically reduces to minimum at the four constrained edges of the skin unit.Since all four edges of the metallic skin are riveted with underneath stiffeners, the maximum deflection was observed at the midpoint of each RSU.The deflection result for the three RSUs is summarized in Table 3.Though RSU 2 is under the highest aerodynamic pressure of 0.92 MPa, it does not deflect the most, due to its smallest size.The difference in computational and analytical deflection is negligible.The RSU 2 was observed to develop maximum stress.

The computational results of RSUs deflection were analytically validated at the mid-point of RSUs.The relationship for maximum deflection of a rectangular plate,constrained at four edges subjected to normal pressure, is expressed by43,44

where ymaxis the maximum deflection of the RSU at midpoint; α is coefficient to be determined from Fig.8.For a length/width ratio of 2.00 (applicable to RSUs 1 and 3),α=0.027.

The analytically calculated deflection for the three RSUs is summarized in Table 3.The difference in computational and analytical deflection is negligible,which indicates the reliability of modelling in ANSYS.The summary of computational stress for the three selected RSUs is also provided in Table 3.The maximum computational stress of 268.3 MPa was observed in RSU 2, as shown in Fig.9.Maximum stress is observed on the longitudinal edges of the unit.The length of the unit is 2.67 times its width, which has developed maximum stress.

7.Selection of alternate optimum material

The selection of an AOM for the skin of the aircraft, equivalent in performance, but less in weight, was a conflicting requirement.Derivation of an objective function was required involving skin unit dimensions, applied pressure, deflection,density, and stiffness.Minimization of the mass was the optimisation criteria for the selection of material.

Table 1 Summary of 65%–70% of aircraft skin unit sizes.

Fig.6 RSU of size 160 mm×60 mm (RSU 2) under a maximum DPL of 0.92 MPa (as indicated in Table 1).

Table 2 Properties of LY12CZ cold-rolled sheet used for fabrication of RSUs.45–47

Mass of the RSU, in terms of density, is represented by

Fig.7 Deflection observed at mid-point of RSU 2(160 mm×60 mm).

Eq.(4)is the proposed objective function for the minimization of RSU mass.Mathematically, minimization of the RSU mass was achievable by reducing functional requirements,geometric parameters, and material properties.However, functional and geometric parameters contain three constraints (a,b,and ymax),which cannot be altered due to aircraft structural design.Therefore, minimizing RSU mass is only possible by the selection of appropriate material.

The candidate materials were those with the highest stiffness and lowest density (highest MI ratio).The candidate materials were selected from the CES data bank (aerospace materials subset) on the lg-lg chart of E vs ρ by drawing MI as a selection guideline.For one material, the MI is represented by a constant value C:

Fig.8 Relationship between dimensional coefficient α and length/width ratio of skin unit.

Fig.9 Maximum stress observed in RSU 2 (160 mm×60 mm).

Eqs.(3)–(6)are valid for rectangular skin units which comprise 65%–70%of the aircraft skin.Eq.(5)is a family of selection guidelines of slope k (k=3 for the model of the thin plate)on a lg-lg plot of E vs ρ.All materials on/above the constant MI guideline are alternatives to the existing material(LY12CZ).There was a total of 674 aerospace materials in the CES database, out of which 280 materials to the left of the MI guideline were found as candidate materials for the application(Fig.10,where the dashed line shows the selection guideline or MI of slope 3 as our structural design requirement of a plate (Eq.(5))).

Three additional filters were applied to the candidate materials for the following reasons:

(1) Filter 1 Materials with a minimum fracture toughness K1cof 15 MPa?m1/2,a value often quoted as a minimum for conventional design.41

(2) Filter 2 Materials with elastic modulus greater than E of LY12CZ (68 GPa).

(3) Filter 3 Materials that can be fabricated as plates.

A total of 180 materials passed the criteria.To further narrow down the selection funnel,a multi-objective approach was applied to select those materials with a high MI and low cost.For this purpose,MI–1was taken on the y-axis and the cost per kg of the material was taken on the x-axis in ascending order to transform the problem into an all-minimisation problem.In this way, those materials with the highest MI and lowest cost/kg accumulated at the left bottom corner of the chart as a nondominated solution (Fig.11, where S is the slop).

A scalar multi-objective function was defined, representing a straight line on the MI–1vs cost chart (Fig.11).

where ρ/E1/3is inverse of MI;Cois the price of material in US,$/kg;w1is weight factor of the function cost;w2is weight factor of the inverse of MI; P is the intercept of the equation on the inverse of the MI axis.

The slope of Eq.(7)is a ratio between the weight factors of the two objectives, which defines the importance of the objective functions.Eq.(7)is drawn as a dashed line with two slopes i.e., 1 (equal importance of MI and cost) and 1/4 (MI is four times more important than cost).CFRP UD prepreg(E=209 GPa) was found to be the optimum material for either of the slopes (Fig.11).

Fig.10 Aerospace material database on log-log chart of E vs ρ.

Fig.11 MI–1-price relationships of optimum material.

There are five CFRPs near non-dominated solution (intersection of the two slope lines near the bottom left corner of Fig.11) which become optimum if the slope (weight factor ratio) of selection guidelines is changed, which are listed in Table 4.The MI of the CFRPs were compared and summarized in Table 4, five shortlisted composite materials are compared for their MI, which shows that CFRP UD prepreg(E=209 GPa) has the highest MI (3.85).

Table 4 Comparison of selected composites’MI.

7.1.Validation of results

To visualize the effect of density and elastic modulus on the mass of selected material, the objective function (Eq.(4))was drawn as a surface.Fig.12 illustrates the mass of aluminium alloy and five candidate optimum materials.The mass of CFRP (E=209 GPa, ρ=1.50 g/cm3) is 44.6% less than that of aluminium alloy (E=68 GPa, ρ=2.71 g/cm3) with the highest MI of 3.85.Since objective function is valid for 65%–70% of the aircraft skin, the reduction in the weight of aircraft skin is approximately 28%–30%.

7.2.Laminate properties determination and validation

Fig.12 Effect of density and elastic modulus on mass of candidate materials.

Fig.13 Isotropy of properties.

The selection of appropriate laminae sequences is instrumental in composite laminate performance.A 0.15 mm lamina was selected for the modelling of laminate.To achieve isotropy of properties in the plane of laminate, symmetric balanced laminae stacking sequence [0/±45/90]swas selected to model CSU laminate.The properties of the laminate were estimated analytically by using the Kirchhoff Classical Lamination Theory (CLT) for the composite plate using MATLAB software.48–51The strength of laminate was estimated using Tsai-Wu failure criteria.Due to the symmetric design of the laminate, the properties are isotropic in the plane of the laminate.The properties of laminate were also estimated using ANSYS software, which confirmed the analytically estimated values(Fig.13, where Elastic moduli E1, E2, and shear modulus G12were evenly distributed in the plane of CSU, assuring isotropy of the properties.These moduli were calculated computationally).The properties of CSU laminate were found superior to those of LY12CZ.The symmetric design of the laminate resulted in isotropy of the properties in the plane of the laminate.Both analytically and computationally estimated properties of CSU are listed in Table 5.

8.CFRP laminate behaviour

8.1.Under DPL

Three laminates of CFRP UD prepreg (E=209 GPa) were modelled in ANSYS software with the same dimensions as the three RSUs.Deflection and stress analysis of these laminates were carried out under DPL to check the performance of optimum materials in comparison with aluminium alloy LY12CZ.Besides, the safety factor of the optimum material skin was also determined to ascertain the risk involved due to the use of optimum material for the skin of the aircraft.These laminates were named Composite Skin Units (CSUs)1, 2 and 3.

The three CSU laminates were modelled in ANSYS software to determine their deflection, stress, and safety factors under DPL.The deflection developed in CSU 2 is shown in Fig.14.The maximum deflection of 0.31 mm was observed at the midpoint of the CSU 2 under aerodynamic pressure of 0.92 MPa.

The computational deflection of the three CSUs is summarized in Table 6 for comparison with the deflection of RSUs under the same aerodynamic pressure.The CSUs with 44.6% less mass deflected almost equal to RSUs.The maximum DPL of 0.92 MPa was estimated for RSU 2.However,the maximum deflection of 0.86 mm was observed in CSU 1(2.5 mm × 200 mm × 100 mm), which is due to the largest planner area of CSU 1.Maximum stress was not observed in CSU 2 (2.5 mm×160 mm×160 mm, the smallest size of the composite units).The level of stress in each size of the CSUs is the combined effect of the planner area of the skin unit and the aerodynamic pressure acting on the skin unit.The comparatively low safety factor in CSUs 1 and 2 is due to the larger planner area.All three CSUs were found safe under DPL.Table 6 shows almost equal deflection of CSUs laminates and metallic RSUs under the same DPL.The difference in CSUs and RSUs deflection was found negligible.

Table 5 Properties of CSU laminate [0/±45/90]s.

Fig.14 Computational results of deformation of CSU 2(160 mm×60 mm).

Table 6 Computational results of RSUs and CSUs’deflection, stress and safety factors.

Stress developed in the CSU 2 is 194.3 MPa as shown in Fig.15.The computational stress of three CSUs is summarized in Table 6.

Table 6 shows that modelled CSUs laminate developed 12.7%–71.5% less stress compared to RSUs.Maximum stress was observed in CSU 3,which was not under maximum DPL.

Fig.15 Computational results of stress of CSU 2(160 mm×60 mm).

The Tsai-Wu failure criterion, considered as one of the principal failure criteria for polymer matrix composite materials,52,53was applied to find out the safety factor for each CSU.The result of the failure analysis for CSU 2 is shown in Fig.16 where a minimum safety factor of 1.6 was observed on two horizontal edges of composite skin unit.The overall results of all three CSUs are summarized in Table 6.

Fig.16 Computational results of safety factor of CSU 2(160 mm×60 mm).

Fig.17 Comparison of safety factors, deflection, and stress between RSU and CSU under the same bending force of 480 N.

The comparatively low safety factor in CSUs 1 and 2 is due to the larger planner area.All three CSUs were found safe under DPL.54

The properties of CSU laminate,its deflection,stresses,and safety factors suggest it to be an optimum material for the skin of understudy aircraft.The selection of CFRP UD as a suitable material for aircraft skin has also been recommended by Yavuz.25

8.2.Under elastic structural deformation

During flying operation, the skin of wings, vertical and horizontal stabilizers are subjected to elastic bending and twisting due to elastic deformation of spars, stringers, and stiffeners under the skin.It was therefore necessary to compare the behaviour of one of the RSUs (160 mm×60 mm) with the same size CSUs.

The RSU was subjected to gradually increasing bending force on one of the longer edges while the other longer edge was fixed.Fig.17 is the comparison of safety factors, deflection, and stress between RSU and CSU under the same bending force of 480 N.The bending force was increased till a minimum safety factor of 1.6 was achieved (Fig.17(a)).The deflection (Fig.17(c)) and stress (Fig.17(e)) were also determined in RSU.The same bending force was applied to CSU,and the safety factor (Fig.17(b)), deflection (Fig.17(d)) and stress (Fig.17(f)) were determined.

The summary of applied bending force,the resulting safety factors,deflection,and stress of RSU and CSU is presented in Table 7.

Like the exercise of bending force, an increasing twisting moment was applied to RSU.The resulting safety factor(Fig.18(a) and (b)), deflection (Fig.18(c) and (d)) and stress(Fig.18(e) and (f)) were determined in RSU and CSU.

Table 7 Summary of safety factors,deflection,and stress of RSU and CSU under a bending force of 480 N and a twisting moment of 20 N?m.

Fig.18 Comparison of safety factors, deflection, and stress between RSU and CSU under same twisting moment of 20 N?m.

The summary of the applied twisting moment,the resulting safety factors, deflection, and stress of RSU and CSU is presented in Table 7.

The results summary of Table 7 shows a negligible difference in safety factor, deflection, and stress of RSU and CSU under bending force and twisting moment.This indicates that CSU can be used to replace RSU with almost the same performance.

9.Conclusions

The objective of this research paper was to suggest a methodology for finding the optimum material for the skin of a medium-sized combat aircraft.The suggested methodology was exercised and prepreg CFRP UD (E=209 GPa) was selected as the AOM for the studied aircraft’s skin.The following conclusions can be drawn:

(1) The properties of CFRP laminate [0/±45/90]sare superior to those of LY12CZ.

(2) The properties of CFRP laminate were found isotropic in the plane of the laminate.

(3) The stresses in CFRP laminate due to DPL were found less, whereas deflection was observed almost equal to that of metallic skin.

(4) The safety factor of CFRP laminate was found adequate(>1.3).

(5) The behaviour of LY12CZ and CFRP laminate skin under bending force and twisting moment was also found compatible.

(6) The optimum material would reduce the weight of the aircraft up to 30% without compromising the safety of the aircraft’s skin design.

Therefore, prepreg CFRP UD (E=209 GPa) laminate [0/±45/90]sis recommended as an AOM for the skin of the aircraft studied.

Since the objective function for the minimization of mass(Eq.(5)) is confined to 65%–70% of rectangular skin units,objective function valid for other shapes of skin units such as triangular,circular,or other miscellaneous shapes is recommended to be derived and used for filtering the aerospace materials database in the future.

Optimisation of laminae orientation and stacking sequence is a mathematical challenge and many papers have been written to address the same.55–57The selection of optimised stacking sequence depends upon the design of the skin and the forces acting on the laminate.It is not possible to define a general, all-purpose laminae stacking sequence.Further research is recommended for the determination of optimised stacking sequence for the skin of main structural parts,such as fuselage,wings, horizontal, and vertical stabilizers.By using the optimised stacking sequence, the stress and deflection can further be reduced, increasing the possibility of using even thinner laminate and reducing the weight of the aircraft skin.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

The authors extend their appreciation to the Deanship of Scientific Research, the King Khalid University of Saudi Arabia,for funding this work through the Large Groups Research Project (No.RGP.2/163/43).