An Optimum Design of a Subsonic Aircraft Wing due to the Aerodynamic Loading

Aircraft designers are mainly interested in finding the level of pressure, stresses, and deformations of the parts of the aircraft wing. In many aviation accidents, the failure of the wing is the main cause of disasters, as it is considered the main surface that generates the necessary lift for the aircraft in addition to its other functions in controlling the transverse stability. In this work, a numerical study was performed to obtain the optimum wing structural design parameters for high strength and minimum weight for the L-39 A/C wing. The wing was modeled as a honeycomb with different thicknesses using the software SOLIDWORKS 2020. The pressure distribution was predicted using the FLUENT 2022 R1 package. Having obtained the aerodynamic pressure, the deformations and stresses were obtained using the ANSYS program. The results were compared with other researchers using other models, such as using ribs and stringers in the interior structure of the wing. The current results were found to be reliable and acceptable from the design point of view of the high stiffness-to-weight ratio.


Introduction
Te design of the internal structure of the aircraft wing mainly depends on the use of ribs and stringers, and the wing structure is divided into many cells which results in a low stifness-toweight ratio.Te new aeroplane design trends are focused on the use of lightweight sections which are capable of supporting the payload and aerodynamic loading, such as the honeycomb structures.Te authors of [1][2][3] presented an experimental and computational study of the bending behaviors regarding honeycomb sandwich panels with diferent shapes of the cores (in other words, circular, hexagonal, and square) and 2 types of facings: one is aluminum and the other is composite.In comparison with the other core shapes, the square honeycomb core had the highest load, which increased due to the increase in facing thickness, and aluminum skin facing had a larger value of the load when compared to composite skin facing.
Crushing behavior related to a honeycomb sandwich structure was investigated via experiments.In addition, a numerical model for capturing some specifc deformation and failure features in the process of crushing was developed using experimental data to ensure its validity.A three-point bending test was performed on an Al honeycomb sandwich panel [4].Te strength of the sandwich structures under bending loads with a variety of face materials was studied theoretically.Titanium and aluminum may be used as face materials.It has been discovered that titanium alloy has superior sandwich construction qualities [5][6][7].
Te bending stress of a glass fber-reinforced plastic (GFRP) sandwich construction was investigated for a lightweight vehicle.Tere have been 3 diferent adhesives used to adhere to the face and core.Te research demonstrated that a lightweight chassis vehicle's honeycomb sandwich panel design with three adhesives might withstand considerable bending stress [8][9][10].Te researchers provided an experimental investigation on honeycomb sandwich panel compression properties in relation to diferent design parameters such as cell size, foil thickness, and size of the sample (i.e., width, length, and height dimensions) regarding the honeycomb structure.Sandwich samples were constructed by bonding Al honeycomb cores and 1 mm thick CFRP laminate faces, and compression tests were performed on them.It could be seen that when the foil thickness and core height decrease, the yield stress increases [11,12].
Te impact of the honeycomb thickness on the vibration response of sandwich panels was studied using experiments with various boundary conditions.Free vibration analysis was performed on diferent support conditions.It was revealed that the impact of core height on the basic natural frequency of the honeycomb sandwich panels is considerable.As the height of the core rises, so does frequency [13][14][15].
Finite and experimental element analytic methods have been used to look at the behavior of aluminum honeycomb structures under the low-speed impacts.Te ASTM D7766 standard was utilized for conducting low-velocity impact tests on the honeycomb structures that were created.Te impact force was investigated as a function of cell width and height.Te maximal impact force values in the honeycomb composite constructions have been found to grow as cell width and height decrease.Te experimental and fnite element approach results are roughly 85 percent in agreement [16][17][18].
Te goal of the current work is to design and analyze a lightweight L-39 aircraft wing using a honeycomb structure which can resist aerodynamic loading.A comparison study will be performed by using wing design with ribs and stringers.

Honeycomb Structures
With regard to sandwich structures, honeycomb cores are available in a range of materials, including paper and card for applications needing low strength and stifness and low loads (like interior doors for homes) and high strength and stifness, incredibly lightweight sections for aviation structures, are available for honeycomb cores used in sandwich structures.Honeycombs can be formed into composite structures which are both fat and curved without needing a lot of mechanical force or heat [19][20][21].A honeycomb's typical shape is shown in Figure 1.Te cells could be hexagonal, triangular, or square.Examples of honeycomb include glass fber-reinforced plastic, aluminum, and honeycomb made of kraft paper.Aluminum and carbon honeycomb cores were used in this experiment.Figure 1 shows a simplifed honeycomb.
Honeycomb characteristics are anisotropic, meaning that they difer between out-plane and in-plane strengths and stifnesses.Te walls of the cells frst bend, and deformation is linear elastic in a case where a honeycomb is squeezed in plane, that is, when stress acts orthogonal to the cell axis; plane X1 X2 is depicted in Figure 2.
Composite sandwich structures, on the other hand, represent a modeling problem due to the fact that their core region is made up of several cells with complex geometries.
Te isotropic beam analysis method in [22][23][24][25] is the most widely used model of unit cells for determining efective characteristic determination.Te author makes an assumption that the honeycomb deformations' linear elastic response and the consequent core characteristics are solely dependent on the bending of the core cell walls.Te stretching and shearing of cell walls were studied as additional deformation modes [26][27][28].FEM has been used in numerous previous publications for estimating efective material characteristics regarding honeycomb architectures.Te core of multifunctional sandwich composites could then be sized using analytical equations in the design process to account for anticipated energy needs as well as desired service loads.Figure 3 provides an illustration of the homogenization approach used in this study.
In Figure 3, the superscript in E 1 1 , E 2 1 , and E 3 1 refers to the layer number and the subscript refers to the principal direction.E ff is the efective modulus, and E core is the core modulus.4, which can be summarized as follows: (1) Tree internal structure confgurations were suggested: 1 cell, 6 cells, and 9 cells.(2) For each case in (1), three diferent air speeds were chosen 0.4, 0.6, and 0.8 Mach numbers.(3) Te aerodynamic pressure distribution on the wing for each case in (2) is obtained using the FLUENT program.(4) For each case in (1), the skin thicknesses of 2, 3, and 4 mm are used.

Material Properties of the
(5) For each skin thickness in (4), three core thicknesses of 2, 4, and 6 mm are used.( 6) Te displacement and stresses are obtained for each tested case in the block diagram using the ANSYS package.Te Scientifc World Journal

Detailed Case Study
Te L-39 A/W wing weight is 6500 kg, with the profle NACA 64A 012.Te span is 9.12 m, the gross area is 18.8 m 2 , the quarter chord line sweepback angle is 1 °45, the leading edge sweepback angle is 6 °26, the taper ratio is 0.475, the aspect ratio is 4.4, the mean aerodynamic chord is 2.15 m, the tip chord is 1.33 m, the root chord is 2.8 m, and the geometric shape is trapezoidal.Te calculations are based on the angle of attack 12 °because of the maximum pressure around the A/C wing model as shown in Table 1.First, a 12 °angle of attack is adopted because at this attitude, the maximum deformations and stresses are developed in the wing structure.Te pressure developed at this position is found using the FLUENT package which is exported directly to the ANSYS package (fuid-structure interaction) which is considered an exact modeling of the wing structure under aerodynamic modeling.Tis was used throughout the work presented here.

Wing One Cell.
Te determination of displacements and stress using diferent structural modeling methods is presented here.Finite element modeling was employed as explained above to predict the pressure distribution to be Step1:Determine effective walmodulus  Te Scientifc World Journal 3 applied on the wing structure, which corresponds to the real case to give the true picture of deformation and stresses on the wing skin.Te efects of the design parameters of the wing structure are discussed as follows: (i) Efects of skin thickness (ii) Efects of the number of cells (iii) Efects of core thickness (invariably of skin thickness) 3.1.1.Efects of Skin Tickness.Using a skin thickness of 2 mm and a core thickness of 2 mm, the maximum deformation of 154.28 mm and the resulted von Mises of 210.17 MPa were obtained, as shown in Figures 4 and 5.
Increasing a skin thickness to 3 mm, the deformation becomes 106.41 mm and the resulted von Mises becomes 143.64 MPa, as shown in Figures 6 and 7. Table 2 shows the results of using diferent thicknesses (invariably of core).Note that in Table 2, some of the points in bold failed because the value of the von Mises stress exceeded a yield strength of 505 N/(mm) 2 .Te least mass was 200.21 kg and the largest mass was 421.71 kg using material Al 7075-T6.Table 2 shows that the change in the total von Mises stress was largest (793.92MPa) at a skin thickness of 2 mm, a core thickness of 4 mm, and Mach 0.8 (failed), while the lowest stress (108.41MPa) was obtained at a skin thickness of 4 mm, a core thickness of 6 mm, and Mach 0.4.It was shown that the largest equivalent strain of 0.0075414 mm/mm was obtained in the model with a skin thickness of 3 mm and a core thickness of 2 mm at Mach 0.8, while the least deviation of 0.0010246 mm/mm was obtained in the model with a skin thickness of 2 mm and a core thickness of 6 mm at Mach 0.8.

Efects of Core Tickness.
Using a skin thickness of 2 mm and a core thickness of 2 mm, the maximum deformation of 338.84 mm and the resulted von Mises of 473.87 MPa were obtained, as shown in Table 3.
Note that in Table 3, some of the points in bold failed because the value of the von Mises stress exceeded a yield strength of 505 N/mm 2 .Te least mass was 200.21 kg, and the largest mass was 421.71 kg.Table 3 shows that the change in the total von Mises stress was largest (793.92MPa) at a skin thickness of 2 mm, a core of thickness 4 mm, and Mach 0.8 (failed), while the lowest stress (108.41MPa) was obtained at a skin thickness of 4 mm, a core thickness of 6 mm, and Mach 0.4.Table 3 also shows that the largest equivalent strain of 0.0075414 mm/mm was obtained in the model with a skin thickness of 3 mm and a core thickness of 2 mm at Mach 0.8, while the least deviation of 0.0010246 mm/mm was obtained in the model with a skin thickness of 2 mm and a core thickness of 6 mm at Mach 0.8.Some cases failed due to the maximum stresses developed compared to the yield stress at the used material (Al 7075-T6) when a stress ratio is less than 1.Tey are labelled in bold.Even the masses are low compared to the mass used in the A/C design.

Wing 6 Cells.
Finite element modeling was used as stated previously to predict the pressure distribution to be applied on the wing structure.Tis corresponds to the real case to give the true picture of deformation and stresses on the wing skin.Te efects of the design parameters of the wing structure are discussed as follows: Table 4 shows the results of using diferent thicknesses (invariably of core).Note that in the table, some of the points in bold failed because the value of the von Mises stress exceeded a yield strength of 505 N/(mm) 2 .Te least mass was 210.46 kg and the largest mass was 451.26 kg using material Al 7075-T6.Table 5 shows that the change in the total von Mises stress was largest (765.07MPa) at a skin thickness of 2 mm, a core thickness of 2 mm, and Mach 0.8 (failed), while the lowest stress (100.77MPa) was obtained at a skin thickness of 4 mm, a core thickness of 6 mm, and Mach 0.4.Tis table also shows that the largest equivalent strain of 0.0011286 mm/mm occurs in the model with a skin thickness of 4 mm and a core thickness of 6 mm at Mach 0.8, while the least deviation is 0.001417 mm/mm obtained in the model with a skin thickness of 2 mm and a core thickness of 6 mm at Mach 0.4.deformation is 104.24 mm and the resulted von Mises is 141.84 MPa, as shown in Figures 12-15.

Efects of
Table 5 shows the results of using diferent thicknesses (invariably of core).Note that in the table, some of the points in bold failed because the value of the von Mises stress exceeded yield strength � 505 N/(mm) 2 .Te least mass was 210.46 kg and the largest mass was 451.26 kg using material Al 7075-T6.mm occurs in the model with a skin thickness of 4 mm and a core thickness of 6 mm at Mach 0.8, while the least deviation of 0.001417 mm/mm was obtained in the model with a skin thickness of 2 mm and a core thickness of 6 mm at Mach 0.4.
Te summary of the results which are extracted from the contours is shown in Table 5.Some cases failed due to the maximum stresses developed compared to the yield stress at the used material (Al 7075-T6) when a stress ratio is less than 1.Tey are labelled in bold.Te Scientifc World Journal

Comparison Study
Te obtained results using the honeycomb structures are compared with the results obtained by using the ribs and stringers as shown in Table 6.
Table 6 shows a comparison study between the suggested modeling and the work achieved by Gargan [29].

Conclusions
From this work, the following points can be concluded: (1) Te efectiveness of using honeycomb in reducing stress is greater than the efectiveness of using the ribs and stringers.
(2) Using 7075-T6 aluminum alloy for both the skin and core gives the least weight of the wing structure with a largest weight (421.71kg) using one cell and a minimum weight using 6 cells (200.2 kg).Te maximum wing mass was 451.26 kg and the minimum mass was 210.46 kg which are considered to be lightweight wings in any case compared to the wings with ribs and stringers with a minimum mass of 414 kg.(3) Te stifness of the wings using the honeycomb structures is greater than that using the ribs and stringers, which results in less deformation, which in turn increases the futter and the divergence speeds and gives a greater chance to avoid failure under the same aerodynamic modeling.Te Scientifc World Journal (4) Finally, the fnite element modeling of a threedimensional wing and using the idea of cells as a stifening element were found to give good results and to determine the areas of most stress and acceptable deformation levels.

Figure 1 :
Figure 1: Schematic of a typical sandwich structure.

Figure 3 :
Figure 3: Overview of the homogenization methodology sought in the current investigation.

Figure 4 :
Figure 4: Contour of the total deformation at one cell skin 2 core 2 (Mach 0.4).

Figure 5 :
Figure 5: Contour of the equivalent stress at one cell skin 2 core 2 (Mach 0.4).

Figure 6 :
Figure 6: Contour of the total deformation at one cell skin 3 core 2 (Mach 0.4).

Figure 7 :
Figure 7: Contour of the equivalent stress at one cell skin 3 core 2 (Mach 0.4).

section 0 skin 2 cor 2
Core Tickness.Using a skin thickness of 2 mm and a core thickness of 2 mm, the maximum deformation is 149.83 mm and the resulted von Mises is 208.83MPa.Increasing a skin thickness of 3 mm, the C:

section 0 skin 3 cor 2
Table 5also shows that the change in the total von Mises stress was largest (765.07MPa) at a skin thickness of 2 mm, a core thickness of 2 mm, and Mach 0.8 (failed), while the lowest stress (100.77MPa) was obtained at a skin thickness of 4 mm, a core thickness of 6 mm, and Mach 0.4.Tis table also shows that the largest equivalent strain of 0.0011286 mm/ F:

Table 4 :
Wing 6 cells at the angle of attack 12

Table 5 :
Te results of using diferent thicknesses (invariably of core).