Design and Analysis of CFRP‐Based Landing Gear for Unmanned Combat Aerial Vehicles

Abstract

With recent technological advancements, the drone industry has been looking into new materials to manufacture parts. The ultimate aim of designing any aircraft component is to minimize its weight and maximize its strength while keeping the costs low to compete with the market. One of the biggest challenges for any drone is to have a safe landing, especially when it has sensitive equipment or goods onboard. Landing gears are supposed to be highly crashworthy and are not expected to fail in their given lifecycle; however, due to the nature of their use, they are always at risk of damage. This study is aimed at finding a way to mitigate this risk by conducting research based on a relatively new material technology called carbon fiber–reinforced polymer (CFRP). A new design for the landing gears is also provided using CFRP as material. CFRPs are highly durable, stronger, and lighter then steel. Equivalent von Mises stresses and strains, and maximum principle stresses were obtained and studied using finite element analysis for multiple models of the landing gear of a selected UAV. The finite element package ANSYS was used for this purpose. Impact analysis was performed using LS Dyna in ANSYS. The new proposed design is validated through various simulations and analysis performed in Ansys Workbench. The results were used to draw a comparison of the factor of safeties of the preferred model and a conclusion was drawn for the usage of CFRP in the manufacturing of landing gears.

1. Introduction

As with most fields of modern technology, aircraft, and by extension unmanned aerial vehicles (UAVs), have seen rapid development in the last two decades. Starting as mere technology demonstrators, UAVs have now become an integral part of several key industries around the world including exploration and mapping, natural and scientific studies, and military applications. As these drones have been adapted to a wider array of tasks and capabilities, there has been an equivalent increase in their operational parameters, including size, weight, and speed (including landing speeds). This is especially true for the jet-powered UAVs and unmanned combat aerial vehicles (UCAVs) that are used by many modern militaries, as these, akin to their manned counterparts, have much higher operational loads and speeds. Consequently, the landing gears of such machines need to be similarly strengthened to the rest of their structures in order to withstand the increased forces these parts will face. According to the Office of Aerospace Medicine of the US Department of Transportation, 47% of crashes in military drones [1] were during the landing procedure. With a majority of these occurring due to the kinds of materials being used in the construction of the landing gears, as opposed to the design [2], the ideal landing gear would consist of the most durable materials, having high crashworthiness and low weight while keeping the overall cost of the landing gear low. Weight is an important factor here because one of the most important performance parameters of a UAV, especially in military applications, is its endurance and flight time, which is closely linked to the weight of the aircraft. Even a few kilograms of extra weight can make a noticeable difference in the total range of a UAV [3].

To overcome all these aforementioned problems, airplane and drone manufacturers have been looking into new materials to design parts with, materials that can not only withstand the increased stresses of these use cases but also not greatly affect the range and cost of their products. In this regard, the use of composites has increased significantly in the manufacture of aircraft parts, especially structural parts [4]. Composites are some of the most ideal materials for manufacturing aircraft landing gears because of their durability. They tend to have high strength, high modulus, low density, excellent resistance to fatigue, creep, creep rupture, corrosion, and wear, and low coefficient of thermal expansion [5]. As Ma in his 2023 study focused on optimizing CFRP structures to replace metal components in rail systems to achieve weight reduction and maintain structural integrity, this study extends the application of CFRP to aerial vehicle landing gear systems [6, 7]. Similarly, considering the same property, another study on lightweight oil pans for automobiles was conducted under Ma in 2021.

The specific material concerning this study is that of carbon fiber–reinforced polymer (CFRP). Carbon fiber is a lightweight, high-strength material that is known for its exceptional mechanical properties. It is composed of thin strands of carbon atoms, typically less than 10 μm in diameter, which are woven together to form a fabric-like structure. These carbon fibers are extremely strong and stiff, providing a high tensile strength and modulus of elasticity [8]. CFRP refers to a composite material that combines carbon fibers with a polymer matrix, usually epoxy resin. The carbon fibers are embedded within the polymer matrix, forming a strong and durable material. CFRP offers a unique combination of properties, including high strength-to-weight ratio, excellent stiffness, corrosion resistance, and low thermal expansion. The manufacturing process of CFRP involves several steps. First, carbon fibers are produced by subjecting a precursor material to high temperatures in an oxygen-depleted environment. Next, the carbon fibers are impregnated with a liquid resin, typically epoxy, to form a composite material. Additional layers of carbon fiber sheets or fabric can be stacked to increase the strength and thickness of the final CFRP part. After impregnation, the CFRP is cured by applying heat and pressure. Once cured, the CFRP part can be further processed, such as by cutting, shaping, or machining, to achieve the desired final shape. It offers significant advantages over traditional materials like steel and aluminum, as it provides comparable strength with significantly lower weight. This lightweight nature contributes to fuel efficiency, improved performance, and increased payload capacity in applications such as aircraft, race cars, and bicycles.

Keeping all of this in mind, this study is aimed at conducting fatigue and impact testing on two different models of the landing gear of a commercial UAV, using CFRP as the construction material and the finite element package as well as the explicit dynamics feature in ANSYS. The results of the two models will be compared to study the factor of safeties.

Although CFRP has been widely studied because of its superior mechanical properties, limited research has been conducted on its use for manufacturing landing gears in aerial vehicles. This research analyzes its use by using comprehensive material properties from literature. This study proposes a new design for landing gear and performs several static and dynamic analyses in Ansys Workbench to verify its validity. Carbon fiber is used as material for this design. The findings serve as a predictive benchmark for the use of CFRPs in landing gears and offer a foundation for future experimental validation and optimization.

1.1. Research Highlights

Designing landing gears comes with a whole host of challenges. These structures are expected to undergo large stresses and rapidly deform/change shape as the aircraft impacts the ground and then settles. These factors make studying the crashworthiness of an aircraft part more challenging [9].

Before conducting any dynamic analysis, it is important to understand the principles of stress and impact analysis. Accurate analysis of the landing gear under fatigue and impact can provide a good estimate of the deformations, stresses, and strains that occur in the gears during landing and hence help in optimizing them both structurally and materially. Due to the recent boom in unmanned aviation, there has been an increase in the number of studies conducted on the crashworthiness of aircraft and their landing gears, many of which use their own methods and conditions for such analysis.

In the examination conducted by Rui Pires [10], Newton′s second law was employed to compute the forces acting in the normal and spin up back directions upon impact. By exclusively focusing on these forces for their assessment, the PATRAN software was employed to derive insights into the stresses, strains, and deflections resulting from the impact. In pursuit of enhancing crashworthiness, an optimization approach was adopted. This involved modifying the shape of the landing gear and introducing curvature adjustments. By varying the curvature, they obtained a number of models while maintaining consistent size and material properties. As a result, this iterative process notably reduced both stress levels and deflection amounts, thereby substantially enhancing the crashworthiness of the landing gear.

In “Design and Manufacture of Composite Landing Gear for a Light Unmanned Aerial Vehicle,” Yen-Chu et al. [11] focused on the design, analysis, fabrication, and performance of a UAV model with thermoplastic extruded composite components. The UAV model showed high stability, maneuverability, and good aerodynamic characteristics. The study highlights the advantages of composite materials, particularly carbon fiber, which include high stiffness, tensile strength, low weight, chemical resistance, and thermal tolerance. Carbon fiber–reinforced composites are preferred for high-performance drone frames. The use of carbon fiber reduces the weight of the structure and improves fatigue and corrosion resistance. Landing gears play a crucial role in ensuring safe operations, and lightweight, high-strength materials are necessary to prevent accidents.

Plabita et al. [12] used CATIA for the modeling of main landing gear (MLG) of a small UAV and calculated the factor of safety (FoS) using FEA. They calculated the loads during landing by kinematic analysis and found von Mises stresses using FEM. They presented their results for different impact velocities of the UAV. The material they used was carbon-Hercules AS4.

Imran et al. [13] made an analysis of structural and spectrum loads on MLG. They used carbon-Hercules AS4 composite material to analyze the strength of the landing gear. Their analysis included the effects due to parameters such as weight as well as static and shock spectrum loads. They deduced from their results that landing gear made of composite material is proven to be more crashworthy because the effect of stresses was less and the deflections were reduced.

Yildrim et al. [14] used different geometries and shapes for their analysis. They used four different models of skid-type landing gear. They did their analysis for stresses, strain, and deformation on ANSYS. Their experiment showed a 10% error for the calculated values of ANSYS. They found that the model was 1.5 times safer when curved and hollow bars were used.

A team led by Camil Lancea at the Transylvania University of Brașov [15] conducted a study that used fused filament fabrication to create landing gear models for an unmanned aircraft, finding that carbon fiber-reinforced polymer material had the highest mechanical performance, while polyethylene terephthalate with short carbon fiber had the best performance among the fabricated landing gears. Microscopic analysis revealed typical defects in the composite filaments. Finite element analysis was conducted to analyze the landing gear models made from different materials. The study compared simulation results with experimental results obtained from bending tests of the landing gear models.

Swati and Khan [16] designed and analyzed weight-optimized MLGs for UAV under impact loading using computational tools. They performed static structural analysis for their first model, evaluating different stresses, strains, and deformations. Afterward, optimizing their model to create a second model, they performed the same analysis on it. The results of the analysis were compared, and the modified model was found to be better than the initial model in terms of weight optimization and structural stability.

In another study, Swati et al. [10] carried out the fatigue and impact analysis of MLG using explicit dynamics. FEA in ANSYS yielded the equivalent von Mises and maximum principal stresses for various materials. The stress formulations and deformations during impact exhibited a high degree of nonlinearity, rendering them more realistic and accurate compared to static structural analysis. In both types of analyses, it was observed that stresses and deformations increased with higher impact velocities, leading to a decrease in the FoS. The static structural analysis was conducted in a manner consistent with a prior study. However, for the impact analysis, the incorporation of remote point masses and displacements enhanced the accuracy and realism of the results. These additions more faithfully simulated the motion of landing gear during landing, resulting in more precise deflections and stress concentrations.

2. Materials and Methods

2.1. Selection of Materials

Some of the common materials used to manufacture landing gears are titanium and aluminum alloys. For this study, the material chosen was CFRP because composites tend to have strong and lightweight properties. They can withstand high loads during impact because of their high durability and resistance to corrosion. As discussed in the research highlights, its properties align with the required material for this research. Hence, CFRP was chosen as the material for our CAD model. The material properties of CFRP and some other materials that are used in manufacturing landing gears are given in Table 1.

Table 1 Material properties of CFRP [17–20].

Properties	CFRP	Ti-15 V-3Sn-3Al-3Cr	Aluminum alloy 7075	Alloys steel 4340	Titanium 6AL-4V
Density (kg/m3)	1800	4704	2.88	7.7	4.43
YS (MPa)	3530	1483	95	472.3	880
Poisson’s ratio	0.27	0.33	0.33	0.33	0.342
Young’s modulus (GPa)	200	82	80	200	113.8

The properties of the woven carbon fiber discussed here are similar to the properties of “pan-based high tensile strength carbon fiber” with a very minute difference as discussed in Xun Chen’s research paper [21]. These fibers are widely used in the aerospace and automotive industries due to their good strength-to-weight ratio and mechanical performance.

2.2. Reference UAVs

The landing gear of RQ-7B [22] is taken as a reference in this study. The MLG Model-1 geometry was taken from a public source and was modified and made similar to that of the RQ-7B in SOLIDWORKS. We further modified the design according to our results to create a new optimized model. Table 2 shows the parameters of our reference UAV that were taken from a private source and some publicly available sources.

Table 2 Dimensions of Model 1.

Bounding box
Length	100 cm
Height	36.56 cm
Width	9.13 cm
Properties
Volume	1.0303e + 06 mm3
Mass	1.8546 kg

2.3. Methodology

Mathematical techniques are used for the structural and impact analysis which are being done on ANSYS. All the geometric parameters of the MLG were obtained through publicly available data sources from the UAV manufacturers. The landing gear was modeled in CAD software Dassault SOLIDWORKS. The material chosen was CFRP. The first model (Model 1) was analyzed for structural and fatigue analysis and various stresses, strains, deformation, and FoS were evaluated. After obtaining the results, the model was optimized to enhance its structural reliability and the FoS and a new model was introduced (Model 2). The same tests as before were performed on Model 2, and the results were compared. After that, both models were utilized for impact analysis of the landing gear, and the results of both models were compared. The focus of the research was proving the viability of composite material for the MLG and to optimize the structure for better results.

MATLAB was used to study and plot the graphs for the results due to its accuracy. It is widely used in research because of its ease of use, versatility, and speed.

The touchdown velocities were specified as between 1.5 and 2.5 m/s in CS-23, a European Aviation Safety Agency′s Certification specification manual [23]. However, in this study, for impact velocities, a range of 2–6 m/s was used for static analysis and 2–8 m/s for impact analysis [10]. Newton′s third law was used to calculate the loads [24].

The model was imported and meshed in the FEA software package ANSYS. The mesh sizing was done at 4 mm. The material properties of CFRP were taken from various sources and added to ANSYS before meshing. The boundary conditions were applied after meshing and the structural and fatigue analyses were performed. The impact study for both models was considered afterwards.

On comparing the material properties provided in Table 1, CFRP emerges as a suitable material because of its high yield strength and Young′s modulus despite having a low density as compared to other materials with the similar properties. CFRP is particularly useful in aerial vehicles where light weight design is of utmost importance. Although it is complex to repair, advances in composite manufacturing are increasingly addressing these limitations.

Aluminum Alloy 7075 despite being lightweight also has low yield strength, making it unsuitable for high stresses in landing gears. Alloy Steel 4340 offers good strength but it is too heavy. Titanium alloys provide a balance between strengths and weight but are more complex to machine and manufacture than CFRP.

2.4. Material Assignment to the Model

Material properties were collected from different authentic sources as given in Table 1 above. These properties were used to define a new material in Ansys Workbench software. All the properties of the material were properly defined in the Engineering Data section of the Ansys Workbench as given in Figure 1, and simulations were carried out using this material.

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Only simulations and theoretical approaches are considered in this paper; practical manufacturing is out of scope for this research paper.

3. Static Structural

3.1. General Assumptions

To facilitate analysis, several general assumptions were established. This study specifically focused on the two-point landing condition. The UAV′s maximum takeoff weight was assumed to be 170 kg. Moments resulting from vertical loads were disregarded. The impact time was set at 1 s. The initial frictional force produced by the tires and tangential forces was both omitted. Typically, UAVs are considered within a touchdown velocity range of 2–3 m/s. However, for a more comprehensive understanding of the FoS in our investigation, we extended the vertical touchdown velocities to a range of 2–8 m/s.

The initial loads were calculated using the equation below [24]: $\begin{array}{}\mathbf{F}=\frac{\mathbf{m}\ast \mathbf{V}}{\Delta \mathbf{t}},\end{array}$ where m is the mass, V is the vertical touchdown velocity, and Δt is the impact time.

3.2. Development of Model 1

The model was designed to be similar to the landing gear of the RQ-7B. A reference model was taken from a public resource and adjusted in SOLIDWORKS software. The dimensions of the model are given in Table 2, while the CAD model is shown in Figure 2.

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For an accurate solution, one of the key parameters to set is the mesh. It is of utmost importance to perform a fine quality mesh for our model. Our mesh was taken to be of size 4 mm. Meshing was done using tetrahedral elements.

elements, and the algorithm used was the patch conforming method, with an element size of 4 mm and smoothing set to high. The details of the mesh are shown in Table 3, along with the mesh itself in Figure 3.

Table 3 Properties of mesh.

Parameters	Mesh 1
Element size	4 mm
Smoothing	High
Nodes	901,312
Elements	624,705
Span angle center	Coarse
Min edge length	9.198E−3 mm
Transition	Fast
Transition ratio	0.272
Maximum layers	5

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The boundary conditions of the landing gear are established in the following manner:

• •

  The horizontal structure of the landing gear is constrained for all degrees of freedom, that is, fixed.

• •

  The self-weight is given in the downward direction (−y direction)

• •

  Reactional force at the tire joints in upward direction (y direction)

The SN curve of a material is very important for any form of analysis; however, there was no publicly available SN curve for the material in question. Considering this, an SN curve was generated using the corresponding data in Table 4 using the equation given by Burhan and Kim [25]. $\begin{array}{}{\mathbf{\sigma }}_{\mathbf{max}}={\mathbf{\sigma }}_{\mathbf{u}\mathbf{T}}{\left(\frac{\mathbf{\alpha }\left(\mathbf{\beta }-\mathbf{1}\right)\left({\mathbf{N}}_{\mathbf{f}}+{\mathbf{N}}_{\mathbf{0}}\right)}{{\mathbf{\sigma }}_{\mathbf{u}\mathbf{T}}^{-\mathbf{\beta }}}+\mathbf{1}\right)}^{\mathbf{1}/\left(\mathbf{1}-\mathbf{\beta }\right)}.\end{array}$

Table 4 Data for SN curve.

Cycles	Alternating stress (MPa)
10	304.07
20	285.82
50	262.95
100	246.73
200	231.46
2000	187.09
10000	161.22
20000	151.2
1E + 05	130.29
2E + 05	122.96
1E + 06	105.29

As a standard ANSYS takes 12 values of the SN CURVE so the values were calculated till the 12th iteration. The used sequence of cycles is also taken as a standard by ANSYS. The resulting curve is given below in Figure 4.

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4. Results of Fatigue Analysis

For each load, the findings were organized in a tabular form, encompassing the von Mises stresses and strains, total deformations, maximum principal stress, and the fatigue FoS as the parameters obtained in this study.

4.1. Result for Model 1

The calculated loads with regard to speed and the tabulated results for Model 1 are shown in Tables 5 and 6 below, respectively.

Table 5 Calculated loads at different landing speeds.

Velocities (m/s)	Impact force (N)
2	340
3	510
4	680
5	850
6	1020
7	1190
8	1360

Table 6 Static Structural Analysis for Model 1.

Force (N)	Total deformation max (m)	Eq. stress min (Pa)	Eq. stress max (Pa)	Max principal stress min (Pa)	Max principal stress max (Pa)	Eq. strain min (mm-1)	Eq. strain max (mm-1)	FoS
340	0.001531903	0.124629655	32,528,464.57	−8,574,181.875	30,398,990.09	8.04E−13	0.000180632	3.236924995
510	0.002297854	0.186944482	48,792,696.4	−12,861,272.74	45,598,484.77	1.21E−12	0.000270948	2.157950016
680	0.003063805	0.24925931	65,056,929.14	−17,148,363.75	60,797,980.19	1.61E−12	0.000361264	1.618462497
850	0.003829756	0.311574142	81,321,159.69	−21,435,455.06	75,997,475.32	2.01E−12	0.000451579	1.294770025
1020	0.004595708	0.373888964	97,585,392.8	−25,722,545.47	91,196,969.54	2.41E−12	0.000541895	1.078975008
1190	0.005361659	0.436203795	113,849,622.9	−30,009,636.03	106,396,465.2	2.81E−12	0.000632211	0.924835738
1360	0.00612761	0.49851862	130,113,858.3	−34,296,727.5	121,595,960.4	3.21E−12	0.000722527	0.809231249
1400	0.006307834	0.513180932	133,940,734.1	−35,305,454.04	125,172,311.4	3.31E−12	0.000743778	0.78611037
1450	0.006533114	0.531508822	138,724,334.3	−36,566,362.95	129,642,753.6	3.43E−12	0.000770341	0.759003102
1500	0.006758393	0.549836723	143,507,931.1	−37,827,271.76	134,113,191.7	3.55E−12	0.000796905	0.733703003
1600	0.007208953	0.586492493	153,075,127.6	−40,349,090.8	143,054,071.6	3.78E−12	0.000850032	0.68784656
1700	0.007659513	0.623148285	162,642,319.4	−42,870,910.13	151,994,950.6	4.02E−12	0.000903159	0.647385013

Comparisons are made between the FoS and varying loads. The FoS is characterized as the ratio of ultimate tensile strength to the maximum allowable stress acting on the landing gear. $\begin{array}{}\mathbf{F}\mathbf{o}\mathbf{S}=\frac{\mathbf{F}\mathbf{U}\mathbf{T}\mathbf{S}}{\mathbf{\sigma }\mathbf{max}}.\end{array}$

Here, it is important to note that the FoS for this model drops below 1 at forces of around 1000 N, which is not acceptable for a UAV of this size and weight. Table 5 shows that at higher velocities, increased load causes the material to deteriorate under fatigue because the FoS falls below the value of 1. This result suggests an improvement in the design of landing gear made using CFRP.

4.2. Design of Model 2

This model was designed as an improvement over the previously discussed model to improve its crashworthiness and FoS; it was achieved by adding skeletonized supporting structures to the frame. However, the materials and the footprint of the landing gear remain the same as before. The CAD model and mesh for this design are shown in Figures 5 and 6, while its dimensions are given in Table 7.

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Table 7 Dimensions of Model 2.

Bounding box
Length	100 cm
Height	36.56 cm
Width	9.13 cm
Properties
Volume	2.8336e + 06 mm3
Mass	5.1004 kg

It can be observed from Tables 2 and 7 that despite having the same dimensions mass and volume of Model 2 is greater than Model 1, it is due to the modified structure of the Model 2. The skeletonized structure added to the Model 2 increased its mass as it can be seen in Figures 2 and 5.

4.3. Results for Model 2

Due to the improvements made to the structure of this model there is a notable increase in almost all the factors under study, but at the understandable cost of weight (which can still be mitigated over conventional landing gear designs due to the low weight of CFRP). In this model. as seen in Table 8, the FoS for this model stays within a safe limit regardless of the forces being applied upon landing or the impact velocity within the chosen ranges.

Table 8 Static structural analysis for Model 2.

Force (N)	Total deformation max (m)	Eq. stress min (Pa)	Eq. stress max (Pa)	Max principal stress min (Pa)	Max principal stress max (Pa)	Eq. strain min (mm-1)	Eq. strain max (mm-1)	FoS
340	7.20E−06	180.2227236	4,822,647.851	−815,737.9683	1,438,328.308	1.86E−09	3.01E−05	15
510	1.08E−05	270.3340721	7,233,971.881	−1,223,606.927	2,157,492.482	2.79E−09	4.51E−05	14.55524
680	1.44E−05	360.4454555	9,645,295.701	−1,631,475.937	2,876,656.616	3.72E−09	6.01E−05	10.91643
850	1.80E−05	450.5567912	12,056,619.72	−2,039,344.84	3,595,820.766	4.66E−09	7.52E−05	8.733144
1020	2.16E−05	540.6681243	14,467,943.76	−2,447,213.854	4,314,984.965	5.59E−09	9.02E−05	7.27762
1190	2.52E−05	630.7795715	16,879,267.83	−2,855,082.847	5,034,149.131	6.52E−09	0.000105241	6.23796
1360	2.88E−05	720.890911	19,290,591.4	−3,262,951.873	5,753,313.233	7.45E−09	0.000120275	5.458215
1400	2.97E−05	742.0933367	19,857,961.79	−3,358,920.873	5,922,528.35	7.67E−09	0.000123813	5.302266
1450	3.07E−05	768.5969282	20,567,174.73	−3,478,882.281	6,134,047.214	7.94E−09	0.000128235	5.119429
1500	3.18E−05	795.1003139	21,276,387.55	−3,598,843.954	6,345,566.09	8.22E−09	0.000132656	4.948782
1600	3.39E−05	848.1068978	22,694,813.45	−3,838,766.955	6,768,603.849	8.76E−09	0.0001415	4.639483
1700	3.60E−05	901.1135824	24,113,239.43	−4,078,689.68	7,191,641.532	9.31E−09	0.000150344	4.366572

4.4. Comparison of Results Between the Two Models

The results in Tables 6 and 8 and the tests from which they were gathered can be used to draw a comparison between the two models using ANSYS simulations and corresponding graphs.

In both models, the maximum total deformation is seen at the lower ends of the structure where the wheels are to be attached, with the minimum deformation being seen at the center point where the assembly is to be attached to the aircraft. While the total area of maximum deformation is higher in Model 2, the actual magnitude of maximum deformation is significantly lower at around 35 μm when subjected to 1600 N compared to over 7 mm at the same applied force as evident from Figure 7. Total deformation in (a,c) Model 1 and (b,d) Model 2 is given in Figure 7. From the figure, (a) shows the total deformation in Model 1, (b) shows total deformation in Model 2, (c) shows the graph of total deformation and force of Model 1, and (d) shows the graph of total deformation and force of Model 2.

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The maximum equivalent stresses on both models are observed around the joints of the landing gear struts, with Model 1 once again exhibiting increased equivalent stresses of around 160 MPa at 1700 N compared to around 24 MPa at the same applied force in Model 2. Minimal equivalent stresses are observed at the connecting points for the wheels as well as the mounting points to the aircraft, as shown in Figure 8. In Figure 8, equivalent von Mises stress graphs are given for both Model 1 (a,c) and Model 2 (b,d). From the figure, (a) shows equilateral stress in Model 1, (b) shows equilateral stress in Model 2, (c) shows the graph of equilateral stress and force of Model 1, and (d) shows the graph of total deformation and force of Model 2.

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As seen in Figure 9, the principal stresses observed are rather uniform over the entirety of Model 1, while they are concentrated around the joints of the added support structure in Model 2,; however the magnitude of these stresses is higher in Model 1 at 150 MPa at 1700 N, while it is 7.2 MPa in model 1. In Figure 10, the maximum principal stress graphs are given for both Model 1 (a,c) and Model 2 (b,d). From the figure, (a) shows maximum principal stress in Model 1, (b) shows maximum principal stress in Model 2, (c) shows the graph of maximum principal stress and force of Model 1, and (d) shows the graph of maximum principal stress and force in Model 2.

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The concentrations of equivalent elastic strains on the model in Figure 11 are similar to those of equivalent stress, around the regions where the struts of the landing gear are joined to the central mounting piece. with the minimum strains being similarly distributed as well. In Model 1, the strain at 1700 N is seen to be 0.9 mm/mm, while in Model 2 it is 0.14 mm/mm. Equivalent elastic strain for Model 1 (a,c) and Model 2 (b, d) is given in Figure 11. Here, (a) shows equilateral strain in Model 1, (b) shows equilateral strain in Model 2, (c) shows the graph of equilateral strain and force of Model 1, and (d) shows the graph of equilateral strain and force in Model 2.

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Lastly, the factors of safety of the two models are shown in Figure 12, where it can be seen that the FoS for Model 1 drops below around 1100 N of force, which is what led to a requirement for a better design. Model 2′s FoS remains above 4 even for the maximum simulated load of 1800 N, rendering it safe for commercial usage. In Figure 12, the comparison between the factors of safety for Model 1 (a) and Model 2 (b) is shown. Here, (a) shows the graph of FoS and force of Model 1 and (b) shows the graph of FoS and force of Model 2.

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Something that is noticeable in all of the graphical results for the experiment is the linearity of the curves. Generally, with stress and strain curves we expect to see some plastic behavior (nonlinearity) at higher stresses; however it is not seen in this study. This is likely due to the strength and material properties of CFRP, as other testing and experimentation conducted in regard to the stress–train characteristics of CFRP have suggested that the material tends to stay in the elastic region for a considerable range of applied stress. Essam et al. [26] studied damage in carbon fiber composites using numerical analysis and vibration measurements; the stress-–strain curve of CFRP from said study is given in Figure 13. The results show that the carbon–flax hybrid material reduces vibration amplitude and frequency compared to other materials. Other studies have also shown that CFRP and similar materials deviate from elastic behavior under stress loads and forces much higher than those being exerted in this experiment. Hence, it may be concluded that the linear behavior of the graphs is not abnormal given the material and load in consideration.

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5. Modal Analysis

Modal analysis is a technique used in structural and mechanical engineering to study the dynamic characteristics of structures or mechanical systems. The primary focus of modal analysis is on determining the natural frequencies, mode shapes, and damping ratios of a system.

Mode shapes represent the spatial patterns of deformation exhibited by a structure at its natural frequencies. These patterns illustrate how different parts of the structure move relative to each other during vibration. They may be real or complex and each of them corresponds to a natural frequency. Natural frequencies are the frequencies at which a structure or component naturally vibrates when disturbed. The determination of modal frequencies is a key outcome of modal analysis. Each mode has its associated modal frequency, and these frequencies are crucial in understanding the dynamic behavior of the structure. The modal frequencies are dependent on the physical properties of the structure, including mass, stiffness, and damping.

The mass distribution of a structure influences its natural frequencies and mode shapes. Heavier components tend to have lower natural frequencies, and the distribution of mass affects the mode shapes. Stiffness is a measure of how a structure resists deformation; higher stiffness leads to higher natural frequencies and influences the mode shapes by determining how the structure deforms under dynamic loading. Damping affects the decay of vibrations. The level of damping influences both the natural frequencies and the shapes of the mode, as higher damping results in faster dissipation of energy. The spatial distribution of mass, stiffness, and damping properties across a structure plays a crucial role in defining mode shapes. Different regions of the structure contribute differently to each mode of vibration.

Constrained and free modal analysis are two approaches used in the field of structural dynamics to study the natural modes of vibration of a mechanical system. Free modal analysis examines the natural modes of vibration of a structure without imposing any restrictions on its movement. This approach is used to obtain crucial information such as natural frequencies, mode shapes, and damping ratios, providing a comprehensive understanding of how the structure naturally responds to dynamic loads. The values for natural frequencies obtained from free modal analysis are shown in Table 9. The contours are shown in Figure 14. For these models, the first three frequencies are zero because they represent translation in the x, y, and z axes. The next three represent rotation in the x, y, and z axes. Figure 15 shows constrained analysis at various frequencies. Here, (a) shows constrained modal analysis at 386.79 Hz frequency, (b) shows constrained modal analysis at 410.5 Hz frequency, (c) shows constrained modal analysis at 491.33 Hz frequency, (d) shows constrained modal analysis at 499.9 Hz frequency, (e) shows constrained modal analysis at 1174.1 Hz frequency, and (f) shows constrained modal analysis at 1221.1 Hz frequency.

Table 9 Natural frequencies.

Mode	Frequency (Hz) free modal	Frequency (Hz) constrained
1	0	386.79
2	0	410.5
3	0	491.33
4	4.81E−04	499.9
5	1.16E−03	1174.1
6	1.71E−03	1221.1
7	253.12	1677.9
8	735.29	1701.6
9	910.77	1722.5
10	954.94	1781.1
11	1173.8	2330
12	1281.2	2375.8
13	1459.2	2578.6
14	1524.4	3073.1
15	1574.8	3092
16	1779.8	3226

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Constrained modal analysis, in contrast, involves restricting or constraining specific degrees of freedom or directions of movement within a structure. By introducing constraints, it can be studied how dynamic behavior is influenced by boundaries, supports, or connections. This method is particularly valuable for detailed investigations, helping identify modes of vibration that are affected by the applied constraints. Constrained modal analysis aids in understanding the impact of specific components on the overall structural dynamics, contributing to the optimization and refinement of mechanical systems. The values for natural frequencies obtained from free modal analysis are shown in Table 9. The contours are shown in Figure 14. A fixed support is added as a constraint shown as Figure 13. The results of free modal analysis are given in Figure 14. Here, (a) shows free modal analysis at 253.12 Hz frequency, (b) shows free modal analysis at 735.29 Hz frequency, (c) shows free modal analysis at 910.77 Hz frequency, (d) shows free modal analysis at 954.94 Hz frequency, (e) shows free modal analysis at 1173.8 Hz frequency, and (f) shows free modal analysis at 1281.2 Hz frequency.

6. Impact Analysis

Impact analysis is essential to test the reliability and safety of landing gear. This part of UAVs is directly affected in case of a crash, so its reliability is important. To perform this analysis, impact velocity has been taken from a range of 2–8 m/s.

6.1. Modeling Setup

As it was analyzed in static analysis that Model 1 failed after 1000 N of stress, only Model 2 was considered for impact analysis. A distributed mass of 170 kg is applied on the top horizontal surface of the landing gear. Two blocks are attached at the base of the landing gear to represent wheels, and a solid block is added to represent ground. Figure 16a represents the complete body of the simulation geometry. The mesh of the geometry is depicted in Figure 16b.

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To improve the results of the analysis and provide as much realistic environment as possible boundary conditions were used such as standard earth gravity. To ensure the movement in the horizontal direction is restricted and to strictly study the vertical impact by applying a velocity in the downward direction, fixed supports are applied on mounting holes and at the side connected to the aerial vehicle as shown in Figures 17c, 17d, and 17f. The fixed support shown in Figure 17f is applied on both ends of the landing gear. The values of impact velocity range from 2 to 8 m/s. A distributed mass of 170 kg is applied at the top horizontal part of the landing gear. The ground is rigid. These boundary conditions are represented in Figure 17.

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As it was observed in static analysis for a stress of about 1700 N, the landing gear had a FoS greater than 1. Considering Standard Earth gravity, that is, 9.81 ms^-2, it is equal to 173.4 kg. Thus, 170 kg of distributed mass was applied at the top horizontal surface. All motion in the horizontal plane is restricted and friction is neglected. The end time was taken as 0.01 s and the time step was 0.9 s. The ground was assumed to be rigid.

The material used for the analysis is a composite called CFRP as it was used in other analyses. For analysis in LS-Dyna, explicit materials are used that also take into account other properties such as temperature, strain rates, and time-related properties. These properties ultimately improve the quality of the analysis.

For impact analysis mesh element size was used to be 4 mm and defeaturing size was taken to be 4 mm. It was because the quality of refined mesh improves the accuracy of the results.

7. Results and Discussions

The results generated in this study were equivalent to von Mises stress, maximum principal stress, total deformation, directional deformation, and shear stress. Results of the impact analysis were graphed at 2, 4, 6, and 8 ms^-1. Their comparisons are given below.

The maximum value of equivalent von Mises stress for 2 m/s initially increases in a linear manner and then decreases in a similar manner. As the impact velocity increases, for 4 m/s the initial pattern is almost similar but after decreasing the equivalent stress shows nonlinear behavior. This characteristic exists in graphs for other larger impact velocities, and it can be seen in Figure 18. The maximum values of equivalent von Mises stress increase with the increase in impact velocity. The minimum values of equivalent stress remain zero throughout the graphs.

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The maximum principal stresses have a similar pattern to equilateral stress for maximum values but for minimum values, they have a mirrored pattern and increase in the decreases in a negative direction. The graphs follow the same pattern of initially increasing linearly and decreasing then behaving nonlinearly. It happens for both maximum and minimum values. The difference being that maximum values increase in the positive direction to make the pattern while minimum values decrease in the negative direction to make the pattern. The graphical results of the maximum principal stress are given in Figure 19.

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The total deformation graphs for impact velocities from 2 to 8 m/s are given in Figure 20. A similar pattern can be observed in them. They show a linear increase initially and then a similar linear decrease in deformation. Finally, after decreasing it starts increasing again in an almost linear manner and keeps on increasing. This behavior is similar throughout all impact velocities. The maximum values of the deformation increase with an increase in the impact velocity.

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The shear stress has a similar pattern to equivalent stress and maximum principal stress. It also increases linearly initially and then decreases followed by a nonlinear behavior. The particular behavior observed here is that it forms an almost mirrored behavior using minimum values of shear stress in the negative direction. The graphical results of the maximum principal stress are given in Figure 21.

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The equilateral stress, maximum principal stress, shear stress, and total deformation at an impact velocity of 8 m/s are given in Figure 22. It can be seen in Figure 22a that the equilateral von Mises stress mostly acts in the skeletonized area of the landing gear. Maximum principal stress is spread almost throughout the landing gear but it can be seen concentrated at some places in the skeletonized area. The shear stress is spread all over the landing gear, but a couple of concentrated parts can be observed in curves in the skeletonized part. The total deformation is found to be concentrated in the top horizontal part of the landing gear which would be in contact with the UAV. It decreases as it moves downward in the landing gear. At the bottom, it increases a bit where the wheels would be attached.

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The FoS decreases as the impact velocity increases, but even at the maximum velocity of 8 m/s, it is recorded to be greater than 1. These values can be observed in Table 10, and the graph is illustrated in Figure 23.

Table 10 Factor of safety (FoS).

Impact velocities (m/s)	Factor of safety (FoS)
2	6.9447
4	2.7714
6	1.1456
8	1.355

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8. Conclusion

The landing gear of RQ-7B was taken as a reference to determine the advantage of the use of composite material such as CFRP for the landing gear of UCAVs. Two models of the landing gear were designed for this purpose. These models were tested under static structural analysis and impact analysis using impact velocities from 2 to 8 m/s to perform a comparison of their factors of safety. Model 1 is the replication of the reference model, and Model 2 is the improved skeletonized landing gear. The landing gears are imitated to determine equivalent von Mises stress, shear stress, maximum principal stress, and total deformation. From the static analysis, Model 2 demonstrated a much higher FoS than Model 1. The FoS of Model 1 decreases below 1 under higher velocities. For impact analysis using LS-DYNA in ANSYS, only Model 2 was considered. Under realistic boundary and loading conditions analysis was performed. Results established the overall FoS of Model 2 greater than 1. The stresses produced during this analysis proved to be nonlinear but overall maximum stresses were within the tolerable range of the landing gears, that is, less than ultimate tensile strength. From both analyses, it was observed that stresses increase with the increase of impact velocity, and the FoS decreases. All the static structural analysis, the modal analysis and the impact analysis proved Model 2 to be better suited as a landing gear than Model 1 as it has a higher FoS and can bear higher stresses than Model 1. The current scope of the research focuses on simulation-based analysis. To ensure the accuracy and reliability of the simulation results, authors extracted material properties of the carbon fiber from literature and used realistic parameters such as boundary conditions to ensure the validity of the results. Similar results were observed in Swati’s study which also validates the results [10].

Data Availability Statement

All data needed to evaluate the conclusions in the paper are present in the paper. No additional material or data is needed to replicate the findings reported in the manuscript.

Conflicts of Interest

The authors declare no conflicts of interest.

Funding

This study was supported by the Sultan Qaboos University, , RF/--/ENG/ECE/25/090.

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