*3.4. Computation*

After the definition of the numerical model, the analysis can be computed. In the authors' approach, computation was realized in three stages. In the first stage, the first 50 natural frequencies were calculated. Knowledge about these frequencies is vital during the aeroelastic validation of the project. In this stage, the model was computed for both no constraints and with constraints applied.

In the second stage of the computation process, the standard structural analysis was performed. Based on the results of this stage, it was possible to evaluate the overall designed structure and detect areas where some problems were expected.

The last computation stage was devoted to performing buckling analysis. This type of research allows the verification of the stiffness of components and finds some potentially problematic elements.

Based on these results, the user can decide if the project needs to be redesign, what require only some parameters values change, thanks to the generative modelling, or to approve the project for the next stage of the designing/manufacturing process.

In the next part of the paper, the authors present how the presented methodology can be used in the use case of unique aircraft design.

## **4. Use Case**

In this part of the paper, the authors present how the developed methodology can be applied in the real case—TWIN STRATOS UAV. TWIN STRATOS is part of the UAV family and was developed as part of the LEADER project implemented by an international consortium consisting of SkyTech eLab LLC, Silesian University of Technology, Universities of Warsaw, and Norwegian Research Center. The section presents a short description of the TWIN STRATOS UAV and further steps that have been made during the design and validation process.

The TWIN STRATOS project is a stratospheric unmanned aerial vehicle (UAV) family project designed for high atmospheric and stratospheric measurements of air pollution. The form of designed UAV family member is shown in Figure 12. The wingspan is 24 m with a 30 kg total payload. Thanks to the use of an electrical drive system and photovoltaic panels, the flight duration, in theory, is unlimited.

**Figure 12.** Visualization of the STRATOS unmanned aerial vehicle (UAV).

#### *4.1. Strain, Stresses and Buckling Analysis*

4.1.1. CAD Model Elaboration

Based on the project assumption, in the first step, the geometry of the UAV was designed. In this process, some load-bearing elements, i.e., spars, ribs, stinger, were intended as part of the generative model. To make this possible, the authors prepared a series of generative models for individual component types. Each model contained geometrical information about different designed elements' shape types, control rules, parameters, etc. As a main geometrical input, airfoil curve was used. This geometrical input was used because it is relatively easy to extract this type of curve along the wing. In the case of a fuselage as the geometrical input, a cross-section profile was used. Using the generative modelling technique allows quick changes to be made in the basic load-bearing structure if it is necessary, which makes the whole process of conceptual design much more comfortable and faster in comparison to the traditional design process. The prepared CAD model for numerical validation is presented in Figure 13.

**Figure 13.** The CAD model prepared for the FEA analysis.

### 4.1.2. Numerical Model Preparation

After geometry development, the phase of the numerical validation of the project must be performed. As presented in the previous section, the delivered CAD geometry must be processed to be usable for the study. In Figure 14, general and detailed images presenting the TWIN STRATOS after the simplification and discretization process are shown. As can be seen, different components have different colors that correspond to the other composite structure, and which are related to the different material and structural properties. All preparation was related to the numerical model, the computation process, and the postprocessing of the results was conducted in Altair HyperWorks software.

**Figure 14.** The simplified and discrete model of the STRATOS.

## 4.1.3. Material Properties

In Table 1, material properties that were used in the study definition are presented. For following approach for the calculations, general material data based on manufacturers' data were adopted.


**Table 1.** Anisotropic material properties used in the study definition.

#### 4.1.4. Loads and Constraints Definition

Preliminary calculations of loads were made due to the similarity with the use of software supporting glider analysis. Unfortunately, the analysis did not allow modelling the case of a double-hulled aircraft due to the different nature of the application. The better weight distribution of the two-hull system ensures that the actual loads will be lower. Load calculations were made for successive heights, flight speeds, angles of attack and flight conditions. In the final stage, a load envelope was developed for the subsequent sections of the wing. The envelope covered the maximum loads recorded in each section, although in adjacent sections they occurred in other flight conditions. In most cases, the maximum loads occur in flight at maximum flight altitudes with high speeds and gusts. Such an envelope was used in the preliminary strength calculations. At the next stages, the calculations were made based on proprietary software, considering the weight distribution system of the two-hull aircraft, and then using the XFLR5 system.

According to the presented method of load application, the authors applied properly calculated loads as well as constraints. An example of applied restraints added to fuselage mounting rings is presented in Figure 15.

## 4.1.5. Obtained Results

The prepared model was used to perform the computation procedure. In the first step, natural frequencies were calculated for both no constraints and with constraints. An example of the commutated natural frequency is shown in Figure 16. In the process, the first 50 frequencies were calculated for further aeroelastic analysis.

In the second step, standard structural analysis was performed. In this case, two analyses were conducted, the first one for the positive loads' envelope, and the second for the negative loads' envelope. As a result of this stage of the study, we obtained colored stress and displacement maps. Examples of the obtained results are presented in Figures 17 and 18.

**Figure 15.** An example of applied restraints.

**Figure 17.** Global stress plot.

**Figure 18.** Global displacement plot.

The last part of the computation process is buckling analysis used for stiffens and stability evaluation. An example of the result of this analysis is presented in Figure 19.

**Figure 19.** Example of stability lose in the central part of the UAV.

Based on the performed computations, it was possible to avoid some potential issues in the design. For example, the buckling analysis showed the area that needed to be revamped, because it is possible that in this area the UAV may lose stability and cause a crash. To address this issue, the authors, using generative modelling for honeycomb structures, changed the thickness to find out the proper value to fulfil the project's assumptions. In this case, the authors used the generative model as a tool to making models of the structure with different thickness. In the tests, the thickness of the filling layer of the sandwich structure was increased without changing the form of the filling. The study was intended to increase the viewer on the loss of stability in compressed structures. Finally, it finds out that in particularly endangered places 10 mm structure is an optimal value. The summary of the most important obtained results is presented in Table 2.



#### *4.2. Aeroelastic Analysis with Flutter Verification*

The mid-fidelity tool ASWING was used to model aircraft aeroelasticity [24,25] ASWING couples interconnected nonlinear (specifically, Bernoulli–Euler) beam models with a general extended lifting line approach. The ASWING software enables the calculation of aircraft deflections, axial strains and shear stresses, aircraft aerodynamic properties, and aircraft stability derivatives and eigenvalues based on input data, including geometric, structural, and aerodynamic parameters airfoil sections along the aircraft wing and other surfaces. During analysis, aircraft stability derivatives and eigenvalues were used because the different outputs were identified using other methods. The model used as the input to ASWING was calculated to form the parametric CAD model (Figure 20); material data assumed for analysis and load distribution were identified using XFLR5 [26]. The data were integrated into excel file and subsequently transferred to a proper format which was used as the input to ASWING (Figure 21).

**Figure 20.** Geometric model used for ASWING analysis.

**Figure 21.** Data processing sequence for aeroelastic analysis using ASWING.

The flutter speed and actual flutter frequency are indicated by one of the eigenvalues crossing over from left to right of the imaginary axis. Flight-dynamic instabilities (e.g., spiral mode) will also have eigenvalues on the right side of the imaginary axis, but these will typically be at a near-zero frequency and will have completely different eigenmodes.

The results of the initial analyses indicated the risk of flutter at a speed of 20 m/s, (Figure 22), which is a speed exceeding the operating speed. A sensitivity analysis was performed during the flutter analysis. The influence of the position of the wing mass was

investigated. The first simplified analysis assumed that the solar panels are positioned proportionally to the wing area. The model was then refined by adding mass points symbolizing solar panels at a distance of 0.4 of the wing chord from the leading edge. In the last iteration of calculations, the influence of shifting the mass of solar panels by 80 (mm) towards the leading edge was investigated. Sensitivity analysis showed the possibility of turning the critical flutter velocity in these cases to 25 and 35 m/s, respectively.

**Figure 22.** Eigenvalues of TWIN STRATOS UAV.

#### *4.3. Comparative Analysis of Morphic Control*

During the study, the main problem that should be solved is the considered design's aerodynamic performance. The airplane structure was reconstructed in XFLR5 software, as shown in Figure 23. The tests were similar to the aeroelasticity analyses (Figure 21) and carried out for various configurations of control systems [27].

The main aircraft wing was divided into several sections with differing chords and dihedrals. Different versions of roll control elements were taken into account. The following analysis compared three control options—classical with ailerons, tail control, wingtip twist morphing (Figure 24).

Figure 24 shows the distribution of the lifting force coefficient (Cl) in the given wing section as a function of the main wingspan and the tail wingspan measured from the symmetry plane for the roll operation for different angle of attack (ACA) (0◦; 5,5◦; 10◦).

The computational simulation results confirmed the legitimacy of applying innovative solutions, both integrated in the tail and morphic wingtips. In both cases, the new control configurations became even 10% more efficient in the entire range of attack angles [27].

**Figure 23.** TWIN STRATOS UAV model in XFLR5 software.

**Figure 24.** TWIN STRATOS UAV comparative analysis of roll operation for different steering arrangements. From above: ailerons, tail compliant trailing edge, wingtip twist morphing.
