# Structural Optimization of MicroMED Dust Analyzer
## 2 Materials and Methods
The material depletion of the design domain (Figure 3), i.e., the only region eligible for the TO, was performed by generating constant height ribs in the direction perpendicular to the OB floor. No voids nor holes throughout the height of the ribs were allowed for the final design. The loading condition applied for the optimization was a quasi-static acceleration of 1000 m/s\({}^{2}\) on each lumped mass, in each direction. Each iteration for Model A concluded only when the result produced a new model having the first natural frequency fulfilling the design dynamic requirement, thus when the first three resonances were equal or larger than the current OB ones. On the other hand, for the Model B development, the optimization was interrupted only when the optimal material distribution was identified, i.e., the one providing the highest value possible for the component's natural frequencies. In this case, the design constraint was set on the mass budget spent on the ribs grid, imposed equal to the current OB one. Moreover, as pointed out in Figure 2, following the TO, a post-processing activity was performed on the optimal solutions, with the aim of smoothing and homogenizing the optimal ribs grid towards a milling/Electrical Discharge Machining (EDM) manufacturing process. Preliminarily, a FEM of the current OB was developed in PTC Creo Parametric/Simulate environment to define the baseline performance to be exploited during the TO. As shown in Figure 4, pin constraints were placed at the OB peripheral holes to simulate the MicroMED instrument mounting interface on the Dust Suite, the ESA ExoMars 2022 lander surface platform. Mesh refinement was applied to the FEM, obtaining an overall of 32,371 finite elements, split between 28,704 solid tetrahedrons and 3667 shell triangles. Likewise, the FEMs for the optimal and post-processed OBs were developed. The performance of the models was estimated relying on the FEAs set:  
* Modal analysis aiming to estimate the first five natural frequencies;
* Quasi-static analyses applying a load of 1000 m/s\({}^{2}\), probing the state of stress distribution of the models considering three different loading directions (i.e., X, Y, and Z according to the reference frame reported in Figure 4) and resembling the excitation expected during the takeoff and landing phases of the mission; and
* Thermoelastic analyses in either non-operational (i.e., the cold case, considering a temperature shift from the reference +20 \({}^{\circ}\)C to the target \(-40\) \({}^{\circ}\)C) or operational (i.e., the hot case, likewise the cold case but within the range +20 \({}^{\circ}\)C and +40 \({}^{\circ}\)C) conditions. The figure of merit to state the quasi-static and thermoelastic FEAs goodness was the Margin of Safety (_MoS_). The _MoS_ was evaluated to highlight the resistance of the  
Figure 4: OB model without (**a**) and with (**b**) the stiffening ribs grid. FEAs features (i.e., lumped masses, rigid links, shells, and constraints) are highlighted. The mesh was applied to the model (**c**). mechanical component during the assessments, relying on the Von Mises yield criterion for ductile materials. The _MoS_ was computed referring to the following formulation:  
\[MoS=\frac{\sigma_{\text{YS}}}{\eta\cdot\sigma_{VM}}-1 \tag{1}\]  
In the equation, \(\sigma_{\text{YS}}\) was the material yielding stress (i.e., 503 MPa for the AI/075-T6), \(\eta\) was the admissible safety factor (i.e., 1.5 as reported in the ECSS-E-ST-33-01C design standard [28]), and \(\sigma_{VM}\) was the maximum Von Mises stress resulting from the simulation. The assessment was considered satisfactory with positive _MoS_. Moreover, the thermal deformations induced within the temperature ranges were probed both for the current and the optimal OBs. The intent was to quantify the impact of the temperature on the structural stability of the MicroMED hardware, i.e., estimating the misalignment between the laser light and the aerosol flux due to the thermal deformations of the mechanical parts for the cold and hot cases.