# Multi-Objective Design Optimization of the Reinforced Composite Roof in a Solar Vehicle
## 3 Results and Discussion
### Multi-Objective Optimization Results at a Glace  
In line with results from similar investigations (as [36]), it is clear how the grid structures are preferable to perforated panels. It is also evident that a grid with a denser mesh is better than those of sparse one with an equivalent weight. However, although the comparisons give unambiguous indications when only mechanical properties are considered, additional criteria should be included. In fact, the optimized option as here detected, i.e., quadridirectional grid with crosses every 250 mm, could present (compared to less dense grids) additional challenges in its applicability such as:  
* Minor free surface for heat transfer, not permitting an efficient the solar cells cooling;
* Greater complexity in fabrication related to a larger number of basic elements (beams). These aspects were not including in the optimization since the beginning and are not considered. A preliminary estimation of the free surface carried out by Ansys with respect to two borderline grids showed a quite low variability (<10%): using a denser grid does not significantly affect the panels cooling. It also depends to the fact that, denser grids are necessarily made by tighter beams (since the precondition of equivalent weight). Regarding the composite roof construction, with an area of approx. 8.0 m\({}^{2}\), its manufacturing can represent a laborious task. A larger number of beams and crosses, to be made and glued, would be preferable only when mechanical properties were significantly better: it is not the present case. Table 9 reports an update in design solutions evaluation, taking into count of additional parameters and objectives of optimization. In particular, the maximum displacement when the lowest natural frequency occurs is included: those parameters have to consider in combination for better analyze the dynamic behavior of the structure. Furthermore, the table also introduces parameters, not strictly related to mechanical properties, as the area available for heat transfer and an indicator of producibility. While the exposed area may be directly detected by Ansys functionalities, an empirical index had to be defined for estimating the producibility, it was done in accordance with information from manufacturer, making its value proportional to the number of operations necessary to build composite structures. As a synthesis, a quadridirectional grid with crosses every 500 mm was adopted. In accordance with previous results, in fact, this structure exhibited good mechanical properties, better than both perforated sandwich panels (especially regarding the resonance frequency [37]), but also compared to an orthogonal grid, thanks to the presence of reinforcing beams in the diagonal directions [38]. However, its medium sparse grid does not entail the construction problems that can occur during production in the case of denser grids. Finally, since it was noticed that a slight increase in the mass of the angular grid provided positive benefits to the quadridirectional grids, it was also preliminary checked the effect of minor changes in the constraint of the minimum width for the orthogonal beams (=30 mm). The basic unit of 500 mm sides was examined, performing a further optimization in Ansys by varying the width of the orthogonal beams between 25 mm and 30 mm and diagonal beams between 30 mm and 50 mm. Since the condition of equal total weight, an increase in the mass of one grid, orthogonal or diagonal, decreases the other. In general terms, the best situation is present when widths