# Multi-Objective Design Optimization of the Reinforced Composite Roof in a Solar Vehicle
## 3 Results and Discussion  
### Shape Topological Optimisation  
In Table 5 a first comparison between geometries at the level of basic unit is reported in terms of performance index (IC) respect to their main dimensional characteristics (sizes).  
Specifically, in the case of laminates dimensions refers to the hole sizes as width (W), height (H) and filled radius (r) for a rounded rectangle or 1 st and 2 nd (A, B) axes for ellipsis.  
In the case of the grids, the dimensions refer to the width of beams that make up the structure: an upper orthogonal (0-90\({}^{\circ}\)) grid, reinforced by a lower diagonal (\(\pm\)45\({}^{\circ}\)) one. A value of 30 mm in width for the upper grid is fixed considering the need to sustain the singular solar cell. Both for laminates and grids 5.2 mm of thickness is fixed since the predetermined composite layout (Table 2).  
In terms of results, it should be noted that, together with the torsional and flexural stiffness, the first (lowest) natural frequency is also reported in the table. This value represents an indication of how sensitive the structure is to the effects of vibrations. The maximum displacement respect to the first natural frequency should be also considered representing the effect of vibrations in terms of intensity (not sensibility).  
By comparing the values of the performance index (IC), it is immediately evident that the best configurations are, in general, grid configurations (as Figure 2c,d) reinforced by several crosses (IC \(\geq\) 0.48) and, specifically, a quadidirectional configuration (IC = 0.79). Despite this, the option of manufacturing a laminate in a single body and then lightening it through holes could be taken into consideration provided the choice of rectangular (IC = 0.61), almost squared (-95 mm vs. 93 mm), and rather large holes (-8800 mm\({}^{2}\)) with rounded borders (-24 mm). In making these considerations, it should be also remembered that all these configurations are obtained keeping the same weight (w = 0.264 \(\pm\) 0.01 kg) as target and, consequently, the same amount of material.  
Outcomes from Table 5 also take into count, as a preliminary optimization (improved below), the way an upper orthogonal grid (orthogrid) can be reinforced by lower transversal crosses leading to double grid configurations. The most interesting options, between many others under consideration,  
\begin{table}
\begin{tabular}{l l c c c c c c} \hline \hline
**Configuration** & \multicolumn{3}{c}{**Laminate**} & \multicolumn{3}{c}{**Grid**} \\ \hline  & **Rectangle** & **Ellipsis** & **Orthogrid** & **Cross** & **Double** & **Coars** & **Quadridirection** \\ \hline Hole Size (mm) & & 94.7 & 95.0 & & & & \\  & 92.8 & 95.0 & & & & \\ Grid Width Size & Upper grid (mm) & & 23.7 & & & & \\  & Lower grid (mm) & & 40.7 & 30.0 & 30.0 & 30.0 \\  & & & & & & 23.5 & 14 \\  & & & & & & & \\  
are displayed in Table 6 where at the investigation level of the basic unit, the impact of a crescent number of crosses is analyzed. The same table also exhibits the effect of changes in cross angles.  
Results, as said, assumed that:  
* All beams in each specific grid have the same dimensions (i.e., width and thickness);
* These dimensions can vary (in general) between the upper and lower grids;
* The thickness, however, is fixed by the specific composite layout;
* The width of beams in the upper grid is fixed (with the scope to permit to sustain the solar cells);
* The width of beams in the lower grid is related to their number (since a constant weight).  
For each configuration, the table reports stiffness in the cases of application of (flexural or torsional) loads along X or Y axes. Differences are evident related the geometrical anisotropies of grids respect to these changes in the axes.