# Multi-Objective Design Optimization of the Reinforced Composite Roof in a Solar Vehicle
## 3 Results and Discussion
### Grid Topological Optimisation  
In Table 7, a second comparison between configurations is reported. It also deals with the best solutions detected in terms of geometry and shapes at the level of basic units (Table 5) but extends results on the mock-up case. In particular, the laminate with rectangular holes where compared with quadridirectional grids in different configurations. Having demonstrated a certain appropriateness (measured through IC) for a specific configuration at the level of basic unit does not necessarily mean, in fact, that this rank remains the same on the mock-up. Such a fact immediately emerges from the table making clear that the laminate with rectangular holes (IC = 0.25) is no longer convenient.  
Having also demonstrated the convenience of using, as general design concept, a grid structure where an upper orthogonal grid (on which the solar panels are laid) are reinforced by a series of diagonal crosses, a different topological optimization study was carried out with respect to the definition of the (lower) grid in terms of number of elements and their arrangement.  
Without entering in unnecessary details, Table 8 exhibits the impact of diagonal crosses at the level of mock-up, both as number, distribution and crosses angles.  
\begin{table}
\begin{tabular}{l l l l l l l l l l l} \hline \hline
**Configuration** & & \multicolumn{6}{c}{**Number of Crosses**} \\ \hline  & & **1** & **1\({}^{1}\)/\({}_{3}\)** & **1\({}^{1}\)/\({}_{3}\)** & **1\({}^{1}\)/\({}_{2}\)** & **1\({}^{1}\)/\({}_{2}\)** & **2** & **2** & **4** & **4** \\ \hline \multirow{3}{*}{Width Size} & Upper grid & \multirow{3}{*}{30} & \multirow{3}{*}{30} & \multirow{3}{*}{30} & \multirow{3}{*}{30} & \multirow{3}{*}{30} & \multirow{3}{*}{30} & \multirow{3}{*}{30} & \multirow{3}{*}{30} & \multirow{3}{*}{30} & \multirow{3}{*}{30} \\  & (mm) & & & & & & & & & & \\  & Lower grid & \multirow{3}{*}{30} & \multirow{3}{*}{28} & \multirow{3}{*}{28} & \multirow{3}{*}{23.5} & \multirow{3}{*}{23.5} & \multirow{3}{*}{20} & \multirow{3}{*}{20} & \multirow{3}{*}{10.5} & \multirow{3}{*}{10.5} \\  & (mm) & & & & & & & & & & \\ Load Direction & \multirow{3}{*}{x or y} & \multirow{3}{*}{x} & \multirow{3}{*}{y} & \multirow{3}{*}{x} & \multirow{3}{*}{y} & \multirow{3}{*}{x} & \multirow{3}{*}{y} & \multirow{3}{*}{x} & \multirow{3}{*}{y} \\  & & & & & & & & & & & \\  & & & & & &  
The beam width in upper grids remains 30 mm (to conveniently host the solar cells), but changes affect the lower ones (from 14 to 50 mm) according to the condition of weight conservation. Spacing parameter (in Tables 8 and A2) provides information on the distance between beams on the lower grid: reducing the distance increases the number of beams (and crosses as reinforce) but, on the other side, as said, reduce their width saving the total weight. Finally, unlike the first analyses on the geometric parameters, where an automatic change for (almost) all the parameters was possible, in these further investigation configurations often involve the development of specific CAD models. Thus, several actions were done manually.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Configuration** & \multicolumn{4}{c}{**Quadridirectional Grid**} \\ \hline  & **Rectangle** & **Low** & **Medium** & **High** \\ \hline  & & & & \\ Lowest Frequency (Hz) & 11.4 & 12.3 & 12.9 & 13.8 \\ Flexural stiffness (N/mm) & 7.7 & 4.4 & 3.5 & 3.6 \\ Torsional stiffness (N mm/rad) & 1851 & 1960 & 2090 & 2665 \\ Element Weight (kg) & 2.090 & 2.047 & 2.031 & 2.028 \\ \hline
**Performance Index** & **0.25** & **0.27**