# Multi-Objective Design Optimization of the Reinforced Composite Roof in a Solar Vehicle
## Materials and Methods
### Design and Simulation Tools  
3D CAD modelling was performed in SolidWorks (by Dassault Systemes, Velizy-Villacoublay, France). Ansys Workbench ver. 18.1 platform (by ANSYS, Inc., Canonsburg, Pennsylvania, USA) was used for structural analysis of composites (by an ACP toolkit) and for design optimization (Design Exploration) by the direct optimization features and the screening and response surface method.  
Specifically, in 3D modelling solid parts were suppressed with the scope to manage 3D surfaces. Discretization was done by shell elements (FE), quadrangular of quadratic order with 8 knots, preferred for precision. After mesh convergence tests, the maximum size for FE was set at 3 mm (in the case of basic units), employing 12,000-18,000 FE for meshing the different configurations.  
In accordance with reality, the thickness of sandwic was made variable along the section by creating cut-off selection rules in ACP and assigning them to the PVC core. The same technique was adopted to manage edges and intersections. A visual example of effects of expedients used for the correct discretisation of composite structures is reported in Figure 4 in the case of rectangular grid. The \(500\times 500\) mm base section, consisting of \(4\times 4\) squares (representing the solar cell frames) are shown highlighting differences in thickness and the final mesh with implemented these changes.  
The so-called single-layered shell method [33], instead of many others (e.g., stacked shell [34]), was chosen and implemented for discretizing the layout. This simplification quite common in analyzing composites in the case of large and complex structures, permits to quickly investigate the main phenomena at the level of macroscale. With a proper conversion in properties, it reduces a multilayered laminate to an equivalent single layer laminate and use shell elements all along the surface with integration points (IP) throughout the thickness [33]. Specifically, in the case an IP was set per each of the seven layers: no additional IP was used to investigate the six interfaces between layers. In such a way it was possible to drastically limit the number of FE speeding up the simulation focusing the attention on in-plane phenomena [33; 34; 35].  
However, this methodological limit has no practical effect on the present study since the roof has no global structural functions [35]. The vehicle was designed around a lower monoc  
Figure 4: Details in sandwich discretization (in the case of rectangular grid): (**a**) the \(500\times 500\) mm base section; (**b**) vertical beams over respect to the horizontal ones; (**c**) sides where the thickness of the sandwich must decrease; (**d**) final mesh (also showing the thickness changes).  
structure (Figure 1b). A rigid frame on the composite structure guarantees the fixing and solidity of the roof which, practically, in addition to its own weight, must only support the solar cells (\(\sim\) 1.2-1.5 kg/m\({}^{2}\)).  
From the Ansys internal library, material models labelled as \"Epoxy Carbon UD (230 GPa) Prepreg\", \"Epoxy Carbon Woven (230 GPa) Prepreg\" and \"PVC Foam (80 kg m\({}^{-3}\))\" were chosen for, T1000, T800 and PVC respectively, but default properties were changed in accordance to Table 1. ACP toolkit permitted to build exact layouts as shown with Table 2. In the grid configuration, in order to correctly orient the fibers according to the direction of the single beam, it was necessary to divide the grid in section subgrouping beams characterized by a same orientation in the fibers.