\section{Discussion}
\label{sec:discuss}

Assumption were made in this design process, and they can probably modify the real behavior of the proposed beam. First, in the FEA, the tire pressure have been transformed into 3 force applied on 3 point for each wheel. This allow us to reduce the complexity of the FEA model and to have faster results. However, a tire is a flexible surface, and a better approximation of its force would be a rectangular region where a pressure is applied. To create such a model, more data regarding the properties of the tire would be required. A better tire simulation can probably change some results, the pressure of the vehicle can be better divided between the support walls and in this case reduce the buckling and the deformation observed during the FEA. In this regard, treating the load from the tires as a series of point loads can be regarded as a safety measure.

Now, looking at the results through the reality perspective, some interesting points can be raised. All the laminates are very thin. The FEA shows that they will handle the loads and forces applied on them, but considerations regarding different damage that can happen during production or transport have not been regarded. Such a bridge will probably be exposed to extreme condition, add a protective shell for the composite or a thicker layup should be considered. This shield layer can increase the mechanical properties of the beam and protect from rock, humidity, heat, or an uneven ground when setting up the bridge.

It is also important to note that the bridge is not symmetrical in the vertical direction. This has facilitated a greatly reduced weight, as the thickness of the bottom surface could be drastically reduced. However, this also implies that the capacity of the bridge will be massively reduced if it is placed the wrong way. If the beam is to be produced, the surfaces must be clearly marked to indicate which side is up, as it will likely fail under its own weight if transported or carried upside down. To mitigate this problem, a custom-made holder that properly secures the beam to the vehicle, and provides support during transportation could be created. Local reinforcement of the ends of the beam may also be a viable way to reduce the danger of breakage during transportation and mounting.

It is possible to test the buckling in a an analytical way, nonetheless this analysis include to solve a second-order, linear ordinary differential equation\cite{matte4}. The expense of time to solve such an equation has been regarded to be is too long compared to the increased precision. Thus, the FEA has been judged to be enough.

\subsection{Manufacturing}

The manufacturing processes for sandwich materials can be the same as those used for other composite materials or specific processes. For manufacturing the solution chosen. The more efficiency way seems to create each sandwich and then assemble them together using plastic welding or addition of joints in each junction.  

Each sandwich part can be created using wet or dry moulding techniques. For wet moulding could use contact molding, vacuum molding, compression molding could be used. For a dry moulding, it is possible to use preimpregnated laminates. Glue technique could be used as well, however to determine which assembly technique is the best for our composite, experimentation would be required. This assembly can modify the mechanical properties, some further research would have to be done if the beam were to be produced.

\section{Conclusion}

\begin{table}[h]
    \centering
    \caption{Optimal beam structures determined by finite element analysis. The letter ''f'' indicates a foam layer.}
    \begin{tabular}{c c c c c c c c}
    \toprule
    \multirow{2}{*}{Beam} & & Top & Bottom & Vertical &  Eigenvalue, 1st & \multirow{2}{*}{$f_E^{\max}$} & \multirow{2}{*}{Mass [kg]}\\
    & & Surface & Surface & Supports & buckling mode & &\\
    \midrule
    \multirow{2}{*}{B} & Orientation & \makecell{[0, 90, 0, 90]$_s$} & [0]$^6$ & [9.5, -9.5]$_s$ & \multirow{2}{*}{1.36} & \multirow{2}{*}{0.002} & \multirow{2}{*}{91.8} \\
     & Thickness & \makecell{[0.5, 0.2, 1.5, 0.1]$_s$} & [0.5]$^6$ & [0.4, 0.4]$_s$ & & \\
     \midrule
     \multirow{2}{*}{D} & Orientation & [0, 90, f]$_s$ & [0] & [9.5, -9.5, f]$_s$ & \multirow{2}{*}{1.70} & \multirow{2}{*}{0.03} & \multirow{2}{*}{57.6}\\
     & Thickness & [0.4, 0.1, 5]$_s$ & [0.6] & [0.1, 0.1, 5]$_s$ & & \\
     \bottomrule
    \end{tabular}
    \label{tab:conclude_layups}
\end{table}

This report show all the thinking and the step through the creation of this car bridge beam. An analytical analysis has been created, using this algorithm one solution have been chosen. Then this solution has been processed through Abaqus software to confirm that the analytical result were valid and to further optimize the solution while taking into account buckling. 

On a deformation and classic material failure, the analytical solution fulfilled all the criterion. However, the buckling analysis showed a huge risk of breakage. Even if, like described in part \ref{Linear_Buckling_Analysis}, we have no actual information on the magnitude of displacements. With some experiments, it could have been possible to determinate these magnitudes and to decide if this solution was feasible or not. Further optimization by FEA resulted in beam B, presented in Table \ref{tab:conclude_layups} with a greatly reduced weight. 

For the second solution, a sandwich structure has been developed. The same geometry is kept, but with a different layups. This structure is based on two skin of carbon/epoxy (a) composite and a core of PVC foam. The structure resulting from the optimization without a sandwich solution was used as an initial configuration, before further optimization with a sandwich solution. The new solution this time validate all the constraint of the problem and is even better than the last one with a lighter design.

The two solutions presented in Table \ref{tab:conclude_layups} are therefore optimal for different conditions. Beam B is more robust with regard to handling and transportation, but with a weight below \SI{100}{\kilo\gram} it can still be regarded as portable. Beam D is optimized for low weight, and can easily be transported by a single person if one end is mounted on wheels, however it is extremely fragile if handled incorrectly, and may be poorly suited to be mounted on uneven ground. This may be solved by good design of the end ramps or local reinforcement of the ends.

This solution has now to be assembly with the ramp to the two extremity and tested in real conditions.