\section{Problem statement}

\begin{frame}
\frametitle{3D body geomery}

\begin{columns}
\begin{column}{0.60\textwidth}
\begin{figure}
		\includegraphics[width=1.00\textwidth]{../Figures/3dbody_l.eps}
\end{figure}
\end{column}
\begin{column}{0.40\textwidth}
\begin{flalign*}
&\Gamma   =\Gamma_0 \cup \Gamma_u \cup \Gamma_t \cup \Gamma_c \\
&\Gamma_c = \Gamma_c^t \cup \Gamma_c^0
\end{flalign*}
\end{column}

\end{columns}
\end{frame}

\subsection{Weak Form}\label{Weak Form}

\begin{frame}[fragile]
\frametitle{Weak form of equilibrium equations}
Find $\bu \in \mathcal{U}$ such that $\forall \bv \in \mathcal{V}$

\begin{equation*}
	\int_{\Omega} \bsigma (\bu):\bepsilon (\bv)\ d\Omega = \int_{\Omega} \bb\cdot\bv \ d\Omega + \int_{\Gamma_t} \bar{\bt}\cdot\bv \ d\Gamma + \int_{\Gamma_c^t} \bar{\bt}_c \cdot\bv \ d\Gamma_c^t
\end{equation*}

where :

\begin{equation*}
	\mathcal{U} = \left\{\bu|\bu \in \left(H^1\left(\Omega\right)\right)^3,\bu = \bar{\bu}  \text{ on }  \Gamma_u \right\}
\end{equation*}

and

\begin{equation*}
	\mathcal{V} = \left\{\bv|\bv \in \left(H^1\left(\Omega\right)\right)^3,\bv = 0  \text{ on }  \Gamma_u \right\}
\end{equation*}

\end{frame}