manual-structuralmechanicsmodel-elements.tex
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manual-structuralmechanicsmodel-elements.tex
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			\section{Structural Elements\index{Elements!Structural}}

			\subsection*{Bernoulli Beam Elements\index{Elements!Bernoulli}}
			These elements allow to compute the displacements and rotations of
			structures constituted by Bernoulli beams. \akantu defines them for
			both 2D and 3D problems respectively in the element types
			\code{\_bernoulli\_beam\_2} and \code{\_bernoulli\_beam\_3}. A
			schematic depiction of a beam element is shown in
			Figure~\ref{fig:elements:bernoulli} and some of its properties are
			listed in Table~\ref{tab:elements:bernoulli}.

			\note{Beam elements are of mixed order: the axial displacement is
			linearly interpolated while transverse displacements and rotations
			use cubic shape functions.}

			\begin{figure}[htb]
			\centering
			\includegraphics[width=0.3\textwidth]{figures/elements/bernoulli_2}
			\caption{Schematic depiction of a Bernoulli beam element (applied to
			2D and 3D) in \akantu. The node numbering as used in \akantu is
			indicated, and also the quadrature points are highlighted (gray
			circles).}
			\label{fig:elements:bernoulli}
			\end{figure}
			\begin{table}[htb]
			\centering
			\begin{tabular}{c\|cccc}
			\toprule
			Element type & Dimension & \# nodes &\# quad. points & \# d.o.f.\\
			\midrule
			\texttt{\_bernoulli\_beam\_2} & 2D& 2& 3& 6\\
			\texttt{\_bernoulli\_beam\_3} & 3D& 2& 3& 12\\
			\bottomrule
			\end{tabular}
			\caption{Some basic properties of the beam elements in \akantu}
			\label{tab:elements:bernoulli}
			\end{table}