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manual-structuralmechanicsmodel-elements.tex

\subsection{Structural Elements\index{Elements!Structural}}
\subsubsection*{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}

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