manual-structuralmechanicsmodel-elements.tex
No OneTemporary
Actions

Subscribers

None

File Metadata

	\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}