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manual-structuralmechanicsmodel-elements.tex
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rAKA akantu
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
}
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