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element_class_triangle_3_inline_impl.hh
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rAKA akantu
element_class_triangle_3_inline_impl.hh
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/**
* @file element_class_triangle_3_inline_impl.hh
*
* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
* @author Mohit Pundir <mohit.pundir@epfl.ch>
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date creation: Fri Jul 16 2010
* @date last modification: Fri Dec 11 2020
*
* @brief Specialization of the element_class class for the type _triangle_3
*
*
* @section LICENSE
*
* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
*
* Akantu is free software: you can redistribute it and/or modify it under the
* terms of the GNU Lesser General Public License as published by the Free
* Software Foundation, either version 3 of the License, or (at your option) any
* later version.
*
* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
* details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
*
*/
/**
* @verbatim
\eta
^
|
x (0,0,1)
|`
| `
| q `
| ° `
x--------x-----> \xi
(1,0,0) (0,1,0)
@endverbatim
*
* @f{eqnarray*}{
* N1 &=& 1 - \xi - \eta \\
* N2 &=& \xi \\
* N3 &=& \eta
* @f}
*
* @f{eqnarray*}{
* \xi_{q0} &=& 1/3 \qquad \eta_{q0} = 1/3
* @f}
*/
/* -------------------------------------------------------------------------- */
#include "element_class.hh"
/* -------------------------------------------------------------------------- */
namespace
akantu
{
/* -------------------------------------------------------------------------- */
AKANTU_DEFINE_ELEMENT_CLASS_PROPERTY
(
_triangle_3
,
_gt_triangle_3
,
_itp_lagrange_triangle_3
,
_ek_regular
,
2
,
_git_triangle
,
1
);
/* -------------------------------------------------------------------------- */
template
<>
template
<
class
D1
,
class
D2
,
aka
::
enable_if_t
<
aka
::
are_vectors
<
D1
,
D2
>::
value
>
*>
inline
void
InterpolationElement
<
_itp_lagrange_triangle_3
>::
computeShapes
(
const
Eigen
::
MatrixBase
<
D1
>
&
X
,
Eigen
::
MatrixBase
<
D2
>
&
N
)
{
N
(
0
)
=
1
-
X
(
0
)
-
X
(
1
);
/// @f$ c0 = 1 - \xi - \eta @f$
N
(
1
)
=
X
(
0
);
/// @f$ c1 = \xi @f$
N
(
2
)
=
X
(
1
);
/// @f$ c2 = \eta @f$
}
/* -------------------------------------------------------------------------- */
template
<>
template
<
class
D1
,
class
D2
>
inline
void
InterpolationElement
<
_itp_lagrange_triangle_3
>::
computeDNDS
(
const
Eigen
::
MatrixBase
<
D1
>
&
/*natural_coords*/
,
Eigen
::
MatrixBase
<
D2
>
&
dnds
)
{
/**
* @f[
* dnds = \left(
* \begin{array}{cccccc}
* \frac{\partial N1}{\partial \xi} & \frac{\partial N2}{\partial
* \xi} & \frac{\partial N3}{\partial \xi} \\
* \frac{\partial N1}{\partial \eta} & \frac{\partial N2}{\partial
* \eta} & \frac{\partial N3}{\partial \eta}
* \end{array}
* \right)
* @f]
*/
dnds
(
0
,
0
)
=
-
1.
;
dnds
(
0
,
1
)
=
1.
;
dnds
(
0
,
2
)
=
0.
;
dnds
(
1
,
0
)
=
-
1.
;
dnds
(
1
,
1
)
=
0.
;
dnds
(
1
,
2
)
=
1.
;
}
/* -------------------------------------------------------------------------- */
template
<>
template
<
class
vector_type
,
class
matrix_type
>
inline
void
InterpolationElement
<
_itp_lagrange_triangle_3
>::
computeD2NDS2
(
const
vector_type
&
/*natural_coords*/
,
matrix_type
&
d2nds2
)
{
d2nds2
.
zero
();
}
/* -------------------------------------------------------------------------- */
template
<>
template
<
class
D
>
inline
Real
GeometricalElement
<
_gt_triangle_3
>::
getInradius
(
const
Eigen
::
MatrixBase
<
D
>
&
coord
)
{
auto
&&
coord1
=
coord
.
col
(
0
);
auto
&&
coord2
=
coord
.
col
(
1
);
auto
&&
coord3
=
coord
.
col
(
2
);
return
2.
*
Math
::
triangle_inradius
(
coord1
,
coord2
,
coord3
);
}
/* -------------------------------------------------------------------------- */
}
// namespace akantu
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