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element_class_segment_2_inline_impl.hh
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rAKA akantu
element_class_segment_2_inline_impl.hh
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/**
* @file element_class_segment_2_inline_impl.hh
*
* @author Emil Gallyamov <emil.gallyamov@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 _segment_2
*
*
* @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
q
--x--------|--------x---> x
-1 0 1
@endverbatim
*
* @f{eqnarray*}{
* w_1(x) &=& 1/2(1 - x) \\
* w_2(x) &=& 1/2(1 + x)
* @f}
*
* @f{eqnarray*}{
* x_{q} &=& 0
* @f}
*/
/* -------------------------------------------------------------------------- */
#include "element_class.hh"
/* -------------------------------------------------------------------------- */
namespace
akantu
{
/* -------------------------------------------------------------------------- */
AKANTU_DEFINE_ELEMENT_CLASS_PROPERTY
(
_segment_2
,
_gt_segment_2
,
_itp_lagrange_segment_2
,
_ek_regular
,
1
,
_git_segment
,
1
);
/* -------------------------------------------------------------------------- */
template
<>
template
<
class
D1
,
class
D2
,
aka
::
enable_if_t
<
aka
::
are_vectors
<
D1
,
D2
>::
value
>
*>
inline
void
InterpolationElement
<
_itp_lagrange_segment_2
>::
computeShapes
(
const
Eigen
::
MatrixBase
<
D1
>
&
natural_coords
,
Eigen
::
MatrixBase
<
D2
>
&
N
)
{
/// natural coordinate
Real
c
=
natural_coords
(
0
);
/// shape functions
N
(
0
)
=
0.5
*
(
1
-
c
);
N
(
1
)
=
0.5
*
(
1
+
c
);
}
/* -------------------------------------------------------------------------- */
template
<>
template
<
class
D1
,
class
D2
>
inline
void
InterpolationElement
<
_itp_lagrange_segment_2
>::
computeDNDS
(
const
Eigen
::
MatrixBase
<
D1
>
&
/*natural_coords*/
,
Eigen
::
MatrixBase
<
D2
>
&
dnds
)
{
/// dN1/de
dnds
(
0
,
0
)
=
-
.5
;
/// dN2/de
dnds
(
0
,
1
)
=
.5
;
}
/* -------------------------------------------------------------------------- */
template
<>
template
<
class
vector_type
,
class
matrix_type
>
inline
void
InterpolationElement
<
_itp_lagrange_segment_2
>::
computeD2NDS2
(
const
vector_type
&
/*natural_coords*/
,
matrix_type
&
d2nds2
)
{
d2nds2
.
zero
();
}
/* -------------------------------------------------------------------------- */
template
<>
template
<
class
D
>
inline
Real
GeometricalElement
<
_gt_segment_2
>::
getInradius
(
const
Eigen
::
MatrixBase
<
D
>
&
coord
)
{
auto
a
{
coord
(
0
)};
auto
b
{
coord
(
1
)};
return
(
b
-
a
).
norm
();
}
/* -------------------------------------------------------------------------- */
template
<>
template
<
class
D1
,
class
D2
>
inline
void
GeometricalElement
<
_gt_segment_2
>::
getNormal
(
const
Eigen
::
MatrixBase
<
D1
>
&
coord
,
Eigen
::
MatrixBase
<
D2
>
&
normal
)
{
AKANTU_DEBUG_ASSERT
(
normal
.
size
()
==
2
,
"The normal is only uniquely defined in 2D"
);
Math
::
normal
(
coord
.
col
(
0
)
-
coord
.
col
(
1
),
normal
);
}
/* -------------------------------------------------------------------------- */
}
// namespace akantu
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