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element_class_segment_3_inline_impl.cc
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rAKA akantu
element_class_segment_3_inline_impl.cc
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/**
* @file element_class_segment_3_inline_impl.cc
*
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date creation: Fri Jul 16 2010
* @date last modification: Sun Oct 19 2014
*
* @brief Specialization of the element_class class for the type _segment_3
*
* @section LICENSE
*
* Copyright (©) 2010-2012, 2014, 2015 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/>.
*
* @section DESCRIPTION
*
* @verbatim
-1 0 1
-----x---------x---------x-----> x
1 3 2
@endverbatim
*
* @subsection coords Nodes coordinates
*
* @f[
* \begin{array}{lll}
* x_{1} = -1 & x_{2} = 1 & x_{3} = 0
* \end{array}
* @f]
*
* @subsection shapes Shape functions
* @f[
* \begin{array}{ll}
* w_1(x) = \frac{x}{2}(x - 1) & w'_1(x) = x - \frac{1}{2}\\
* w_2(x) = \frac{x}{2}(x + 1) & w'_2(x) = x + \frac{1}{2}\\
* w_3(x) = 1-x^2 & w'_3(x) = -2x
* \end{array}
* @f]
*
* @subsection quad_points Position of quadrature points
* @f[
* \begin{array}{ll}
* x_{q1} = -1/\sqrt{3} & x_{q2} = 1/\sqrt{3}
* \end{array}
* @f]
*/
/* -------------------------------------------------------------------------- */
AKANTU_DEFINE_ELEMENT_CLASS_PROPERTY
(
_segment_3
,
_gt_segment_3
,
_itp_lagrange_segment_3
,
_ek_regular
,
1
,
_git_segment
,
2
);
AKANTU_DEFINE_SHAPE
(
_gt_segment_3
,
_gst_square
);
/* -------------------------------------------------------------------------- */
template
<>
template
<
class
vector_type
>
inline
void
InterpolationElement
<
_itp_lagrange_segment_3
>::
computeShapes
(
const
vector_type
&
natural_coords
,
vector_type
&
N
)
{
Real
c
=
natural_coords
(
0
);
N
(
0
)
=
(
c
-
1
)
*
c
/
2
;
N
(
1
)
=
(
c
+
1
)
*
c
/
2
;
N
(
2
)
=
1
-
c
*
c
;
}
/* -------------------------------------------------------------------------- */
template
<>
template
<
class
vector_type
,
class
matrix_type
>
inline
void
InterpolationElement
<
_itp_lagrange_segment_3
>::
computeDNDS
(
const
vector_type
&
natural_coords
,
matrix_type
&
dnds
){
Real
c
=
natural_coords
(
0
);
dnds
(
0
,
0
)
=
c
-
.5
;
dnds
(
0
,
1
)
=
c
+
.5
;
dnds
(
0
,
2
)
=
-
2
*
c
;
}
/* -------------------------------------------------------------------------- */
template
<>
inline
void
InterpolationElement
<
_itp_lagrange_segment_3
>::
computeSpecialJacobian
(
const
Matrix
<
Real
>
&
dxds
,
Real
&
jac
)
{
jac
=
Math
::
norm2
(
dxds
.
storage
());
}
/* -------------------------------------------------------------------------- */
template
<>
inline
Real
GeometricalElement
<
_gt_segment_3
>::
getInradius
(
const
Matrix
<
Real
>
&
coord
)
{
Real
dist1
=
std
::
abs
(
coord
(
0
,
0
)
-
coord
(
0
,
1
));
Real
dist2
=
std
::
abs
(
coord
(
0
,
1
)
-
coord
(
0
,
2
));
return
std
::
min
(
dist1
,
dist2
);
}
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