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element_class_triangle_3_inline_impl.cc
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rAKA akantu
element_class_triangle_3_inline_impl.cc
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/**
* @file element_class_triangle_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 _triangle_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
\eta
^
|
x (0,0,1)
|`
| `
| q `
| ° `
x--------x-----> \xi
(1,0,0) (0,1,0)
@endverbatim
*
* @subsection shapes Shape functions
* @f{eqnarray*}{
* N1 &=& 1 - \xi - \eta \\
* N2 &=& \xi \\
* N3 &=& \eta
* @f}
*
* @subsection quad_points Position of quadrature points
* @f{eqnarray*}{
* \xi_{q0} &=& 1/3 \qquad \eta_{q0} = 1/3
* @f}
*/
/* -------------------------------------------------------------------------- */
AKANTU_DEFINE_ELEMENT_CLASS_PROPERTY
(
_triangle_3
,
_gt_triangle_3
,
_itp_lagrange_triangle_3
,
_ek_regular
,
2
,
_git_triangle
,
1
);
AKANTU_DEFINE_SHAPE
(
_gt_triangle_3
,
_gst_triangle
);
/* -------------------------------------------------------------------------- */
template
<>
template
<
class
vector_type
>
inline
void
InterpolationElement
<
_itp_lagrange_triangle_3
>::
computeShapes
(
const
vector_type
&
natural_coords
,
vector_type
&
N
)
{
/// Natural coordinates
Real
c0
=
1
-
natural_coords
(
0
)
-
natural_coords
(
1
);
/// @f$ c0 = 1 - \xi - \eta @f$
Real
c1
=
natural_coords
(
0
);
/// @f$ c1 = \xi @f$
Real
c2
=
natural_coords
(
1
);
/// @f$ c2 = \eta @f$
N
(
0
)
=
c0
;
/// N1(q_0)
N
(
1
)
=
c1
;
/// N2(q_0)
N
(
2
)
=
c2
;
/// N3(q_0)
}
/* -------------------------------------------------------------------------- */
template
<>
template
<
class
vector_type
,
class
matrix_type
>
inline
void
InterpolationElement
<
_itp_lagrange_triangle_3
>::
computeDNDS
(
__attribute__
((
unused
))
const
vector_type
&
natural_coords
,
matrix_type
&
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
<>
inline
void
InterpolationElement
<
_itp_lagrange_triangle_3
>::
computeSpecialJacobian
(
const
Matrix
<
Real
>
&
J
,
Real
&
jac
)
{
Vector
<
Real
>
vprod
(
J
.
cols
());
Matrix
<
Real
>
Jt
(
J
.
transpose
(),
true
);
vprod
.
crossProduct
(
Jt
(
0
),
Jt
(
1
));
jac
=
vprod
.
norm
();
}
/* -------------------------------------------------------------------------- */
template
<>
inline
Real
GeometricalElement
<
_gt_triangle_3
>::
getInradius
(
const
Matrix
<
Real
>
&
coord
)
{
return
Math
::
triangle_inradius
(
coord
(
0
).
storage
(),
coord
(
1
).
storage
(),
coord
(
2
).
storage
());
}
/* -------------------------------------------------------------------------- */
// template<> inline bool ElementClass<_triangle_3>::contains(const Vector<Real> & natural_coords) {
// if (natural_coords[0] < 0.) return false;
// if (natural_coords[0] > 1.) return false;
// if (natural_coords[1] < 0.) return false;
// if (natural_coords[1] > 1.) return false;
// if (natural_coords[0]+natural_coords[1] > 1.) return false;
// return true;
// }
/* -------------------------------------------------------------------------- */
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