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element_class_bernoulli_beam_inline_impl.cc
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rAKA akantu
element_class_bernoulli_beam_inline_impl.cc
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/**
* @file element_class_bernoulli_beam_inline_impl.cc
*
* @author Fabian Barras <fabian.barras@epfl.ch>
*
* @date creation: Fri Jul 15 2011
* @date last modification: Sun Oct 19 2014
*
* @brief Specialization of the element_class class for the type
_bernoulli_beam_2
*
* @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
--x-----q1----|----q2-----x---> x
-a 0 a
@endverbatim
*
* @subsection coords Nodes coordinates
*
* @f[
* \begin{array}{ll}
* x_{1} = -a & x_{2} = a
* \end{array}
* @f]
*
* @subsection shapes Shape functions
* @f[
* \begin{array}{ll}
* N_1(x) &= \frac{1-x}{2a}\\
* N_2(x) &= \frac{1+x}{2a}
* \end{array}
*
* \begin{array}{ll}
* M_1(x) &= 1/4(x^{3}/a^{3}-3x/a+2)\\
* M_2(x) &= -1/4(x^{3}/a^{3}-3x/a-2)
* \end{array}
*
* \begin{array}{ll}
* L_1(x) &= a/4(x^{3}/a^{3}-x^{2}/a^{2}-x/a+1)\\
* L_2(x) &= a/4(x^{3}/a^{3}+x^{2}/a^{2}-x/a-1)
* \end{array}
*
* \begin{array}{ll}
* M'_1(x) &= 3/4a(x^{2}/a^{2}-1)\\
* M'_2(x) &= -3/4a(x^{2}/a^{2}-1)
* \end{array}
*
* \begin{array}{ll}
* L'_1(x) &= 1/4(3x^{2}/a^{2}-2x/a-1)\\
* L'_2(x) &= 1/4(3x^{2}/a^{2}+2x/a-1)
* \end{array}
*@f]
*
* @subsection dnds Shape derivatives
*
*@f[
* \begin{array}{ll}
* N'_1(x) &= -1/2a\\
* N'_2(x) &= 1/2a
* \end{array}]
*
* \begin{array}{ll}
* -M''_1(x) &= -3x/(2a^{3})\\
* -M''_2(x) &= 3x/(2a^{3})\\
* \end{array}
*
* \begin{array}{ll}
* -L''_1(x) &= -1/2a(3x/a-1)\\
* -L''_2(x) &= -1/2a(3x/a+1)
* \end{array}
*@f]
*
* @subsection quad_points Position of quadrature points
*
* @f[
* \begin{array}{ll}
* x_{q1} = -a/\sqrt{3} & x_{q2} = a/\sqrt{3}
* \end{array}
* @f]
*/
/* -------------------------------------------------------------------------- */
#include "aka_static_if.hh"
#include "element_class_structural.hh"
/* -------------------------------------------------------------------------- */
#ifndef __AKANTU_ELEMENT_CLASS_BERNOULLI_BEAM_INLINE_IMPL_CC__
#define __AKANTU_ELEMENT_CLASS_BERNOULLI_BEAM_INLINE_IMPL_CC__
namespace
akantu
{
/* -------------------------------------------------------------------------- */
AKANTU_DEFINE_STRUCTURAL_INTERPOLATION_TYPE_PROPERTY
(
_itp_bernoulli_beam_2
,
_itp_lagrange_segment_2
,
2
,
3
,
2
);
AKANTU_DEFINE_STRUCTURAL_INTERPOLATION_TYPE_PROPERTY
(
_itp_bernoulli_beam_3
,
_itp_lagrange_segment_2
,
3
,
6
,
4
);
AKANTU_DEFINE_STRUCTURAL_ELEMENT_CLASS_PROPERTY
(
_bernoulli_beam_2
,
_gt_segment_2
,
_itp_bernoulli_beam_2
,
_segment_2
,
_ek_structural
,
2
,
_git_segment
,
5
);
AKANTU_DEFINE_STRUCTURAL_ELEMENT_CLASS_PROPERTY
(
_bernoulli_beam_3
,
_gt_segment_2
,
_itp_bernoulli_beam_3
,
_segment_2
,
_ek_structural
,
3
,
_git_segment
,
5
);
/* -------------------------------------------------------------------------- */
/* -------------------------------------------------------------------------- */
namespace
{
namespace
details
{
template
<
InterpolationType
type
>
void
computeShapes
(
const
Vector
<
Real
>
&
natural_coords
,
Matrix
<
Real
>
&
N
,
const
Matrix
<
Real
>
&
real_coord
)
{
/// Compute the dimension of the beam
Vector
<
Real
>
x1
=
real_coord
(
0
);
Vector
<
Real
>
x2
=
real_coord
(
1
);
Real
a
=
x1
.
distance
(
x2
)
/
2.
;
/// natural coordinate
Real
c
=
natural_coords
(
0
);
auto
N0
=
(
1
-
c
)
/
2.
;
auto
N1
=
(
1
+
c
)
/
2.
;
auto
M0
=
(
c
*
c
*
c
-
3.
*
c
+
2.
)
/
4.
;
auto
M1
=
-
(
c
*
c
*
c
-
3.
*
c
-
2.
)
/
4.
;
auto
L0
=
a
*
(
c
*
c
*
c
-
c
*
c
-
c
+
1.
)
/
4.
;
auto
L1
=
a
*
(
c
*
c
*
c
+
c
*
c
-
c
-
1.
)
/
4.
;
auto
Mp0
=
3.
/
a
*
(
c
*
c
-
1.
)
/
4.
;
auto
Mp1
=
-
3.
/
a
*
(
c
*
c
-
1.
)
/
4.
;
auto
Lp0
=
(
3.
*
c
*
c
-
2.
*
c
-
1.
)
/
4.
;
auto
Lp1
=
(
3.
*
c
*
c
+
2.
*
c
-
1.
)
/
4.
;
static_if
(
type
==
_itp_bernoulli_beam_2
)
.
then
([
&
](
auto
&&
N
)
{
// clang-format off
// 0 1 2 3 4 5
N
=
{{
N0
,
0.
,
0.
,
N1
,
0.
,
0.
},
{
0.
,
M0
,
L0
,
0.
,
M1
,
L1
},
{
0.
,
Mp0
,
Lp0
,
0.
,
Mp1
,
Lp1
}};
// clang-format on
})
.
else_if
(
type
==
_itp_bernoulli_beam_3
)
.
then
([
&
](
auto
&&
N
)
{
// clang-format off
// 0 1 2 3 4 5 6 7 8 9 10 11
N
=
{{
N0
,
0.
,
0.
,
0.
,
0.
,
0.
,
N1
,
0.
,
0.
,
0.
,
0.
,
0.
},
{
0.
,
M0
,
0.
,
0.
,
0.
,
L0
,
0.
,
M1
,
0.
,
0.
,
0.
,
L1
},
{
0.
,
0.
,
M0
,
0.
,
-
L0
,
0.
,
0.
,
0.
,
M1
,
0.
,
-
L1
,
0.
},
{
0.
,
0.
,
0.
,
N0
,
0.
,
0.
,
0.
,
0.
,
0.
,
N1
,
0.
,
0.
},
{
0.
,
0.
,
Mp0
,
0.
,
-
Lp0
,
0.
,
0.
,
0.
,
Mp1
,
0.
,
-
Lp1
,
0.
},
{
0.
,
Mp0
,
0.
,
0.
,
0.
,
Lp0
,
0.
,
Mp1
,
0.
,
0.
,
0.
,
Lp1
}};
// clang-format on
})
.
else_
([](
auto
&&
/*unused*/
)
{
AKANTU_EXCEPTION
(
"Should not be in this part of the code"
);
})(
std
::
forward
<
decltype
(
N
)
>
(
N
));
}
/* ---------------------------------------------------------------------- */
template
<
InterpolationType
type
>
void
computeDNDS
(
const
Vector
<
Real
>
&
natural_coords
,
Matrix
<
Real
>
&
B
,
const
Matrix
<
Real
>
&
real_nodes_coord
)
{
/// Compute the dimension of the beam
Vector
<
Real
>
x1
=
real_nodes_coord
(
0
);
Vector
<
Real
>
x2
=
real_nodes_coord
(
1
);
Real
a
=
.5
*
x1
.
distance
(
x2
);
/// natural coordinate
Real
c
=
natural_coords
(
0
)
*
a
;
auto
Np0
=
-
1.
/
(
2.
*
a
);
auto
Np1
=
1.
/
(
2.
*
a
);
auto
Mpp0
=
-
3.
*
c
/
(
2.
*
pow
(
a
,
3.
));
auto
Mpp1
=
3.
*
c
/
(
2.
*
pow
(
a
,
3.
));
auto
Lpp0
=
-
1.
/
(
2.
*
a
)
*
(
3.
*
c
/
a
-
1.
);
auto
Lpp1
=
-
1.
/
(
2.
*
a
)
*
(
3.
*
c
/
a
+
1.
);
static_if
(
type
==
_itp_bernoulli_beam_2
)
.
then
([
&
](
auto
&&
B
)
{
// clang-format off
// 0 1 2 3 4 5
B
=
{{
Np0
,
0.
,
0.
,
Np1
,
0.
,
0.
},
{
0.
,
Mpp0
,
Lpp0
,
0.
,
Mpp1
,
Lpp1
}};
// clang-format on
})
.
else_if
(
type
==
_itp_bernoulli_beam_3
)
.
then
([
&
](
auto
&&
B
)
{
// clang-format off
// 0 1 2 3 4 5 6 7 8 9 10 11
B
=
{{
Np0
,
0.
,
0.
,
0.
,
0.
,
0.
,
Np1
,
0.
,
0.
,
0.
,
0.
,
0.
},
{
0.
,
Mpp0
,
0.
,
0.
,
0.
,
Lpp0
,
0.
,
Mpp1
,
0.
,
0.
,
0.
,
Lpp1
},
{
0.
,
0.
,
Mpp0
,
0.
,
-
Lpp0
,
0.
,
0.
,
0.
,
Mpp1
,
0.
,
-
Lpp1
,
0.
},
{
0.
,
0.
,
0.
,
Np0
,
0.
,
0.
,
0.
,
0.
,
0.
,
Np1
,
0.
,
0.
}};
// clang-format on
})
.
else_
([](
auto
&&
/*unused*/
)
{
AKANTU_EXCEPTION
(
"Should not be in this part of the code"
);
})(
std
::
forward
<
decltype
(
B
)
>
(
B
));
}
}
// namespace details
}
// namespace
/* -------------------------------------------------------------------------- */
template
<>
inline
void
InterpolationElement
<
_itp_bernoulli_beam_2
,
_itk_structural
>::
computeShapes
(
const
Vector
<
Real
>
&
natural_coords
,
Matrix
<
Real
>
&
N
,
const
Matrix
<
Real
>
&
real_coord
)
{
details
::
computeShapes
<
_itp_bernoulli_beam_2
>
(
natural_coords
,
N
,
real_coord
);
}
template
<>
inline
void
InterpolationElement
<
_itp_bernoulli_beam_3
,
_itk_structural
>::
computeShapes
(
const
Vector
<
Real
>
&
natural_coords
,
Matrix
<
Real
>
&
N
,
const
Matrix
<
Real
>
&
real_coord
)
{
details
::
computeShapes
<
_itp_bernoulli_beam_3
>
(
natural_coords
,
N
,
real_coord
);
}
/* -------------------------------------------------------------------------- */
template
<>
inline
void
InterpolationElement
<
_itp_bernoulli_beam_2
,
_itk_structural
>::
computeDNDS
(
const
Vector
<
Real
>
&
natural_coords
,
Matrix
<
Real
>
&
B
,
const
Matrix
<
Real
>
&
real_nodes_coord
)
{
details
::
computeDNDS
<
_itp_bernoulli_beam_2
>
(
natural_coords
,
B
,
real_nodes_coord
);
}
template
<>
inline
void
InterpolationElement
<
_itp_bernoulli_beam_3
,
_itk_structural
>::
computeDNDS
(
const
Vector
<
Real
>
&
natural_coords
,
Matrix
<
Real
>
&
B
,
const
Matrix
<
Real
>
&
real_nodes_coord
)
{
details
::
computeDNDS
<
_itp_bernoulli_beam_3
>
(
natural_coords
,
B
,
real_nodes_coord
);
}
}
// namespace akantu
#endif
/* __AKANTU_ELEMENT_CLASS_BERNOULLI_BEAM_INLINE_IMPL_CC__ */
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