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element_class_bernoulli_beam_inline_impl.hh
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rAKA akantu
element_class_bernoulli_beam_inline_impl.hh
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/**
* @file element_class_bernoulli_beam_inline_impl.hh
*
* @author Fabian Barras <fabian.barras@epfl.ch>
* @author Lucas Frerot <lucas.frerot@epfl.ch>
*
* @date creation: Fri Jul 15 2011
* @date last modification: Mon Feb 19 2018
*
* @brief Specialization of the element_class class for the type
* _bernoulli_beam_2
*
*
* Copyright (©) 2010-2018 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
--x-----q1----|----q2-----x---> x
-1 0 1
@endverbatim
*
*/
/* -------------------------------------------------------------------------- */
#include "aka_static_if.hh"
#include "element_class_structural.hh"
//#include "aka_element_classes_info.hh"
/* -------------------------------------------------------------------------- */
#ifndef __AKANTU_ELEMENT_CLASS_BERNOULLI_BEAM_INLINE_IMPL_HH__
#define __AKANTU_ELEMENT_CLASS_BERNOULLI_BEAM_INLINE_IMPL_HH__
namespace
akantu
{
/* -------------------------------------------------------------------------- */
AKANTU_DEFINE_STRUCTURAL_INTERPOLATION_TYPE_PROPERTY
(
_itp_bernoulli_beam_2
,
_itp_lagrange_segment_2
,
3
,
2
,
6
);
AKANTU_DEFINE_STRUCTURAL_INTERPOLATION_TYPE_PROPERTY
(
_itp_bernoulli_beam_3
,
_itp_lagrange_segment_2
,
6
,
4
,
6
);
AKANTU_DEFINE_STRUCTURAL_ELEMENT_CLASS_PROPERTY
(
_bernoulli_beam_2
,
_gt_segment_2
,
_itp_bernoulli_beam_2
,
_segment_2
,
_ek_structural
,
2
,
_git_segment
,
3
);
AKANTU_DEFINE_STRUCTURAL_ELEMENT_CLASS_PROPERTY
(
_bernoulli_beam_3
,
_gt_segment_2
,
_itp_bernoulli_beam_3
,
_segment_2
,
_ek_structural
,
3
,
_git_segment
,
3
);
/* -------------------------------------------------------------------------- */
template
<>
inline
void
InterpolationElement
<
_itp_bernoulli_beam_2
,
_itk_structural
>::
computeShapes
(
const
Vector
<
Real
>
&
natural_coords
,
const
Matrix
<
Real
>
&
real_coord
,
Matrix
<
Real
>
&
N
)
{
Vector
<
Real
>
L
(
2
);
InterpolationElement
<
_itp_lagrange_segment_2
,
_itk_lagrangian
>::
computeShapes
(
natural_coords
,
L
);
Matrix
<
Real
>
H
(
2
,
4
);
InterpolationElement
<
_itp_hermite_2
,
_itk_structural
>::
computeShapes
(
natural_coords
,
real_coord
,
H
);
// clang-format off
// u1 v1 t1 u2 v2 t2
N
=
{{
L
(
0
),
0
,
0
,
L
(
1
),
0
,
0
},
// u
{
0
,
H
(
0
,
0
),
H
(
0
,
1
),
0
,
H
(
0
,
2
),
H
(
0
,
3
)},
// v
{
0
,
H
(
1
,
0
),
H
(
1
,
1
),
0
,
H
(
1
,
2
),
H
(
1
,
3
)}};
// theta
// clang-format on
}
template
<>
inline
void
InterpolationElement
<
_itp_bernoulli_beam_3
,
_itk_structural
>::
computeShapes
(
const
Vector
<
Real
>
&
natural_coords
,
const
Matrix
<
Real
>
&
real_coord
,
Matrix
<
Real
>
&
N
)
{
Vector
<
Real
>
L
(
2
);
InterpolationElement
<
_itp_lagrange_segment_2
,
_itk_lagrangian
>::
computeShapes
(
natural_coords
,
L
);
Matrix
<
Real
>
H
(
2
,
4
);
InterpolationElement
<
_itp_hermite_2
,
_itk_structural
>::
computeShapes
(
natural_coords
,
real_coord
,
H
);
// clang-format off
// u1 v1 w1 x1 y1 z1 u2 v2 w2 x2 y2 z2
N
=
{{
L
(
0
),
0
,
0
,
0
,
0
,
0
,
L
(
1
),
0
,
0
,
0
,
0
,
0
},
// u
{
0
,
H
(
0
,
0
),
0
,
0
,
H
(
0
,
1
),
0
,
0
,
H
(
0
,
2
),
0
,
0
,
H
(
0
,
3
),
0
},
// v
{
0
,
0
,
H
(
0
,
0
),
0
,
0
,
H
(
0
,
1
),
0
,
0
,
H
(
0
,
2
),
0
,
0
,
H
(
0
,
3
)},
// w
{
0
,
0
,
0
,
L
(
0
),
0
,
0
,
0
,
0
,
0
,
L
(
1
),
0
,
0
},
// thetax
{
0
,
H
(
1
,
0
),
0
,
0
,
H
(
1
,
1
),
0
,
0
,
H
(
1
,
2
),
0
,
0
,
H
(
1
,
3
),
0
},
// thetay
{
0
,
0
,
H
(
1
,
0
),
0
,
0
,
H
(
1
,
1
),
0
,
0
,
H
(
1
,
2
),
0
,
0
,
H
(
1
,
3
)}};
// thetaz
// clang-format on
}
/* -------------------------------------------------------------------------- */
template
<>
inline
void
InterpolationElement
<
_itp_bernoulli_beam_2
,
_itk_structural
>::
computeDNDS
(
const
Vector
<
Real
>
&
natural_coords
,
const
Matrix
<
Real
>
&
real_coord
,
Matrix
<
Real
>
&
dnds
)
{
Matrix
<
Real
>
L
(
1
,
2
);
InterpolationElement
<
_itp_lagrange_segment_2
,
_itk_lagrangian
>::
computeDNDS
(
natural_coords
,
L
);
Matrix
<
Real
>
H
(
1
,
4
);
InterpolationElement
<
_itp_hermite_2
,
_itk_structural
>::
computeDNDS
(
natural_coords
,
real_coord
,
H
);
// Storing the derivatives in dnds
dnds
.
block
(
L
,
0
,
0
);
dnds
.
block
(
H
,
0
,
2
);
}
/* -------------------------------------------------------------------------- */
template
<>
inline
void
InterpolationElement
<
_itp_bernoulli_beam_2
,
_itk_structural
>::
arrangeInVoigt
(
const
Matrix
<
Real
>
&
dnds
,
Matrix
<
Real
>
&
B
)
{
auto
L
=
dnds
.
block
(
0
,
0
,
1
,
2
);
// Lagrange shape derivatives
auto
H
=
dnds
.
block
(
0
,
2
,
1
,
4
);
// Hermite shape derivatives
// clang-format off
// u1 v1 t1 u2 v2 t2
B
=
{{
L
(
0
,
0
),
0
,
0
,
L
(
0
,
1
),
0
,
0
},
{
0
,
H
(
0
,
0
),
H
(
0
,
1
),
0
,
H
(
0
,
2
),
H
(
0
,
3
)}};
// clang-format on
}
/* -------------------------------------------------------------------------- */
template
<>
inline
void
InterpolationElement
<
_itp_bernoulli_beam_3
,
_itk_structural
>::
computeDNDS
(
const
Vector
<
Real
>
&
natural_coords
,
const
Matrix
<
Real
>
&
real_coord
,
Matrix
<
Real
>
&
dnds
)
{
InterpolationElement
<
_itp_bernoulli_beam_2
,
_itk_structural
>::
computeDNDS
(
natural_coords
,
real_coord
,
dnds
);
}
/* -------------------------------------------------------------------------- */
template
<>
inline
void
InterpolationElement
<
_itp_bernoulli_beam_3
,
_itk_structural
>::
arrangeInVoigt
(
const
Matrix
<
Real
>
&
dnds
,
Matrix
<
Real
>
&
B
)
{
auto
L
=
dnds
.
block
(
0
,
0
,
1
,
2
);
// Lagrange shape derivatives
auto
H
=
dnds
.
block
(
0
,
2
,
1
,
4
);
// Hermite shape derivatives
// clang-format off
// u1 v1 w1 x1 y1 z1 u2 v2 w2 x2 y2 z2
B
=
{{
L
(
0
,
0
),
0
,
0
,
0
,
0
,
0
,
L
(
0
,
1
),
0
,
0
,
0
,
0
,
0
},
// eps
{
0
,
H
(
0
,
0
),
0
,
0
,
0
,
H
(
0
,
1
),
0
,
H
(
0
,
2
),
0
,
0
,
0
,
H
(
0
,
3
)},
// chi strong axis
{
0
,
0
,
-
H
(
0
,
0
),
0
,
H
(
0
,
1
),
0
,
0
,
0
,
-
H
(
0
,
2
),
0
,
H
(
0
,
3
),
0
},
// chi weak axis
{
0
,
0
,
0
,
L
(
0
,
0
),
0
,
0
,
0
,
0
,
0
,
L
(
0
,
1
),
0
,
0
}};
// chi torsion
// clang-format on
}
/* -------------------------------------------------------------------------- */
template
<>
inline
void
ElementClass
<
_bernoulli_beam_2
>::
computeRotationMatrix
(
Matrix
<
Real
>
&
R
,
const
Matrix
<
Real
>
&
X
,
const
Vector
<
Real
>
&
)
{
Vector
<
Real
>
x2
=
X
(
1
);
// X2
Vector
<
Real
>
x1
=
X
(
0
);
// X1
auto
cs
=
(
x2
-
x1
);
cs
.
normalize
();
auto
c
=
cs
(
0
);
auto
s
=
cs
(
1
);
// clang-format off
/// Definition of the rotation matrix
R
=
{{
c
,
s
,
0.
},
{
-
s
,
c
,
0.
},
{
0.
,
0.
,
1.
}};
// clang-format on
}
/* -------------------------------------------------------------------------- */
template
<>
inline
void
ElementClass
<
_bernoulli_beam_3
>::
computeRotationMatrix
(
Matrix
<
Real
>
&
R
,
const
Matrix
<
Real
>
&
X
,
const
Vector
<
Real
>
&
n
)
{
Vector
<
Real
>
x2
=
X
(
1
);
// X2
Vector
<
Real
>
x1
=
X
(
0
);
// X1
auto
dim
=
X
.
rows
();
auto
x
=
(
x2
-
x1
);
x
.
normalize
();
auto
x_n
=
x
.
crossProduct
(
n
);
Matrix
<
Real
>
Pe
=
{{
1.
,
0.
,
0.
},
{
0.
,
-
1.
,
0.
},
{
0.
,
0.
,
1.
}};
Matrix
<
Real
>
Pg
(
dim
,
dim
);
Pg
(
0
)
=
x
;
Pg
(
1
)
=
x_n
;
Pg
(
2
)
=
n
;
Pe
*=
Pg
.
inverse
();
R
.
clear
();
/// Definition of the rotation matrix
for
(
UInt
i
=
0
;
i
<
dim
;
++
i
)
for
(
UInt
j
=
0
;
j
<
dim
;
++
j
)
R
(
i
+
dim
,
j
+
dim
)
=
R
(
i
,
j
)
=
Pe
(
i
,
j
);
}
}
// namespace akantu
#endif
/* __AKANTU_ELEMENT_CLASS_BERNOULLI_BEAM_INLINE_IMPL_HH__ */
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