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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>
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date creation: Fri Jul 15 2011
* @date last modification: Fri Feb 05 2021
*
* @brief Specialization of the element_class class for the type
* _bernoulli_beam_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
--x-----q1----|----q2-----x---> x
-1 0 1
@endverbatim
*
*/
/* -------------------------------------------------------------------------- */
//#include "element_class_structural.hh"
/* -------------------------------------------------------------------------- */
#ifndef AKANTU_ELEMENT_CLASS_BERNOULLI_BEAM_INLINE_IMPL_HH_
#define AKANTU_ELEMENT_CLASS_BERNOULLI_BEAM_INLINE_IMPL_HH_
namespace
akantu
{
/* -------------------------------------------------------------------------- */
template
<>
template
<
typename
D1
,
typename
D2
,
typename
D3
>
inline
void
InterpolationElement
<
_itp_bernoulli_beam_2
,
_itk_structural
>::
computeShapes
(
const
Eigen
::
MatrixBase
<
D1
>
&
natural_coords
,
const
Eigen
::
MatrixBase
<
D2
>
&
real_coord
,
Eigen
::
MatrixBase
<
D3
>
&
N
)
{
Eigen
::
Matrix
<
Real
,
2
,
1
>
L
;
InterpolationElement
<
_itp_lagrange_segment_2
,
_itk_lagrangian
>::
computeShapes
(
natural_coords
,
L
);
Eigen
::
Matrix
<
Real
,
2
,
4
>
H
;
InterpolationElement
<
_itp_hermite_2
,
_itk_structural
>::
computeShapes
(
natural_coords
,
real_coord
,
H
);
// clang-format off
// u1 v1 t1 u2 v2 t2
N
=
Matrix
<
Real
,
3
,
6
>
{{
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
<>
template
<
typename
D1
,
typename
D2
,
typename
D3
>
inline
void
InterpolationElement
<
_itp_bernoulli_beam_3
,
_itk_structural
>::
computeShapes
(
const
Eigen
::
MatrixBase
<
D1
>
&
natural_coords
,
const
Eigen
::
MatrixBase
<
D2
>
&
real_coord
,
Eigen
::
MatrixBase
<
D3
>
&
N
)
{
Eigen
::
Matrix
<
Real
,
2
,
1
>
L
;
InterpolationElement
<
_itp_lagrange_segment_2
,
_itk_lagrangian
>::
computeShapes
(
natural_coords
,
L
);
Eigen
::
Matrix
<
Real
,
2
,
4
>
H
;
InterpolationElement
<
_itp_hermite_2
,
_itk_structural
>::
computeShapes
(
natural_coords
,
real_coord
,
H
);
// clang-format off
// u1 v1 w1 tx1 ty1 tz1 u2 v2 w2 tx2 ty2 tz2
N
=
Matrix
<
Real
,
6
,
12
>
{{
L
(
0
),
0
,
0
,
0
,
0
,
0
,
L
(
1
),
0
,
0
,
0
,
0
,
0
},
// u
{
0
,
H
(
0
,
0
),
0
,
0
,
0
,
H
(
0
,
1
),
0
,
H
(
0
,
2
),
0
,
0
,
0
,
H
(
0
,
3
)},
// v
{
0
,
0
,
H
(
0
,
0
),
0
,
-
H
(
0
,
1
),
0
,
0
,
0
,
H
(
0
,
2
),
0
,
-
H
(
0
,
3
),
0
},
// w
{
0
,
0
,
0
,
L
(
0
),
0
,
0
,
0
,
0
,
0
,
L
(
1
),
0
,
0
},
// thetax
{
0
,
0
,
H
(
1
,
0
),
0
,
-
H
(
1
,
1
),
0
,
0
,
0
,
H
(
1
,
2
),
0
,
-
H
(
1
,
3
),
0
},
// thetay
{
0
,
H
(
1
,
0
),
0
,
0
,
0
,
H
(
1
,
1
),
0
,
H
(
1
,
2
),
0
,
0
,
0
,
H
(
1
,
3
)}};
// thetaz
// clang-format on
}
/* -------------------------------------------------------------------------- */
#if 0
template <>
inline void
InterpolationElement<_itp_bernoulli_beam_3, _itk_structural>::computeShapesDisplacements(
const Vector<Real> & natural_coords, const Matrix<Real> & real_coord,
Matrix<Real> & N) {
}
#endif
/* -------------------------------------------------------------------------- */
template
<>
template
<
class
D1
,
class
D2
,
class
D3
>
inline
void
InterpolationElement
<
_itp_bernoulli_beam_2
,
_itk_structural
>::
computeDNDS
(
const
Eigen
::
MatrixBase
<
D1
>
&
Xs
,
const
Eigen
::
MatrixBase
<
D2
>
&
xs
,
Eigen
::
MatrixBase
<
D3
>
&
dnds
)
{
Eigen
::
Matrix
<
Real
,
1
,
2
>
L
;
InterpolationElement
<
_itp_lagrange_segment_2
,
_itk_lagrangian
>::
computeDNDS
(
Xs
,
L
);
Eigen
::
Matrix
<
Real
,
1
,
4
>
H
;
InterpolationElement
<
_itp_hermite_2
,
_itk_structural
>::
computeDNDS
(
Xs
,
xs
,
H
);
// Storing the derivatives in dnds
dnds
.
template
block
<
1
,
2
>
(
0
,
0
)
=
L
;
dnds
.
template
block
<
1
,
4
>
(
0
,
2
)
=
H
;
}
/* -------------------------------------------------------------------------- */
template
<>
template
<
class
D1
,
class
D2
>
inline
void
InterpolationElement
<
_itp_bernoulli_beam_2
,
_itk_structural
>::
arrangeInVoigt
(
const
Eigen
::
MatrixBase
<
D1
>
&
dnds
,
Eigen
::
MatrixBase
<
D2
>
&
B
)
{
auto
L
=
dnds
.
template
block
<
1
,
2
>
(
0
,
0
);
// Lagrange shape derivatives
auto
H
=
dnds
.
template
block
<
1
,
4
>
(
0
,
2
);
// Hermite shape derivatives
// clang-format off
// u1 v1 t1 u2 v2 t2
B
=
Matrix
<
Real
,
2
,
6
>
{{
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
<>
template
<
class
D1
,
class
D2
,
class
D3
>
inline
void
InterpolationElement
<
_itp_bernoulli_beam_3
,
_itk_structural
>::
computeDNDS
(
const
Eigen
::
MatrixBase
<
D1
>
&
natural_coords
,
const
Eigen
::
MatrixBase
<
D2
>
&
real_coord
,
Eigen
::
MatrixBase
<
D3
>
&
dnds
)
{
InterpolationElement
<
_itp_bernoulli_beam_2
,
_itk_structural
>::
computeDNDS
(
natural_coords
,
real_coord
,
dnds
);
}
/* -------------------------------------------------------------------------- */
template
<>
template
<
class
D1
,
class
D2
>
inline
void
InterpolationElement
<
_itp_bernoulli_beam_3
,
_itk_structural
>::
arrangeInVoigt
(
const
Eigen
::
MatrixBase
<
D1
>
&
dnds
,
Eigen
::
MatrixBase
<
D2
>
&
B
)
{
auto
L
=
dnds
.
template
block
<
1
,
2
>
(
0
,
0
);
// Lagrange shape derivatives
auto
H
=
dnds
.
template
block
<
1
,
4
>
(
0
,
2
);
// Hermite shape derivatives
// clang-format off
// u1 v1 w1 x1 y1 z1 u2 v2 w2 x2 y2 z2
B
=
Matrix
<
Real
,
4
,
12
>
{{
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
<>
template
<
class
D1
,
class
D2
,
class
D3
>
inline
void
ElementClass
<
_bernoulli_beam_2
>::
computeRotationMatrix
(
Eigen
::
MatrixBase
<
D1
>
&
R
,
const
Eigen
::
MatrixBase
<
D2
>
&
X
,
const
Eigen
::
MatrixBase
<
D3
>
&
)
{
auto
&&
x2
=
X
(
1
);
// X2
auto
&&
x1
=
X
(
0
);
// X1
auto
cs
=
(
x2
-
x1
)
/
(
x2
-
x1
).
norm
();
auto
c
=
cs
(
0
);
auto
s
=
cs
(
1
);
// clang-format off
/// Definition of the rotation matrix
R
=
Matrix
<
Real
,
3
,
3
>
{{
c
,
s
,
0.
},
{
-
s
,
c
,
0.
},
{
0.
,
0.
,
1.
}};
// clang-format on
}
/* -------------------------------------------------------------------------- */
template
<>
template
<
class
D1
,
class
D2
,
class
D3
>
inline
void
ElementClass
<
_bernoulli_beam_3
>::
computeRotationMatrix
(
Eigen
::
MatrixBase
<
D1
>
&
R
,
const
Eigen
::
MatrixBase
<
D2
>
&
X
,
const
Eigen
::
MatrixBase
<
D3
>
&
n
)
{
auto
dim
=
X
.
rows
();
Eigen
::
Matrix
<
Real
,
1
,
3
>
x
=
(
X
(
1
)
-
X
(
0
));
Eigen
::
Matrix
<
Real
,
1
,
3
>
nv
=
n
;
x
.
normalize
();
auto
x_n
=
x
.
cross
(
nv
);
Matrix
<
Real
>
Pe
(
dim
,
dim
);
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
.
zero
();
/// Definition of the rotation matrix
for
(
Int
i
=
0
;
i
<
dim
;
++
i
)
{
for
(
Int
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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