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test_fe_engine_precomputation_bernoulli_2.cc
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Wed, Sep 18, 10:43
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Fri, Sep 20, 10:43 (2 d)
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rAKA akantu
test_fe_engine_precomputation_bernoulli_2.cc
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/**
* @file test_fe_engine_precomputation_bernoulli_2.cc
*
* @author Lucas Frerot <lucas.frerot@epfl.ch>
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date creation: Mon Jun 14 2010
* @date last modification: Thu Jan 25 2018
*
* @brief test of the fem class
*
*
* 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/>.
*
*/
/* -------------------------------------------------------------------------- */
#include "fe_engine.hh"
#include "integrator_gauss.hh"
#include "shape_structural.hh"
/* -------------------------------------------------------------------------- */
#include <cmath>
#include <functional>
#include <iostream>
/* -------------------------------------------------------------------------- */
using
namespace
akantu
;
Matrix
<
Real
>
globalToLocalRotation
(
Real
theta
)
{
// clang-format off
return
{{
std
::
cos
(
theta
),
std
::
sin
(
theta
),
0
},
{
-
std
::
sin
(
theta
),
std
::
cos
(
theta
),
0
},
{
0
,
0
,
1
}};
// clang-format on
}
Vector
<
Real
>
axialReference
(
Real
xq
)
{
return
{(
1.
-
xq
)
/
2
,
0
,
0
,
(
1.
+
xq
)
/
2
,
0
,
0
};
}
Vector
<
Real
>
bendingReference
(
Real
xq
)
{
return
{
0
,
1.
/
4.
*
Math
::
pow
<
2
>
(
xq
-
1
)
*
(
xq
+
2
),
1.
/
4.
*
Math
::
pow
<
2
>
(
xq
-
1
)
*
(
xq
+
1
),
0
,
1.
/
4.
*
Math
::
pow
<
2
>
(
xq
+
1
)
*
(
2
-
xq
),
1.
/
4.
*
Math
::
pow
<
2
>
(
xq
+
1
)
*
(
xq
-
1
)};
}
Vector
<
Real
>
bendingRotationReference
(
Real
xq
)
{
return
{
0
,
3.
/
4.
*
(
xq
*
xq
-
1
),
1.
/
4.
*
(
3
*
xq
*
xq
-
2
*
xq
-
1
),
0
,
3.
/
4.
*
(
1
-
xq
*
xq
),
1.
/
4.
*
(
3
*
xq
*
xq
+
2
*
xq
-
1
)};
}
bool
testBending
(
const
Array
<
Real
>
&
shape_functions
,
UInt
shape_line_index
,
std
::
function
<
Vector
<
Real
>
(
Real
)
>
reference
)
{
Real
xq
=
-
1.
/
std
::
sqrt
(
3.
);
// Testing values for bending rotations shapes on quadrature points
for
(
auto
&&
N
:
make_view
(
shape_functions
,
3
,
6
))
{
auto
Nt
=
N
.
transpose
();
Vector
<
Real
>
N_bending
=
Nt
(
shape_line_index
);
auto
bending_reference
=
reference
(
xq
);
if
(
!
Math
::
are_vector_equal
(
6
,
N_bending
.
storage
(),
bending_reference
.
storage
()))
return
false
;
xq
*=
-
1
;
}
std
::
cout
.
flush
();
return
true
;
}
int
main
(
int
argc
,
char
*
argv
[])
{
akantu
::
initialize
(
argc
,
argv
);
// debug::setDebugLevel(dblTest);
constexpr
ElementType
type
=
_bernoulli_beam_2
;
UInt
dim
=
ElementClass
<
type
>::
getSpatialDimension
();
Mesh
mesh
(
dim
);
// creating nodes
Vector
<
Real
>
node
=
{
0
,
0
};
mesh
.
getNodes
().
push_back
(
node
);
node
=
{
3.
/
5.
,
4.
/
5.
};
mesh
.
getNodes
().
push_back
(
node
);
node
=
{
2
*
3.
/
5.
,
0
};
mesh
.
getNodes
().
push_back
(
node
);
mesh
.
addConnectivityType
(
type
);
auto
&
connectivity
=
mesh
.
getConnectivity
(
type
);
// creating elements
Vector
<
UInt
>
elem
=
{
0
,
1
};
connectivity
.
push_back
(
elem
);
elem
=
{
1
,
2
};
connectivity
.
push_back
(
elem
);
elem
=
{
0
,
2
};
connectivity
.
push_back
(
elem
);
using
FE
=
FEEngineTemplate
<
IntegratorGauss
,
ShapeStructural
,
_ek_structural
>
;
using
ShapeStruct
=
ShapeStructural
<
_ek_structural
>
;
auto
fem
=
std
::
make_unique
<
FE
>
(
mesh
,
dim
,
"test_fem"
);
fem
->
initShapeFunctions
();
auto
&
shape
=
dynamic_cast
<
const
ShapeStruct
&>
(
fem
->
getShapeFunctions
());
Array
<
Real
>
angles
;
angles
.
push_back
(
std
::
atan
(
4.
/
3.
));
angles
.
push_back
(
-
std
::
atan
(
4.
/
3.
));
angles
.
push_back
(
0
);
/// Testing the rotation matrices
for
(
auto
&&
tuple
:
zip
(
make_view
(
shape
.
getRotations
(
type
),
3
,
3
),
angles
))
{
auto
&&
rotation
=
std
::
get
<
0
>
(
tuple
);
auto
theta
=
std
::
get
<
1
>
(
tuple
);
auto
reference
=
globalToLocalRotation
(
theta
);
if
(
!
Math
::
are_vector_equal
(
9
,
reference
.
storage
(),
rotation
.
storage
()))
return
1
;
}
auto
&
shape_functions
=
shape
.
getShapes
(
type
);
if
(
!
testBending
(
shape_functions
,
0
,
axialReference
))
return
1
;
// if (!testBending(shape_functions, 1, bendingReference))
// return 1;
// if (!testBending(shape_functions, 2, bendingRotationReference))
// return 1;
std
::
cout
.
flush
();
finalize
();
return
0
;
}
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