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test_structural_mechanics_model_bernoulli_beam_dynamics.cc
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rAKA akantu
test_structural_mechanics_model_bernoulli_beam_dynamics.cc
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/**
* @file test_structural_mechanics_model_bernoulli_beam_dynamics.cc
*
* @author Sébastien Hartmann <sebastien.hartmann@epfl.ch>
*
* @date creation: Mon Jul 07 2014
* @date last modification: Wed Feb 03 2016
*
* @brief Test for _bernouilli_beam in dynamic
*
*
* Copyright (©) 2014-2018 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 "test_structural_mechanics_model_fixture.hh"
/* -------------------------------------------------------------------------- */
#include "dof_manager.hh"
#include "mesh_accessor.hh"
#include "non_linear_solver_newton_raphson.hh"
#include "structural_mechanics_model.hh"
/* -------------------------------------------------------------------------- */
#include <fstream>
#include <iostream>
#include <limits>
/* -------------------------------------------------------------------------- */
using
namespace
akantu
;
/* -------------------------------------------------------------------------- */
static
Real
analytical_solution
(
Real
time
,
Real
L
,
Real
rho
,
Real
E
,
__attribute__
((
unused
))
Real
A
,
Real
I
,
Real
F
)
{
Real
omega
=
M_PI
*
M_PI
/
L
/
L
*
sqrt
(
E
*
I
/
rho
);
Real
sum
=
0.
;
UInt
i
=
5
;
for
(
UInt
n
=
1
;
n
<=
i
;
n
+=
2
)
{
sum
+=
(
1.
-
cos
(
n
*
n
*
omega
*
time
))
/
pow
(
n
,
4
);
}
return
2.
*
F
*
pow
(
L
,
3
)
/
pow
(
M_PI
,
4
)
/
E
/
I
*
sum
;
}
template
<
class
Type
>
class
TestStructBernoulliDynamic
:
public
TestStructuralFixture
<
Type
>
{
using
parent
=
TestStructuralFixture
<
Type
>
;
public
:
const
UInt
nb_element
{
40
};
const
Real
L
{
2
};
const
Real
le
{
L
/
nb_element
};
const
UInt
nb_nodes
{
nb_element
+
1
};
const
Real
F
{
1e4
};
StructuralMaterial
mat
;
void
readMesh
(
std
::
string
/*filename*/
)
override
{
MeshAccessor
mesh_accessor
(
*
this
->
mesh
);
auto
&
nodes
=
mesh_accessor
.
getNodes
();
nodes
.
resize
(
nb_nodes
);
nodes
.
set
(
0.
);
for
(
auto
&&
data
:
enumerate
(
make_view
(
nodes
,
this
->
spatial_dimension
)))
{
auto
&
node
=
std
::
get
<
1
>
(
data
);
UInt
i
=
std
::
get
<
0
>
(
data
);
node
[
_x
]
=
i
*
le
;
}
this
->
mesh
->
addConnectivityType
(
parent
::
type
);
auto
&
connectivities
=
mesh_accessor
.
getConnectivity
(
parent
::
type
);
connectivities
.
resize
(
nb_element
);
for
(
auto
&&
data
:
enumerate
(
make_view
(
connectivities
,
2
)))
{
UInt
i
=
std
::
get
<
0
>
(
data
);
auto
&
connectivity
=
std
::
get
<
1
>
(
data
);
connectivity
=
{
i
,
i
+
1
};
}
mesh_accessor
.
makeReady
();
}
void
setNormals
()
override
{
if
(
this
->
spatial_dimension
!=
3
)
{
return
;
}
auto
&
normals
=
this
->
mesh
->
template
getData
<
Real
>
(
"extra_normal"
,
parent
::
type
);
normals
.
resize
(
nb_element
);
for
(
auto
&&
normal
:
make_view
(
normals
,
this
->
spatial_dimension
))
{
normal
=
{
0.
,
0.
,
1.
};
}
}
AnalysisMethod
getAnalysisMethod
()
const
override
{
return
_implicit_dynamic
;
}
void
addMaterials
()
override
{
this
->
mat
.
E
=
1e9
;
this
->
mat
.
rho
=
10
;
this
->
mat
.
I
=
1
;
this
->
mat
.
Iz
=
1
;
this
->
mat
.
Iy
=
1
;
this
->
mat
.
A
=
1
;
this
->
mat
.
GJ
=
1
;
this
->
model
->
addMaterial
(
mat
);
}
void
setDirichletBCs
()
override
{
auto
&
boundary
=
this
->
model
->
getBlockedDOFs
();
boundary
.
set
(
false
);
boundary
(
0
,
_x
)
=
true
;
boundary
(
0
,
_y
)
=
true
;
boundary
(
nb_nodes
-
1
,
_y
)
=
true
;
if
(
this
->
spatial_dimension
==
3
)
{
boundary
(
0
,
_z
)
=
true
;
boundary
(
nb_nodes
-
1
,
_z
)
=
true
;
}
}
void
setNeumannBCs
()
override
{
auto
node_to_print
=
nb_nodes
/
2
;
// Forces
auto
&
forces
=
this
->
model
->
getExternalForce
();
forces
.
zero
();
forces
(
node_to_print
,
_y
)
=
F
;
}
void
assignMaterials
()
override
{
this
->
model
->
getElementMaterial
(
parent
::
type
).
set
(
0
);
}
};
using
beam_types
=
gtest_list_t
<
std
::
tuple
<
element_type_t
<
_bernoulli_beam_2
>
,
element_type_t
<
_bernoulli_beam_3
>>>
;
TYPED_TEST_SUITE
(
TestStructBernoulliDynamic
,
beam_types
,
);
template
<
class
Type
>
void
getElementMassMatrix
(
const
StructuralMaterial
&
/*material*/
,
Real
/*l*/
,
Matrix
<
Real
>
&
/*M*/
)
{}
template
<
class
Type
>
void
getElementStifnessMatrix
(
const
StructuralMaterial
&
/*material*/
,
Real
/*l*/
,
Matrix
<
Real
>
&
/*M*/
)
{}
template
<>
void
getElementMassMatrix
<
element_type_t
<
_bernoulli_beam_2
>>
(
const
StructuralMaterial
&
material
,
Real
l
,
Matrix
<
Real
>
&
M
)
{
auto
A
=
material
.
A
;
auto
rho
=
material
.
rho
;
// clang-format off
M
=
rho
*
A
*
l
/
420.
*
Matrix
<
Real
>
({
{
140
,
0
,
0
,
70
,
0
,
0
},
{
0
,
156
,
22
*
l
,
0
,
54
,
-
13
*
l
},
{
0
,
22
*
l
,
4
*
l
*
l
,
0
,
13
*
l
,
-
3
*
l
*
l
},
{
70
,
0
,
0
,
140
,
0
,
0
},
{
0
,
54
,
13
*
l
,
0
,
156
,
-
22
*
l
},
{
0
,
-
13
*
l
,
-
3
*
l
*
l
,
0
,
-
22
*
l
,
4
*
l
*
l
}});
// clang-format on
}
template
<>
void
getElementStifnessMatrix
<
element_type_t
<
_bernoulli_beam_2
>>
(
const
StructuralMaterial
&
material
,
Real
l
,
Matrix
<
Real
>
&
K
)
{
auto
E
=
material
.
E
;
auto
A
=
material
.
A
;
auto
I
=
material
.
I
;
auto
l_2
=
l
*
l
;
auto
l_3
=
l
*
l
*
l
;
// clang-format off
K
=
Matrix
<
Real
>
({
{
E
*
A
/
l
,
0
,
0
,
-
E
*
A
/
l
,
0
,
0
},
{
0
,
12
*
E
*
I
/
l_3
,
6
*
E
*
I
/
l_2
,
0
,
-
12
*
E
*
I
/
l_3
,
6
*
E
*
I
/
l_2
},
{
0
,
6
*
E
*
I
/
l_2
,
4
*
E
*
I
/
l
,
0
,
-
6
*
E
*
I
/
l_2
,
2
*
E
*
I
/
l
},
{
-
E
*
A
/
l
,
0
,
0
,
E
*
A
/
l
,
0
,
0
},
{
0
,
-
12
*
E
*
I
/
l_3
,
-
6
*
E
*
I
/
l_2
,
0
,
12
*
E
*
I
/
l_3
,
-
6
*
E
*
I
/
l_2
},
{
0
,
6
*
E
*
I
/
l_2
,
2
*
E
*
I
/
l
,
0
,
-
6
*
E
*
I
/
l_2
,
4
*
E
*
I
/
l
}});
// clang-format on
}
template
<>
void
getElementMassMatrix
<
element_type_t
<
_bernoulli_beam_3
>>
(
const
StructuralMaterial
&
material
,
Real
l
,
Matrix
<
Real
>
&
M
)
{
auto
A
=
material
.
A
;
auto
rho
=
material
.
rho
;
// clang-format off
M
=
rho
*
A
*
l
/
420.
*
Matrix
<
Real
>
({
{
140
,
0
,
0
,
0
,
0
,
0
,
70
,
0
,
0
,
0
,
0
,
0
},
{
0
,
156
,
0
,
0
,
0
,
22
*
l
,
0
,
54
,
0
,
0
,
0
,
-
13
*
l
},
{
0
,
0
,
156
,
0
,
-
22
*
l
,
0
,
0
,
0
,
54
,
0
,
13
*
l
,
0
},
{
0
,
0
,
0
,
140
,
0
,
0
,
0
,
0
,
0
,
70
,
0
,
0
},
{
0
,
0
,
-
22
*
l
,
0
,
4
*
l
*
l
,
0
,
0
,
0
,
-
13
*
l
,
0
,
-
3
*
l
*
l
,
0
},
{
0
,
22
*
l
,
0
,
0
,
0
,
4
*
l
*
l
,
0
,
13
*
l
,
0
,
0
,
0
,
-
3
*
l
*
l
},
{
70
,
0
,
0
,
0
,
0
,
0
,
140
,
0
,
0
,
0
,
0
,
0
},
{
0
,
54
,
0
,
0
,
0
,
13
*
l
,
0
,
156
,
0
,
0
,
0
,
-
22
*
l
},
{
0
,
0
,
54
,
0
,
-
13
*
l
,
0
,
0
,
0
,
156
,
0
,
22
*
l
,
0
},
{
0
,
0
,
0
,
70
,
0
,
0
,
0
,
0
,
0
,
140
,
0
,
0
},
{
0
,
0
,
13
*
l
,
0
,
-
3
*
l
*
l
,
0
,
0
,
0
,
22
*
l
,
0
,
4
*
l
*
l
,
0
},
{
0
,
-
13
*
l
,
0
,
0
,
0
,
-
3
*
l
*
l
,
0
,
-
22
*
l
,
0
,
0
,
0
,
4
*
l
*
l
}});
// clang-format on
}
template
<>
void
getElementStifnessMatrix
<
element_type_t
<
_bernoulli_beam_3
>>
(
const
StructuralMaterial
&
material
,
Real
l
,
Matrix
<
Real
>
&
K
)
{
auto
E
=
material
.
E
;
auto
A
=
material
.
A
;
auto
Iy
=
material
.
Iy
;
auto
Iz
=
material
.
Iz
;
auto
GJ
=
material
.
GJ
;
auto
a1
=
E
*
A
/
l
;
auto
b1
=
12
*
E
*
Iz
/
l
/
l
/
l
;
auto
b2
=
6
*
E
*
Iz
/
l
/
l
;
auto
b3
=
4
*
E
*
Iz
/
l
;
auto
b4
=
2
*
E
*
Iz
/
l
;
auto
c1
=
12
*
E
*
Iy
/
l
/
l
/
l
;
auto
c2
=
6
*
E
*
Iy
/
l
/
l
;
auto
c3
=
4
*
E
*
Iy
/
l
;
auto
c4
=
2
*
E
*
Iy
/
l
;
auto
d1
=
GJ
/
l
;
// clang-format off
K
=
Matrix
<
Real
>
({
{
a1
,
0
,
0
,
0
,
0
,
0
,
-
a1
,
0
,
0
,
0
,
0
,
0
},
{
0
,
b1
,
0
,
0
,
0
,
b2
,
0
,
-
b1
,
0
,
0
,
0
,
b2
},
{
0
,
0
,
c1
,
0
,
-
c2
,
0
,
0
,
0
,
-
c1
,
0
,
-
c2
,
0
},
{
0
,
0
,
0
,
d1
,
0
,
0
,
0
,
0
,
0
,
-
d1
,
0
,
0
},
{
0
,
0
,
-
c2
,
0
,
c3
,
0
,
0
,
0
,
c2
,
0
,
c4
,
0
},
{
0
,
b2
,
0
,
0
,
0
,
b3
,
0
,
-
b2
,
0
,
0
,
0
,
b4
},
{
-
a1
,
0
,
0
,
0
,
0
,
0
,
a1
,
0
,
0
,
0
,
0
,
0
},
{
0
,
-
b1
,
0
,
0
,
0
,
-
b2
,
0
,
b1
,
0
,
0
,
0
,
-
b2
},
{
0
,
0
,
-
c1
,
0
,
c2
,
0
,
0
,
0
,
c1
,
0
,
c2
,
0
},
{
0
,
0
,
0
,
-
d1
,
0
,
0
,
0
,
0
,
0
,
d1
,
0
,
0
},
{
0
,
0
,
-
c2
,
0
,
c4
,
0
,
0
,
0
,
c2
,
0
,
c3
,
0
},
{
0
,
b2
,
0
,
0
,
0
,
b4
,
0
,
-
b2
,
0
,
0
,
0
,
b3
}});
// clang-format on
}
TYPED_TEST
(
TestStructBernoulliDynamic
,
TestBeamMatrices
)
{
this
->
model
->
assembleMatrix
(
"M"
);
this
->
model
->
assembleMatrix
(
"K"
);
const
auto
&
K
=
this
->
model
->
getDOFManager
().
getMatrix
(
"K"
);
const
auto
&
M
=
this
->
model
->
getDOFManager
().
getMatrix
(
"M"
);
Matrix
<
Real
>
Ka
(
this
->
nb_nodes
*
this
->
ndof
,
this
->
nb_nodes
*
this
->
ndof
,
0.
);
Matrix
<
Real
>
Ma
(
this
->
nb_nodes
*
this
->
ndof
,
this
->
nb_nodes
*
this
->
ndof
,
0.
);
Matrix
<
Real
>
Ke
(
this
->
ndof
*
2
,
this
->
ndof
*
2
);
Matrix
<
Real
>
Me
(
this
->
ndof
*
2
,
this
->
ndof
*
2
);
getElementMassMatrix
<
TypeParam
>
(
this
->
mat
,
this
->
le
,
Me
);
getElementStifnessMatrix
<
TypeParam
>
(
this
->
mat
,
this
->
le
,
Ke
);
auto
assemble
=
[
&
](
auto
&&
nodes
,
auto
&&
M
,
auto
&&
Me
)
{
auto
n1
=
nodes
[
0
];
auto
n2
=
nodes
[
1
];
for
(
auto
i
:
arange
(
this
->
ndof
))
{
for
(
auto
j
:
arange
(
this
->
ndof
))
{
M
(
n1
*
this
->
ndof
+
i
,
n1
*
this
->
ndof
+
j
)
+=
Me
(
i
,
j
);
M
(
n2
*
this
->
ndof
+
i
,
n2
*
this
->
ndof
+
j
)
+=
Me
(
this
->
ndof
+
i
,
this
->
ndof
+
j
);
M
(
n1
*
this
->
ndof
+
i
,
n2
*
this
->
ndof
+
j
)
+=
Me
(
i
,
this
->
ndof
+
j
);
M
(
n2
*
this
->
ndof
+
i
,
n1
*
this
->
ndof
+
j
)
+=
Me
(
this
->
ndof
+
i
,
j
);
}
}
};
auto
&&
connectivities
=
this
->
mesh
->
getConnectivity
(
this
->
type
);
for
(
auto
&&
connectivity
:
make_view
(
connectivities
,
2
))
{
assemble
(
connectivity
,
Ka
,
Ke
);
assemble
(
connectivity
,
Ma
,
Me
);
}
auto
tol
=
1e-13
;
auto
Ka_max
=
Ka
.
template
norm
<
L_inf
>
();
auto
Ma_max
=
Ma
.
template
norm
<
L_inf
>
();
for
(
auto
i
:
arange
(
Ka
.
rows
()))
{
for
(
auto
j
:
arange
(
Ka
.
cols
()))
{
EXPECT_NEAR
(
Ka
(
i
,
j
),
K
(
i
,
j
),
tol
*
Ka_max
);
EXPECT_NEAR
(
Ma
(
i
,
j
),
M
(
i
,
j
),
tol
*
Ma_max
);
}
}
}
TYPED_TEST
(
TestStructBernoulliDynamic
,
TestBeamOscilation
)
{
Real
time_step
=
1e-6
;
this
->
model
->
setTimeStep
(
time_step
);
auto
&
solver
=
this
->
model
->
getNonLinearSolver
();
solver
.
set
(
"max_iterations"
,
100
);
solver
.
set
(
"threshold"
,
1e-8
);
solver
.
set
(
"convergence_type"
,
SolveConvergenceCriteria
::
_solution
);
auto
node_to_print
=
this
->
nb_nodes
/
2
;
auto
&
d
=
this
->
model
->
getDisplacement
()(
node_to_print
,
_y
);
std
::
ofstream
pos
;
std
::
string
filename
=
"position"
+
std
::
to_string
(
this
->
type
)
+
".csv"
;
pos
.
open
(
filename
);
if
(
not
pos
.
good
())
{
AKANTU_ERROR
(
"Cannot open file
\"
position.csv
\"
"
);
}
pos
<<
"id,time,position,solution"
<<
std
::
endl
;
//#define debug
#ifdef debug
this
->
model
->
addDumpFieldVector
(
"displacement"
);
this
->
model
->
addDumpField
(
"blocked_dofs"
);
this
->
model
->
addDumpFieldVector
(
"external_force"
);
this
->
model
->
addDumpFieldVector
(
"internal_force"
);
this
->
model
->
addDumpFieldVector
(
"acceleration"
);
this
->
model
->
addDumpFieldVector
(
"velocity"
);
this
->
model
->
dump
();
#endif
this
->
model
->
getDisplacement
().
set
(
0.
);
Real
tol
=
1e-6
;
Real
time
=
0.
;
for
(
UInt
s
=
1
;
s
<
300
;
++
s
)
{
EXPECT_NO_THROW
(
this
->
model
->
solveStep
());
time
=
s
*
time_step
;
auto
da
=
analytical_solution
(
time
,
this
->
L
,
this
->
mat
.
rho
,
this
->
mat
.
E
,
this
->
mat
.
A
,
this
->
mat
.
Iy
,
this
->
F
);
pos
<<
s
<<
","
<<
time
<<
","
<<
d
<<
","
<<
da
<<
std
::
endl
;
#ifdef debug
this
->
model
->
dump
();
#endif
EXPECT_NEAR
(
d
,
da
,
tol
);
}
}
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