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test_model_solver_dynamic.cc
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rAKA akantu
test_model_solver_dynamic.cc
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/**
* @file test_dof_manager_default.cc
*
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date Wed Feb 24 12:28:44 2016
*
* @brief Test default dof manager
*
* @section LICENSE
*
* Copyright (©) 2010-2011 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 "model_solver.hh"
#include "mesh.hh"
#include "mesh_accessor.hh"
#include "dof_manager.hh"
#include "sparse_matrix.hh"
using
namespace
akantu
;
class
MyModel
;
static
void
genMesh
(
Mesh
&
mesh
,
UInt
nb_nodes
);
/**
* =\o-----o-----o-> F
* | |
* |---- L ----|
*/
class
MyModel
:
public
ModelSolver
{
public
:
MyModel
(
Real
F
,
Mesh
&
mesh
,
bool
lumped
)
:
ModelSolver
(
mesh
,
"model_solver"
,
0
),
displacement
(
mesh
.
getNbNodes
(),
1
,
"disp"
),
velocity
(
mesh
.
getNbNodes
(),
1
,
"velo"
),
acceleration
(
mesh
.
getNbNodes
(),
1
,
"accel"
),
blocked
(
mesh
.
getNbNodes
(),
1
,
"blocked"
),
forces
(
mesh
.
getNbNodes
(),
1
,
"force_ext"
),
internal_forces
(
mesh
.
getNbNodes
(),
1
,
"force_int"
),
mesh
(
mesh
),
nb_dofs
(
mesh
.
getNbNodes
()),
E
(
1.
),
A
(
1.
),
rho
(
1.
),
lumped
(
lumped
)
{
this
->
initDOFManager
(
"mumps"
);
this
->
getDOFManager
().
registerDOFs
(
"disp"
,
displacement
,
_dst_nodal
);
this
->
getDOFManager
().
registerDOFsDerivative
(
"disp"
,
1
,
velocity
);
this
->
getDOFManager
().
registerDOFsDerivative
(
"disp"
,
2
,
acceleration
);
this
->
getDOFManager
().
registerBlockedDOFs
(
"disp"
,
blocked
);
this
->
getDOFManager
().
getNewMatrix
(
"K"
,
_symmetric
);
this
->
getDOFManager
().
getNewMatrix
(
"M"
,
"K"
);
this
->
getDOFManager
().
getNewMatrix
(
"J"
,
"K"
);
this
->
getDOFManager
().
getNewLumpedMatrix
(
"M"
);
if
(
lumped
)
{
this
->
assembleLumpedMass
();
}
else
{
this
->
assembleMass
();
this
->
assembleStiffness
();
}
this
->
assembleJacobian
();
displacement
.
set
(
0.
);
velocity
.
set
(
0.
);
acceleration
.
set
(
0.
);
forces
.
set
(
0.
);
blocked
.
set
(
false
);
forces
(
nb_dofs
-
1
,
_x
)
=
F
;
// displacement(nb_dofs - 1, _x) = .1;
blocked
(
0
,
_x
)
=
true
;
}
void
assembleLumpedMass
()
{
Array
<
Real
>
&
M
=
this
->
getDOFManager
().
getLumpedMatrix
(
"M"
);
M
.
clear
();
Array
<
Real
>
m_all_el
(
this
->
nb_dofs
-
1
,
2
);
Array
<
Real
>::
vector_iterator
m_it
=
m_all_el
.
begin
(
2
);
Array
<
UInt
>::
const_vector_iterator
cit
=
this
->
mesh
.
getConnectivity
(
_segment_2
).
begin
(
2
);
Array
<
UInt
>::
const_vector_iterator
cend
=
this
->
mesh
.
getConnectivity
(
_segment_2
).
end
(
2
);
for
(;
cit
!=
cend
;
++
cit
,
++
m_it
)
{
const
Vector
<
UInt
>
&
conn
=
*
cit
;
UInt
n1
=
conn
(
0
);
UInt
n2
=
conn
(
1
);
Real
p1
=
this
->
mesh
.
getNodes
()(
n1
,
_x
);
Real
p2
=
this
->
mesh
.
getNodes
()(
n2
,
_x
);
Real
L
=
std
::
abs
(
p2
-
p1
);
Real
M_n
=
rho
*
A
*
L
/
2
;
(
*
m_it
)(
0
)
=
(
*
m_it
)(
1
)
=
M_n
;
}
this
->
getDOFManager
().
assembleElementalArrayLocalArray
(
m_all_el
,
M
,
_segment_2
,
_not_ghost
);
}
void
assembleMass
()
{
SparseMatrix
&
M
=
this
->
getDOFManager
().
getMatrix
(
"M"
);
M
.
clear
();
Array
<
Real
>
m_all_el
(
this
->
nb_dofs
-
1
,
4
);
Array
<
Real
>::
matrix_iterator
m_it
=
m_all_el
.
begin
(
2
,
2
);
Array
<
UInt
>::
const_vector_iterator
cit
=
this
->
mesh
.
getConnectivity
(
_segment_2
).
begin
(
2
);
Array
<
UInt
>::
const_vector_iterator
cend
=
this
->
mesh
.
getConnectivity
(
_segment_2
).
end
(
2
);
Matrix
<
Real
>
m
(
2
,
2
);
m
(
0
,
0
)
=
m
(
1
,
1
)
=
2
;
m
(
0
,
1
)
=
m
(
1
,
0
)
=
1
;
// under integrated
// m(0, 0) = m(1, 1) = 3./2.;
// m(0, 1) = m(1, 0) = 3./2.;
// lumping the mass matrix
// m(0, 0) += m(0, 1);
// m(1, 1) += m(1, 0);
// m(0, 1) = m(1, 0) = 0;
for
(;
cit
!=
cend
;
++
cit
,
++
m_it
)
{
const
Vector
<
UInt
>
&
conn
=
*
cit
;
UInt
n1
=
conn
(
0
);
UInt
n2
=
conn
(
1
);
Real
p1
=
this
->
mesh
.
getNodes
()(
n1
,
_x
);
Real
p2
=
this
->
mesh
.
getNodes
()(
n2
,
_x
);
Real
L
=
std
::
abs
(
p2
-
p1
);
Matrix
<
Real
>
&
m_el
=
*
m_it
;
m_el
=
m
;
m_el
*=
rho
*
A
*
L
/
6.
;
}
this
->
getDOFManager
().
assembleElementalMatricesToMatrix
(
"M"
,
"disp"
,
m_all_el
,
_segment_2
);
}
void
assembleJacobian
()
{}
void
assembleStiffness
()
{
SparseMatrix
&
K
=
this
->
getDOFManager
().
getMatrix
(
"K"
);
K
.
clear
();
Matrix
<
Real
>
k
(
2
,
2
);
k
(
0
,
0
)
=
k
(
1
,
1
)
=
1
;
k
(
0
,
1
)
=
k
(
1
,
0
)
=
-
1
;
Array
<
Real
>
k_all_el
(
this
->
nb_dofs
-
1
,
4
);
Array
<
Real
>::
matrix_iterator
k_it
=
k_all_el
.
begin
(
2
,
2
);
Array
<
UInt
>::
const_vector_iterator
cit
=
this
->
mesh
.
getConnectivity
(
_segment_2
).
begin
(
2
);
Array
<
UInt
>::
const_vector_iterator
cend
=
this
->
mesh
.
getConnectivity
(
_segment_2
).
end
(
2
);
for
(;
cit
!=
cend
;
++
cit
,
++
k_it
)
{
const
Vector
<
UInt
>
&
conn
=
*
cit
;
UInt
n1
=
conn
(
0
);
UInt
n2
=
conn
(
1
);
Real
p1
=
this
->
mesh
.
getNodes
()(
n1
,
_x
);
Real
p2
=
this
->
mesh
.
getNodes
()(
n2
,
_x
);
Real
L
=
std
::
abs
(
p2
-
p1
);
Matrix
<
Real
>
&
k_el
=
*
k_it
;
k_el
=
k
;
k_el
*=
E
*
A
/
L
;
}
this
->
getDOFManager
().
assembleElementalMatricesToMatrix
(
"K"
,
"disp"
,
k_all_el
,
_segment_2
);
}
void
assembleResidual
()
{
this
->
getDOFManager
().
assembleToResidual
(
"disp"
,
forces
);
Array
<
Real
>
forces_internal_el
(
this
->
nb_dofs
-
1
,
2
);
Array
<
Real
>::
vector_iterator
f_it
=
forces_internal_el
.
begin
(
2
);
Array
<
UInt
>::
const_vector_iterator
cit
=
this
->
mesh
.
getConnectivity
(
_segment_2
).
begin
(
2
);
Array
<
UInt
>::
const_vector_iterator
cend
=
this
->
mesh
.
getConnectivity
(
_segment_2
).
end
(
2
);
for
(;
cit
!=
cend
;
++
cit
,
++
f_it
)
{
const
Vector
<
UInt
>
&
conn
=
*
cit
;
UInt
n1
=
conn
(
0
);
UInt
n2
=
conn
(
1
);
Real
p1
=
this
->
mesh
.
getNodes
()(
n1
,
_x
);
Real
p2
=
this
->
mesh
.
getNodes
()(
n2
,
_x
);
Real
L
=
std
::
abs
(
p2
-
p1
);
Real
u1
=
this
->
displacement
(
n1
,
_x
);
Real
u2
=
this
->
displacement
(
n2
,
_x
);
Real
f_n
=
E
*
A
/
L
*
(
u2
-
u1
);
Vector
<
Real
>
&
f
=
*
f_it
;
f
(
0
)
=
-
f_n
;
f
(
1
)
=
f_n
;
}
internal_forces
.
clear
();
this
->
getDOFManager
().
assembleElementalArrayLocalArray
(
forces_internal_el
,
internal_forces
,
_segment_2
,
_not_ghost
);
this
->
getDOFManager
().
assembleToResidual
(
"disp"
,
internal_forces
,
-
1.
);
}
Real
getPotentialEnergy
()
{
Real
res
=
0
;
if
(
!
lumped
)
{
res
=
this
->
mulVectMatVect
(
this
->
displacement
,
this
->
getDOFManager
().
getMatrix
(
"K"
),
this
->
displacement
);
}
else
{
Array
<
UInt
>::
const_vector_iterator
cit
=
this
->
mesh
.
getConnectivity
(
_segment_2
).
begin
(
2
);
Array
<
UInt
>::
const_vector_iterator
cend
=
this
->
mesh
.
getConnectivity
(
_segment_2
).
end
(
2
);
for
(;
cit
!=
cend
;
++
cit
)
{
const
Vector
<
UInt
>
&
conn
=
*
cit
;
UInt
n1
=
conn
(
0
);
UInt
n2
=
conn
(
1
);
Real
p1
=
this
->
mesh
.
getNodes
()(
n1
,
_x
);
Real
p2
=
this
->
mesh
.
getNodes
()(
n2
,
_x
);
Real
L
=
std
::
abs
(
p2
-
p1
);
Real
u1
=
this
->
displacement
(
n1
,
_x
);
Real
u2
=
this
->
displacement
(
n2
,
_x
);
Real
strain
=
(
u2
-
u1
)
/
L
;
res
+=
strain
*
E
*
strain
*
A
*
L
;
}
}
return
res
/
2.
;
}
Real
getKineticEnergy
()
{
Real
res
=
0
;
if
(
!
lumped
)
{
res
=
this
->
mulVectMatVect
(
this
->
velocity
,
this
->
getDOFManager
().
getMatrix
(
"M"
),
this
->
velocity
);
}
else
{
Array
<
Real
>
&
m
=
this
->
getDOFManager
().
getLumpedMatrix
(
"M"
);
Array
<
Real
>::
const_scalar_iterator
it
=
velocity
.
begin
();
Array
<
Real
>::
const_scalar_iterator
end
=
velocity
.
end
();
Array
<
Real
>::
const_scalar_iterator
m_it
=
m
.
begin
();
for
(;
it
!=
end
;
++
it
,
++
m_it
)
{
res
+=
*
m_it
*
*
it
*
*
it
;
}
}
return
res
/
2.
;
}
Real
mulVectMatVect
(
const
Array
<
Real
>
&
x
,
const
SparseMatrix
&
A
,
const
Array
<
Real
>
&
y
)
{
Array
<
Real
>
Ay
(
this
->
nb_dofs
);
A
.
matVecMul
(
y
,
Ay
);
Real
res
=
0.
;
Array
<
Real
>::
const_scalar_iterator
it
=
Ay
.
begin
();
Array
<
Real
>::
const_scalar_iterator
end
=
Ay
.
end
();
Array
<
Real
>::
const_scalar_iterator
x_it
=
x
.
begin
();
for
(;
it
!=
end
;
++
it
,
++
x_it
)
{
res
+=
*
x_it
*
*
it
;
}
return
res
;
}
void
predictor
()
{}
void
corrector
()
{}
Array
<
Real
>
displacement
;
Array
<
Real
>
velocity
;
Array
<
Real
>
acceleration
;
Array
<
bool
>
blocked
;
Array
<
Real
>
forces
;
Array
<
Real
>
internal_forces
;
private
:
Mesh
&
mesh
;
UInt
nb_dofs
;
Real
E
,
A
,
rho
;
bool
lumped
;
};
/* -------------------------------------------------------------------------- */
int
main
(
int
argc
,
char
*
argv
[])
{
initialize
(
argc
,
argv
);
UInt
nb_nodes
=
201
;
UInt
max_steps
=
5000
;
Real
time_step
=
0.001
;
Mesh
mesh
(
1
);
Real
F
=
9.81
;
bool
_explicit
=
false
;
genMesh
(
mesh
,
nb_nodes
);
MyModel
model
(
F
,
mesh
,
_explicit
);
if
(
!
_explicit
)
{
model
.
getNewSolver
(
"dynamic"
,
_tsst_dynamic
,
_nls_newton_raphson
);
model
.
setIntegrationScheme
(
"dynamic"
,
"disp"
,
_ist_trapezoidal_rule_2
,
IntegrationScheme
::
_displacement
);
}
else
{
model
.
getNewSolver
(
"dynamic"
,
_tsst_dynamic_lumped
,
_nls_lumped
);
model
.
setIntegrationScheme
(
"dynamic"
,
"disp"
,
_ist_central_difference
,
IntegrationScheme
::
_acceleration
);
}
model
.
setTimeStep
(
time_step
);
const
Array
<
Real
>
&
disp
=
model
.
displacement
;
const
Array
<
Real
>
&
velo
=
model
.
velocity
;
const
Array
<
Real
>
&
reac
=
model
.
internal_forces
;
std
::
cout
<<
std
::
setw
(
8
)
<<
"time"
<<
", "
<<
std
::
setw
(
8
)
<<
"disp"
<<
", "
<<
std
::
setw
(
8
)
<<
"velo"
<<
", "
<<
std
::
setw
(
8
)
<<
"reac"
<<
", "
<<
std
::
setw
(
8
)
<<
"wext"
<<
", "
<<
std
::
setw
(
8
)
<<
"epot"
<<
", "
<<
std
::
setw
(
8
)
<<
"ekin"
<<
std
::
endl
;
Real
wext
=
0
;
for
(
UInt
i
=
1
;
i
<
max_steps
+
1
;
++
i
)
{
model
.
solveStep
();
wext
+=
F
*
velo
(
nb_nodes
-
1
,
0
)
*
time_step
;
Real
epot
=
model
.
getPotentialEnergy
();
Real
ekin
=
model
.
getKineticEnergy
();
std
::
cout
<<
std
::
setw
(
8
)
<<
time_step
*
i
<<
", "
<<
std
::
setw
(
8
)
<<
disp
(
nb_nodes
-
1
,
_x
)
<<
", "
<<
std
::
setw
(
8
)
<<
velo
(
nb_nodes
-
1
,
_x
)
<<
", "
<<
std
::
setw
(
8
)
<<
(
-
reac
(
0
,
_x
))
<<
", "
<<
std
::
setw
(
8
)
<<
wext
<<
", "
<<
std
::
setw
(
8
)
<<
epot
<<
", "
<<
std
::
setw
(
8
)
<<
ekin
<<
std
::
endl
;
}
finalize
();
return
EXIT_SUCCESS
;
}
/* -------------------------------------------------------------------------- */
void
genMesh
(
Mesh
&
mesh
,
UInt
nb_nodes
)
{
MeshAccessor
mesh_accessor
(
mesh
);
Array
<
Real
>
&
nodes
=
mesh_accessor
.
getNodes
();
Array
<
UInt
>
&
conn
=
mesh_accessor
.
getConnectivity
(
_segment_2
);
nodes
.
resize
(
nb_nodes
);
for
(
UInt
n
=
0
;
n
<
nb_nodes
;
++
n
)
{
nodes
(
n
,
_x
)
=
n
*
(
1.
/
(
nb_nodes
-
1
));
}
conn
.
resize
(
nb_nodes
-
1
);
for
(
UInt
n
=
0
;
n
<
nb_nodes
-
1
;
++
n
)
{
conn
(
n
,
0
)
=
n
;
conn
(
n
,
1
)
=
n
+
1
;
}
}
Event Timeline
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