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rAKA akantu
newmark-beta.cc
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/**
* @file newmark-beta.cc
*
* @author David Simon Kammer <david.kammer@epfl.ch>
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date creation: Fri Oct 23 2015
* @date last modification: Wed Mar 27 2019
*
* @brief implementation of the newmark-@f$\beta@f$ integration scheme. This
* implementation is taken from Méthodes numériques en mécanique des solides by
* Alain Curnier \note{ISBN: 2-88074-247-1}
*
*
* @section LICENSE
*
* Copyright (©) 2015-2021 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/>.
*
*/
/* -------------------------------------------------------------------------- */
#include "newmark-beta.hh"
#include "dof_manager.hh"
#include "sparse_matrix.hh"
/* -------------------------------------------------------------------------- */
namespace
akantu
{
/* -------------------------------------------------------------------------- */
NewmarkBeta
::
NewmarkBeta
(
DOFManager
&
dof_manager
,
const
ID
&
dof_id
,
Real
alpha
,
Real
beta
)
:
IntegrationScheme2ndOrder
(
dof_manager
,
dof_id
),
beta
(
beta
),
alpha
(
alpha
),
k
(
0.
),
h
(
0.
),
m_release
(
0
),
k_release
(
0
),
c_release
(
0
)
{
this
->
registerParam
(
"alpha"
,
this
->
alpha
,
alpha
,
_pat_parsmod
,
"The alpha parameter"
);
this
->
registerParam
(
"beta"
,
this
->
beta
,
beta
,
_pat_parsmod
,
"The beta parameter"
);
}
/* -------------------------------------------------------------------------- */
/*
* @f$ \tilde{u_{n+1}} = u_{n} + \Delta t \dot{u}_n + \frac{\Delta t^2}{2}
* \ddot{u}_n @f$
* @f$ \tilde{\dot{u}_{n+1}} = \dot{u}_{n} + \Delta t \ddot{u}_{n} @f$
* @f$ \tilde{\ddot{u}_{n}} = \ddot{u}_{n} @f$
*/
void
NewmarkBeta
::
predictor
(
Real
delta_t
,
Array
<
Real
>
&
u
,
Array
<
Real
>
&
u_dot
,
Array
<
Real
>
&
u_dot_dot
,
const
Array
<
bool
>
&
blocked_dofs
)
const
{
AKANTU_DEBUG_IN
();
UInt
nb_nodes
=
u
.
size
();
UInt
nb_degree_of_freedom
=
u
.
getNbComponent
()
*
nb_nodes
;
Real
*
u_val
=
u
.
storage
();
Real
*
u_dot_val
=
u_dot
.
storage
();
Real
*
u_dot_dot_val
=
u_dot_dot
.
storage
();
bool
*
blocked_dofs_val
=
blocked_dofs
.
storage
();
for
(
UInt
d
=
0
;
d
<
nb_degree_of_freedom
;
d
++
)
{
if
(
!
(
*
blocked_dofs_val
))
{
Real
dt_a_n
=
delta_t
*
*
u_dot_dot_val
;
*
u_val
+=
(
1
-
k
*
alpha
)
*
delta_t
*
*
u_dot_val
+
(
.5
-
h
*
alpha
*
beta
)
*
delta_t
*
dt_a_n
;
*
u_dot_val
=
(
1
-
k
)
*
*
u_dot_val
+
(
1
-
h
*
beta
)
*
dt_a_n
;
*
u_dot_dot_val
=
(
1
-
h
)
*
*
u_dot_dot_val
;
}
u_val
++
;
u_dot_val
++
;
u_dot_dot_val
++
;
blocked_dofs_val
++
;
}
AKANTU_DEBUG_OUT
();
}
/* -------------------------------------------------------------------------- */
void
NewmarkBeta
::
corrector
(
const
SolutionType
&
type
,
Real
delta_t
,
Array
<
Real
>
&
u
,
Array
<
Real
>
&
u_dot
,
Array
<
Real
>
&
u_dot_dot
,
const
Array
<
bool
>
&
blocked_dofs
,
const
Array
<
Real
>
&
delta
)
const
{
AKANTU_DEBUG_IN
();
switch
(
type
)
{
case
_acceleration:
{
this
->
allCorrector
<
_acceleration
>
(
delta_t
,
u
,
u_dot
,
u_dot_dot
,
blocked_dofs
,
delta
);
break
;
}
case
_velocity:
{
this
->
allCorrector
<
_velocity
>
(
delta_t
,
u
,
u_dot
,
u_dot_dot
,
blocked_dofs
,
delta
);
break
;
}
case
_displacement:
{
this
->
allCorrector
<
_displacement
>
(
delta_t
,
u
,
u_dot
,
u_dot_dot
,
blocked_dofs
,
delta
);
break
;
}
default
:
AKANTU_EXCEPTION
(
"The corrector type : "
<<
type
<<
" is not supported by this type of integration scheme"
);
}
AKANTU_DEBUG_OUT
();
}
/* -------------------------------------------------------------------------- */
Real
NewmarkBeta
::
getAccelerationCoefficient
(
const
SolutionType
&
type
,
Real
delta_t
)
const
{
switch
(
type
)
{
case
_acceleration:
return
1.
;
case
_velocity:
return
1.
/
(
beta
*
delta_t
);
case
_displacement:
return
1.
/
(
alpha
*
beta
*
delta_t
*
delta_t
);
default
:
AKANTU_EXCEPTION
(
"The corrector type : "
<<
type
<<
" is not supported by this type of integration scheme"
);
}
}
/* -------------------------------------------------------------------------- */
Real
NewmarkBeta
::
getVelocityCoefficient
(
const
SolutionType
&
type
,
Real
delta_t
)
const
{
switch
(
type
)
{
case
_acceleration:
return
beta
*
delta_t
;
case
_velocity:
return
1.
;
case
_displacement:
return
1.
/
(
alpha
*
delta_t
);
default
:
AKANTU_EXCEPTION
(
"The corrector type : "
<<
type
<<
" is not supported by this type of integration scheme"
);
}
}
/* -------------------------------------------------------------------------- */
Real
NewmarkBeta
::
getDisplacementCoefficient
(
const
SolutionType
&
type
,
Real
delta_t
)
const
{
switch
(
type
)
{
case
_acceleration:
return
alpha
*
beta
*
delta_t
*
delta_t
;
case
_velocity:
return
alpha
*
delta_t
;
case
_displacement:
return
1.
;
default
:
AKANTU_EXCEPTION
(
"The corrector type : "
<<
type
<<
" is not supported by this type of integration scheme"
);
}
}
/* -------------------------------------------------------------------------- */
template
<
IntegrationScheme
::
SolutionType
type
>
void
NewmarkBeta
::
allCorrector
(
Real
delta_t
,
Array
<
Real
>
&
u
,
Array
<
Real
>
&
u_dot
,
Array
<
Real
>
&
u_dot_dot
,
const
Array
<
bool
>
&
blocked_dofs
,
const
Array
<
Real
>
&
delta
)
const
{
AKANTU_DEBUG_IN
();
UInt
nb_nodes
=
u
.
size
();
UInt
nb_degree_of_freedom
=
u
.
getNbComponent
()
*
nb_nodes
;
Real
c
=
getAccelerationCoefficient
(
type
,
delta_t
);
Real
d
=
getVelocityCoefficient
(
type
,
delta_t
);
Real
e
=
getDisplacementCoefficient
(
type
,
delta_t
);
Real
*
u_val
=
u
.
storage
();
Real
*
u_dot_val
=
u_dot
.
storage
();
Real
*
u_dot_dot_val
=
u_dot_dot
.
storage
();
Real
*
delta_val
=
delta
.
storage
();
bool
*
blocked_dofs_val
=
blocked_dofs
.
storage
();
for
(
UInt
dof
=
0
;
dof
<
nb_degree_of_freedom
;
dof
++
)
{
if
(
!
(
*
blocked_dofs_val
))
{
*
u_val
+=
e
*
*
delta_val
;
*
u_dot_val
+=
d
*
*
delta_val
;
*
u_dot_dot_val
+=
c
*
*
delta_val
;
}
u_val
++
;
u_dot_val
++
;
u_dot_dot_val
++
;
delta_val
++
;
blocked_dofs_val
++
;
}
AKANTU_DEBUG_OUT
();
}
/* -------------------------------------------------------------------------- */
void
NewmarkBeta
::
assembleJacobian
(
const
SolutionType
&
type
,
Real
delta_t
)
{
AKANTU_DEBUG_IN
();
SparseMatrix
&
J
=
this
->
dof_manager
.
getMatrix
(
"J"
);
const
SparseMatrix
&
M
=
this
->
dof_manager
.
getMatrix
(
"M"
);
const
SparseMatrix
&
K
=
this
->
dof_manager
.
getMatrix
(
"K"
);
bool
does_j_need_update
=
false
;
does_j_need_update
|=
M
.
getRelease
()
!=
m_release
;
does_j_need_update
|=
K
.
getRelease
()
!=
k_release
;
if
(
this
->
dof_manager
.
hasMatrix
(
"C"
))
{
const
SparseMatrix
&
C
=
this
->
dof_manager
.
getMatrix
(
"C"
);
does_j_need_update
|=
C
.
getRelease
()
!=
c_release
;
}
does_j_need_update
|=
this
->
dof_manager
.
hasBlockedDOFsChanged
();
if
(
!
does_j_need_update
)
{
AKANTU_DEBUG_OUT
();
return
;
}
J
.
copyProfile
(
K
);
// J.zero();
Real
c
=
this
->
getAccelerationCoefficient
(
type
,
delta_t
);
Real
e
=
this
->
getDisplacementCoefficient
(
type
,
delta_t
);
if
(
!
(
e
==
0.
))
{
// in explicit this coefficient is exactly 0.
J
.
add
(
K
,
e
);
}
J
.
add
(
M
,
c
);
m_release
=
M
.
getRelease
();
k_release
=
K
.
getRelease
();
if
(
this
->
dof_manager
.
hasMatrix
(
"C"
))
{
Real
d
=
this
->
getVelocityCoefficient
(
type
,
delta_t
);
const
SparseMatrix
&
C
=
this
->
dof_manager
.
getMatrix
(
"C"
);
J
.
add
(
C
,
d
);
c_release
=
C
.
getRelease
();
}
AKANTU_DEBUG_OUT
();
}
/* -------------------------------------------------------------------------- */
}
// namespace akantu
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