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rAKA akantu
structural_mechanics_model_inline_impl.cc
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/**
* @file structural_mechanics_model_inline_impl.cc
*
* @author Fabian Barras <fabian.barras@epfl.ch>
* @author Sébastien Hartmann <sebastien.hartmann@epfl.ch>
* @author Nicolas Richart <nicolas.richart@epfl.ch>
* @author Damien Spielmann <damien.spielmann@epfl.ch>
*
* @date creation: Fri Jul 15 2011
* @date last modification: Thu Oct 15 2015
*
* @brief Implementation of inline functions of StructuralMechanicsModel
*
* @section LICENSE
*
* Copyright (©) 2010-2012, 2014, 2015 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 "structural_mechanics_model.hh"
/* -------------------------------------------------------------------------- */
#ifndef __AKANTU_STRUCTURAL_MECHANICS_MODEL_INLINE_IMPL_CC__
#define __AKANTU_STRUCTURAL_MECHANICS_MODEL_INLINE_IMPL_CC__
namespace
akantu
{
/* -------------------------------------------------------------------------- */
template
<
ElementType
type
>
void
StructuralMechanicsModel
::
computeTangentModuli
(
Array
<
Real
>
&
tangent_moduli
)
{
AKANTU_DEBUG_TO_IMPLEMENT
();
}
}
// namespace akantu
#include "structural_element_bernoulli_beam_2.hh"
#include "structural_element_bernoulli_beam_3.hh"
#include "structural_element_kirchhoff_shell.hh"
namespace
akantu
{
/* -------------------------------------------------------------------------- */
template
<
ElementType
type
>
void
StructuralMechanicsModel
::
assembleStiffnessMatrix
()
{
AKANTU_DEBUG_IN
();
auto
nb_element
=
getFEEngine
().
getMesh
().
getNbElement
(
type
);
auto
nb_nodes_per_element
=
Mesh
::
getNbNodesPerElement
(
type
);
auto
nb_quadrature_points
=
getFEEngine
().
getNbIntegrationPoints
(
type
);
auto
tangent_size
=
ElementClass
<
type
>::
getVoigtSize
();
auto
tangent_moduli
=
std
::
make_unique
<
Array
<
Real
>>
(
nb_element
*
nb_quadrature_points
,
tangent_size
*
tangent_size
,
"tangent_stiffness_matrix"
);
computeTangentModuli
<
type
>
(
*
tangent_moduli
);
/// compute @f$\mathbf{B}^t * \mathbf{D} * \mathbf{B}@f$
UInt
bt_d_b_size
=
nb_degree_of_freedom
*
nb_nodes_per_element
;
auto
bt_d_b
=
std
::
make_unique
<
Array
<
Real
>>
(
nb_element
*
nb_quadrature_points
,
bt_d_b_size
*
bt_d_b_size
,
"B^t*D*B"
);
const
auto
&
b
=
getFEEngine
().
getShapesDerivatives
(
type
);
Matrix
<
Real
>
Bt_D
(
bt_d_b_size
,
tangent_size
);
auto
B
=
b
.
begin
(
tangent_size
,
bt_d_b_size
);
auto
D
=
tangent_moduli
->
begin
(
tangent_size
,
tangent_size
);
auto
Bt_D_B
=
bt_d_b
->
begin
(
bt_d_b_size
,
bt_d_b_size
);
auto
T
=
rotation_matrix
(
type
).
begin
(
bt_d_b_size
,
bt_d_b_size
);
for
(
UInt
e
=
0
;
e
<
nb_element
;
++
e
,
++
T
)
{
for
(
UInt
q
=
0
;
q
<
nb_quadrature_points
;
++
q
,
++
B
,
++
D
,
++
Bt_D_B
)
{
auto
BT
=
*
B
*
*
T
;
Bt_D
.
mul
<
true
,
false
>
(
BT
,
*
D
);
Bt_D_B
->
mul
<
false
,
false
>
(
Bt_D
,
BT
);
}
}
/// compute @f$ k_e = \int_e \mathbf{B}^t * \mathbf{D} * \mathbf{B}@f$
auto
int_bt_d_b
=
std
::
make_unique
<
Array
<
Real
>>
(
nb_element
,
bt_d_b_size
*
bt_d_b_size
,
"int_B^t*D*B"
);
getFEEngine
().
integrate
(
*
bt_d_b
,
*
int_bt_d_b
,
bt_d_b_size
*
bt_d_b_size
,
type
);
getDOFManager
().
assembleElementalMatricesToMatrix
(
"K"
,
"displacement"
,
*
int_bt_d_b
,
type
,
_not_ghost
,
_symmetric
);
AKANTU_DEBUG_OUT
();
}
/* -------------------------------------------------------------------------- */
template
<
ElementType
type
>
void
StructuralMechanicsModel
::
computeStressOnQuad
()
{
AKANTU_DEBUG_IN
();
Array
<
Real
>
&
sigma
=
stress
(
type
,
_not_ghost
);
auto
nb_element
=
mesh
.
getNbElement
(
type
);
auto
nb_nodes_per_element
=
Mesh
::
getNbNodesPerElement
(
type
);
auto
nb_quadrature_points
=
getFEEngine
().
getNbIntegrationPoints
(
type
);
auto
tangent_size
=
ElementClass
<
type
>::
getVoigtSize
();
auto
tangent_moduli
=
std
::
make_unique
<
Array
<
Real
>>
(
nb_element
*
nb_quadrature_points
,
tangent_size
*
tangent_size
,
"tangent_stiffness_matrix"
);
computeTangentModuli
<
type
>
(
*
tangent_moduli
);
/// compute DB
auto
d_b_size
=
nb_degree_of_freedom
*
nb_nodes_per_element
;
auto
d_b
=
std
::
make_unique
<
Array
<
Real
>>
(
nb_element
*
nb_quadrature_points
,
d_b_size
*
tangent_size
,
"D*B"
);
const
auto
&
b
=
getFEEngine
().
getShapesDerivatives
(
type
);
auto
B
=
b
.
begin
(
tangent_size
,
d_b_size
);
auto
D
=
tangent_moduli
->
begin
(
tangent_size
,
tangent_size
);
auto
D_B
=
d_b
->
begin
(
tangent_size
,
d_b_size
);
for
(
UInt
e
=
0
;
e
<
nb_element
;
++
e
)
{
for
(
UInt
q
=
0
;
q
<
nb_quadrature_points
;
++
q
,
++
B
,
++
D
,
++
D_B
)
{
D_B
->
mul
<
false
,
false
>
(
*
D
,
*
B
);
}
}
/// compute DBu
D_B
=
d_b
->
begin
(
tangent_size
,
d_b_size
);
auto
DBu
=
sigma
.
begin
(
tangent_size
);
Vector
<
Real
>
ul
(
d_b_size
);
Array
<
Real
>
u_el
(
0
,
d_b_size
);
FEEngine
::
extractNodalToElementField
(
mesh
,
*
displacement_rotation
,
u_el
,
type
);
auto
ug
=
u_el
.
begin
(
d_b_size
);
auto
T
=
rotation_matrix
(
type
).
begin
(
d_b_size
,
d_b_size
);
for
(
UInt
e
=
0
;
e
<
nb_element
;
++
e
,
++
T
,
++
ug
)
{
ul
.
mul
<
false
>
(
*
T
,
*
ug
);
for
(
UInt
q
=
0
;
q
<
nb_quadrature_points
;
++
q
,
++
D_B
,
++
DBu
)
{
DBu
->
mul
<
false
>
(
*
D_B
,
ul
);
}
}
delete
d_b
;
AKANTU_DEBUG_OUT
();
}
/* -------------------------------------------------------------------------- */
template
<
ElementType
type
>
void
StructuralMechanicsModel
::
computeForcesByLocalTractionArray
(
const
Array
<
Real
>
&
tractions
)
{
AKANTU_DEBUG_IN
();
UInt
nb_element
=
getFEEngine
().
getMesh
().
getNbElement
(
type
);
UInt
nb_nodes_per_element
=
getFEEngine
().
getMesh
().
getNbNodesPerElement
(
type
);
UInt
nb_quad
=
getFEEngine
().
getNbIntegrationPoints
(
type
);
// check dimension match
AKANTU_DEBUG_ASSERT
(
Mesh
::
getSpatialDimension
(
type
)
==
getFEEngine
().
getElementDimension
(),
"element type dimension does not match the dimension of boundaries : "
<<
getFEEngine
().
getElementDimension
()
<<
" != "
<<
Mesh
::
getSpatialDimension
(
type
));
// check size of the vector
AKANTU_DEBUG_ASSERT
(
tractions
.
size
()
==
nb_quad
*
nb_element
,
"the size of the vector should be the total number of quadrature points"
);
// check number of components
AKANTU_DEBUG_ASSERT
(
tractions
.
getNbComponent
()
==
nb_degree_of_freedom
,
"the number of components should be the spatial "
"dimension of the problem"
);
Array
<
Real
>
Nvoigt
(
nb_element
*
nb_quad
,
nb_degree_of_freedom
*
nb_degree_of_freedom
*
nb_nodes_per_element
);
transferNMatrixToSymVoigtNMatrix
<
type
>
(
Nvoigt
);
Array
<
Real
>::
const_matrix_iterator
N_it
=
Nvoigt
.
begin
(
nb_degree_of_freedom
,
nb_degree_of_freedom
*
nb_nodes_per_element
);
Array
<
Real
>::
const_matrix_iterator
T_it
=
rotation_matrix
(
type
).
begin
(
nb_degree_of_freedom
*
nb_nodes_per_element
,
nb_degree_of_freedom
*
nb_nodes_per_element
);
Array
<
Real
>::
const_vector_iterator
te_it
=
tractions
.
begin
(
nb_degree_of_freedom
);
Array
<
Real
>
funct
(
nb_element
*
nb_quad
,
nb_degree_of_freedom
*
nb_nodes_per_element
,
0.
);
Array
<
Real
>::
iterator
<
Vector
<
Real
>>
Fe_it
=
funct
.
begin
(
nb_degree_of_freedom
*
nb_nodes_per_element
);
Vector
<
Real
>
fe
(
nb_degree_of_freedom
*
nb_nodes_per_element
);
for
(
UInt
e
=
0
;
e
<
nb_element
;
++
e
,
++
T_it
)
{
const
Matrix
<
Real
>
&
T
=
*
T_it
;
for
(
UInt
q
=
0
;
q
<
nb_quad
;
++
q
,
++
N_it
,
++
te_it
,
++
Fe_it
)
{
const
Matrix
<
Real
>
&
N
=
*
N_it
;
const
Vector
<
Real
>
&
te
=
*
te_it
;
Vector
<
Real
>
&
Fe
=
*
Fe_it
;
// compute N^t tl
fe
.
mul
<
true
>
(
N
,
te
);
// turn N^t tl back in the global referential
Fe
.
mul
<
true
>
(
T
,
fe
);
}
}
// allocate the vector that will contain the integrated values
std
::
stringstream
name
;
name
<<
id
<<
type
<<
":integral_boundary"
;
Array
<
Real
>
int_funct
(
nb_element
,
nb_degree_of_freedom
*
nb_nodes_per_element
,
name
.
str
());
// do the integration
getFEEngine
().
integrate
(
funct
,
int_funct
,
nb_degree_of_freedom
*
nb_nodes_per_element
,
type
);
// assemble the result into force vector
getFEEngine
().
assembleArray
(
int_funct
,
*
force_momentum
,
dof_synchronizer
->
getLocalDOFEquationNumbers
(),
nb_degree_of_freedom
,
type
);
AKANTU_DEBUG_OUT
();
}
/* -------------------------------------------------------------------------- */
template
<
ElementType
type
>
void
StructuralMechanicsModel
::
computeForcesByGlobalTractionArray
(
const
Array
<
Real
>
&
traction_global
)
{
AKANTU_DEBUG_IN
();
UInt
nb_element
=
mesh
.
getNbElement
(
type
);
UInt
nb_quad
=
getFEEngine
().
getNbIntegrationPoints
(
type
);
UInt
nb_nodes_per_element
=
getFEEngine
().
getMesh
().
getNbNodesPerElement
(
type
);
std
::
stringstream
name
;
name
<<
id
<<
":structuralmechanics:imposed_linear_load"
;
Array
<
Real
>
traction_local
(
nb_element
*
nb_quad
,
nb_degree_of_freedom
,
name
.
str
());
Array
<
Real
>::
const_matrix_iterator
T_it
=
rotation_matrix
(
type
).
begin
(
nb_degree_of_freedom
*
nb_nodes_per_element
,
nb_degree_of_freedom
*
nb_nodes_per_element
);
Array
<
Real
>::
const_iterator
<
Vector
<
Real
>>
Te_it
=
traction_global
.
begin
(
nb_degree_of_freedom
);
Array
<
Real
>::
iterator
<
Vector
<
Real
>>
te_it
=
traction_local
.
begin
(
nb_degree_of_freedom
);
Matrix
<
Real
>
R
(
nb_degree_of_freedom
,
nb_degree_of_freedom
);
for
(
UInt
e
=
0
;
e
<
nb_element
;
++
e
,
++
T_it
)
{
const
Matrix
<
Real
>
&
T
=
*
T_it
;
for
(
UInt
i
=
0
;
i
<
nb_degree_of_freedom
;
++
i
)
for
(
UInt
j
=
0
;
j
<
nb_degree_of_freedom
;
++
j
)
R
(
i
,
j
)
=
T
(
i
,
j
);
for
(
UInt
q
=
0
;
q
<
nb_quad
;
++
q
,
++
Te_it
,
++
te_it
)
{
const
Vector
<
Real
>
&
Te
=
*
Te_it
;
Vector
<
Real
>
&
te
=
*
te_it
;
// turn the traction in the local referential
te
.
mul
<
false
>
(
R
,
Te
);
}
}
computeForcesByLocalTractionArray
<
type
>
(
traction_local
);
AKANTU_DEBUG_OUT
();
}
/* -------------------------------------------------------------------------- */
/**
* @param myf pointer to a function that fills a vector/tensor with respect to
* passed coordinates
*/
template
<
ElementType
type
>
inline
void
StructuralMechanicsModel
::
computeForcesFromFunction
(
BoundaryFunction
myf
,
BoundaryFunctionType
function_type
)
{
/** function type is
** _bft_forces : linear load is given
** _bft_stress : stress function is given -> Not already done for this kind
*of model
*/
std
::
stringstream
name
;
name
<<
id
<<
":structuralmechanics:imposed_linear_load"
;
Array
<
Real
>
lin_load
(
0
,
nb_degree_of_freedom
,
name
.
str
());
name
.
clear
();
UInt
offset
=
nb_degree_of_freedom
;
// prepare the loop over element types
UInt
nb_quad
=
getFEEngine
().
getNbIntegrationPoints
(
type
);
UInt
nb_element
=
getFEEngine
().
getMesh
().
getNbElement
(
type
);
name
.
clear
();
name
<<
id
<<
":structuralmechanics:quad_coords"
;
Array
<
Real
>
quad_coords
(
nb_element
*
nb_quad
,
spatial_dimension
,
"quad_coords"
);
getFEEngineClass
<
MyFEEngineType
>
()
.
getShapeFunctions
()
.
interpolateOnIntegrationPoints
<
type
>
(
getFEEngine
().
getMesh
().
getNodes
(),
quad_coords
,
spatial_dimension
);
getFEEngineClass
<
MyFEEngineType
>
()
.
getShapeFunctions
()
.
interpolateOnIntegrationPoints
<
type
>
(
getFEEngine
().
getMesh
().
getNodes
(),
quad_coords
,
spatial_dimension
,
_not_ghost
,
empty_filter
,
true
,
0
,
1
,
1
);
if
(
spatial_dimension
==
3
)
getFEEngineClass
<
MyFEEngineType
>
()
.
getShapeFunctions
()
.
interpolateOnIntegrationPoints
<
type
>
(
getFEEngine
().
getMesh
().
getNodes
(),
quad_coords
,
spatial_dimension
,
_not_ghost
,
empty_filter
,
true
,
0
,
2
,
2
);
lin_load
.
resize
(
nb_element
*
nb_quad
);
Real
*
imposed_val
=
lin_load
.
storage
();
/// sigma/load on each quadrature points
Real
*
qcoord
=
quad_coords
.
storage
();
for
(
UInt
el
=
0
;
el
<
nb_element
;
++
el
)
{
for
(
UInt
q
=
0
;
q
<
nb_quad
;
++
q
)
{
myf
(
qcoord
,
imposed_val
,
NULL
,
0
);
imposed_val
+=
offset
;
qcoord
+=
spatial_dimension
;
}
}
switch
(
function_type
)
{
case
_bft_traction_local:
computeForcesByLocalTractionArray
<
type
>
(
lin_load
);
break
;
case
_bft_traction:
computeForcesByGlobalTractionArray
<
type
>
(
lin_load
);
break
;
default
:
break
;
}
}
}
// namespace akantu
#endif
/* __AKANTU_STRUCTURAL_MECHANICS_MODEL_INLINE_IMPL_CC__ */
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