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rAKA akantu
structural_mechanics_model_inline_impl.hh
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/**
* @file structural_mechanics_model_inline_impl.hh
*
* @author Fabian Barras <fabian.barras@epfl.ch>
* @author Lucas Frerot <lucas.frerot@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: Tue Feb 20 2018
*
* @brief Implementation of inline functions of StructuralMechanicsModel
*
*
* 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 "structural_mechanics_model.hh"
/* -------------------------------------------------------------------------- */
#ifndef AKANTU_STRUCTURAL_MECHANICS_MODEL_INLINE_IMPL_HH_
#define AKANTU_STRUCTURAL_MECHANICS_MODEL_INLINE_IMPL_HH_
namespace
akantu
{
/* -------------------------------------------------------------------------- */
template
<
ElementType
type
>
void
StructuralMechanicsModel
::
computeTangentModuli
(
Array
<
Real
>
&
/*tangent_moduli*/
)
{
AKANTU_TO_IMPLEMENT
();
}
/* -------------------------------------------------------------------------- */
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
>::
getNbStressComponents
();
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
>
BtD
(
bt_d_b_size
,
tangent_size
);
for
(
auto
&&
tuple
:
zip
(
make_view
(
b
,
tangent_size
,
bt_d_b_size
),
make_view
(
*
tangent_moduli
,
tangent_size
,
tangent_size
),
make_view
(
*
bt_d_b
,
bt_d_b_size
,
bt_d_b_size
)))
{
auto
&
B
=
std
::
get
<
0
>
(
tuple
);
auto
&
D
=
std
::
get
<
1
>
(
tuple
);
auto
&
BtDB
=
std
::
get
<
2
>
(
tuple
);
BtD
.
mul
<
true
,
false
>
(
B
,
D
);
BtDB
.
template
mul
<
false
,
false
>
(
BtD
,
B
);
}
/// 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
();
auto
&
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
>::
getNbStressComponents
();
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
->
template
mul
<
false
,
false
>
(
*
D
,
*
B
);
}
}
/// compute DBu
D_B
=
d_b
->
begin
(
tangent_size
,
d_b_size
);
auto
DBu
=
sigma
.
begin
(
tangent_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
);
// No need to rotate because B is post-multiplied
for
(
UInt
e
=
0
;
e
<
nb_element
;
++
e
,
++
ug
)
{
for
(
UInt
q
=
0
;
q
<
nb_quadrature_points
;
++
q
,
++
D_B
,
++
DBu
)
{
DBu
->
template
mul
<
false
>
(
*
D_B
,
*
ug
);
}
}
AKANTU_DEBUG_OUT
();
}
/* -------------------------------------------------------------------------- */
template
<
ElementType
type
>
void
StructuralMechanicsModel
::
computeForcesByLocalTractionArray
(
const
Array
<
Real
>
&
tractions
)
{
AKANTU_DEBUG_IN
();
auto
nb_element
=
getFEEngine
().
getMesh
().
getNbElement
(
type
);
auto
nb_nodes_per_element
=
getFEEngine
().
getMesh
().
getNbNodesPerElement
(
type
);
auto
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
>
Ntbs
(
nb_element
*
nb_quad
,
nb_degree_of_freedom
*
nb_nodes_per_element
);
auto
&
fem
=
getFEEngine
();
fem
.
computeNtb
(
tractions
,
Ntbs
,
type
);
// allocate the vector that will contain the integrated values
auto
name
=
id
+
std
::
to_string
(
type
)
+
":integral_boundary"
;
Array
<
Real
>
int_funct
(
nb_element
,
nb_degree_of_freedom
*
nb_nodes_per_element
,
name
);
// do the integration
getFEEngine
().
integrate
(
Ntbs
,
int_funct
,
nb_degree_of_freedom
*
nb_nodes_per_element
,
type
);
// assemble the result into force vector
getDOFManager
().
assembleElementalArrayLocalArray
(
int_funct
,
*
external_force
,
type
,
_not_ghost
,
1
);
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
());
auto
T_it
=
rotation_matrix
(
type
).
begin
(
nb_degree_of_freedom
*
nb_nodes_per_element
,
nb_degree_of_freedom
*
nb_nodes_per_element
);
auto
Te_it
=
traction_global
.
begin
(
nb_degree_of_freedom
);
auto
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
auto
&
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
auto
&
Te
=
*
Te_it
;
auto
&
te
=
*
te_it
;
// turn the traction in the local referential
te
.
template
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
*/
#if 0
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.zero();
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.zero();
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;
}
}
#endif
}
// namespace akantu
#endif
/* AKANTU_STRUCTURAL_MECHANICS_MODEL_INLINE_IMPL_HH_ */
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