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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 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
*
* @section LICENSE
*
* 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_CC__
#define __AKANTU_STRUCTURAL_MECHANICS_MODEL_INLINE_IMPL_CC__
namespace
akantu
{
/* -------------------------------------------------------------------------- */
inline
UInt
StructuralMechanicsModel
::
getNbDegreeOfFreedom
(
const
ElementType
&
type
)
const
{
UInt
ndof
=
0
;
#define GET_(type) ndof = ElementClass<type>::getNbDegreeOfFreedom()
AKANTU_BOOST_KIND_ELEMENT_SWITCH
(
GET_
,
_ek_structural
);
#undef GET_
return
ndof
;
}
/* -------------------------------------------------------------------------- */
template
<
ElementType
type
>
void
StructuralMechanicsModel
::
computeTangentModuli
(
Array
<
Real
>
&
/*tangent_moduli*/
)
{
AKANTU_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
>::
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
();
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
>::
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
();
#if 0
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);
auto 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);
#endif
AKANTU_DEBUG_OUT
();
}
/* -------------------------------------------------------------------------- */
template
<
ElementType
type
>
void
StructuralMechanicsModel
::
computeForcesByGlobalTractionArray
(
const
Array
<
Real
>
&
/*traction_global*/
)
{
AKANTU_DEBUG_IN
();
#if 0
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);
#endif
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.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;
}
}
#endif
}
// namespace akantu
#endif
/* __AKANTU_STRUCTURAL_MECHANICS_MODEL_INLINE_IMPL_CC__ */
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