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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);
Array<Real> TtNtbs(nb_element * nb_quad,
nb_degree_of_freedom * nb_nodes_per_element);
auto & fem = getFEEngine();
fem.computeNtb(tractions, Ntbs, type);
auto T_it =
rotation_matrix(type).begin(nb_degree_of_freedom * nb_nodes_per_element,
nb_degree_of_freedom * nb_nodes_per_element);
auto Ntb_it = Ntbs.begin(nb_degree_of_freedom * nb_nodes_per_element);
auto TtNtb_it = TtNtbs.begin(nb_degree_of_freedom * nb_nodes_per_element);
for (UInt e = 0; e < nb_element; ++e, ++T_it) {
const auto & T = *T_it;
for (UInt q = 0; q < nb_quad; ++q, ++Ntb_it, ++TtNtb_it) {
const auto & Ntb = *Ntb_it;
auto & TtNtb = *TtNtb_it;
// turn N^t tl back in the global referential
TtNtb.mul<true>(T, Ntb);
}
}
// 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(TtNtbs, 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.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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