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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>
inline UInt StructuralMechanicsModel::getTangentStiffnessVoigtSize() {
AKANTU_DEBUG_TO_IMPLEMENT();
return 0;
}
/* -------------------------------------------------------------------------- */
template <ElementType type>
void StructuralMechanicsModel::assembleStiffnessMatrix() {
AKANTU_DEBUG_IN();
UInt nb_element = getFEEngine().getMesh().getNbElement(type);
UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
UInt nb_quadrature_points = getFEEngine().getNbIntegrationPoints(type);
UInt tangent_size = getTangentStiffnessVoigtSize<type>();
Array<Real> tangent_moduli(nb_element * nb_quadrature_points,
tangent_size * tangent_size, 0.,
"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;
Array<Real> bt_d_b(nb_element * nb_quadrature_points,
bt_d_b_size * bt_d_b_size, "B^t*D*B");
Array<Real> b(nb_element * nb_quadrature_points, tangent_size * bt_d_b_size,
"B");
transferBMatrixToSymVoigtBMatrix<type>(b);
Matrix<Real> Bt_D(bt_d_b_size, tangent_size);
Matrix<Real> BT(tangent_size, bt_d_b_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) {
BT.mul<false, false>(*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$
Array<Real> int_bt_d_b(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);
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <ElementType type>
void StructuralMechanicsModel::computeTangentModuli(Array<Real> &) {
AKANTU_DEBUG_TO_IMPLEMENT();
}
/* -------------------------------------------------------------------------- */
template <ElementType type>
void StructuralMechanicsModel::transferBMatrixToSymVoigtBMatrix(Array<Real> &,
bool) {
AKANTU_DEBUG_TO_IMPLEMENT();
}
/* -------------------------------------------------------------------------- */
template <ElementType type>
void StructuralMechanicsModel::computeStressOnQuad() {
AKANTU_DEBUG_IN();
Array<Real> & sigma = stress(type, _not_ghost);
sigma.clear();
const Mesh & mesh = getFEEngine().getMesh();
UInt nb_element = mesh.getNbElement(type);
UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
UInt nb_quadrature_points = getFEEngine().getNbIntegrationPoints(type);
UInt tangent_size = getTangentStiffnessVoigtSize<type>();
Array<Real> * tangent_moduli =
new Array<Real>(nb_element * nb_quadrature_points,
tangent_size * tangent_size, "tangent_stiffness_matrix");
tangent_moduli->clear();
computeTangentModuli<type>(*tangent_moduli);
/// compute DB
UInt d_b_size = nb_degree_of_freedom * nb_nodes_per_element;
Array<Real> * d_b = new Array<Real>(nb_element * nb_quadrature_points,
d_b_size * tangent_size, "D*B");
Array<Real> * b = new Array<Real>(nb_element * nb_quadrature_points,
tangent_size * d_b_size, "B");
transferBMatrixToSymVoigtBMatrix<type>(*b);
Array<Real>::matrix_iterator B = b->begin(tangent_size, d_b_size);
Array<Real>::matrix_iterator D =
tangent_moduli->begin(tangent_size, tangent_size);
Array<Real>::matrix_iterator 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);
}
}
delete b;
delete tangent_moduli;
/// compute DBu
D_B = d_b->begin(tangent_size, d_b_size);
Array<Real>::iterator<Vector<Real>> 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);
Array<Real>::vector_iterator ug = u_el.begin(d_b_size);
Array<Real>::matrix_iterator 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);
auto N_it = Nvoigt.begin(nb_degree_of_freedom,
nb_degree_of_freedom * nb_nodes_per_element);
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 = tractions.begin(nb_degree_of_freedom);
Array<Real> funct(nb_element * nb_quad,
nb_degree_of_freedom * nb_nodes_per_element, 0.);
auto 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
Array<Real> int_funct(nb_element, nb_degree_of_freedom * nb_nodes_per_element,
std::string(id + ":integral_boundary"));
// do the integration
getFEEngine().integrate(funct, int_funct,
nb_degree_of_freedom * nb_nodes_per_element, type);
// assemble the result into force vector
getDOFManager().assembleElementalArrayLocalArray(
int_funct, *internal_force_momentum, type, _not_ghost);
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <ElementType type>
void StructuralMechanicsModel::computeForcesByGlobalTractionArray(
const Array<Real> & traction_global) {
AKANTU_DEBUG_IN();
UInt nb_element = getFEEngine().getMesh().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 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>(mesh.getNodes(), quad_coords,
// spatial_dimension);
// getFEEngineClass<MyFEEngineType>()
// .getShapeFunctions()
// .interpolateOnIntegrationPoints<type>(mesh.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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