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structural_mechanics_model_inline_impl.cc
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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>
* @date Thu May 5 19:48:07 2011
*
* @brief
*
* @section LICENSE
*
* Copyright (©) 2010-2011 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/>.
*
*/
/* -------------------------------------------------------------------------- */
template<ElementType type>
inline UInt StructuralMechanicsModel::getTangentStiffnessVoigtSize() {
AKANTU_DEBUG_TO_IMPLEMENT();
return 0;
}
template<>
inline UInt StructuralMechanicsModel::getTangentStiffnessVoigtSize<_bernoulli_beam_2>() {
return 2;
}
template<>
inline UInt StructuralMechanicsModel::getTangentStiffnessVoigtSize<_bernoulli_beam_3>() {
return 4;
}
/* -------------------------------------------------------------------------- */
template <ElementType type>
void StructuralMechanicsModel::assembleStiffnessMatrix() {
AKANTU_DEBUG_IN();
SparseMatrix & K = *stiffness_matrix;
UInt nb_element = getFEEngine().getMesh().getNbElement(type);
UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
UInt nb_quadrature_points = getFEEngine().getNbQuadraturePoints(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 @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 = new Array<Real>(nb_element*nb_quadrature_points,
bt_d_b_size * bt_d_b_size,
"B^t*D*B");
Array<Real> * b = new Array<Real>(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);
Array<Real>::matrix_iterator B = b->begin(tangent_size, bt_d_b_size);
Array<Real>::matrix_iterator D = tangent_moduli->begin(tangent_size, tangent_size);
Array<Real>::matrix_iterator Bt_D_B = bt_d_b->begin(bt_d_b_size, bt_d_b_size);
Array<Real>::matrix_iterator 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);
}
}
delete b;
delete tangent_moduli;
/// compute @f$ k_e = \int_e \mathbf{B}^t * \mathbf{D} * \mathbf{B}@f$
Array<Real> * int_bt_d_b = new 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);
delete bt_d_b;
getFEEngine().assembleMatrix(*int_bt_d_b, K, nb_degree_of_freedom, type);
delete int_bt_d_b;
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template<ElementType type>
void StructuralMechanicsModel::computeTangentModuli(Array<Real> & tangent_moduli) {
AKANTU_DEBUG_TO_IMPLEMENT();
}
/* -------------------------------------------------------------------------- */
template<ElementType type>
void StructuralMechanicsModel::transferBMatrixToSymVoigtBMatrix(Array<Real> & b, bool local) {
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().getNbQuadraturePoints(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().getNbQuadraturePoints(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.getSize() == 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 = getFEEngine().getMesh().getNbElement(type);
UInt nb_quad = getFEEngine().getNbQuadraturePoints(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>
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().getNbQuadraturePoints(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().interpolateOnControlPoints<type>(getFEEngine().getMesh().getNodes(),
quad_coords,
spatial_dimension);
getFEEngineClass<MyFEEngineType>().getShapeFunctions().interpolateOnControlPoints<type>(getFEEngine().getMesh().getNodes(),
quad_coords,
spatial_dimension,
_not_ghost,
empty_filter,
true,
0,
1,
1);
if(spatial_dimension == 3)
getFEEngineClass<MyFEEngineType>().getShapeFunctions().interpolateOnControlPoints<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;
}
}
/* -------------------------------------------------------------------------- */
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