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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/>.
*
*/
/* -------------------------------------------------------------------------- */
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<>
inline UInt StructuralMechanicsModel::getTangentStiffnessVoigtSize<_kirchhoff_shell>() {
return 6;
}
/* -------------------------------------------------------------------------- */
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().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 @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().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.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().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);
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>(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;
}
}
/* -------------------------------------------------------------------------- */
template<>
inline void StructuralMechanicsModel::assembleMass<_bernoulli_beam_2>() {
AKANTU_DEBUG_IN();
GhostType ghost_type = _not_ghost;
ElementType type = _bernoulli_beam_2;
MyFEEngineType & fem = getFEEngineClass<MyFEEngineType>();
UInt nb_element = getFEEngine().getMesh().getNbElement(type);
UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
UInt nb_quadrature_points = getFEEngine().getNbIntegrationPoints(type);
UInt nb_fields_to_interpolate = getTangentStiffnessVoigtSize<_bernoulli_beam_2>();
UInt nt_n_field_size = nb_degree_of_freedom * nb_nodes_per_element;
Array<Real> * n = new Array<Real>(nb_element*nb_quadrature_points,
nb_fields_to_interpolate * nt_n_field_size,
"N");
n->clear();
Array<Real> * rho_field = new Array<Real>(nb_element*nb_quadrature_points,
"Rho");
rho_field->clear();
computeRho(*rho_field, type, _not_ghost);
bool sign = true;
/* -------------------------------------------------------------------------- */
fem.computeShapesMatrix(type, nb_degree_of_freedom, nb_nodes_per_element, n, 0, 0, 0, sign, ghost_type); // Ni ui -> u
fem.computeShapesMatrix(type, nb_degree_of_freedom, nb_nodes_per_element, n, 1, 1, 1, sign, ghost_type); // Mi vi -> v
fem.computeShapesMatrix(type, nb_degree_of_freedom, nb_nodes_per_element, n, 2, 2, 1, sign, ghost_type); // Li Theta_i -> v
/* -------------------------------------------------------------------------- */
fem.assembleFieldMatrix(*rho_field, nb_degree_of_freedom, *mass_matrix, n, rotation_matrix, type, ghost_type);
delete n;
delete rho_field;
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template<>
inline void StructuralMechanicsModel::assembleMass<_bernoulli_beam_3>() {
AKANTU_DEBUG_IN();
GhostType ghost_type = _not_ghost;
ElementType type = _bernoulli_beam_3;
MyFEEngineType & fem = getFEEngineClass<MyFEEngineType>();
UInt nb_element = getFEEngine().getMesh().getNbElement(type);
UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
UInt nb_quadrature_points = getFEEngine().getNbIntegrationPoints(type);
UInt nb_fields_to_interpolate = getTangentStiffnessVoigtSize<_bernoulli_beam_3>();
UInt nt_n_field_size = nb_degree_of_freedom * nb_nodes_per_element;
Array<Real> * n = new Array<Real>(nb_element*nb_quadrature_points,
nb_fields_to_interpolate * nt_n_field_size,
"N");
n->clear();
Array<Real> * rho_field = new Array<Real>(nb_element * nb_quadrature_points,
"Rho");
rho_field->clear();
computeRho(*rho_field, type, _not_ghost);
/* -------------------------------------------------------------------------- */
fem.computeShapesMatrix(type, nb_degree_of_freedom, nb_nodes_per_element, n, 0, 0, 0, true, ghost_type); // Ni ui -> u
fem.computeShapesMatrix(type, nb_degree_of_freedom, nb_nodes_per_element, n, 1, 1, 1, true, ghost_type); // Mi vi -> v
fem.computeShapesMatrix(type, nb_degree_of_freedom, nb_nodes_per_element, n, 2, 5, 1, true, ghost_type); // Li Theta_z_i -> v
fem.computeShapesMatrix(type, nb_degree_of_freedom, nb_nodes_per_element, n, 1, 2, 2, true, ghost_type); // Mi wi -> w
fem.computeShapesMatrix(type, nb_degree_of_freedom, nb_nodes_per_element, n, 2, 4, 2, false,ghost_type);// -Li Theta_y_i -> w
fem.computeShapesMatrix(type, nb_degree_of_freedom, nb_nodes_per_element, n, 0, 3, 3, true, ghost_type); // Ni Theta_x_i->Theta_x
/* -------------------------------------------------------------------------- */
fem.assembleFieldMatrix(*rho_field, nb_degree_of_freedom, *mass_matrix, n, rotation_matrix, type, ghost_type);
delete n;
delete rho_field;
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template<>
inline void StructuralMechanicsModel::assembleMass<_kirchhoff_shell>() {
AKANTU_DEBUG_TO_IMPLEMENT();
}
/* -------------------------------------------------------------------------- */
/* -------------------------------------------------------------------------- */
template<SolveConvergenceMethod cmethod, SolveConvergenceCriteria criteria>
bool StructuralMechanicsModel::solveStep(Real tolerance,
UInt max_iteration) {
Real error = 0.;
return this->template solveStep<cmethod,criteria>(tolerance,
error,
max_iteration);
}
/* -------------------------------------------------------------------------- */
template<SolveConvergenceMethod cmethod, SolveConvergenceCriteria criteria>
bool StructuralMechanicsModel::solveStep(Real tolerance, Real & error, UInt max_iteration) {
this->implicitPred();
this->updateResidual();
AKANTU_DEBUG_ASSERT(stiffness_matrix != NULL,
"You should first initialize the implicit solver and assemble the stiffness matrix");
if (method==_implicit_dynamic) {
AKANTU_DEBUG_ASSERT(mass_matrix != NULL,
"You should first initialize the implicit solver and assemble the mass matrix");
}
switch (cmethod) {
case _scm_newton_raphson_tangent:
case _scm_newton_raphson_tangent_not_computed:
break;
case _scm_newton_raphson_tangent_modified:
this->assembleStiffnessMatrix();
break;
default:
AKANTU_DEBUG_ERROR("The resolution method " << cmethod << " has not been implemented!");
}
UInt iter = 0;
bool converged = false;
error = 0.;
if(criteria == _scc_residual) {
converged = this->testConvergence<criteria> (tolerance, error);
if(converged) return converged;
}
do {
if (cmethod == _scm_newton_raphson_tangent)
this->assembleStiffnessMatrix();
solve<NewmarkBeta::_displacement_corrector> (*increment);
this->implicitCorr();
if(criteria == _scc_residual) this->updateResidual();
converged = this->testConvergence<criteria> (tolerance, error);
if(criteria == _scc_increment && !converged) this->updateResidual();
//this->dump();
iter++;
AKANTU_DEBUG_INFO("[" << criteria << "] Convergence iteration "
<< std::setw(std::log10(max_iteration)) << iter
<< ": error " << error << (converged ? " < " : " > ") << tolerance);
} while (!converged && iter < max_iteration);
if (converged) {
} else if(iter == max_iteration) {
AKANTU_DEBUG_WARNING("[" << criteria << "] Convergence not reached after "
<< std::setw(std::log10(max_iteration)) << iter <<
" iteration" << (iter == 1 ? "" : "s") << "!" << std::endl);
}
return converged;
}
/* -------------------------------------------------------------------------- */
template<NewmarkBeta::IntegrationSchemeCorrectorType type>
void StructuralMechanicsModel::solve(Array<Real> & increment,
Real block_val) {
jacobian_matrix->clear();
//updateResidualInternal(); //doesn't do anything for static
Real c = 0.,d = 0.,e = 0.;
if(method == _static) {
AKANTU_DEBUG_INFO("Solving K inc = r");
e = 1.;
} else {
AKANTU_DEBUG_INFO("Solving (c M + d C + e K) inc = r");
NewmarkBeta * nmb_int = dynamic_cast<NewmarkBeta *>(integrator);
c = nmb_int->getAccelerationCoefficient<type>(time_step);
d = nmb_int->getVelocityCoefficient<type>(time_step);
e = nmb_int->getDisplacementCoefficient<type>(time_step);
}
// J = c M + d C + e K
if(stiffness_matrix)
jacobian_matrix->add(*stiffness_matrix, e);
// if(type != NewmarkBeta::_acceleration_corrector)
// jacobian_matrix->add(*stiffness_matrix, e);
if(mass_matrix)
jacobian_matrix->add(*mass_matrix, c);
#if !defined(AKANTU_NDEBUG)
if(mass_matrix && AKANTU_DEBUG_TEST(dblDump))
mass_matrix->saveMatrix("M.mtx");
#endif
if(velocity_damping_matrix)
jacobian_matrix->add(*velocity_damping_matrix, d);
jacobian_matrix->applyBoundary(*blocked_dofs);
#if !defined(AKANTU_NDEBUG)
if(AKANTU_DEBUG_TEST(dblDump))
jacobian_matrix->saveMatrix("J.mtx");
#endif
solver->setRHS(*residual);
// solve @f[ J \delta w = r @f]
solver->factorize();
solver->solve(increment);
}

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