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rAKA/src/model/structural_mechanics/structural_mechanics_model_mass.cc
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structural_mechanics_model_mass.cc
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/**
* Copyright (©) 2014-2023 EPFL (Ecole Polytechnique Fédérale de Lausanne)
* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
*
* This file is part of Akantu
*
* 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 "aka_math.hh"
#include "integrator_gauss.hh"
#include "material.hh"
#include "shape_structural.hh"
#include "structural_mechanics_model.hh"
/* -------------------------------------------------------------------------- */
namespace akantu {
class ComputeRhoFunctorStruct {
public:
explicit ComputeRhoFunctorStruct(const StructuralMechanicsModel & model)
: model(model){};
void operator()(Matrix<Real> & rho, const Element & element) const {
const auto & mat = model.getMaterialByElement(element);
const Real mat_rho = mat.rho; // This is the density
const Real mat_A = mat.A; // This is the cross section
const Real mat_mass_per_length =
mat_rho * mat_A; // Mass of the beam per unit length
rho.set(
mat_mass_per_length); // The integrator _recquiers_ mass per unit length
}
private:
const StructuralMechanicsModel & model;
};
/* -------------------------------------------------------------------------- */
void StructuralMechanicsModel::assembleMassMatrix() {
AKANTU_DEBUG_IN();
if (not need_to_reassemble_mass) {
return;
}
if (not getDOFManager().hasMatrix("M")) {
getDOFManager().getNewMatrix("M", getMatrixType("M"));
}
this->getDOFManager().zeroMatrix("M");
assembleMassMatrix(_not_ghost);
need_to_reassemble_mass = false;
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
void StructuralMechanicsModel::assembleMassMatrix(GhostType ghost_type) {
AKANTU_DEBUG_IN();
auto & fem = getFEEngineClass<MyFEEngineType>();
ComputeRhoFunctorStruct compute_rho(*this);
for (auto type :
mesh.elementTypes(spatial_dimension, ghost_type, _ek_structural)) {
fem.assembleFieldMatrix(compute_rho, "M", "displacement",
this->getDOFManager(), type, ghost_type);
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
void StructuralMechanicsModel::assembleLumpedMassMatrix() {
if (not this->need_to_reassemble_lumped_mass) {
return;
}
allocNodalField(this->mass, nb_degree_of_freedom, "lumped_mass");
if (!this->getDOFManager().hasLumpedMatrix("M")) {
this->getDOFManager().getNewLumpedMatrix("M");
}
this->getDOFManager().zeroLumpedMatrix("M");
// Preparing
const UInt nb_nodes = mesh.getNbNodes();
const auto & nodes = mesh.getNodes();
const auto & node_it = make_view(nodes, spatial_dimension).begin();
auto & lumped_mass = *(this->mass);
lumped_mass.zero(); // Set the lumped mass to zero
Array<Real> volumes(nb_nodes, 1, 0., "volumes");
/// We now compute the mass and the volume, but not the inertia
for (auto type :
mesh.elementTypes(spatial_dimension, _not_ghost, _ek_structural)) {
const auto & element_material_id = this->element_material(type);
const auto & connectivity = mesh.getConnectivity(type);
// const auto nb_element = connectivity.size();
if (type != _bernoulli_beam_3 and type != _bernoulli_beam_2) {
AKANTU_EXCEPTION(
"The lumped mass was not implemented for non Bernoulli Beams");
}
// Now iterate through all the connectivity
for (auto && data : zip(make_view(connectivity, 2), element_material_id)) {
const auto & conn = std::get<0>(data);
auto node1 = conn(0);
auto node2 = conn(0);
const auto & material = this->materials.at(std::get<1>(data));
const auto rho = material.rho;
const auto cross_section = material.A;
auto && coord_node_1 = node_it[node1];
auto && coord_node_2 = node_it[node2];
const auto length = coord_node_1.distance(coord_node_2);
const auto volume = length * cross_section;
const auto mass = volume * rho;
// Now distribute the mass at the right places
for (auto d : arange(spatial_dimension)) {
lumped_mass(node1, d) += mass / 2.;
lumped_mass(node2, d) += mass / 2.;
}; // end for(d):
volumes(node1) += volume / 2.; // this entry never point to mass
volumes(node2) += volume / 2.;
}
}
const auto pi = std::atan(1.) * 4;
// We now compute the inertia.
if (spatial_dimension == 2) {
/* This is the 2D case, so we are assuming that the mass is inside a disc.
* Which is given as
* \begin{align}
* I := m \cdot r^2
* \end{align}
*
* The radius is obtained by assuming that the volume, that is associated to
* a beam, forms a uniformly disc. From this volume we can compute the
* radius.
*/
for (auto && data :
zip(make_view(lumped_mass, nb_degree_of_freedom), volumes)) {
const Real volume = std::get<1>(data);
auto & masses = std::get<0>(data);
const Real r2 = volume / pi; // The square of the volume
const Real inertia = masses(0) * r2;
masses(spatial_dimension) = inertia;
}
} else if (spatial_dimension == 3) {
/* This is essentially the same as for 2D only that we assume here,
* that the mass is uniformly distributed inside a sphere.
* And thus we have
* \begin{align}
* I := \frac{2}{5} m \cdot r^2
* \end{align}
*
* We also have to set three values, for the three axis.
* But since we assume a sphere, they are all the same.
*/
for (auto && data :
zip(make_view(lumped_mass, nb_degree_of_freedom), volumes)) {
const Real volume = std::get<1>(data);
auto & masses = std::get<0>(data);
const Real r2 = std::pow((volume * 3.) / (4 * pi), 2. / 3.);
const Real inertia = (2. / 5.) * masses(0) * r2;
for (auto && m : masses) {
m = inertia;
}
}
} else {
AKANTU_EXCEPTION("The dimension " << spatial_dimension << " is not known.");
}
this->getDOFManager().assembleToLumpedMatrix("displacement", lumped_mass,
"M");
this->need_to_reassemble_lumped_mass = false;
}
} // namespace akantu
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