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test_solid_mechanics_model_dynamics.cc
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test_solid_mechanics_model_dynamics.cc
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/**
* @file test_solid_mechanics_model_cube3d.cc
*
* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
*
* @date creation: Wed Aug 04 2010
* @date last modification: Thu Aug 06 2015
*
* @brief test of the class SolidMechanicsModel on the 3d cube
*
* @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 "boundary_condition_functor.hh"
#include "test_solid_mechanics_model_fixture.hh"
/* -------------------------------------------------------------------------- */
using namespace akantu;
namespace {
constexpr Real A = 1e-1;
constexpr Real E = 1.;
constexpr Real poisson = .3;
constexpr Real lambda = E * poisson / (1. + poisson) / (1. - 2. * poisson);
constexpr Real mu = E / 2 / (1. + poisson);
constexpr Real rho = 1.;
const Real cp = std::sqrt((lambda + 2 * mu) / rho);
const Real cs = std::sqrt(mu / rho);
const Real c = std::sqrt(E / rho);
const Vector<Real> k = {.5, 0., 0.};
const Vector<Real> psi1 = {0., 0., 1.};
const Vector<Real> psi2 = {0., 1., 0.};
const Real knorm = k.norm();
template <UInt spatial_dimension> auto solution_disp = 1;
template <UInt spatial_dimension> auto solution_vel = 1;
template <>
auto solution_disp<1> =
[](Vector<Real> & disp, const Vector<Real> & coord, Real current_time) {
const auto & x = coord(_x);
const Real omega = c * k[0];
disp(_x) = A * cos(k[0] * x - omega * current_time);
};
template <>
auto solution_vel<1> =
[](Vector<Real> & vel, const Vector<Real> & coord, Real current_time) {
const auto & x = coord(_x);
const Real omega = c * k[0];
vel(_x) = omega * A * sin(k[0] * x - omega * current_time);
};
template <>
auto solution_disp<2> =
[](Vector<Real> & disp, const Vector<Real> & coord, Real current_time) {
const auto & X = coord;
Vector<Real> kshear = {k[1], k[0]};
Vector<Real> kpush = {k[0], k[1]};
const Real omega_p = knorm * cp;
const Real omega_s = knorm * cs;
Real phase_p = X.dot(kpush) - omega_p * current_time;
Real phase_s = X.dot(kpush) - omega_s * current_time;
disp = A * (kpush * cos(phase_p) + kshear * cos(phase_s));
};
template <>
auto solution_vel<2> = [](Vector<Real> & vel, const Vector<Real> & coord,
Real current_time) {
const auto & X = coord;
Vector<Real> kshear = {k[1], k[0]};
Vector<Real> kpush = {k[0], k[1]};
const Real omega_p = knorm * cp;
const Real omega_s = knorm * cs;
Real phase_p = X.dot(kpush) - omega_p * current_time;
Real phase_s = X.dot(kpush) - omega_s * current_time;
vel = A * (kpush * omega_p * cos(phase_p) + kshear * omega_s * cos(phase_s));
};
template <>
auto solution_disp<3> =
[](Vector<Real> & disp, const Vector<Real> & coord, Real current_time) {
const auto & X = coord;
Vector<Real> kpush = k;
Vector<Real> kshear1(3);
Vector<Real> kshear2(3);
kshear1.crossProduct(k, psi1);
kshear2.crossProduct(k, psi2);
const Real omega_p = knorm * cp;
const Real omega_s = knorm * cs;
Real phase_p = X.dot(kpush) - omega_p * current_time;
Real phase_s = X.dot(kpush) - omega_s * current_time;
disp = A * (kpush * cos(phase_p) + kshear1 * cos(phase_s) +
kshear2 * cos(phase_s));
};
template <>
auto solution_vel<3> = [](Vector<Real> & vel, const Vector<Real> & coord,
Real current_time) {
const auto & X = coord;
Vector<Real> kpush = k;
Vector<Real> kshear1(3);
Vector<Real> kshear2(3);
kshear1.crossProduct(k, psi1);
kshear2.crossProduct(k, psi2);
const Real omega_p = knorm * cp;
const Real omega_s = knorm * cs;
Real phase_p = X.dot(kpush) - omega_p * current_time;
Real phase_s = X.dot(kpush) - omega_s * current_time;
vel = A * (kpush * omega_p * cos(phase_p) + kshear1 * omega_s * cos(phase_s) +
kshear2 * omega_s * cos(phase_s));
};
template <ElementType _type>
class SolutionFunctor : public BC::Dirichlet::DirichletFunctor {
public:
SolutionFunctor(Real current_time, SolidMechanicsModel & model)
: current_time(current_time), model(model) {}
public:
// static constexpr UInt dim = DimensionHelper<_type>::dim;
static constexpr UInt dim = ElementClass<_type>::getSpatialDimension();
inline void operator()(UInt node, Vector<bool> & flags, Vector<Real> & primal,
const Vector<Real> & coord) const {
flags(0) = true;
auto & vel = model.getVelocity();
auto itVel = vel.begin(model.getSpatialDimension());
Vector<Real> v = itVel[node];
solution_disp<dim>(primal, coord, current_time);
solution_vel<dim>(v, coord, current_time);
}
private:
Real current_time;
SolidMechanicsModel & model;
};
template <ElementType _type, typename AM>
void test_body(SolidMechanicsModel & model, AM analysis_method) {
// constexpr UInt dim = DimensionHelper<_type>::dim;
static constexpr UInt dim = ElementClass<_type>::getSpatialDimension();
getStaticParser().parse("test_solid_mechanics_model_"
"dynamics_material.dat");
model.initFull(SolidMechanicsModelOptions(analysis_method));
bool dump_paraview = false;
if (dump_paraview) {
std::stringstream base_name;
base_name << "bar" << analysis_method << _type;
model.setBaseName(base_name.str());
model.addDumpFieldVector("displacement");
model.addDumpField("mass");
model.addDumpField("velocity");
model.addDumpField("acceleration");
model.addDumpFieldVector("external_force");
model.addDumpFieldVector("internal_force");
model.addDumpField("stress");
model.addDumpField("strain");
}
Real time_step = model.getStableTimeStep() / 10.;
model.setTimeStep(time_step);
std::cout << "timestep: " << time_step << std::endl;
UInt nb_nodes = model.getMesh().getNbNodes();
UInt spatial_dimension = model.getSpatialDimension();
auto & nodes = model.getMesh().getNodes();
auto & disp = model.getDisplacement();
auto & vel = model.getVelocity();
Array<Real> disp_solution(nb_nodes, spatial_dimension);
Real current_time = 0;
auto itNodes = nodes.begin(spatial_dimension);
auto itDisp = disp.begin(spatial_dimension);
auto itVel = vel.begin(spatial_dimension);
for (UInt n = 0; n < nb_nodes; ++n, ++itNodes, ++itDisp, ++itVel) {
solution_disp<dim>(*itDisp, *itNodes, current_time);
solution_vel<dim>(*itVel, *itNodes, current_time);
}
if (dump_paraview)
model.dump();
/// boundary conditions
model.applyBC(SolutionFunctor<_type>(current_time, model), "BC");
Real max_error = 0.;
Real wave_velocity = 1.; // sqrt(E/rho) = sqrt(1/1) = 1
Real simulation_time = 5 / wave_velocity;
UInt max_steps = simulation_time / time_step; // 100
UInt ndump = 50;
UInt dump_freq = max_steps / ndump;
std::cout << "max_steps: " << max_steps << std::endl;
for (UInt s = 0; s < max_steps; ++s, current_time += time_step) {
if (s % dump_freq == 0 && dump_paraview)
model.dump();
/// boundary conditions
model.applyBC(SolutionFunctor<_type>(current_time, model), "BC");
// compute the disp solution
auto itDispSolution = disp_solution.begin(spatial_dimension);
itNodes = nodes.begin(spatial_dimension);
for (UInt n = 0; n < nb_nodes; ++n, ++itNodes, ++itDispSolution) {
solution_disp<dim>(*itDispSolution, *itNodes, current_time);
}
// compute the error solution
itDispSolution = disp_solution.begin(spatial_dimension);
itDisp = disp.begin(spatial_dimension);
Real disp_error = 0.;
for (UInt n = 0; n < nb_nodes; ++n, ++itDispSolution, ++itDisp) {
auto diff = *itDispSolution - *itDisp;
for (UInt i = 0; i < spatial_dimension; ++i) {
disp_error += diff(i) * diff(i);
}
}
disp_error = sqrt(disp_error) / nb_nodes;
max_error = std::max(disp_error, max_error);
ASSERT_NEAR(disp_error, 0., 1e-3);
model.solveStep();
}
std::cout << "max error: " << max_error << std::endl;
}
#ifdef AKANTU_IMPLICIT
TYPED_TEST(TestSMMFixtureBar, DynamicsImplicit) {
test_body<this->type>(*(this->model), _implicit_dynamic);
}
#endif
TYPED_TEST(TestSMMFixtureBar, DynamicsExplicit) {
test_body<TestFixture::type>(*(this->model), _explicit_lumped_mass);
}
}

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