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implicit_dynamic.cc
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implicit_dynamic.cc
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/**
* @file implicit_dynamic.cc
*
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date creation: Sun Oct 19 2014
* @date last modification: Fri Feb 28 2020
*
* @brief Example of solid mechanics in implicit dynamic
*
*
* @section LICENSE
*
* Copyright (©) 2015-2021 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 "communicator.hh"
#include "non_linear_solver.hh"
#include "solid_mechanics_model.hh"
/* -------------------------------------------------------------------------- */
#include <fstream>
/* -------------------------------------------------------------------------- */
using namespace akantu;
/* -------------------------------------------------------------------------- */
const Real bar_length = 10.;
const Real bar_height = 1.;
const Real bar_depth = 1.;
const Real F = 5e3;
const Real L = bar_length;
const Real I = bar_depth * bar_height * bar_height * bar_height / 12.;
const Real E = 12e7;
const Real rho = 1000;
const Real m = rho * bar_height * bar_depth;
static Real w(UInt n) {
return n * n * M_PI * M_PI / (L * L) * sqrt(E * I / m);
}
static Real analytical_solution(Real time) {
return 2 * F * L * L * L / (pow(M_PI, 4) * E * I) *
((1. - cos(w(1) * time)) + (1. - cos(w(3) * time)) / 81. +
(1. - cos(w(5) * time)) / 625.);
}
const UInt spatial_dimension = 2;
const Real time_step = 1e-4;
const Real max_time = 0.62;
/* -------------------------------------------------------------------------- */
int main(int argc, char * argv[]) {
initialize("material_dynamic.dat", argc, argv);
Mesh mesh(spatial_dimension);
const auto & comm = Communicator::getStaticCommunicator();
Int prank = comm.whoAmI();
if (prank == 0)
mesh.read("beam.msh");
mesh.distribute();
SolidMechanicsModel model(mesh);
/// model initialization
model.initFull(_analysis_method = _implicit_dynamic);
Material & mat = model.getMaterial(0);
mat.setParam("E", E);
mat.setParam("rho", rho);
Array<Real> & force = model.getExternalForce();
Array<Real> & displacment = model.getDisplacement();
// boundary conditions
model.applyBC(BC::Dirichlet::FixedValue(0.0, _x), "blocked");
model.applyBC(BC::Dirichlet::FixedValue(0.0, _y), "blocked");
model.applyBC(BC::Dirichlet::FixedValue(0.0, _y), "roller");
const Array<UInt> & trac_nodes =
mesh.getElementGroup("traction").getNodeGroup().getNodes();
bool dump_node = false;
if (trac_nodes.size() > 0 && mesh.isLocalOrMasterNode(trac_nodes(0))) {
force(trac_nodes(0), 1) = F;
dump_node = true;
}
// output setup
std::ofstream pos;
pos.open("position.csv");
if (!pos.good())
AKANTU_ERROR("Cannot open file \"position.csv\"");
pos << "id,time,position,solution" << std::endl;
model.setBaseName("dynamic");
model.addDumpFieldVector("displacement");
model.addDumpField("velocity");
model.addDumpField("acceleration");
model.addDumpField("external_force");
model.addDumpField("internal_force");
model.dump();
model.setTimeStep(time_step);
auto & solver = model.getNonLinearSolver();
solver.set("max_iterations", 100);
solver.set("threshold", 1e-12);
solver.set("convergence_type", SolveConvergenceCriteria::_solution);
/// time loop
Real time = 0.;
for (UInt s = 1; time < max_time; ++s, time += time_step) {
if (prank == 0)
std::cout << s << "\r" << std::flush;
model.solveStep();
if (dump_node)
pos << s << "," << time << "," << displacment(trac_nodes(0), 1) << ","
<< analytical_solution(s * time_step) << std::endl;
if (s % 100 == 0)
model.dump();
}
std::cout << std::endl;
pos.close();
finalize();
return EXIT_SUCCESS;
}

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