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rAKA/examples/structural_mechanics/bernoulli_beam_2_exemple.cc
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/**
* @file bernoulli_beam_2_exemple.cc
*
* @author Fabian Barras <fabian.barras@epfl.ch>
*
* @date creation: Mon Jan 18 2016
*
* @brief Computation of the analytical exemple 1.1 in the TGC vol 6
*
*
* Copyright (©) 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 "structural_mechanics_model.hh"
/* -------------------------------------------------------------------------- */
#include <iostream>
/* -------------------------------------------------------------------------- */
#define TYPE _bernoulli_beam_2
using namespace akantu;
// Linear load function
static void lin_load(double * position, double * load,
__attribute__((unused)) Real * normal,
__attribute__((unused)) UInt surface_id) {
memset(load, 0, sizeof(Real) * 3);
if (position[0] <= 10) {
load[1] = -6000;
}
}
/* -------------------------------------------------------------------------- */
int main(int argc, char * argv[]) {
initialize(argc, argv);
// Defining the mesh
Mesh beams(2);
UInt nb_nodes = 3;
UInt nb_nodes_1 = 1;
UInt nb_nodes_2 = nb_nodes - nb_nodes_1 - 1;
UInt nb_element = nb_nodes - 1;
Array<Real> & nodes = const_cast<Array<Real> &>(beams.getNodes());
nodes.resize(nb_nodes);
beams.addConnectivityType(_bernoulli_beam_2);
Array<UInt> & connectivity =
const_cast<Array<UInt> &>(beams.getConnectivity(_bernoulli_beam_2));
connectivity.resize(nb_element);
for (UInt i = 0; i < nb_nodes; ++i) {
nodes(i, 1) = 0;
}
for (UInt i = 0; i < nb_nodes_1; ++i) {
nodes(i, 0) = 10. * i / ((Real)nb_nodes_1);
}
nodes(nb_nodes_1, 0) = 10;
for (UInt i = 0; i < nb_nodes_2; ++i) {
nodes(nb_nodes_1 + i + 1, 0) = 10 + 8. * (i + 1) / ((Real)nb_nodes_2);
}
for (UInt i = 0; i < nb_element; ++i) {
connectivity(i, 0) = i;
connectivity(i, 1) = i + 1;
}
// Defining the materials
StructuralMechanicsModel model(beams);
StructuralMaterial mat1;
mat1.E = 3e10;
mat1.I = 0.0025;
mat1.A = 0.01;
model.addMaterial(mat1);
StructuralMaterial mat2;
mat2.E = 3e10;
mat2.I = 0.00128;
mat2.A = 0.01;
model.addMaterial(mat2);
// Defining the forces
model.initFull();
const Real M = -3600; // Momentum at 3
Array<Real> & forces = model.getForce();
Array<Real> & displacement = model.getDisplacement();
Array<bool> & boundary = model.getBlockedDOFs();
const Array<Real> & N_M = model.getStress(_bernoulli_beam_2);
Array<UInt> & element_material = model.getElementMaterial(_bernoulli_beam_2);
forces.zero();
displacement.zero();
for (UInt i = 0; i < nb_nodes_2; ++i) {
element_material(i + nb_nodes_1) = 1;
}
forces(nb_nodes - 1, 2) += M;
model.computeForcesFromFunction<_bernoulli_beam_2>(lin_load, _bft_traction);
// Defining the boundary conditions
boundary(0, 0) = true;
boundary(0, 1) = true;
boundary(0, 2) = true;
boundary(nb_nodes_1, 1) = true;
boundary(nb_nodes - 1, 1) = true;
// Solve
Real error;
model.assembleStiffnessMatrix();
UInt count = 0;
model.addDumpFieldVector("displacement");
model.addDumpField("rotation");
model.addDumpFieldVector("force");
model.addDumpField("momentum");
do {
if (count != 0)
std::cerr << count << " - " << error << std::endl;
model.updateResidual();
model.solve();
count++;
} while (!model.testConvergenceIncrement(1e-10, error) && count < 10);
std::cerr << count << " - " << error << std::endl;
/* --------------------------------------------------------------------------
*/
// Post-Processing
model.computeStresses();
std::cout << " d1 = " << displacement(nb_nodes_1, 2) << std::endl;
std::cout << " d2 = " << displacement(nb_nodes - 1, 2) << std::endl;
std::cout << " M1 = " << N_M(0, 1) << std::endl;
std::cout << " M2 = " << N_M(2 * (nb_nodes - 2), 1) << std::endl;
model.dump();
finalize();
}
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