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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: Thu Jun 12 2014
* @date last modification: Thu Jun 12 2014
*
* @brief Computation of the analytical exemple 1.1 in the TGC vol 6
*
* @section LICENSE
*
* Copyright (©) 2014 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 <limits>
#include <fstream>
/* -------------------------------------------------------------------------- */
#include "aka_common.hh"
#include "mesh.hh"
#include "mesh_io.hh"
#include "mesh_io_msh.hh"
#include "structural_mechanics_model.hh"
#include "material.hh"
/* -------------------------------------------------------------------------- */
#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);
debug::setDebugLevel(dblWarning);
/* -------------------------------------------------------------------------- */
// 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.clear();
displacement.clear();
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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