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bernoulli_beam_2_example.cc
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bernoulli_beam_2_example.cc
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/**
* @file bernoulli_beam_2_example.cc
*
* @author Fabian Barras <fabian.barras@epfl.ch>
*
* @date creation: Fri Jul 15 2011
* @date last modification: Mon Mar 15 2021
*
* @brief Computation of the analytical exemple 1.1 in the TGC vol 6
*
*
* @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 "mesh_accessor.hh"
#include "structural_mechanics_model.hh"
/* -------------------------------------------------------------------------- */
#include <iostream>
/* -------------------------------------------------------------------------- */
#define TYPE _bernoulli_beam_2
using namespace akantu;
/* -------------------------------------------------------------------------- */
int main(int argc, char * argv[]) {
initialize(argc, argv);
// Defining the mesh
Mesh beams(2);
const auto q = 6000.;
const auto L = 10.;
const auto M = -3600.; // Momentum at 3
auto nb_nodes = 3;
auto nb_element = nb_nodes - 1;
MeshAccessor mesh_accessor(beams);
Array<Real> & nodes = mesh_accessor.getNodes();
nodes.resize(nb_nodes);
beams.addConnectivityType(_bernoulli_beam_2);
Array<UInt> & connectivity = mesh_accessor.getConnectivity(_bernoulli_beam_2);
connectivity.resize(nb_element);
nodes.zero();
nodes(1, 0) = 10;
nodes(2, 0) = 18;
for (int i = 0; i < nb_element; ++i) {
connectivity(i, 0) = i;
connectivity(i, 1) = i + 1;
}
mesh_accessor.makeReady();
// 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();
auto & forces = model.getExternalForce();
auto & displacement = model.getDisplacement();
auto & boundary = model.getBlockedDOFs();
const auto & N_M = model.getStress(_bernoulli_beam_2);
auto & element_material = model.getElementMaterial(_bernoulli_beam_2);
boundary.set(false);
forces.zero();
displacement.zero();
element_material(1) = 1;
forces(0, 1) = -q * L / 2.;
forces(0, 2) = -q * L * L / 12.;
forces(1, 1) = -q * L / 2.;
forces(1, 2) = q * L * L / 12.;
forces(2, 2) = M;
forces(2, 0) = mat2.E * mat2.A / 18;
// Defining the boundary conditions
boundary(0, 0) = true;
boundary(0, 1) = true;
boundary(0, 2) = true;
boundary(1, 1) = true;
boundary(2, 1) = true;
model.addDumpFieldVector("displacement");
model.addDumpField("rotation");
model.addDumpFieldVector("force");
model.addDumpField("momentum");
model.solveStep();
model.assembleResidual();
// Post-Processing
std::cout << " d1 = " << displacement(1, 2) << std::endl;
std::cout << " d2 = " << displacement(2, 2) << std::endl;
std::cout << " d3 = " << displacement(1, 0) << 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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