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rAKA/test/test_model/test_solid_mechanics_model/test_embedded_interface/test_embedded_interface_model_prestress.cc
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test_embedded_interface_model_prestress.cc
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/**
* @file test_embedded_interface_model_prestress.cc
*
* @author Lucas Frerot <lucas.frerot@epfl.ch>
*
* @date creation: mar. avril 28 2015
* @date last modification: mar. avril 28 2015
*
* @brief Embedded model test for prestressing (bases on stress norm)
*
* @section LICENSE
*
* Copyright (©) 2010-2015 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 "aka_common.hh"
#include "embedded_interface_model.hh"
/* -------------------------------------------------------------------------- */
using namespace akantu;
#define YG 0.483644859
#define I_eq 0.012488874
#define A_eq (1e-2 + 1. / 7. * 1.)
/* -------------------------------------------------------------------------- */
struct StressSolution : public BC::Neumann::FromHigherDim {
Real M;
Real I;
Real yg;
Real pre_stress;
StressSolution(UInt dim, Real M, Real I, Real yg = 0, Real pre_stress = 0) :
BC::Neumann::FromHigherDim(Matrix<Real>(dim, dim)),
M(M), I(I), yg(yg), pre_stress(pre_stress)
{}
void operator()(const QuadraturePoint & quad_point,
Vector<Real> & dual,
const Vector<Real> & coord,
const Vector<Real> & normals) const {
UInt dim = coord.size();
if (dim < 2) AKANTU_DEBUG_ERROR("Solution not valid for 1D");
Matrix<Real> stress(dim, dim); stress.clear();
stress(0, 0) = this->stress(coord(1));
dual.mul<false>(stress, normals);
}
inline Real stress(Real height) const {
return -M / I * (height - yg) + pre_stress;
}
inline Real neutral_axis() const {
return -I * pre_stress / M + yg;
}
};
/* -------------------------------------------------------------------------- */
int main (int argc, char * argv[]) {
initialize("prestress.dat", argc, argv);
debug::setDebugLevel(dblError);
Math::setTolerance(1e-6);
const UInt dim = 2;
/* -------------------------------------------------------------------------- */
Mesh mesh(dim);
mesh.read("embedded_mesh_prestress.msh");
mesh.createGroupsFromMeshData<std::string>("physical_names");
Mesh reinforcement_mesh(dim, "reinforcement_mesh");
try {
reinforcement_mesh.read("embedded_mesh_prestress_reinforcement.msh");
} catch(debug::Exception & e) {}
reinforcement_mesh.createGroupsFromMeshData<std::string>("physical_names");
EmbeddedInterfaceModel model(mesh, reinforcement_mesh, dim);
model.initFull(SolidMechanicsModelOptions(_static));
/* -------------------------------------------------------------------------- */
/* Computation of analytical residual */
/* -------------------------------------------------------------------------- */
/*
* q = 1000 N/m
* L = 20 m
* a = 1 m
*/
Real steel_area = model.getMaterial("reinforcement").getParam<Real>("area");
Real pre_stress = 1e6;
Real stress_norm = 0.;
StressSolution * concrete_stress = NULL, * steel_stress = NULL;
Real pre_force = pre_stress * steel_area;
Real pre_moment = -pre_force * (YG - 0.25);
Real neutral_axis = YG - I_eq / A_eq * pre_force / pre_moment;
concrete_stress = new StressSolution(dim, pre_moment, 7. * I_eq, YG, -pre_force / (7. * A_eq));
steel_stress = new StressSolution(dim, pre_moment, I_eq, YG, pre_stress - pre_force / A_eq);
stress_norm = std::abs(concrete_stress->stress(1)) * (1 - neutral_axis) * 0.5
+ std::abs(concrete_stress->stress(0)) * neutral_axis * 0.5
+ std::abs(steel_stress->stress(0.25)) * steel_area;
model.applyBC(*concrete_stress, "XBlocked");
ElementGroup & end_node = mesh.getElementGroup("EndNode");
NodeGroup & end_node_group = end_node.getNodeGroup();
NodeGroup::const_node_iterator end_node_it = end_node_group.begin();
Vector<Real> end_node_force = model.getForce().begin(dim)[*end_node_it];
end_node_force(0) += steel_stress->stress(0.25) * steel_area;
Array<Real> analytical_residual(mesh.getNbNodes(), dim, "analytical_residual");
analytical_residual.copy(model.getForce());
model.getForce().clear();
delete concrete_stress;
delete steel_stress;
/* -------------------------------------------------------------------------- */
model.applyBC(BC::Dirichlet::FixedValue(0.0, _x), "XBlocked");
model.applyBC(BC::Dirichlet::FixedValue(0.0, _y), "YBlocked");
// Assemble the global stiffness matrix
model.assembleStiffnessMatrix();
model.updateResidual();
if (!model.solveStatic<_scm_newton_raphson_tangent_not_computed, _scc_residual>(1e-6, 1))
return EXIT_FAILURE;
model.updateResidual();
/* -------------------------------------------------------------------------- */
/* Computation of FEM residual norm */
/* -------------------------------------------------------------------------- */
ElementGroup & xblocked = mesh.getElementGroup("XBlocked");
NodeGroup & boundary_nodes = xblocked.getNodeGroup();
NodeGroup::const_node_iterator
nodes_it = boundary_nodes.begin(),
nodes_end = boundary_nodes.end();
Array<Real>::vector_iterator com_res = model.getResidual().begin(dim);
Array<Real>::vector_iterator ana_res = analytical_residual.begin(dim);
Array<Real>::vector_iterator position = mesh.getNodes().begin(dim);
Real res_sum = 0.;
UInt lower_node = -1;
UInt upper_node = -1;
Real lower_dist = 1;
Real upper_dist = 1;
for (; nodes_it != nodes_end ; ++nodes_it) {
UInt node_number = *nodes_it;
const Vector<Real> res = com_res[node_number];
const Vector<Real> ana = ana_res[node_number];
const Vector<Real> pos = position[node_number];
if (!Math::are_float_equal(pos(1), 0.25)) {
if ((std::abs(pos(1) - 0.25) < lower_dist) && (pos(1) < 0.25)) {
lower_dist = std::abs(pos(1) - 0.25);
lower_node = node_number;
}
if ((std::abs(pos(1) - 0.25) < upper_dist) && (pos(1) > 0.25)) {
upper_dist = std::abs(pos(1) - 0.25);
upper_node = node_number;
}
}
for (UInt i = 0 ; i < dim ; i++) {
if (!Math::are_float_equal(pos(1), 0.25)) {
res_sum += std::abs(res(i));
}
}
}
const Vector<Real> upper_res = com_res[upper_node], lower_res = com_res[lower_node];
const Vector<Real> end_node_res = com_res[*end_node_it];
Vector<Real> delta = upper_res - lower_res;
delta *= lower_dist / (upper_dist + lower_dist);
Vector<Real> concrete_residual = lower_res + delta;
Vector<Real> steel_residual = end_node_res - concrete_residual;
for (UInt i = 0 ; i < dim ; i++) {
res_sum += std::abs(concrete_residual(i));
res_sum += std::abs(steel_residual(i));
}
Real relative_error = std::abs(res_sum - stress_norm) / stress_norm;
if (relative_error > 1e-3)
return EXIT_FAILURE;
finalize();
return 0;
}
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