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test_solid_mechanics_model_igfem.cc
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test_solid_mechanics_model_igfem.cc
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/**
* @file test_solid_mechanics_model_igfem.cc
*
* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
*
*
* @brief test the solidmechancis model for IGFEM analysis
*
* @section LICENSE
*
* Copyright (©) 2010-2012, 2014 EPFL (Ecole Polytechnique Fédérale de Lausanne)
* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
*
*/
/* -------------------------------------------------------------------------- */
#include "aka_common.hh"
#include "dumper_paraview.hh"
#include "material_elastic.hh"
#include "mesh_geom_common.hh"
#include "solid_mechanics_model_igfem.hh"
#include <cmath>
#include <cstdlib>
#include <fstream>
#include <iostream>
#include <math.h>
/* -------------------------------------------------------------------------- */
using namespace akantu;
/* -------------------------------------------------------------------------- */
void outputArray(const Mesh & mesh, const Array<Real> & array) {
StaticCommunicator & comm = StaticCommunicator::getStaticCommunicator();
Int prank = comm.whoAmI();
UInt spatial_dimension = mesh.getSpatialDimension();
UInt nb_global_nodes = mesh.getNbGlobalNodes();
Array<Real> solution(nb_global_nodes, spatial_dimension, 0.);
Array<Real>::vector_iterator solution_begin =
solution.begin(spatial_dimension);
Array<Real>::const_vector_iterator array_it = array.begin(spatial_dimension);
for (UInt n = 0; n < mesh.getNbNodes(); ++n, ++array_it) {
if (mesh.isLocalOrMasterNode(n))
solution_begin[mesh.getNodeGlobalId(n)] = *array_it;
}
comm.allReduce(solution.storage(),
solution.getSize() * solution.getNbComponent(), _so_sum);
std::cout << std::fixed;
std::cout << std::setprecision(6);
if (prank == 0) {
Array<Real>::const_vector_iterator sol_it =
solution.begin(spatial_dimension);
for (UInt n = 0; n < nb_global_nodes; ++n, ++sol_it)
// Print absolute values to avoid parasite negative sign in machine
// precision zeros
std::cout << std::abs((*sol_it)(0)) << "," << std::abs((*sol_it)(1))
<< std::endl;
}
}
/* -------------------------------------------------------------------------- */
class Sphere {
public:
Sphere(const Vector<Real> & center, Real radius, Real tolerance = 0.)
: center(center), radius(radius), tolerance(tolerance) {}
bool isInside(const Vector<Real> & point) const {
return (point.distance(center) < radius + tolerance);
}
const Vector<Real> & getCenter() const { return center; }
Real & getRadius() { return radius; }
protected:
Vector<Real> center;
Real radius, tolerance;
};
void growGel(std::list<SK::Sphere_3> & query_list, Real new_radius) {
std::list<SK::Sphere_3>::const_iterator query_it = query_list.begin(),
query_end = query_list.end();
std::list<SK::Sphere_3> sphere_list;
for (; query_it != query_end; ++query_it) {
SK::Sphere_3 sphere(query_it->center(), new_radius * new_radius);
sphere_list.push_back(sphere);
}
query_list.clear();
query_list = sphere_list;
}
Real computeAlpha(Real inner_radius, Real outer_radius,
const Vector<Real> & lambda, const Vector<Real> & mu) {
Real alpha = (lambda(1) + mu(1) + mu(0)) * outer_radius * outer_radius /
((lambda(0) + mu(0)) * inner_radius * inner_radius +
(lambda(1) + mu(1)) * (outer_radius * outer_radius -
inner_radius * inner_radius) +
(mu(0) * outer_radius * outer_radius));
return alpha;
}
void applyBoundaryConditions(SolidMechanicsModelIGFEM & model,
Real inner_radius, Real outer_radius,
const Vector<Real> & lambda,
const Vector<Real> & mu) {
/// boundary conditions for circular inclusion:
Real alpha = computeAlpha(inner_radius, outer_radius, lambda, mu);
Mesh & mesh = model.getMesh();
mesh.computeBoundingBox();
const Vector<Real> & lowerBounds = mesh.getLowerBounds();
const Vector<Real> & upperBounds = mesh.getUpperBounds();
Real bottom = lowerBounds(1);
Real top = upperBounds(1);
Real left = lowerBounds(0);
Real right = upperBounds(0);
Real eps = std::abs((top - bottom) * 1e-12);
const Array<Real> & pos = mesh.getNodes();
Array<Real> & disp = model.getDisplacement();
Array<bool> & boun = model.getBlockedDOFs();
Real radius = 0;
Real phi = 0;
disp.clear();
boun.clear();
/// absolute confinement
for (UInt i = 0; i < mesh.getNbNodes(); ++i) {
if (std::abs(pos(i, 0) - left) < eps) {
radius = std::sqrt(pos(i, 0) * pos(i, 0) + pos(i, 1) * pos(i, 1));
phi = std::atan2(pos(i, 1), pos(i, 0));
boun(i, 0) = true;
disp(i, 0) = cos(phi) * ((radius - 4. / radius) * alpha + 4. / radius);
boun(i, 1) = true;
disp(i, 1) = sin(phi) * ((radius - 4. / radius) * alpha + 4. / radius);
}
if (std::abs(pos(i, 0) - right) < eps) {
radius = std::sqrt(pos(i, 0) * pos(i, 0) + pos(i, 1) * pos(i, 1));
phi = std::atan2(pos(i, 1), pos(i, 0));
boun(i, 0) = true;
disp(i, 0) = cos(phi) * ((radius - 4. / radius) * alpha + 4. / radius);
boun(i, 1) = true;
disp(i, 1) = sin(phi) * ((radius - 4. / radius) * alpha + 4. / radius);
}
if (std::abs(pos(i, 1) - top) < eps) {
radius = std::sqrt(pos(i, 0) * pos(i, 0) + pos(i, 1) * pos(i, 1));
phi = std::atan2(pos(i, 1), pos(i, 0));
boun(i, 0) = true;
disp(i, 0) = cos(phi) * ((radius - 4. / radius) * alpha + 4. / radius);
boun(i, 1) = true;
disp(i, 1) = sin(phi) * ((radius - 4. / radius) * alpha + 4. / radius);
}
if (std::abs(pos(i, 1) - bottom) < eps) {
radius = std::sqrt(pos(i, 0) * pos(i, 0) + pos(i, 1) * pos(i, 1));
phi = std::atan2(pos(i, 1), pos(i, 0));
boun(i, 0) = true;
disp(i, 0) = cos(phi) * ((radius - 4. / radius) * alpha + 4. / radius);
boun(i, 1) = true;
disp(i, 1) = sin(phi) * ((radius - 4. / radius) * alpha + 4. / radius);
}
}
}
class SphereMaterialSelector : public DefaultMaterialIGFEMSelector {
public:
SphereMaterialSelector(std::vector<Sphere> & sphere_list,
SolidMechanicsModelIGFEM & model)
: DefaultMaterialIGFEMSelector(model), model(model),
spheres(sphere_list) {}
UInt operator()(const Element & elem) {
if (Mesh::getKind(elem.type) == _ek_igfem)
return this->fallback_value_igfem;
// return 2;//2model.getMaterialIndex(2);
const Mesh & mesh = model.getMesh();
UInt spatial_dimension = model.getSpatialDimension();
Vector<Real> barycenter(spatial_dimension);
mesh.getBarycenter(elem, barycenter);
std::vector<Sphere>::const_iterator iit = spheres.begin();
std::vector<Sphere>::const_iterator eit = spheres.end();
for (; iit != eit; ++iit) {
const Sphere & sp = *iit;
if (sp.isInside(barycenter)) {
return 1; // model.getMaterialIndex("inside");;
}
}
return 0;
// return DefaultMaterialSelector::operator()(elem);
}
void update(Real new_radius) {
std::vector<Sphere>::iterator iit = spheres.begin();
std::vector<Sphere>::iterator eit = spheres.end();
for (; iit != eit; ++iit) {
Real & radius = iit->getRadius();
radius = new_radius;
}
}
protected:
SolidMechanicsModelIGFEM & model;
std::vector<Sphere> spheres;
};
typedef Spherical SK;
/// the following modeling problem is explained in:
/// T.-P. Fries "A corrected XFEM approximation without problems in blending
/// elements", 2008
int main(int argc, char * argv[]) {
initialize("material.dat", argc, argv);
/// problem dimension
const UInt spatial_dimension = 2;
StaticCommunicator & comm = StaticCommunicator::getStaticCommunicator();
Int psize = comm.getNbProc();
Int prank = comm.whoAmI();
/// mesh creation
Mesh mesh(spatial_dimension);
akantu::MeshPartition * partition = NULL;
if (prank == 0) {
mesh.read("plate.msh");
partition = new MeshPartitionScotch(mesh, spatial_dimension);
partition->partitionate(psize);
}
/// model creation
SolidMechanicsModelIGFEM model(mesh);
model.initParallel(partition);
delete partition;
Math::setTolerance(1e-14);
/// geometry of IGFEM interface: circular inclusion
Real radius_inclusion = 0.401;
Vector<Real> center(spatial_dimension, 0.);
/// @todo: Simplify this: need to create two type of spheres:
/// one for the geometry and one for the material selector
SK::Sphere_3 sphere(SK::Point_3(center(0), center(1), 0),
radius_inclusion * radius_inclusion);
std::list<SK::Sphere_3> sphere_list;
sphere_list.push_back(sphere);
ID domain_name = "gel";
SphereMaterialSelector * mat_selector;
/// set material selector and initialize the model completely
std::vector<Sphere> spheres;
spheres.push_back(Sphere(center, radius_inclusion, 1.e-12));
mat_selector = new SphereMaterialSelector(spheres, model);
model.setMaterialSelector(*mat_selector);
model.initFull();
/// register the sphere list in the model
model.registerGeometryObject(sphere_list, domain_name);
/// add fields that should be dumped
model.setBaseName("regular_elements");
model.setBaseNameToDumper("igfem elements", "igfem elements");
model.addDumpField("material_index");
model.addDumpField("partitions");
model.addDumpFieldVector("displacement");
model.addDumpField("blocked_dofs");
model.addDumpField("stress");
model.addDumpFieldToDumper("igfem elements", "lambda");
model.addDumpFieldVectorToDumper("igfem elements", "real_displacement");
model.addDumpFieldVectorToDumper("igfem elements", "displacement");
model.addDumpFieldToDumper("igfem elements", "material_index");
model.addDumpFieldToDumper("igfem elements", "stress");
model.addDumpFieldToDumper("igfem elements", "partitions");
/// dump mesh before the IGFEM interface is created
model.dump();
model.dump("igfem elements");
/// create the interface
model.update(domain_name);
/* --------------------------------------------------------------------------
*/
/// apply exact solution for the displacement along the outer boundary
Real outer_radius = 2.0;
/// get the Lame constants for the two non-igfem materials (frist two
/// materials in the material file):
/// Needed for compuation of boundary conditions
Vector<Real> lambda(2);
Vector<Real> mu(2);
for (UInt m = 0; m < 2; ++m) {
MaterialElastic<spatial_dimension> & mat =
dynamic_cast<MaterialElastic<spatial_dimension> &>(
model.getMaterial(m));
lambda(m) = mat.getLambda();
mu(m) = mat.getMu();
}
applyBoundaryConditions(model, radius_inclusion, outer_radius, lambda, mu);
/// dump the mesh after the IGFEM interface has been created
model.dump();
model.dump("igfem elements");
/// solve the system
bool factorize = false;
bool converged = false;
Real error;
converged = model.solveStep<_scm_newton_raphson_tangent,
SolveConvergenceCriteria::_increment>(
1e-12, error, 2, factorize);
if (!converged) {
std::cout << "Solving step did not yield a converged solution, error: "
<< error << std::endl;
return EXIT_FAILURE;
}
/// dump the solution
model.dump();
model.dump("igfem elements");
/// output the displacement in parallel
outputArray(mesh, model.getDisplacement());
finalize();
return EXIT_SUCCESS;
}

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