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/*===========================================================================
Copyright (C) 2009-2020 Konstantinos Poulios.
This file is a part of GetFEM
GetFEM 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 along with the GCC Runtime Library
Exception either version 3.1 or (at your option) any later version.
This program 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 and GCC Runtime Library Exception for more details.
You should have received a copy of the GNU Lesser General Public License
along with this program; if not, write to the Free Software Foundation,
Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA.
===========================================================================*/
#include "getfem/getfem_model_solvers.h"
#include "getfem/getfem_import.h" /* import functions (load a mesh from file) */
#include "getfem/getfem_export.h" /* export functions (save solution in a file) */
#include "getfem/getfem_contact_and_friction_nodal.h"
#include "getfem/getfem_contact_and_friction_integral.h"
#include "getfem/getfem_contact_and_friction_large_sliding.h"
#include "gmm/gmm.h"
using std::endl; using std::cout; using std::cerr;
using std::ends; using std::cin;
/* some GetFEM types that we will be using */
using bgeot::dim_type;
using bgeot::size_type; /* = unsigned long */
using bgeot::short_type;
using bgeot::scalar_type; /* = double */
using bgeot::base_node; /* geometrical nodes (derived from base_small_vector)*/
using bgeot::base_matrix; /* small dense matrix. */
/* definition of some matrix/vector types. These ones are built
* using the predefined types in Gmm++
*/
typedef getfem::model_real_plain_vector plain_vector;
/*
structure for the elastostatic problem
*/
struct elastostatic_contact_problem {
enum { DIRICHLET_BOUNDARY_1 = 0, DIRICHLET_BOUNDARY_2 = 1,
CONTACT_BOUNDARY_1 = 1001, CONTACT_BOUNDARY_2 = 1002 };
getfem::mesh mesh1, mesh2; /* the meshes */
getfem::mesh_im mim1, mim2; /* the integration methods */
getfem::mesh_fem mf_u1; /* 1st mesh_fem, for the elastostatic solution */
getfem::mesh_fem mf_u2; /* 2nd mesh_fem, for the elastostatic solution */
getfem::mesh_fem mf_rhs1; /* 1st mesh_fem for the right hand side */
getfem::mesh_fem mf_rhs2; /* 2nd mesh_fem for the right hand side */
getfem::mesh_fem mf_mult1; /* 1st mesh_fem for the multipliers. */
scalar_type lambda, mu; /* elastic coefficients. */
scalar_type residual; /* max residual for the iterative solvers */
scalar_type rot_angle; /* rotation angle of the pinion gear */
scalar_type frict_coeff; /* friction coefficient */
//scalar_type threshold; /* threshold distance for contact finding */
size_type N; /* dimension of the problem */
bool frictionless; /* flag for frictionless model */
int contact_algo; /* contact algorithm (0:nodal, 1-4: integral
>=5:integral large sliding) */
// Vectors holding the ids of mesh region pairs expected to come in contact
// with each other
std::vector<size_type> cb_rgs1, cb_rgs2;
std::string datafilename;
bgeot::md_param PARAM;
bool solve(void);
void init(void);
elastostatic_contact_problem(void) : mim1(mesh1), mim2(mesh2),
mf_u1(mesh1), mf_u2(mesh2), mf_rhs1(mesh1), mf_rhs2(mesh2),
mf_mult1(mesh1) {}
};
/* Define the problem parameters, import the mesh, set finite element
and integration methods and detect the boundaries.
*/
void elastostatic_contact_problem::init(void) {
std::string FEM_TYPE = PARAM.string_value("FEM_TYPE","FEM name");
std::string INTEGRATION = PARAM.string_value("INTEGRATION",
"Name of integration method");
/* First step : import the mesh */
std::string meshname_1 = PARAM.string_value("MESHNAME_GEAR1",
"Mesh filename for the 1st gear");
std::string meshname_2 = PARAM.string_value("MESHNAME_GEAR2",
"Mesh filename for the 2nd gear");
size_type nb_cf_pairs;
for (size_type swap = 0; swap <= 1; swap++) {
std::vector<size_type> &cfs = swap ? cb_rgs2 : cb_rgs1;
// Contact faces
const std::vector<bgeot::md_param::param_value> &cf_params
= PARAM.array_value( swap ? "CONTACT_FACES_2" : "CONTACT_FACES_1" );
if (swap == 0) nb_cf_pairs = cf_params.size();
else GMM_ASSERT1(nb_cf_pairs == cf_params.size(),
"Vectors CONTACT_FACES_1 and CONTACT_FACES_2 " <<
"should have the same size.");
gmm::resize(cfs, nb_cf_pairs);
for (size_type i = 0; i < cfs.size(); ++i) {
GMM_ASSERT1(cf_params[i].type_of_param() == bgeot::md_param::REAL_VALUE,
(swap ? "CONTACT_FACES_2" : "CONTACT_FACES_1")
<< " should be an integer array.");
cfs[i] = size_type(cf_params[i].real()+0.5);
}
// Dirichlet faces
const std::vector<bgeot::md_param::param_value> &df_params
= PARAM.array_value(swap ? "DIRICHLET_FACES_2" : "DIRICHLET_FACES_1");
std::vector<size_type> dfs(df_params.size());
for (size_type i = 0; i < dfs.size(); ++i) {
GMM_ASSERT1(df_params[i].type_of_param() == bgeot::md_param::REAL_VALUE,
(swap ? "DIRICHLET_FACES_2" : "DIRICHLET_FACES_1")
<< " should be an integer array.");
dfs[i] = size_type(df_params[i].real()+0.5);
}
getfem::mesh tmpmesh;
getfem::import_mesh(swap ? meshname_2 : meshname_1, tmpmesh);
N = tmpmesh.dim();
base_node Pmin(N), Pmax(N);
tmpmesh.bounding_box(Pmin, Pmax);
bool reduce_dim = false;
if (gmm::abs(Pmax[N-1] - Pmin[N-1]) < 1.E-10) reduce_dim = true;
getfem::mesh &mesh = swap ? mesh2 : mesh1;
getfem::mesh_region dirichlet_boundary =
mesh.region(swap ? DIRICHLET_BOUNDARY_2 : DIRICHLET_BOUNDARY_1);
// Add convexes to the mesh
for (dal::bv_visitor cv(tmpmesh.convex_index()); !cv.finished(); ++cv) {
size_type newcv;
if (reduce_dim) {
std::vector<base_node> pt_tab;
for (size_type i=0; i < tmpmesh.nb_points_of_convex(cv); ++i) {
base_node PP = tmpmesh.points_of_convex(cv)[i];
base_node P(N-1);
for (size_type j=0; j < N-1; ++j) P[j] = PP[j];
pt_tab.push_back(P);
}
newcv =
mesh.add_convex_by_points(tmpmesh.trans_of_convex(cv), pt_tab.begin());
} else {
newcv =
mesh.add_convex_by_points(tmpmesh.trans_of_convex(cv),
tmpmesh.points_of_convex(cv).begin());
}
for (short_type f = 0; f < tmpmesh.structure_of_convex(cv)->nb_faces(); f++) {
for (size_type i = 0; i < dfs.size(); ++i)
if (tmpmesh.region(dfs[i]).is_in(cv,f)) {
dirichlet_boundary.add(newcv,f);
break;
}
for (size_type i = 0; i < cfs.size(); ++i)
if (tmpmesh.region(cfs[i]).is_in(cv,f)) {
GMM_ASSERT1(!dirichlet_boundary.is_in(newcv,f),
"Overlapping contact and dirichlet regions");
mesh.region(cfs[i]).add(newcv,f);
}
}
}
}
N = mesh1.dim();
GMM_ASSERT1(N == mesh2.dim(),"Meshes should be of the same dim.");
residual = PARAM.real_value("RESIDUAL", "Residual for Newton solver");
if (residual == 0.) residual = 1e-10;
rot_angle = PARAM.real_value("ROT_ANGLE", "Rotation angle of the first gear");
frict_coeff = PARAM.real_value("FRICTION_COEFFICIENT", "Friction coefficient");
if (frict_coeff == 0.) frictionless = true;
else frictionless = false;
// threshold = 10.; //FIXME
mu = PARAM.real_value("MU", "Lamé coefficient mu");
lambda = PARAM.real_value("LAMBDA", "Lamé coefficient lambda");
mf_u1.set_qdim(dim_type(N));
mf_u2.set_qdim(dim_type(N));
/* set the finite element on the mf_u */
getfem::pfem pf_u = getfem::fem_descriptor(FEM_TYPE);
mf_u1.set_finite_element(pf_u);
mf_u2.set_finite_element(pf_u);
GMM_ASSERT1(pf_u->is_lagrange(), "You are using a non-lagrange FEM. "
<< "For this problem you need a lagrange FEM.");
getfem::pintegration_method ppi = getfem::int_method_descriptor(INTEGRATION);
mim1.set_integration_method(ppi);
mim2.set_integration_method(ppi);
/* set the finite element on mf_rhs */
mf_rhs1.set_finite_element(getfem::fem_descriptor(FEM_TYPE));
mf_rhs2.set_finite_element(getfem::fem_descriptor(FEM_TYPE));
datafilename = PARAM.string_value("ROOTFILENAME","Base name of data files.");
contact_algo = int(PARAM.int_value("CONTACT_ALGO","Algorithm for imposing the contact condition."));
if (contact_algo != 0) { // integral contact
std::string MULT_FEM_TYPE = PARAM.string_value("MULT_FEM_TYPE","FEM name for the multipliers");
if (frictionless && contact_algo >= 1 && contact_algo <= 4)
mf_mult1.set_qdim(dim_type(1));
else
mf_mult1.set_qdim(dim_type(N));
getfem::pfem pf_mult = getfem::fem_descriptor(MULT_FEM_TYPE);
mf_mult1.set_finite_element(pf_mult);
getfem::mesh_region &mr1 = mesh1.region(CONTACT_BOUNDARY_1);
getfem::mesh_region &mr2 = mesh2.region(CONTACT_BOUNDARY_2);
for (std::vector<size_type>::const_iterator rg_it=cb_rgs1.begin();
rg_it != cb_rgs1.end(); rg_it++)
mr1 = getfem::mesh_region::merge(mr1, mesh1.region(*rg_it));
for (std::vector<size_type>::const_iterator rg_it=cb_rgs2.begin();
rg_it != cb_rgs2.end(); rg_it++)
mr2 = getfem::mesh_region::merge(mr2, mesh2.region(*rg_it));
dal::bit_vector dol1 = mf_mult1.basic_dof_on_region(CONTACT_BOUNDARY_1);
mf_mult1.reduce_to_basic_dof(dol1);
}
}
/* Construction and solution of the Model.
*/
bool elastostatic_contact_problem::solve() {
size_type nb_dof_rhs1 = mf_rhs1.nb_dof();
size_type nb_dof_rhs2 = mf_rhs2.nb_dof();
cout << "mf_u1.nb_dof() :" << mf_u1.nb_dof() << endl;
cout << "mf_u2.nb_dof() :" << mf_u2.nb_dof() << endl;
getfem::model md;
md.add_fem_variable("u1", mf_u1);
md.add_fem_variable("u2", mf_u2);
// Linearized elasticity brick.
md.add_initialized_scalar_data("lambda", lambda);
md.add_initialized_scalar_data("mu", mu);
getfem::add_isotropic_linearized_elasticity_brick(md, mim1, "u1", "lambda", "mu");
getfem::add_isotropic_linearized_elasticity_brick(md, mim2, "u2", "lambda", "mu");
// Defining the contact condition.
md.add_initialized_scalar_data
("r", mu * (3*lambda + 2*mu) / (lambda + mu) ); // r ~= Young modulus
std::string multname_n, multname_t;
if (contact_algo == 0) {
if (frictionless) {
getfem::add_nodal_contact_between_nonmatching_meshes_brick
(md, mim1, mim2, "u1", "u2", multname_n, "r",
cb_rgs1, cb_rgs2);
} else {
std::string dataname_frict_coeff="friction_coefficient";
md.add_initialized_scalar_data(dataname_frict_coeff, frict_coeff);
getfem::add_nodal_contact_between_nonmatching_meshes_brick
(md, mim1, mim2, "u1", "u2", multname_n, multname_t,
"r", dataname_frict_coeff, cb_rgs1, cb_rgs2);
}
} else {
md.add_fem_variable("mult1", mf_mult1);
if (contact_algo >= 1 && contact_algo <= 4) { // integral contact
if (frictionless)
getfem::add_integral_contact_between_nonmatching_meshes_brick
(md, mim1, "u1", "u2", "mult1", "r",
CONTACT_BOUNDARY_1, CONTACT_BOUNDARY_2, contact_algo);
else {
md.add_initialized_scalar_data("f_coeff", frict_coeff);
getfem::add_integral_contact_between_nonmatching_meshes_brick
(md, mim1, "u1", "u2", "mult1", "r", "f_coeff",
CONTACT_BOUNDARY_1, CONTACT_BOUNDARY_2, contact_algo);
}
}
else { // large sliding is for the moment always frictionless
std::string u01_str(""), u02_str("");
// if (frict_coeff > scalar_type(0)) {
// u01_str = "u01";
// u02_str = "u02";
// md.add_fem_variable(u01_str, mf_u1);
// md.add_fem_variable(u02_str, mf_u2);
// }
md.add_initialized_scalar_data("f_coeff", frict_coeff);
size_type indb =
getfem::add_integral_large_sliding_contact_brick_raytracing
(md, "r", 20., "f_coeff", "1", false, false);
getfem::add_contact_boundary_to_large_sliding_contact_brick
(md, indb, mim1, CONTACT_BOUNDARY_1, false, true, "u1", "mult1", u01_str);
getfem::add_contact_boundary_to_large_sliding_contact_brick
(md, indb, mim2, CONTACT_BOUNDARY_2, true, false, "u2", "", u02_str);
}
}
// Defining the DIRICHLET condition.
plain_vector F(nb_dof_rhs1 * N);
dal::bit_vector
cn = mf_rhs1.basic_dof_on_region(mesh1.region(DIRICHLET_BOUNDARY_1));
for (dal::bv_visitor i(cn); !i.finished(); ++i) {
base_node node = mf_rhs1.point_of_basic_dof(i);
F[i*N] = -node[1] * rot_angle;
F[i*N+1] = node[0] * rot_angle;
}
md.add_initialized_fem_data("DirichletData1", mf_rhs1, F);
getfem::add_Dirichlet_condition_with_multipliers
(md, mim1, "u1", mf_u1, DIRICHLET_BOUNDARY_1, "DirichletData1");
gmm::resize(F, nb_dof_rhs2 * N);
gmm::clear(F);
md.add_initialized_fem_data("DirichletData2", mf_rhs2, F);
getfem::add_Dirichlet_condition_with_multipliers
(md, mim2, "u2", mf_u2, DIRICHLET_BOUNDARY_2, "DirichletData2");
cout << "md.nb_dof() :" << md.nb_dof() << endl;
gmm::iteration iter(residual, 1, 40000);
// getfem::default_newton_line_search ls;
getfem::simplest_newton_line_search ls(50, 5., 5., 0.6, 1e-1);
#if defined(GMM_USES_MUMPS)
getfem::standard_solve(md, iter, getfem::rselect_linear_solver(md,"mumps"), ls);
#else
getfem::standard_solve(md, iter, getfem::default_linear_solver<getfem::model_real_sparse_matrix, getfem::model_real_plain_vector>(md), ls);
#endif
if (!iter.converged()) return false; // Solution has not converged
plain_vector VM1(mf_rhs1.nb_dof()), VM2(mf_rhs2.nb_dof());
getfem::compute_isotropic_linearized_Von_Mises_or_Tresca
(md, "u1", "lambda", "mu", mf_rhs1, VM1, false);
getfem::compute_isotropic_linearized_Von_Mises_or_Tresca
(md, "u2", "lambda", "mu", mf_rhs2, VM2, false);
if (!getfem::MPI_IS_MASTER())
return true;
// Prepare results
plain_vector U1(mf_u1.nb_dof()), U2(mf_u2.nb_dof());
plain_vector RHS(md.nb_dof());
plain_vector Forces1(mf_u1.nb_dof()), Forces2(mf_u2.nb_dof());
plain_vector NCForces1(mf_u1.nb_dof()), NCForces2(mf_u2.nb_dof());
plain_vector TCForces1(0), TCForces2(0);
gmm::copy(md.real_variable("u1"), U1);
gmm::copy(md.real_variable("u2"), U2);
gmm::copy(md.real_rhs(), RHS);
gmm::copy(gmm::sub_vector(RHS, md.interval_of_variable("u1")), Forces1);
gmm::scale(Forces1, -1.0);
gmm::copy(gmm::sub_vector(RHS, md.interval_of_variable("u2")), Forces2);
gmm::scale(Forces2, -1.0);
// Export results
mesh1.write_to_file(datafilename + "1.mesh");
mesh2.write_to_file(datafilename + "2.mesh");
mf_u1.write_to_file(datafilename + "1.mf", true);
mf_u2.write_to_file(datafilename + "2.mf", true);
mf_rhs1.write_to_file(datafilename + "1.mfd", true);
mf_rhs2.write_to_file(datafilename + "2.mfd", true);
gmm::vecsave(datafilename + "1.U", U1);
gmm::vecsave(datafilename + "2.U", U2);
gmm::vecsave(datafilename + "12.RHS", RHS);
getfem::vtk_export exp1(datafilename + "1.vtk", true);
getfem::vtk_export exp2(datafilename + "2.vtk", true);
exp1.exporting(mesh1);
exp2.exporting(mesh2);
exp1.write_point_data(mf_u1, U1, "elastostatic_displacement_1");
exp2.write_point_data(mf_u2, U2, "elastostatic_displacement_2");
exp1.write_point_data(mf_u1, Forces1, "forces_1");
exp2.write_point_data(mf_u2, Forces2, "forces_2");
exp1.write_point_data(mf_rhs1, VM1, "von_mises_stresses_1");
exp2.write_point_data(mf_rhs2, VM2, "von_mises_stresses_2");
if (contact_algo == 0) {
gmm::mult(gmm::sub_matrix(md.real_tangent_matrix(),
md.interval_of_variable("u1"),
md.interval_of_variable(multname_n) ),
md.real_variable(multname_n),
NCForces1);
gmm::scale(NCForces1, -1.0);
gmm::mult(gmm::sub_matrix(md.real_tangent_matrix(),
md.interval_of_variable("u2"),
md.interval_of_variable(multname_n) ),
md.real_variable(multname_n),
NCForces2);
gmm::scale(NCForces2, -1.0);
exp1.write_point_data(mf_u1, NCForces1, "normal_contact_forces_1");
exp2.write_point_data(mf_u2, NCForces2, "normal_contact_forces_2");
if (!frictionless) {
gmm::resize(TCForces1, mf_u1.nb_dof());
gmm::mult(gmm::sub_matrix(md.real_tangent_matrix(),
md.interval_of_variable("u1"),
md.interval_of_variable(multname_t) ),
md.real_variable(multname_t),
TCForces1);
gmm::scale(TCForces1, -1.0);
gmm::resize(TCForces2, mf_u2.nb_dof());
gmm::mult(gmm::sub_matrix(md.real_tangent_matrix(),
md.interval_of_variable("u2"),
md.interval_of_variable(multname_t) ),
md.real_variable(multname_t),
TCForces2);
gmm::scale(TCForces2, -1.0);
exp1.write_point_data(mf_u1, TCForces1, "tangential_contact_forces_1");
exp2.write_point_data(mf_u2, TCForces2, "tangential_contact_forces_2");
}
}
return true; // Solution has converged
}
/**************************************************************************/
/* main program. */
/**************************************************************************/
int main(int argc, char *argv[]) {
GETFEM_MPI_INIT(argc, argv); // For parallelized version
elastostatic_contact_problem p;
p.PARAM.read_command_line(argc, argv);
p.init();
if (!p.solve()) cout << "Solve has failed\n";
GETFEM_MPI_FINALIZE;
return 0;
}
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