You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
93 lines
3.3 KiB
93 lines
3.3 KiB
#include <medusa/Medusa_fwd.hpp>
|
|
#include <medusa/bits/domains/GeneralFill.hpp>
|
|
#include <Eigen/SparseCore>
|
|
#include <Eigen/IterativeLinearSolvers>
|
|
|
|
|
|
/// Classical 2D Point contact problem.
|
|
/// http://e6.ijs.si/medusa/wiki/index.php/Linear_elasticity#Point_contact_2D
|
|
|
|
using namespace mm; // NOLINT
|
|
|
|
int main() {
|
|
// Physical parameters
|
|
const double E = 72.1e9;
|
|
const double nu = 0.33;
|
|
const double P = 1000;
|
|
|
|
// Derived parameters
|
|
double lam = E * nu / (1 - 2 * nu) / (1 + nu);
|
|
const double mu = E / 2 / (1 + nu);
|
|
|
|
// Closed form solution
|
|
std::function<Vec2d(Vec2d)> analytical = [=](const Vec2d& p) {
|
|
double x = p[0], y = p[1], r2 = x*x + y*y, factor = -P / (4.0*PI*mu);
|
|
double ux = 2*x*y/r2 + 2*mu/(lam + mu)*std::atan2(y, x);
|
|
double uy = (y*y-x*x)/r2 - (lam + 2*mu)/(lam + mu)*std::log(r2);
|
|
return Vec2d(factor*ux, factor*uy);
|
|
};
|
|
|
|
// Domain definition
|
|
Vec2d low(-1, -1), high(1, -0.1);
|
|
BoxShape<Vec2d> box(low, high);
|
|
|
|
double step = 0.025;
|
|
DomainDiscretization<Vec2d> domain = box.discretizeBoundaryWithStep(step);
|
|
GeneralFill<Vec2d> fill; fill.seed(0);
|
|
fill(domain, step);
|
|
int N = domain.size();
|
|
prn(N);
|
|
domain.findSupport(FindClosest(9)); // the support for each node is the closest 9 nodes
|
|
|
|
// Construct the approximation engine, in this case a weighted least squares using monomials as
|
|
// basis functions, no weight, and scale to farthest.
|
|
WLS<Gaussians<Vec2d>, GaussianWeight<Vec2d>, ScaleToFarthest> wls({9, 100.0}, 1.0);
|
|
|
|
// Compute the shapes using the defined approximation engine.
|
|
auto shapes = domain.computeShapes(wls);
|
|
std::cerr << "Shapes computed, solving system." << std::endl;
|
|
|
|
Eigen::SparseMatrix<double, Eigen::RowMajor> M(2*N, 2*N);
|
|
Eigen::VectorXd rhs(2*N); rhs.setZero();
|
|
M.reserve(shapes.supportSizesVec());
|
|
|
|
// Construct implicit operators over our storage.
|
|
auto op = shapes.implicitVectorOperators(M, rhs);
|
|
|
|
// Set the governing equations and the boundary conditions.
|
|
for (int i : domain.interior()) {
|
|
(lam+mu)*op.graddiv(i) + mu*op.lap(i) = 0.0;
|
|
}
|
|
for (int i : domain.boundary()) {
|
|
op.value(i) = analytical(domain.pos(i));
|
|
}
|
|
|
|
Eigen::BiCGSTAB<decltype(M), Eigen::IncompleteLUT<double>> solver;
|
|
solver.preconditioner().setFillfactor(20);
|
|
solver.preconditioner().setDroptol(1e-4);
|
|
solver.compute(M);
|
|
Eigen::VectorXd solution = solver.solve(rhs);
|
|
prn(solver.iterations());
|
|
prn(solver.error());
|
|
VectorField2d u = VectorField2d::fromLinear(solution);
|
|
|
|
VectorField3d stress(N);
|
|
auto eop = shapes.explicitVectorOperators();
|
|
for (int i = 0; i < N; ++i) {
|
|
auto grad = eop.grad(u, i);
|
|
stress(i, 0) = (2*mu + lam)*grad(0, 0) + lam*grad(1, 1);
|
|
stress(i, 1) = lam*grad(0, 0) + (2*mu+lam)*grad(1, 1);
|
|
stress(i, 2) = mu*(grad(0, 1)+grad(1, 0));
|
|
}
|
|
|
|
// Write the solution into a file.
|
|
std::ofstream out_file("point_contact2d_data.m");
|
|
out_file << "E = " << E << ";\n";
|
|
out_file << "nu = " << nu << ";\n";
|
|
out_file << "P = " << P << ";\n";
|
|
out_file << "positions = " << domain.positions() << ";\n";
|
|
out_file << "displacement = " << u << ";" << ";\n";
|
|
out_file << "stress = " << stress << ";" << std::endl;
|
|
out_file.close();
|
|
return 0;
|
|
}
|
|
|