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rGOOSEFEM/docs/examples/Statics/LinearElasticity/main.cpp
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main.cpp
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#include <Eigen/Eigen>
#include <GooseFEM/GooseFEM.h>
#include <GMatLinearElastic/Cartesian3d.h>
#include <xtensor-io/xhighfive.hpp>
int main()
{
// mesh
// ----
// define mesh
GooseFEM::Mesh::Quad4::Regular mesh(5,5);
// mesh dimensions
size_t nelem = mesh.nelem();
size_t nne = mesh.nne();
size_t ndim = mesh.ndim();
// mesh definitions
xt::xtensor<double,2> coor = mesh.coor();
xt::xtensor<size_t,2> conn = mesh.conn();
xt::xtensor<size_t,2> dofs = mesh.dofs();
// node sets
xt::xtensor<size_t,1> nodesLeft = mesh.nodesLeftEdge();
xt::xtensor<size_t,1> nodesRight = mesh.nodesRightEdge();
xt::xtensor<size_t,1> nodesTop = mesh.nodesTopEdge();
xt::xtensor<size_t,1> nodesBottom = mesh.nodesBottomEdge();
// fixed displacements DOFs
// ------------------------
xt::xtensor<size_t,1> iip = xt::concatenate(xt::xtuple(
xt::view(dofs, xt::keep(nodesRight ), 0),
xt::view(dofs, xt::keep(nodesTop ), 1),
xt::view(dofs, xt::keep(nodesLeft ), 0),
xt::view(dofs, xt::keep(nodesBottom), 1)
));
// simulation variables
// --------------------
// vector definition
GooseFEM::VectorPartitioned vector(conn, dofs, iip);
// nodal quantities
xt::xtensor<double,2> disp = xt::zeros<double>(coor.shape());
xt::xtensor<double,2> fint = xt::zeros<double>(coor.shape());
xt::xtensor<double,2> fext = xt::zeros<double>(coor.shape());
xt::xtensor<double,2> fres = xt::zeros<double>(coor.shape());
// element vectors
xt::xtensor<double,3> ue = xt::empty<double>({nelem, nne, ndim});
xt::xtensor<double,3> fe = xt::empty<double>({nelem, nne, ndim});
xt::xtensor<double,3> Ke = xt::empty<double>({nelem, nne*ndim, nne*ndim});
// element/material definition
// ---------------------------
GooseFEM::Element::Quad4::QuadraturePlanar elem(vector.AsElement(coor));
size_t nip = elem.nip();
GMatLinearElastic::Cartesian3d::Matrix mat(nelem, nip, 1., 1.);
// solve
// -----
// allocate tensors
size_t d = 3;
xt::xtensor<double,4> Eps = xt::empty<double>({nelem, nip, d, d });
xt::xtensor<double,4> Sig = xt::empty<double>({nelem, nip, d, d });
xt::xtensor<double,6> C = xt::empty<double>({nelem, nip, d, d, d, d});
// allocate system matrix
GooseFEM::MatrixPartitioned K(conn, dofs, iip);
// strain
vector.asElement(disp, ue);
elem.symGradN_vector(ue, Eps);
// stress & tangent
mat.tangent(Eps, Sig, C);
// internal force
elem.int_gradN_dot_tensor2_dV(Sig, fe);
vector.assembleNode(fe, fint);
// stiffness matrix
elem.int_gradN_dot_tensor4_dot_gradNT_dV(C, Ke);
K.assemble(Ke);
// set fixed displacements
xt::view(disp, xt::keep(nodesRight ), 0) = +0.1;
xt::view(disp, xt::keep(nodesTop ), 1) = -0.1;
xt::view(disp, xt::keep(nodesLeft ), 0) = 0.0;
xt::view(disp, xt::keep(nodesBottom), 1) = 0.0;
// residual
xt::noalias(fres) = fext - fint;
// solve
K.solve(fres, disp);
// post-process
// ------------
// compute strain and stress
vector.asElement(disp, ue);
elem.symGradN_vector(ue, Eps);
mat.stress(Eps, Sig);
// internal force
elem.int_gradN_dot_tensor2_dV(Sig, fe);
vector.assembleNode(fe, fint);
// apply reaction force
vector.copy_p(fint, fext);
// residual
xt::noalias(fres) = fext - fint;
// print residual
std::cout << xt::sum(xt::abs(fres))[0] / xt::sum(xt::abs(fext))[0] << std::endl;
// average stress per node
xt::xtensor<double,4> dV = elem.DV(2);
xt::xtensor<double,3> SigAv = xt::average(Sig, dV, {1});
// write output
HighFive::File file("main.h5", HighFive::File::Overwrite);
xt::dump(file, "/coor", coor);
xt::dump(file, "/conn", conn);
xt::dump(file, "/disp", disp);
xt::dump(file, "/Sig" , SigAv);
return 0;
}
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