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rGOOSEFEM/test/basic/ElementHex8.cpp
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ElementHex8.cpp
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#include <catch2/catch.hpp>
#include <xtensor/xrandom.hpp>
#include <xtensor/xmath.hpp>
#include <GooseFEM/GooseFEM.h>
#define ISCLOSE(a,b) REQUIRE_THAT((a), Catch::WithinAbs((b), 1.e-12));
TEST_CASE("GooseFEM::ElementHex8", "ElementHex8.h")
{
SECTION("dV - Gauss")
{
GooseFEM::Mesh::Hex8::Regular mesh(2, 2, 2);
auto coor = mesh.coor();
auto top = mesh.nodesTop();
auto right = mesh.nodesRight();
auto back = mesh.nodesBack();
xt::view(coor, xt::keep(back), xt::keep(2)) += 1.0;
xt::view(coor, xt::keep(top), xt::keep(1)) += 1.0;
xt::view(coor, xt::keep(right), xt::keep(0)) += 1.0;
GooseFEM::Vector vec(mesh.conn(), mesh.dofs());
GooseFEM::Element::Hex8::Quadrature quad(vec.AsElement(coor));
auto dV = quad.dV();
auto dV_tensor = quad.AsTensor<2>(dV);
REQUIRE(xt::allclose(xt::view(dV, xt::keep(0)), 1.0 / 8.0));
REQUIRE(xt::allclose(xt::view(dV, xt::keep(1)), 2.0 / 8.0));
REQUIRE(xt::allclose(xt::view(dV, xt::keep(2)), 2.0 / 8.0));
REQUIRE(xt::allclose(xt::view(dV, xt::keep(3)), 4.0 / 8.0));
REQUIRE(xt::allclose(xt::view(dV, xt::keep(4)), 2.0 / 8.0));
REQUIRE(xt::allclose(xt::view(dV, xt::keep(5)), 4.0 / 8.0));
REQUIRE(xt::allclose(xt::view(dV, xt::keep(6)), 4.0 / 8.0));
REQUIRE(xt::allclose(xt::view(dV, xt::keep(7)), 8.0 / 8.0));
for (size_t e = 0; e < mesh.nelem(); ++e) {
for (size_t q = 0; q < quad.nip(); ++q) {
REQUIRE(xt::allclose(xt::view(dV_tensor, xt::keep(e), xt::keep(q)), dV(e, q)));
}
}
}
SECTION("dV - Nodal")
{
GooseFEM::Mesh::Hex8::Regular mesh(2, 2, 2);
auto coor = mesh.coor();
auto top = mesh.nodesTop();
auto right = mesh.nodesRight();
auto back = mesh.nodesBack();
xt::view(coor, xt::keep(back), xt::keep(2)) += 1.0;
xt::view(coor, xt::keep(top), xt::keep(1)) += 1.0;
xt::view(coor, xt::keep(right), xt::keep(0)) += 1.0;
GooseFEM::Vector vec(mesh.conn(), mesh.dofs());
GooseFEM::Element::Hex8::Quadrature quad(
vec.AsElement(coor),
GooseFEM::Element::Hex8::Nodal::xi(),
GooseFEM::Element::Hex8::Nodal::w());
auto dV = quad.dV();
auto dV_tensor = quad.AsTensor<2>(dV);
REQUIRE(xt::allclose(xt::view(dV, xt::keep(0)), 1. / 8.));
REQUIRE(xt::allclose(xt::view(dV, xt::keep(1)), 2. / 8.));
REQUIRE(xt::allclose(xt::view(dV, xt::keep(2)), 2. / 8.));
REQUIRE(xt::allclose(xt::view(dV, xt::keep(3)), 4. / 8.));
REQUIRE(xt::allclose(xt::view(dV, xt::keep(4)), 2. / 8.));
REQUIRE(xt::allclose(xt::view(dV, xt::keep(5)), 4. / 8.));
REQUIRE(xt::allclose(xt::view(dV, xt::keep(6)), 4. / 8.));
REQUIRE(xt::allclose(xt::view(dV, xt::keep(7)), 8. / 8.));
for (size_t e = 0; e < mesh.nelem(); ++e) {
for (size_t q = 0; q < quad.nip(); ++q) {
REQUIRE(xt::allclose(xt::view(dV_tensor, xt::keep(e), xt::keep(q)), dV(e, q)));
}
}
}
SECTION("int_N_scalar_NT_dV")
{
GooseFEM::Mesh::Hex8::Regular mesh(3, 3, 3);
GooseFEM::Vector vec(mesh.conn(), mesh.dofsPeriodic());
GooseFEM::MatrixDiagonal mat(mesh.conn(), mesh.dofsPeriodic());
GooseFEM::Element::Hex8::Quadrature quad(
vec.AsElement(mesh.coor()),
GooseFEM::Element::Hex8::Nodal::xi(),
GooseFEM::Element::Hex8::Nodal::w());
xt::xtensor<double, 2> rho = xt::ones<double>({mesh.nelem(), quad.nip()});
mat.assemble(quad.Int_N_scalar_NT_dV(rho));
auto M = mat.AsDiagonal();
REQUIRE(M.size() == vec.ndof());
REQUIRE(xt::allclose(M, 1.));
}
SECTION("symGradN_vector")
{
GooseFEM::Mesh::Hex8::FineLayer mesh(27, 27, 27);
GooseFEM::Vector vec(mesh.conn(), mesh.dofs());
GooseFEM::Element::Hex8::Quadrature quad(vec.AsElement(mesh.coor()));
xt::xtensor<double, 2> F = xt::zeros<double>({3, 3});
xt::xtensor<double, 2> EPS = xt::zeros<double>({3, 3});
F(0, 1) = 0.1;
EPS(0, 1) = 0.05;
EPS(1, 0) = 0.05;
auto coor = mesh.coor();
xt::xtensor<double, 2> disp = xt::zeros<double>(coor.shape());
for (size_t n = 0; n < mesh.nnode(); ++n) {
for (size_t i = 0; i < F.shape()[0]; ++i) {
for (size_t j = 0; j < F.shape()[1]; ++j) {
disp(n, i) += F(i, j) * coor(n, j);
}
}
}
auto eps = quad.SymGradN_vector(vec.AsElement(disp));
auto dV = quad.AsTensor<2>(quad.dV());
auto epsbar = xt::average(eps, dV, {0, 1});
REQUIRE(eps.shape()[0] == mesh.nelem());
REQUIRE(eps.shape()[1] == quad.nip());
REQUIRE(eps.shape()[2] == mesh.ndim());
REQUIRE(eps.shape()[3] == mesh.ndim());
for (size_t e = 0; e < mesh.nelem(); ++e) {
for (size_t q = 0; q < quad.nip(); ++q) {
REQUIRE(xt::allclose(xt::view(eps, e, q), EPS));
}
}
REQUIRE(xt::allclose(epsbar, EPS));
}
SECTION("symGradN_vector, int_gradN_dot_tensor2s_dV")
{
GooseFEM::Mesh::Hex8::FineLayer mesh(27, 27, 27);
GooseFEM::Vector vec(mesh.conn(), mesh.dofsPeriodic());
GooseFEM::Element::Hex8::Quadrature quad(vec.AsElement(mesh.coor()));
xt::xtensor<double, 2> F = xt::zeros<double>({3, 3});
F(0, 1) = 0.1;
auto coor = mesh.coor();
xt::xtensor<double, 2> disp = xt::zeros<double>(coor.shape());
for (size_t n = 0; n < mesh.nnode(); ++n) {
for (size_t i = 0; i < F.shape()[0]; ++i) {
for (size_t j = 0; j < F.shape()[1]; ++j) {
disp(n, i) += F(i, j) * coor(n, j);
}
}
}
auto eps = quad.SymGradN_vector(vec.AsElement(disp));
auto Fi = vec.AssembleDofs(quad.Int_gradN_dot_tensor2_dV(eps));
REQUIRE(Fi.size() == vec.ndof());
REQUIRE(xt::allclose(Fi, 0.));
}
}
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