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rGOOSEFEM/tests/basic/ElementHex8.cpp
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ElementHex8.cpp
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#include <GooseFEM/GooseFEM.h>
#include <catch2/catch_all.hpp>
#include <xtensor/xmath.hpp>
#include <xtensor/xrandom.hpp>
#define ISCLOSE(a, b) REQUIRE_THAT((a), Catch::Matchers::WithinAbs((b), 1.e-12));
TEST_CASE("GooseFEM::ElementHex8", "ElementHex8.h")
{
SECTION("GradN")
{
GooseFEM::Mesh::Hex8::Regular mesh(3, 3, 3);
GooseFEM::Vector vec(mesh.conn(), mesh.dofs());
GooseFEM::Element::Hex8::Quadrature quad(vec.AsElement(mesh.coor()));
auto dNdx = quad.GradN();
REQUIRE(xt::has_shape(dNdx, {mesh.nelem(), quad.nip(), mesh.nne(), mesh.ndim()}));
}
SECTION("dV")
{
GooseFEM::Mesh::Hex8::Regular mesh(3, 3, 3);
GooseFEM::Vector vec(mesh.conn(), mesh.dofs());
GooseFEM::Element::Hex8::Quadrature quad(vec.AsElement(mesh.coor()));
auto dV = quad.dV();
REQUIRE(xt::has_shape(dV, quad.shape_qtensor<0>()));
REQUIRE(xt::has_shape(dV, quad.shape_qscalar()));
REQUIRE(xt::allclose(dV, 0.5 * 0.5 * 0.5));
}
SECTION("InterpQuad_vector")
{
GooseFEM::Mesh::Hex8::Regular mesh(3, 3, 3);
GooseFEM::Vector vector(mesh.conn(), mesh.dofsPeriodic());
GooseFEM::Element::Hex8::Quadrature quad(vector.AsElement(mesh.coor()));
auto u = vector.allocate_nodevec(1.0);
auto ue = vector.AsElement(u);
auto uq = quad.InterpQuad_vector(ue);
REQUIRE(xt::allclose(uq, 1.0));
}
SECTION("GradN_vector")
{
GooseFEM::Mesh::Hex8::Regular mesh(3, 3, 3);
GooseFEM::Vector vec(mesh.conn(), mesh.dofs());
GooseFEM::Element::Hex8::Quadrature quad(vec.AsElement(mesh.coor()));
size_t td = mesh.ndim();
xt::xtensor<double, 2> F = xt::zeros<double>({td, td});
xt::xtensor<double, 2> EPS = xt::zeros<double>({td, td});
F(0, 1) = 0.1;
auto coor = mesh.coor();
auto disp = xt::zeros_like(coor);
for (size_t n = 0; n < mesh.nnode(); ++n) {
for (size_t i = 0; i < mesh.ndim(); ++i) {
for (size_t j = 0; j < mesh.ndim(); ++j) {
disp(n, i) += F(i, j) * coor(n, j);
}
}
}
auto f = quad.GradN_vector(vec.AsElement(disp));
REQUIRE(xt::has_shape(f, {mesh.nelem(), quad.nip(), td, td}));
REQUIRE(xt::has_shape(f, quad.shape_qtensor<2>()));
for (size_t e = 0; e < mesh.nelem(); ++e) {
for (size_t q = 0; q < quad.nip(); ++q) {
REQUIRE(xt::allclose(xt::view(f, e, q), xt::transpose(F)));
}
}
}
SECTION("GradN_vector_T")
{
GooseFEM::Mesh::Hex8::Regular mesh(3, 3, 3);
GooseFEM::Vector vec(mesh.conn(), mesh.dofs());
GooseFEM::Element::Hex8::Quadrature quad(vec.AsElement(mesh.coor()));
size_t td = mesh.ndim();
xt::xtensor<double, 2> F = xt::zeros<double>({td, td});
xt::xtensor<double, 2> EPS = xt::zeros<double>({td, td});
F(0, 1) = 0.1;
auto coor = mesh.coor();
auto disp = xt::zeros_like(coor);
for (size_t n = 0; n < mesh.nnode(); ++n) {
for (size_t i = 0; i < mesh.ndim(); ++i) {
for (size_t j = 0; j < mesh.ndim(); ++j) {
disp(n, i) += F(i, j) * coor(n, j);
}
}
}
auto f = quad.GradN_vector_T(vec.AsElement(disp));
REQUIRE(xt::has_shape(f, {mesh.nelem(), quad.nip(), td, td}));
REQUIRE(xt::has_shape(f, quad.shape_qtensor<2>()));
for (size_t e = 0; e < mesh.nelem(); ++e) {
for (size_t q = 0; q < quad.nip(); ++q) {
REQUIRE(xt::allclose(xt::view(f, e, q), F));
}
}
}
SECTION("SymGradN_vector")
{
GooseFEM::Mesh::Hex8::Regular mesh(3, 3, 3);
GooseFEM::Vector vec(mesh.conn(), mesh.dofs());
GooseFEM::Element::Hex8::Quadrature quad(vec.AsElement(mesh.coor()));
size_t td = mesh.ndim();
xt::xtensor<double, 2> F = xt::zeros<double>({td, td});
xt::xtensor<double, 2> EPS = xt::zeros<double>({td, td});
F(0, 1) = 0.1;
EPS(0, 1) = 0.05;
EPS(1, 0) = 0.05;
auto coor = mesh.coor();
auto disp = xt::zeros_like(coor);
for (size_t n = 0; n < mesh.nnode(); ++n) {
for (size_t i = 0; i < mesh.ndim(); ++i) {
for (size_t j = 0; j < mesh.ndim(); ++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(xt::has_shape(eps, {mesh.nelem(), quad.nip(), td, td}));
REQUIRE(xt::has_shape(eps, quad.shape_qtensor<2>()));
REQUIRE(xt::has_shape(dV, {mesh.nelem(), quad.nip(), td, td}));
REQUIRE(xt::has_shape(dV, quad.shape_qtensor<2>()));
REQUIRE(xt::has_shape(epsbar, {td, td}));
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("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.Todiagonal();
REQUIRE(M.size() == vec.ndof());
REQUIRE(xt::allclose(M, 1.0));
}
SECTION("Int_gradN_dot_tensor2_dV")
{
GooseFEM::Mesh::Hex8::Regular mesh(3, 3, 3);
GooseFEM::Vector vec(mesh.conn(), mesh.dofsPeriodic());
GooseFEM::Element::Hex8::Quadrature quad(vec.AsElement(mesh.coor()));
size_t td = mesh.ndim();
xt::xtensor<double, 2> F = xt::zeros<double>({td, td});
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 < mesh.ndim(); ++i) {
for (size_t j = 0; j < mesh.ndim(); ++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, 0.0));
}
}
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