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ElementHex8.cpp
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Fri, Nov 1, 20:27

ElementHex8.cpp
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#include "support.h"
using T2 = cppmat::tiny::cartesian::tensor2 <double,3>;
using T2s = cppmat::tiny::cartesian::tensor2s<double,3>;
// =================================================================================================
TEST_CASE("GooseFEM::ElementHex8", "ElementHex8.h")
{
// =================================================================================================
SECTION( "int_N_scalar_NT_dV" )
{
// mesh
GooseFEM::Mesh::Hex8::Regular mesh(3,3,3);
// vector-definition, and a diagonal matrix
GooseFEM::Vector vec(mesh.conn(), mesh.dofsPeriodic());
GooseFEM::MatrixDiagonal mat(mesh.conn(), mesh.dofsPeriodic());
// element definition, with nodal quadrature
GooseFEM::Element::Hex8::Quadrature quad(
vec.asElement(mesh.coor()),
GooseFEM::Element::Hex8::Nodal::xi(),
GooseFEM::Element::Hex8::Nodal::w()
);
// scalar per quadrature point (e.g. mass-density "rho")
GooseFEM::ArrD rho = GooseFEM::ArrD::Constant({mesh.nelem(), quad.nip()}, 1.);
// evaluate integral and assemble diagonal matrix (e.g. mass matrix)
mat.assemble(quad.int_N_scalar_NT_dV(rho));
// check matrix
// - get the matrix
GooseFEM::ColD M = mat.asDiagonal();
// - check the size
REQUIRE( M.size() == vec.ndof() );
// - check each component
for ( auto i = 0 ; i < M.size() ; ++i )
EQ( M(i), 1 );
}
// =================================================================================================
SECTION( "symGradN_vector" )
{
// mesh
GooseFEM::Mesh::Hex8::FineLayer mesh(27,27,27);
// vector-definition
GooseFEM::Vector vec(mesh.conn(), mesh.dofs());
// element definition, with Gauss quadrature
GooseFEM::Element::Hex8::Quadrature quad( vec.asElement(mesh.coor()) );
// macroscopic deformation gradient
// - allocate
T2 F;
// - zero-initialize
F.setZero();
// - set non-zero components
F(0,1) = 0.1;
// convert the macroscopic strain tensor
T2 EPS = .5 * ( F + F.T() );
// nodal coordinates
GooseFEM::MatD coor = mesh.coor();;
// nodal displacement
// - allocate
GooseFEM::MatD disp(mesh.nnode(), mesh.ndim());
// - zero-initialize
disp.setZero();
// apply macroscopic deformation gradient
for ( size_t n = 0 ; n < mesh.nnode() ; ++n )
for ( size_t i = 0 ; i < F.ndim() ; ++i )
for ( size_t j = 0 ; j < F.ndim() ; ++j )
disp(n,i) += F(i,j) * coor(n,j);
// compute quadrature point tensors
GooseFEM::ArrD eps = quad.symGradN_vector(vec.asElement(disp));
// compute volume averaged tensor
GooseFEM::ArrD epsbar = eps.average(quad.dV(eps.shape(-1)), {0,1});
// check
// - temporary tensor, to view the tensors
cppmat::view::cartesian::tensor2s<double,3> Eps;
// - check sizes
REQUIRE( eps.shape(0) == mesh.nelem() );
REQUIRE( eps.shape(1) == quad.nip() );
REQUIRE( eps.shape(2) == Eps.size() );
// - check all components
for ( size_t e = 0 ; e < mesh.nelem() ; ++e ) {
for ( size_t k = 0 ; k < quad.nip() ; ++k ) {
Eps.setMap(&eps(e,k));
for ( size_t i = 0 ; i < Eps.ndim() ; ++i )
for ( size_t j = 0 ; j < Eps.ndim() ; ++j )
EQ( Eps(i,j), EPS(i,j) );
}
}
// check macroscopic tensor
// - convert to tensor object
T2s Epsbar = T2s::Copy(epsbar.begin(), epsbar.end());
// - check all components
for ( size_t i = 0 ; i < Epsbar.ndim() ; ++i )
for ( size_t j = 0 ; j < Epsbar.ndim() ; ++j )
EQ( Epsbar(i,j), EPS(i,j) );
}
// =================================================================================================
SECTION( "symGradN_vector, int_gradN_dot_tensor2s_dV" )
{
// mesh
GooseFEM::Mesh::Hex8::FineLayer mesh(27,27,27);
// vector-definition
GooseFEM::Vector vec(mesh.conn(), mesh.dofsPeriodic());
// element definition, with Gauss quadrature
GooseFEM::Element::Hex8::Quadrature quad( vec.asElement(mesh.coor()) );
// macroscopic deformation gradient
// - allocate
T2 F;
// - zero-initialize
F.setZero();
// - set non-zero components
F(0,1) = 0.1;
// nodal coordinates
GooseFEM::MatD coor = mesh.coor();;
// nodal displacement
// - allocate
GooseFEM::MatD disp(mesh.nnode(), mesh.ndim());
// - zero-initialize
disp.setZero();
// apply macroscopic deformation gradient
for ( size_t n = 0 ; n < mesh.nnode() ; ++n )
for ( size_t i = 0 ; i < F.ndim() ; ++i )
for ( size_t j = 0 ; j < F.ndim() ; ++j )
disp(n,i) += F(i,j) * coor(n,j);
// compute quadrature point tensors
GooseFEM::ArrD eps = quad.symGradN_vector(vec.asElement(disp));
// nodal force vector (should be zero, as it is only sensitive to periodic fluctuations)
GooseFEM::ColD Fi = vec.assembleDofs(quad.int_gradN_dot_tensor2s_dV(eps));
for ( size_t i = 0 ; i < vec.ndof() ; ++i )
if ( std::abs(Fi(i)) > 1.e-12 )
std::cout << i << ", " << Fi(i) << std::endl;
// check
// - size
REQUIRE( Fi.size() == vec.ndof() );
// - check all components
for ( size_t i = 0 ; i < vec.ndof() ; ++i )
EQ( Fi(i), 0 );
}
// =================================================================================================
}

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