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rAKA/test/test_fe_engine/test_fe_engine_precomputation_structural.cc
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test_fe_engine_precomputation_structural.cc
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/**
* @file test_fe_engine_precomputation_structural.cc
*
* @author Lucas Frérot
*
* @date creation: Fri Feb 26 2018
*
* @brief test of the structural precomputations
*
* @section LICENSE
*
* Copyright (©) 2010-2012, 2014, 2015 EPFL (Ecole Polytechnique Fédérale de
* Lausanne) Laboratory (LSMS - Laboratoire de Simulation en Mécanique des
* Solides)
*
* Akantu is free software: you can redistribute it and/or modify it under the
* terms of the GNU Lesser General Public License as published by the Free
* Software Foundation, either version 3 of the License, or (at your option) any
* later version.
*
* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
* details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
*
*/
/* -------------------------------------------------------------------------- */
#include "fe_engine.hh"
#include "integrator_gauss.hh"
#include "shape_structural.hh"
#include "test_fe_engine_structural_fixture.hh"
/* -------------------------------------------------------------------------- */
using namespace akantu;
/* -------------------------------------------------------------------------- */
// Need a special fixture for the extra normal
class TestBernoulliB3
: public TestFEMStructuralFixture<element_type_t<_bernoulli_beam_3>> {
using parent = TestFEMStructuralFixture<element_type_t<_bernoulli_beam_3>>;
public:
/// Load the mesh and provide extra normal direction
void readMesh(std::string filename) override {
parent::readMesh(filename);
auto & normals = this->mesh->registerData<Real>("extra_normal")
.alloc(0, dim, type, _not_ghost);
Vector<Real> normal = {-36. / 65, -48. / 65, 5. / 13};
normals.push_back(normal);
}
};
/* -------------------------------------------------------------------------- */
/// Type alias
using TestBernoulliB2 =
TestFEMStructuralFixture<element_type_t<_bernoulli_beam_2>>;
using TestDKT18 =
TestFEMStructuralFixture<element_type_t<_discrete_kirchhoff_triangle_18>>;
/* -------------------------------------------------------------------------- */
/// Solution for 2D rotation matrices
Matrix<Real> globalToLocalRotation(Real theta) {
auto c = std::cos(theta);
auto s = std::sin(theta);
return {{c, s, 0}, {-s, c, 0}, {0, 0, 1}};
}
/* -------------------------------------------------------------------------- */
TEST_F(TestBernoulliB2, PrecomputeRotations) {
this->fem->initShapeFunctions();
using ShapeStruct = ShapeStructural<_ek_structural>;
auto & shape = dynamic_cast<const ShapeStruct &>(fem->getShapeFunctions());
auto & rot = shape.getRotations(type);
Real a = std::atan(4. / 3);
std::vector<Real> angles = {a, -a, 0};
Math::setTolerance(1e-15);
for (auto && tuple : zip(make_view(rot, ndof, ndof), angles)) {
auto rotation = std::get<0>(tuple);
auto angle = std::get<1>(tuple);
auto rotation_error = (rotation - globalToLocalRotation(angle)).norm<L_2>();
EXPECT_NEAR(rotation_error, 0., Math::getTolerance());
}
}
/* -------------------------------------------------------------------------- */
TEST_F(TestBernoulliB3, PrecomputeRotations) {
this->fem->initShapeFunctions();
using ShapeStruct = ShapeStructural<_ek_structural>;
auto & shape = dynamic_cast<const ShapeStruct &>(fem->getShapeFunctions());
auto & rot = shape.getRotations(type);
Matrix<Real> ref = {{3. / 13, 4. / 13, 12. / 13},
{-4. / 5, 3. / 5, 0},
{-36. / 65, -48. / 65, 5. / 13}};
Matrix<Real> solution{ndof, ndof};
solution.block(ref, 0, 0);
solution.block(ref, dim, dim);
// The default tolerance is too much, really
Math::setTolerance(1e-15);
for (auto & rotation : make_view(rot, ndof, ndof)) {
auto rotation_error = (rotation - solution).norm<L_2>();
EXPECT_NEAR(rotation_error, 0., Math::getTolerance());
}
}
/* -------------------------------------------------------------------------- */
TEST_F(TestDKT18, PrecomputeRotations) {
this->fem->initShapeFunctions();
using ShapeStruct = ShapeStructural<_ek_structural>;
auto & shape = dynamic_cast<const ShapeStruct &>(fem->getShapeFunctions());
auto & rot = shape.getRotations(type);
for (auto & rotation : make_view(rot, ndof, ndof)) {
std::cout << rotation << "\n";
}
std::cout.flush();
}
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