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rAKA/test/test_fe_engine/test_fe_engine_precomputation_bernoulli_2.cc
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test_fe_engine_precomputation_bernoulli_2.cc
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/**
* @file test_fe_engine_precomputation.cc
*
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date creation: Mon Jun 14 2010
* @date last modification: Mon Jul 13 2015
*
* @brief test of the fem class
*
* @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 <cmath>
#include <iostream>
#include <functional>
/* -------------------------------------------------------------------------- */
using namespace akantu;
Matrix<Real> globalToLocalRotation(Real theta) {
// clang-format off
return {{ std::cos(theta), std::sin(theta), 0},
{-std::sin(theta), std::cos(theta), 0},
{ 0, 0, 1}};
// clang-format on
}
Vector<Real> axialReference(Real xq) {
return {(1. - xq) / 2, 0, 0, (1. + xq) / 2, 0, 0};
}
Vector<Real> bendingReference(Real xq) {
return {0,
1. / 4. * Math::pow<2>(xq - 1) * (xq + 2),
1. / 4. * Math::pow<2>(xq - 1) * (xq + 1),
0,
1. / 4. * Math::pow<2>(xq + 1) * (2 - xq),
1. / 4. * Math::pow<2>(xq + 1) * (xq - 1)};
}
Vector<Real> bendingRotationReference(Real xq) {
return {0, 3. / 4. * (xq * xq - 1), 1. / 4. * (3 * xq * xq - 2 * xq - 1),
0, 3. / 4. * (1 - xq * xq), 1. / 4. * (3 * xq * xq + 2 * xq - 1)};
}
bool testBending(const Array<Real> & shape_functions, UInt shape_line_index,
std::function<Vector<Real>(Real)> reference) {
Real xq = -1. / std::sqrt(3.);
// Testing values for bending rotations shapes on quadrature points
for (auto && N : make_view(shape_functions, 3, 6)) {
auto Nt = N.transpose();
Vector<Real> N_bending = Nt(shape_line_index);
auto bending_reference = reference(xq);
if (!Math::are_vector_equal(6, N_bending.storage(),
bending_reference.storage()))
return false;
xq *= -1;
}
std::cout.flush();
return true;
}
int main(int argc, char * argv[]) {
akantu::initialize(argc, argv);
//debug::setDebugLevel(dblTest);
constexpr ElementType type = _bernoulli_beam_2;
UInt dim = ElementClass<type>::getSpatialDimension();
Mesh mesh(dim);
// creating nodes
Vector<Real> node = {0, 0};
mesh.getNodes().push_back(node);
node = {3. / 5., 4. / 5.};
mesh.getNodes().push_back(node);
node = {2 * 3. / 5., 0};
mesh.getNodes().push_back(node);
mesh.addConnectivityType(type);
auto & connectivity = mesh.getConnectivity(type);
// creating elements
Vector<UInt> elem = {0, 1};
connectivity.push_back(elem);
elem = {1, 2};
connectivity.push_back(elem);
elem = {0, 2};
connectivity.push_back(elem);
using FE = FEEngineTemplate<IntegratorGauss, ShapeStructural, _ek_structural>;
using ShapeStruct = ShapeStructural<_ek_structural>;
auto fem = std::make_unique<FE>(mesh, dim, "test_fem");
fem->initShapeFunctions();
auto & shape = dynamic_cast<const ShapeStruct &>(fem->getShapeFunctions());
Array<Real> angles;
angles.push_back(std::atan(4. / 3.));
angles.push_back(-std::atan(4. / 3.));
angles.push_back(0);
/// Testing the rotation matrices
for (auto && tuple : zip(make_view(shape.getRotations(type), 3, 3), angles)) {
auto && rotation = std::get<0>(tuple);
auto theta = std::get<1>(tuple);
auto reference = globalToLocalRotation(theta);
if (!Math::are_vector_equal(9, reference.storage(), rotation.storage()))
return 1;
}
auto & shape_functions = shape.getShapes(type);
if (!testBending(shape_functions, 0, axialReference))
return 1;
if (!testBending(shape_functions, 1, bendingReference))
return 1;
if (!testBending(shape_functions, 2, bendingRotationReference))
return 1;
std::cout.flush();
finalize();
return 0;
}
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