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test_structural_mechanics_model_bernoulli_beam_3.cc
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test_structural_mechanics_model_bernoulli_beam_3.cc
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/**
* @file test_structural_mechanics_model_bernoulli_beam_3.cc
*
* @author Lucas Frérot <lucas.frerot@epfl.ch>
*
* @date creation: Mon Jan 22 2018
*
* @brief Computation of the analytical exemple 1.1 in the TGC vol 6
*
* @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 "aka_common.hh"
#include "mesh.hh"
#include "sparse_matrix_aij.hh"
#include "sparse_solver.hh"
#include "structural_mechanics_model.hh"
// #include "test_gtest_utils.hh"
/* -------------------------------------------------------------------------- */
#include <gtest/gtest.h>
/* -------------------------------------------------------------------------- */
using namespace akantu;
TEST(TestBernoulliBeam3, TestDisplacements) {
constexpr ElementType type = _bernoulli_beam_3;
constexpr UInt dim = 3;
const UInt ndof = ElementClass<type>::getNbDegreeOfFreedom();
const Real a = std::sqrt(2) / 2; // cos(pi/4)
Mesh mesh(dim, "test_bernoulli_beam_3");
// Pushing nodes
auto & nodes = mesh.getNodes();
Vector<Real> node = {0, 0, 0};
nodes.push_back(node);
node = {a, a, 0};
// node = {1, 0, 0};
nodes.push_back(node);
node = {a, -a, 0};
// node = {0, 1, 0};
nodes.push_back(node);
// Pushing connectivity
mesh.addConnectivityType(type);
auto & connectivity = mesh.getConnectivity(type);
Vector<UInt> element = {0, 1};
connectivity.push_back(element);
element = {0, 2};
connectivity.push_back(element);
// Pushing normals
auto & normals =
mesh.registerData<Real>("extra_normal").alloc(0, dim, type, _not_ghost);
Vector<Real> normal = {0, 0, 1};
normals.push_back(normal);
normal = {0, 0, 1};
normals.push_back(normal);
// Creating model
StructuralMechanicsModel model(mesh, dim, "test_bernoulli_beam_3");
// Unit material
StructuralMaterial mat;
mat.E = 1;
mat.Iz = 1;
mat.Iy = 1;
mat.A = 1;
mat.GJ = 1;
model.addMaterial(mat);
model.initFull();
// Boundary conditions (blocking all DOFs of nodes 2 & 3)
auto boundary = ++model.getBlockedDOFs().begin(ndof);
// clang-format off
*boundary = {true, true, true, true, true, true}; ++boundary;
*boundary = {true, true, true, true, true, true}; ++boundary;
// clang-format on
// Forces
Real P = 1; // N
auto & forces = model.getExternalForce();
forces.clear();
forces(0, 2) = -P; // vertical force on first node
// Setting same material for all elements
model.getElementMaterial(type).set(0);
try {
model.solveStep();
} catch (debug::SingularMatrixException & e) {
std::cerr << e.what() << std::endl;
e.matrix.saveMatrix("jacobian.mtx");
}
model.getDOFManager().getMatrix("K").saveMatrix("stiffness.mtx");
model.getDOFManager().getMatrix("J").saveMatrix("jacobian.mtx");
auto vz = model.getDisplacement()(0, 2);
auto thy = model.getDisplacement()(0, 4);
auto thx = model.getDisplacement()(0, 3);
auto thz = model.getDisplacement()(0, 5);
Real tol = Math::getTolerance();
EXPECT_NEAR(vz, -5. / 48, tol);
EXPECT_NEAR(thy, -std::sqrt(2) / 8, tol);
EXPECT_NEAR(thz, 0, tol);
EXPECT_NEAR(thx, 0, tol);
}

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