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test_structural_mechanics_model_bernoulli_beam_dynamics.cc
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/**
* @file test_structural_mechanics_model_bernoulli_beam_dynamics.cc
*
* @author Sébastien Hartmann <sebastien.hartmann@epfl.ch>
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date creation: Sun Oct 19 2014
* @date last modification: Mon Mar 15 2021
*
* @brief Test for _bernouilli_beam in dynamic
*
*
* @section LICENSE
*
* Copyright (©) 2014-2021 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 "test_structural_mechanics_model_fixture.hh"
/* -------------------------------------------------------------------------- */
#include "dof_manager.hh"
#include "mesh_accessor.hh"
#include "non_linear_solver_newton_raphson.hh"
#include "structural_mechanics_model.hh"
/* -------------------------------------------------------------------------- */
#include <fstream>
#include <iostream>
#include <limits>
/* -------------------------------------------------------------------------- */
using namespace akantu;
/* -------------------------------------------------------------------------- */
static Real analytical_solution(Real time, Real L, Real rho, Real E,
__attribute__((unused)) Real A, Real I,
Real F) {
Real omega = M_PI * M_PI / L / L * sqrt(E * I / rho);
Real sum = 0.;
UInt i = 5;
for (UInt n = 1; n <= i; n += 2) {
sum += (1. - cos(n * n * omega * time)) / pow(n, 4);
}
return 2. * F * pow(L, 3) / pow(M_PI, 4) / E / I * sum;
}
template <class Type>
class TestStructBernoulliDynamic : public TestStructuralFixture<Type> {
using parent = TestStructuralFixture<Type>;
public:
const UInt nb_element{40};
const Real L{2};
const Real le{L / nb_element};
const UInt nb_nodes{nb_element + 1};
const Real F{1e4};
StructuralMaterial mat;
void readMesh(std::string /*filename*/) override {
MeshAccessor mesh_accessor(*this->mesh);
auto & nodes = mesh_accessor.getNodes();
nodes.resize(nb_nodes);
nodes.set(0.);
for (auto && data : enumerate(make_view(nodes, this->spatial_dimension))) {
auto & node = std::get<1>(data);
UInt i = std::get<0>(data);
node[_x] = i * le;
}
this->mesh->addConnectivityType(parent::type);
auto & connectivities = mesh_accessor.getConnectivity(parent::type);
connectivities.resize(nb_element);
for (auto && data : enumerate(make_view(connectivities, 2))) {
UInt i = std::get<0>(data);
auto & connectivity = std::get<1>(data);
connectivity = {i, i + 1};
}
mesh_accessor.makeReady();
}
void setNormals() override {
if (this->spatial_dimension != 3) {
return;
}
auto & normals =
this->mesh->template getData<Real>("extra_normal", parent::type);
normals.resize(nb_element);
for (auto && normal : make_view(normals, this->spatial_dimension)) {
normal = {0., 0., 1.};
}
}
AnalysisMethod getAnalysisMethod() const override {
return _implicit_dynamic;
}
void addMaterials() override {
this->mat.E = 1e9;
this->mat.rho = 10;
this->mat.I = 1;
this->mat.Iz = 1;
this->mat.Iy = 1;
this->mat.A = 1;
this->mat.GJ = 1;
this->model->addMaterial(mat);
}
void setDirichletBCs() override {
auto & boundary = this->model->getBlockedDOFs();
boundary.set(false);
boundary(0, _x) = true;
boundary(0, _y) = true;
boundary(nb_nodes - 1, _y) = true;
if (this->spatial_dimension == 3) {
boundary(0, _z) = true;
boundary(nb_nodes - 1, _z) = true;
}
}
void setNeumannBCs() override {
auto node_to_print = nb_nodes / 2;
// Forces
auto & forces = this->model->getExternalForce();
forces.zero();
forces(node_to_print, _y) = F;
}
void assignMaterials() override {
this->model->getElementMaterial(parent::type).set(0);
}
};
using beam_types = gtest_list_t<std::tuple<element_type_t<_bernoulli_beam_2>,
element_type_t<_bernoulli_beam_3>>>;
TYPED_TEST_SUITE(TestStructBernoulliDynamic, beam_types, );
template <class Type>
void getElementMassMatrix(const StructuralMaterial & /*material*/, Real /*l*/,
Matrix<Real> & /*M*/) {}
template <class Type>
void getElementStifnessMatrix(const StructuralMaterial & /*material*/,
Real /*l*/, Matrix<Real> & /*M*/) {}
template <>
void getElementMassMatrix<element_type_t<_bernoulli_beam_2>>(
const StructuralMaterial & material, Real l, Matrix<Real> & M) {
auto A = material.A;
auto rho = material.rho;
// clang-format off
M = rho * A * l / 420. * Matrix<Real>({
{140, 0, 0, 70, 0, 0},
{ 0, 156, 22*l, 0, 54, -13*l},
{ 0, 22*l, 4*l*l, 0, 13*l, -3*l*l},
{ 70, 0, 0, 140, 0, 0},
{ 0, 54, 13*l, 0, 156, -22*l},
{ 0,-13*l, -3*l*l, 0, -22*l, 4*l*l}});
// clang-format on
}
template <>
void getElementStifnessMatrix<element_type_t<_bernoulli_beam_2>>(
const StructuralMaterial & material, Real l, Matrix<Real> & K) {
auto E = material.E;
auto A = material.A;
auto I = material.I;
auto l_2 = l * l;
auto l_3 = l * l * l;
// clang-format off
K = Matrix<Real>({
{ E*A/l, 0, 0, -E*A/l, 0, 0},
{ 0, 12*E*I/l_3, 6*E*I/l_2, 0, -12*E*I/l_3, 6*E*I/l_2},
{ 0, 6*E*I/l_2, 4*E*I/l, 0, -6*E*I/l_2, 2*E*I/l},
{-E*A/l, 0, 0, E*A/l, 0, 0},
{ 0, -12*E*I/l_3, -6*E*I/l_2, 0, 12*E*I/l_3, -6*E*I/l_2},
{ 0, 6*E*I/l_2, 2*E*I/l, 0, -6*E*I/l_2, 4*E*I/l}});
// clang-format on
}
template <>
void getElementMassMatrix<element_type_t<_bernoulli_beam_3>>(
const StructuralMaterial & material, Real l, Matrix<Real> & M) {
auto A = material.A;
auto rho = material.rho;
// clang-format off
M = rho * A * l / 420. * Matrix<Real>({
{140, 0, 0, 0, 0, 0, 70, 0, 0, 0, 0, 0},
{ 0, 156, 0, 0, 0, 22*l, 0, 54, 0, 0, 0, -13*l},
{ 0, 0, 156, 0, -22*l, 0, 0, 0, 54, 0, 13*l, 0},
{ 0, 0, 0, 140, 0, 0, 0, 0, 0, 70, 0, 0},
{ 0, 0, -22*l, 0, 4*l*l, 0, 0, 0, -13*l, 0, -3*l*l, 0},
{ 0, 22*l, 0, 0, 0, 4*l*l, 0, 13*l, 0, 0, 0, -3*l*l},
{ 70, 0, 0, 0, 0, 0, 140, 0, 0, 0, 0, 0},
{ 0, 54, 0, 0, 0, 13*l, 0, 156, 0, 0, 0, -22*l},
{ 0, 0, 54, 0, -13*l, 0, 0, 0, 156, 0, 22*l, 0},
{ 0, 0, 0, 70, 0, 0, 0, 0, 0, 140, 0, 0},
{ 0, 0, 13*l, 0, -3*l*l, 0, 0, 0, 22*l, 0, 4*l*l, 0},
{ 0, -13*l, 0, 0, 0, -3*l*l, 0, -22*l, 0, 0, 0, 4*l*l}});
// clang-format on
}
template <>
void getElementStifnessMatrix<element_type_t<_bernoulli_beam_3>>(
const StructuralMaterial & material, Real l, Matrix<Real> & K) {
auto E = material.E;
auto A = material.A;
auto Iy = material.Iy;
auto Iz = material.Iz;
auto GJ = material.GJ;
auto a1 = E * A / l;
auto b1 = 12 * E * Iz / l / l / l;
auto b2 = 6 * E * Iz / l / l;
auto b3 = 4 * E * Iz / l;
auto b4 = 2 * E * Iz / l;
auto c1 = 12 * E * Iy / l / l / l;
auto c2 = 6 * E * Iy / l / l;
auto c3 = 4 * E * Iy / l;
auto c4 = 2 * E * Iy / l;
auto d1 = GJ / l;
// clang-format off
K = Matrix<Real>({
{ a1, 0, 0, 0, 0, 0, -a1, 0, 0, 0, 0, 0},
{ 0, b1, 0, 0, 0, b2, 0, -b1, 0, 0, 0, b2},
{ 0, 0, c1, 0, -c2, 0, 0, 0, -c1, 0, -c2, 0},
{ 0, 0, 0, d1, 0, 0, 0, 0, 0, -d1, 0, 0},
{ 0, 0, -c2, 0, c3, 0, 0, 0, c2, 0, c4, 0},
{ 0, b2, 0, 0, 0, b3, 0, -b2, 0, 0, 0, b4},
{ -a1, 0, 0, 0, 0, 0, a1, 0, 0, 0, 0, 0},
{ 0, -b1, 0, 0, 0, -b2, 0, b1, 0, 0, 0, -b2},
{ 0, 0, -c1, 0, c2, 0, 0, 0, c1, 0, c2, 0},
{ 0, 0, 0, -d1, 0, 0, 0, 0, 0, d1, 0, 0},
{ 0, 0, -c2, 0, c4, 0, 0, 0, c2, 0, c3, 0},
{ 0, b2, 0, 0, 0, b4, 0, -b2, 0, 0, 0, b3}});
// clang-format on
}
TYPED_TEST(TestStructBernoulliDynamic, TestBeamMatrices) {
this->model->assembleMatrix("M");
this->model->assembleMatrix("K");
const auto & K = this->model->getDOFManager().getMatrix("K");
const auto & M = this->model->getDOFManager().getMatrix("M");
Matrix<Real> Ka(this->nb_nodes * this->ndof, this->nb_nodes * this->ndof, 0.);
Matrix<Real> Ma(this->nb_nodes * this->ndof, this->nb_nodes * this->ndof, 0.);
Matrix<Real> Ke(this->ndof * 2, this->ndof * 2);
Matrix<Real> Me(this->ndof * 2, this->ndof * 2);
getElementMassMatrix<TypeParam>(this->mat, this->le, Me);
getElementStifnessMatrix<TypeParam>(this->mat, this->le, Ke);
auto assemble = [&](auto && nodes, auto && M, auto && Me) {
auto n1 = nodes[0];
auto n2 = nodes[1];
for (auto i : arange(this->ndof)) {
for (auto j : arange(this->ndof)) {
M(n1 * this->ndof + i, n1 * this->ndof + j) += Me(i, j);
M(n2 * this->ndof + i, n2 * this->ndof + j) +=
Me(this->ndof + i, this->ndof + j);
M(n1 * this->ndof + i, n2 * this->ndof + j) += Me(i, this->ndof + j);
M(n2 * this->ndof + i, n1 * this->ndof + j) += Me(this->ndof + i, j);
}
}
};
auto && connectivities = this->mesh->getConnectivity(this->type);
for (auto && connectivity : make_view(connectivities, 2)) {
assemble(connectivity, Ka, Ke);
assemble(connectivity, Ma, Me);
}
auto tol = 1e-13;
auto Ka_max = Ka.template norm<L_inf>();
auto Ma_max = Ma.template norm<L_inf>();
for (auto i : arange(Ka.rows())) {
for (auto j : arange(Ka.cols())) {
EXPECT_NEAR(Ka(i, j), K(i, j), tol * Ka_max);
EXPECT_NEAR(Ma(i, j), M(i, j), tol * Ma_max);
}
}
}
TYPED_TEST(TestStructBernoulliDynamic, TestBeamOscilation) {
Real time_step = 1e-6;
this->model->setTimeStep(time_step);
auto & solver = this->model->getNonLinearSolver();
solver.set("max_iterations", 100);
solver.set("threshold", 1e-8);
solver.set("convergence_type", SolveConvergenceCriteria::_solution);
auto node_to_print = this->nb_nodes / 2;
auto & d = this->model->getDisplacement()(node_to_print, _y);
std::ofstream pos;
std::string filename = "position" + std::to_string(this->type) + ".csv";
pos.open(filename);
if (not pos.good()) {
AKANTU_ERROR("Cannot open file \"position.csv\"");
}
pos << "id,time,position,solution" << std::endl;
//#define debug
#ifdef debug
this->model->addDumpFieldVector("displacement");
this->model->addDumpField("blocked_dofs");
this->model->addDumpFieldVector("external_force");
this->model->addDumpFieldVector("internal_force");
this->model->addDumpFieldVector("acceleration");
this->model->addDumpFieldVector("velocity");
this->model->dump();
#endif
this->model->getDisplacement().set(0.);
Real tol = 1e-6;
Real time = 0.;
for (UInt s = 1; s < 300; ++s) {
EXPECT_NO_THROW(this->model->solveStep());
time = s * time_step;
auto da = analytical_solution(time, this->L, this->mat.rho, this->mat.E,
this->mat.A, this->mat.Iy, this->F);
pos << s << "," << time << "," << d << "," << da << std::endl;
#ifdef debug
this->model->dump();
#endif
EXPECT_NEAR(d, da, tol);
}
}

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