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rAKA/src/model/structural_mechanics/structural_elements/structural_element_bernoulli_beam_3.hh
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structural_element_bernoulli_beam_3.hh
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/**
* @file structural_element_bernoulli_beam_3.hh
*
* @author Fabian Barras <fabian.barras@epfl.ch>
* @author Sébastien Hartmann <sebastien.hartmann@epfl.ch>
* @author Nicolas Richart <nicolas.richart@epfl.ch>
* @author Damien Spielmann <damien.spielmann@epfl.ch>
*
* @date creation Tue Sep 19 2017
*
* @brief Specific functions for bernoulli beam 3d
*
* @section LICENSE
*
* Copyright (©) 2010-2011 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/>.
*
*/
/* -------------------------------------------------------------------------- */
#ifndef __AKANTU_STRUCTURAL_ELEMENT_BERNOULLI_BEAM_3_HH__
#define __AKANTU_STRUCTURAL_ELEMENT_BERNOULLI_BEAM_3_HH__
#include "structural_mechanics_model.hh"
namespace akantu {
inline UInt
StructuralMechanicsModel::getTangentStiffnessVoigtSize<_bernoulli_beam_3>() {
return 4;
}
/* -------------------------------------------------------------------------- */
template <>
inline void StructuralMechanicsModel::assembleMass<_bernoulli_beam_3>() {
AKANTU_DEBUG_IN();
GhostType ghost_type = _not_ghost;
ElementType type = _bernoulli_beam_3;
MyFEEngineType & fem = getFEEngineClass<MyFEEngineType>();
UInt nb_element = getFEEngine().getMesh().getNbElement(type);
UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
UInt nb_quadrature_points = getFEEngine().getNbIntegrationPoints(type);
UInt nb_fields_to_interpolate =
getTangentStiffnessVoigtSize<_bernoulli_beam_3>();
UInt nt_n_field_size = nb_degree_of_freedom * nb_nodes_per_element;
Array<Real> * n =
new Array<Real>(nb_element * nb_quadrature_points,
nb_fields_to_interpolate * nt_n_field_size, "N");
n->clear();
Array<Real> * rho_field =
new Array<Real>(nb_element * nb_quadrature_points, "Rho");
rho_field->clear();
computeRho(*rho_field, type, _not_ghost);
/* --------------------------------------------------------------------------
*/
fem.computeShapesMatrix(type, nb_degree_of_freedom, nb_nodes_per_element, n,
0, 0, 0, true, ghost_type); // Ni ui -> u
fem.computeShapesMatrix(type, nb_degree_of_freedom, nb_nodes_per_element, n,
1, 1, 1, true, ghost_type); // Mi vi -> v
fem.computeShapesMatrix(type, nb_degree_of_freedom, nb_nodes_per_element, n,
2, 5, 1, true, ghost_type); // Li Theta_z_i -> v
fem.computeShapesMatrix(type, nb_degree_of_freedom, nb_nodes_per_element, n,
1, 2, 2, true, ghost_type); // Mi wi -> w
fem.computeShapesMatrix(type, nb_degree_of_freedom, nb_nodes_per_element, n,
2, 4, 2, false, ghost_type); // -Li Theta_y_i -> w
fem.computeShapesMatrix(type, nb_degree_of_freedom, nb_nodes_per_element, n,
0, 3, 3, true, ghost_type); // Ni Theta_x_i->Theta_x
/* --------------------------------------------------------------------------
*/
fem.assembleFieldMatrix(*rho_field, nb_degree_of_freedom, *mass_matrix, n,
rotation_matrix, type, ghost_type);
delete n;
delete rho_field;
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <>
void StructuralMechanicsModel::computeRotationMatrix<_bernoulli_beam_3>(
Array<Real> & rotations) {
ElementType type = _bernoulli_beam_3;
Mesh & mesh = getFEEngine().getMesh();
UInt nb_element = mesh.getNbElement(type);
Array<Real>::vector_iterator n_it =
mesh.getNormals(type).begin(spatial_dimension);
Array<UInt>::iterator<Vector<UInt> > connec_it =
mesh.getConnectivity(type).begin(2);
Array<Real>::vector_iterator nodes_it =
mesh.getNodes().begin(spatial_dimension);
Matrix<Real> Pe(spatial_dimension, spatial_dimension);
Matrix<Real> Pg(spatial_dimension, spatial_dimension);
Matrix<Real> inv_Pg(spatial_dimension, spatial_dimension);
Vector<Real> x_n(spatial_dimension); // x vect n
Array<Real>::matrix_iterator R_it =
rotations.begin(nb_degree_of_freedom, nb_degree_of_freedom);
for (UInt e = 0; e < nb_element; ++e, ++n_it, ++connec_it, ++R_it) {
Vector<Real> & n = *n_it;
Matrix<Real> & R = *R_it;
Vector<UInt> & connec = *connec_it;
Vector<Real> x;
x = nodes_it[connec(1)]; // X2
Vector<Real> y;
y = nodes_it[connec(0)]; // X1
Real l = x.distance(y);
x -= y; // X2 - X1
x_n.crossProduct(x, n);
Pe.eye();
Pe(0, 0) *= l;
Pe(1, 1) *= -l;
Pg(0, 0) = x(0);
Pg(0, 1) = x_n(0);
Pg(0, 2) = n(0);
Pg(1, 0) = x(1);
Pg(1, 1) = x_n(1);
Pg(1, 2) = n(1);
Pg(2, 0) = x(2);
Pg(2, 1) = x_n(2);
Pg(2, 2) = n(2);
inv_Pg.inverse(Pg);
Pe *= inv_Pg;
for (UInt i = 0; i < spatial_dimension; ++i) {
for (UInt j = 0; j < spatial_dimension; ++j) {
R(i, j) = Pe(i, j);
R(i + spatial_dimension, j + spatial_dimension) = Pe(i, j);
}
}
}
}
/* -------------------------------------------------------------------------- */
template <>
void StructuralMechanicsModel::computeTangentModuli<_bernoulli_beam_3>(
Array<Real> & tangent_moduli) {
UInt nb_element = getFEEngine().getMesh().getNbElement(_bernoulli_beam_3);
UInt nb_quadrature_points =
getFEEngine().getNbIntegrationPoints(_bernoulli_beam_3);
UInt tangent_size = 4;
Array<Real>::matrix_iterator D_it =
tangent_moduli.begin(tangent_size, tangent_size);
for (UInt e = 0; e < nb_element; ++e) {
UInt mat = element_material(_bernoulli_beam_3, _not_ghost)(e);
Real E = materials[mat].E;
Real A = materials[mat].A;
Real Iz = materials[mat].Iz;
Real Iy = materials[mat].Iy;
Real GJ = materials[mat].GJ;
for (UInt q = 0; q < nb_quadrature_points; ++q, ++D_it) {
Matrix<Real> & D = *D_it;
D(0, 0) = E * A;
D(1, 1) = E * Iz;
D(2, 2) = E * Iy;
D(3, 3) = GJ;
}
}
}
/* -------------------------------------------------------------------------- */
template <>
void StructuralMechanicsModel::transferBMatrixToSymVoigtBMatrix<
_bernoulli_beam_3>(Array<Real> & b, bool) {
MyFEEngineType & fem = getFEEngineClass<MyFEEngineType>();
UInt nb_element = getFEEngine().getMesh().getNbElement(_bernoulli_beam_3);
UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(_bernoulli_beam_3);
UInt nb_quadrature_points =
getFEEngine().getNbIntegrationPoints(_bernoulli_beam_3);
Array<Real>::const_vector_iterator shape_Np =
fem.getShapesDerivatives(_bernoulli_beam_3, _not_ghost, 0)
.begin(nb_nodes_per_element);
Array<Real>::const_vector_iterator shape_Mpp =
fem.getShapesDerivatives(_bernoulli_beam_3, _not_ghost, 1)
.begin(nb_nodes_per_element);
Array<Real>::const_vector_iterator shape_Lpp =
fem.getShapesDerivatives(_bernoulli_beam_3, _not_ghost, 2)
.begin(nb_nodes_per_element);
UInt tangent_size = getTangentStiffnessVoigtSize<_bernoulli_beam_3>();
UInt bt_d_b_size = nb_nodes_per_element * nb_degree_of_freedom;
b.clear();
Array<Real>::matrix_iterator B_it = b.begin(tangent_size, bt_d_b_size);
for (UInt e = 0; e < nb_element; ++e) {
for (UInt q = 0; q < nb_quadrature_points; ++q) {
Matrix<Real> & B = *B_it;
const Vector<Real> & Np = *shape_Np;
const Vector<Real> & Lpp = *shape_Lpp;
const Vector<Real> & Mpp = *shape_Mpp;
B(0, 0) = Np(0);
B(0, 6) = Np(1);
B(1, 1) = Mpp(0);
B(1, 5) = Lpp(0);
B(1, 7) = Mpp(1);
B(1, 11) = Lpp(1);
B(2, 2) = Mpp(0);
B(2, 4) = -Lpp(0);
B(2, 8) = Mpp(1);
B(2, 10) = -Lpp(1);
B(3, 3) = Np(0);
B(3, 9) = Np(1);
++B_it;
++shape_Np;
++shape_Mpp;
++shape_Lpp;
}
}
}
} // akantu
#endif /* __AKANTU_STRUCTURAL_ELEMENT_BERNOULLI_BEAM_3_HH__ */
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