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structural_element_kirchhoff_shell.hh
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structural_element_kirchhoff_shell.hh
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/**
* @file structural_element_bernoulli_kirchhoff_shell.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 kirchhoff shell
*
* @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_KIRCHHOFF_SHELL_HH__
#define __AKANTU_STRUCTURAL_ELEMENT_BERNOULLI_KIRCHHOFF_SHELL_HH__
namespace akantu {
inline UInt
StructuralMechanicsModel::getTangentStiffnessVoigtSize<_bernoulli_kirchhoff_shell>() {
return 6;
}
/* -------------------------------------------------------------------------- */
template <>
inline void StructuralMechanicsModel::assembleMass<_kirchhoff_shell>() {
AKANTU_DEBUG_TO_IMPLEMENT();
}
/* -------------------------------------------------------------------------- */
template <>
void StructuralMechanicsModel::computeRotationMatrix<_kirchhoff_shell>(
Array<Real> & rotations) {
ElementType type = _kirchhoff_shell;
Mesh & mesh = getFEEngine().getMesh();
UInt nb_element = mesh.getNbElement(type);
Array<UInt>::iterator<Vector<UInt> > connec_it =
mesh.getConnectivity(type).begin(3);
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);
Array<Real>::matrix_iterator R_it =
rotations.begin(nb_degree_of_freedom, nb_degree_of_freedom);
for (UInt e = 0; e < nb_element; ++e, ++connec_it, ++R_it) {
Pe.eye();
Matrix<Real> & R = *R_it;
Vector<UInt> & connec = *connec_it;
Vector<Real> x2;
x2 = nodes_it[connec(1)]; // X2
Vector<Real> x1;
x1 = nodes_it[connec(0)]; // X1
Vector<Real> x3;
x3 = nodes_it[connec(2)]; // X3
Vector<Real> Pg_col_1 = x2 - x1;
Vector<Real> Pg_col_2 = x3 - x1;
Vector<Real> Pg_col_3(spatial_dimension);
Pg_col_3.crossProduct(Pg_col_1, Pg_col_2);
for (UInt i = 0; i < spatial_dimension; ++i) {
Pg(i, 0) = Pg_col_1(i);
Pg(i, 1) = Pg_col_2(i);
Pg(i, 2) = Pg_col_3(i);
}
inv_Pg.inverse(Pg);
// Pe *= inv_Pg;
Pe.eye();
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<
_kirchhoff_shell>(Array<Real> & b, __attribute__((unused)) bool local) {
MyFEEngineType & fem = getFEEngineClass<MyFEEngineType>();
UInt nb_element = getFEEngine().getMesh().getNbElement(_kirchhoff_shell);
UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(_kirchhoff_shell);
UInt nb_quadrature_points =
getFEEngine().getNbIntegrationPoints(_kirchhoff_shell);
Array<Real>::const_matrix_iterator shape_Np =
fem.getShapesDerivatives(_kirchhoff_shell, _not_ghost, 0)
.begin(2, nb_nodes_per_element);
Array<Real>::const_matrix_iterator shape_Nx1p =
fem.getShapesDerivatives(_kirchhoff_shell, _not_ghost, 1)
.begin(2, nb_nodes_per_element);
Array<Real>::const_matrix_iterator shape_Nx2p =
fem.getShapesDerivatives(_kirchhoff_shell, _not_ghost, 2)
.begin(2, nb_nodes_per_element);
Array<Real>::const_matrix_iterator shape_Nx3p =
fem.getShapesDerivatives(_kirchhoff_shell, _not_ghost, 3)
.begin(2, nb_nodes_per_element);
Array<Real>::const_matrix_iterator shape_Ny1p =
fem.getShapesDerivatives(_kirchhoff_shell, _not_ghost, 4)
.begin(2, nb_nodes_per_element);
Array<Real>::const_matrix_iterator shape_Ny2p =
fem.getShapesDerivatives(_kirchhoff_shell, _not_ghost, 5)
.begin(2, nb_nodes_per_element);
Array<Real>::const_matrix_iterator shape_Ny3p =
fem.getShapesDerivatives(_kirchhoff_shell, _not_ghost, 6)
.begin(2, nb_nodes_per_element);
UInt tangent_size = getTangentStiffnessVoigtSize<_kirchhoff_shell>();
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 Matrix<Real> & Np = *shape_Np;
const Matrix<Real> & Nx1p = *shape_Nx1p;
const Matrix<Real> & Nx2p = *shape_Nx2p;
const Matrix<Real> & Nx3p = *shape_Nx3p;
const Matrix<Real> & Ny1p = *shape_Ny1p;
const Matrix<Real> & Ny2p = *shape_Ny2p;
const Matrix<Real> & Ny3p = *shape_Ny3p;
B(0, 0) = Np(0, 0);
B(0, 6) = Np(0, 1);
B(0, 12) = Np(0, 2);
B(1, 1) = Np(1, 0);
B(1, 7) = Np(1, 1);
B(1, 13) = Np(1, 2);
B(2, 0) = Np(1, 0);
B(2, 1) = Np(0, 0);
B(2, 6) = Np(1, 1);
B(2, 7) = Np(0, 1);
B(2, 12) = Np(1, 2);
B(2, 13) = Np(0, 2);
B(3, 2) = Nx1p(0, 0);
B(3, 3) = Nx2p(0, 0);
B(3, 4) = Nx3p(0, 0);
B(3, 8) = Nx1p(0, 1);
B(3, 9) = Nx2p(0, 1);
B(3, 10) = Nx3p(0, 1);
B(3, 14) = Nx1p(0, 2);
B(3, 15) = Nx2p(0, 2);
B(3, 16) = Nx3p(0, 2);
B(4, 2) = Ny1p(1, 0);
B(4, 3) = Ny2p(1, 0);
B(4, 4) = Ny3p(1, 0);
B(4, 8) = Ny1p(1, 1);
B(4, 9) = Ny2p(1, 1);
B(4, 10) = Ny3p(1, 1);
B(4, 14) = Ny1p(1, 2);
B(4, 15) = Ny2p(1, 2);
B(4, 16) = Ny3p(1, 2);
B(5, 2) = Nx1p(1, 0) + Ny1p(0, 0);
B(5, 3) = Nx2p(1, 0) + Ny2p(0, 0);
B(5, 4) = Nx3p(1, 0) + Ny3p(0, 0);
B(5, 8) = Nx1p(1, 1) + Ny1p(0, 1);
B(5, 9) = Nx2p(1, 1) + Ny2p(0, 1);
B(5, 10) = Nx3p(1, 1) + Ny3p(0, 1);
B(5, 14) = Nx1p(1, 2) + Ny1p(0, 2);
B(5, 15) = Nx2p(1, 2) + Ny2p(0, 2);
B(5, 16) = Nx3p(1, 2) + Ny3p(0, 2);
++B_it;
++shape_Np;
++shape_Nx1p;
++shape_Nx2p;
++shape_Nx3p;
++shape_Ny1p;
++shape_Ny2p;
++shape_Ny3p;
}
}
}
} // akantu
#endif /* __AKANTU_STRUCTURAL_ELEMENT_BERNOULLI_KIRCHHOFF_SHELL_HH__ */

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