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aka_voigthelper.hh
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/**
* @file aka_voigthelper.hh
*
* @author Lucas Frerot <lucas.frerot@epfl.ch>
* @author Till Junge <till.junge@epfl.ch>
* @author Daniel Pino Muñoz <daniel.pinomunoz@epfl.ch>
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date creation: Fri Dec 20 2013
* @date last modification: Fri Jan 22 2016
*
* @brief Helper file for Voigt notation
*
* @section LICENSE
*
* Copyright (©) 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/>.
*
*/
#ifndef __AKA_VOIGTHELPER_HH__
#define __AKA_VOIGTHELPER_HH__
#include "aka_common.hh"
#include "aka_types.hh"
__BEGIN_AKANTU__
/* -------------------------------------------------------------------------- */
template <UInt dim> class VoigtHelper {
public:
/// transfer the B matrix to a Voigt notation B matrix
inline static void transferBMatrixToSymVoigtBMatrix(
const Matrix<Real> & B, Matrix<Real> & Bvoigt, UInt nb_nodes_per_element);
/// transfer the BNL matrix to a Voigt notation B matrix (See Bathe et al.
/// IJNME vol 9, 1975)
inline static void transferBMatrixToBNL(const Matrix<Real> & B,
Matrix<Real> & Bvoigt,
UInt nb_nodes_per_element);
/// transfer the BL2 matrix to a Voigt notation B matrix (See Bathe et al.
/// IJNME vol 9, 1975)
inline static void transferBMatrixToBL2(const Matrix<Real> & B,
const Matrix<Real> & grad_u,
Matrix<Real> & Bvoigt,
UInt nb_nodes_per_element);
public:
const static UInt size;
// matrix of vector index I as function of tensor indices i,j
const static UInt mat[dim][dim];
// array of matrix indices ij as function of vector index I
const static UInt vec[dim * dim][2];
// factors to multiply the strain by for voigt notation
const static Real factors[dim * (dim - (dim - 1) / 2)];
};
template <UInt dim> const UInt VoigtHelper<dim>::size = dim*(dim-(dim-1)/2.);
/* -------------------------------------------------------------------------- */
template <UInt dim>
inline void VoigtHelper<dim>::transferBMatrixToSymVoigtBMatrix(
const Matrix<Real> & B, Matrix<Real> & Bvoigt, UInt nb_nodes_per_element) {
Bvoigt.clear();
for (UInt i = 0; i < dim; ++i)
for (UInt n = 0; n < nb_nodes_per_element; ++n)
Bvoigt(i, i + n * dim) = B(i, n);
if (dim == 2) {
/// in 2D, fill the @f$ [\frac{\partial N_i}{\partial x}, \frac{\partial
/// N_i}{\partial y}]@f$ row
for (UInt n = 0; n < nb_nodes_per_element; ++n) {
Bvoigt(2, 1 + n * 2) = B(0, n);
Bvoigt(2, 0 + n * 2) = B(1, n);
}
}
if (dim == 3) {
for (UInt n = 0; n < nb_nodes_per_element; ++n) {
Real dndx = B(0, n);
Real dndy = B(1, n);
Real dndz = B(2, n);
/// in 3D, fill the @f$ [0, \frac{\partial N_i}{\partial y},
/// \frac{N_i}{\partial z}]@f$ row
Bvoigt(3, 1 + n * 3) = dndz;
Bvoigt(3, 2 + n * 3) = dndy;
/// in 3D, fill the @f$ [\frac{\partial N_i}{\partial x}, 0,
/// \frac{N_i}{\partial z}]@f$ row
Bvoigt(4, 0 + n * 3) = dndz;
Bvoigt(4, 2 + n * 3) = dndx;
/// in 3D, fill the @f$ [\frac{\partial N_i}{\partial x},
/// \frac{N_i}{\partial y}, 0]@f$ row
Bvoigt(5, 0 + n * 3) = dndy;
Bvoigt(5, 1 + n * 3) = dndx;
}
}
}
/* -------------------------------------------------------------------------- */
template <UInt dim>
inline void VoigtHelper<dim>::transferBMatrixToBNL(const Matrix<Real> & B,
Matrix<Real> & Bvoigt,
UInt nb_nodes_per_element) {
Bvoigt.clear();
// see Finite element formulations for large deformation dynamic analysis,
// Bathe et al. IJNME vol 9, 1975, page 364 B_{NL}
for (UInt i = 0; i < dim; ++i) {
for (UInt m = 0; m < nb_nodes_per_element; ++m) {
for (UInt n = 0; n < dim; ++n) {
// std::cout << B(n, m) << std::endl;
Bvoigt(i * dim + n, m * dim + i) = B(n, m);
}
}
}
// TODO: Verify the 2D and 1D case
}
/* -------------------------------------------------------------------------- */
template <>
inline void VoigtHelper<1>::transferBMatrixToBL2(const Matrix<Real> & B,
const Matrix<Real> & grad_u,
Matrix<Real> & Bvoigt,
UInt nb_nodes_per_element) {
Bvoigt.clear();
for (UInt j = 0; j < nb_nodes_per_element; ++j)
for (UInt k = 0; k < 2; ++k)
Bvoigt(0, j * 2 + k) = grad_u(k, 0) * B(0, j);
}
/* -------------------------------------------------------------------------- */
template <>
inline void VoigtHelper<3>::transferBMatrixToBL2(const Matrix<Real> & B,
const Matrix<Real> & grad_u,
Matrix<Real> & Bvoigt,
UInt nb_nodes_per_element) {
Bvoigt.clear();
for (UInt i = 0; i < 3; ++i)
for (UInt j = 0; j < nb_nodes_per_element; ++j)
for (UInt k = 0; k < 3; ++k)
Bvoigt(i, j * 3 + k) = grad_u(k, i) * B(i, j);
for (UInt i = 3; i < 6; ++i) {
for (UInt j = 0; j < nb_nodes_per_element; ++j) {
for (UInt k = 0; k < 3; ++k) {
UInt aux = i - 3;
for (UInt m = 0; m < 3; ++m) {
if (m != aux) {
UInt index1 = m;
UInt index2 = 3 - m - aux;
Bvoigt(i, j * 3 + k) += grad_u(k, index1) * B(index2, j);
}
}
}
}
}
}
/* -------------------------------------------------------------------------- */
template <>
inline void VoigtHelper<2>::transferBMatrixToBL2(const Matrix<Real> & B,
const Matrix<Real> & grad_u,
Matrix<Real> & Bvoigt,
UInt nb_nodes_per_element) {
Bvoigt.clear();
for (UInt i = 0; i < 2; ++i)
for (UInt j = 0; j < nb_nodes_per_element; ++j)
for (UInt k = 0; k < 2; ++k)
Bvoigt(i, j * 2 + k) = grad_u(k, i) * B(i, j);
for (UInt j = 0; j < nb_nodes_per_element; ++j) {
for (UInt k = 0; k < 2; ++k) {
for (UInt m = 0; m < 2; ++m) {
UInt index1 = m;
UInt index2 = (2 - 1) - m;
Bvoigt(2, j * 2 + k) += grad_u(k, index1) * B(index2, j);
}
}
}
}
__END_AKANTU__
#endif

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