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resolution_utils.hh
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resolution_utils.hh
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/**
* Copyright (©) 2019-2023 EPFL (Ecole Polytechnique Fédérale de Lausanne)
* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
*
* This file is part of Akantu
*
* 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 "contact_element.hh"
#include "contact_mechanics_model.hh"
#include "fe_engine.hh"
/* -------------------------------------------------------------------------- */
#ifndef AKANTU_RESOLUTION_UTILS_HH_
#define AKANTU_RESOLUTION_UTILS_HH_
/* -------------------------------------------------------------------------- */
namespace akantu {
class ResolutionUtils {
/* ------------------------------------------------------------------------ */
/* Methods */
/* ------------------------------------------------------------------------ */
public:
/// computes the shape function matric for the contact element (@f$A
/// @f$) where row is equal to spatial dimension and cols is equal
/// to spatial dimension times number of nodes in contact element
template <class Derived>
static Matrix<Real>
computeShapeFunctionMatrix(const ContactElement & element,
const Eigen::MatrixBase<Derived> & projection) {
const auto type = element.master.type;
const auto surface_dimension = Mesh::getSpatialDimension(type);
const auto spatial_dimension = surface_dimension + 1;
const auto nb_nodes_per_contact = element.getNbNodes();
Matrix<Real> shape_matrix(spatial_dimension,
spatial_dimension * nb_nodes_per_contact);
shape_matrix.zero();
auto && shapes = ElementClassHelper<_ek_regular>::getN(projection, type);
for (auto i : arange(nb_nodes_per_contact)) {
for (auto j : arange(spatial_dimension)) {
if (i == 0) {
shape_matrix(j, i * spatial_dimension + j) = 1;
continue;
}
shape_matrix(j, i * spatial_dimension + j) = -shapes[i - 1];
}
}
return shape_matrix;
}
template <class Derived>
static Tensor3<Real> computeDerivativeShapeFunctionMatrix(
const ContactElement & element,
const Eigen::MatrixBase<Derived> & projection) {
const auto type = element.master.type;
// computing shape derivatives
auto && shape_derivatives =
ElementClassHelper<_ek_regular>::getDNDS(projection, type);
const auto surface_dimension = shape_derivatives.rows();
const auto spatial_dimension = shape_derivatives.rows() + 1;
const auto nb_nodes_per_contact = shape_derivatives.cols() + 1;
Tensor3<Real> derivative_shape_matrix(
spatial_dimension, spatial_dimension * nb_nodes_per_contact,
surface_dimension);
derivative_shape_matrix.zero();
for (auto && [dnds, Aj] :
zip(shape_derivatives.transpose(), derivative_shape_matrix)) {
for (auto i : arange(nb_nodes_per_contact)) {
for (auto j : arange(spatial_dimension)) {
if (i == 0) {
Aj(j, i * spatial_dimension + j) = 0;
continue;
}
Aj(j, i * spatial_dimension + j) = dnds(i - 1);
}
}
}
return derivative_shape_matrix;
}
};
} // namespace akantu
#endif /* AKANTU_RESOLUTION_UTILS_HH_ */

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