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element_class_pentahedron_6_inline_impl.hh
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element_class_pentahedron_6_inline_impl.hh
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/**
* @file element_class_pentahedron_6_inline_impl.hh
*
* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
* @author Marion Estelle Chambart <mchambart@stucky.ch>
* @author Mauro Corrado <mauro.corrado@epfl.ch>
* @author Thomas Menouillard <tmenouillard@stucky.ch>
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date creation: Mon Mar 14 2011
* @date last modification: Tue Sep 29 2020
*
* @brief Specialization of the element_class class for the type _pentahedron_6
*
*
* @section LICENSE
*
* Copyright (©) 2010-2021 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/>.
*
*/
/**
* @verbatim
/z
|
|
| 1
| /|\
|/ | \
/ | \
/ | \
/ | \
4 2-----0
| \ / /
| \/ /
| \ /----------/y
| / \ /
|/ \ /
5---.--3
/
/
/
\x
x y z
* N0 -1 1 0
* N1 -1 0 1
* N2 -1 0 0
* N3 1 1 0
* N4 1 0 1
* N5 1 0 0
\endverbatim
*/
/* -------------------------------------------------------------------------- */
#include "element_class.hh"
/* -------------------------------------------------------------------------- */
namespace akantu {
/* -------------------------------------------------------------------------- */
AKANTU_DEFINE_ELEMENT_CLASS_PROPERTY(_pentahedron_6, _gt_pentahedron_6,
_itp_lagrange_pentahedron_6, _ek_regular,
3, _git_pentahedron, 1);
/* -------------------------------------------------------------------------- */
template <>
template <class D1, class D2,
aka::enable_if_t<aka::are_vectors<D1, D2>::value> *>
inline void InterpolationElement<_itp_lagrange_pentahedron_6>::computeShapes(
const Eigen::MatrixBase<D1> &c, Eigen::MatrixBase<D2> &N) {
/// Natural coordinates
N(0) = 0.5 * c(1) * (1 - c(0)); // N1(q)
N(1) = 0.5 * c(2) * (1 - c(0)); // N2(q)
N(2) = 0.5 * (1 - c(1) - c(2)) * (1 - c(0)); // N3(q)
N(3) = 0.5 * c(1) * (1 + c(0)); // N4(q)
N(4) = 0.5 * c(2) * (1 + c(0)); // N5(q)
N(5) = 0.5 * (1 - c(1) - c(2)) * (1 + c(0)); // N6(q)
}
/* -------------------------------------------------------------------------- */
template <>
template <class D1, class D2>
inline void InterpolationElement<_itp_lagrange_pentahedron_6>::computeDNDS(
const Eigen::MatrixBase<D1> &c, Eigen::MatrixBase<D2> &dnds) {
dnds(0, 0) = -0.5 * c(1);
dnds(0, 1) = -0.5 * c(2);
dnds(0, 2) = -0.5 * (1 - c(1) - c(2));
dnds(0, 3) = 0.5 * c(1);
dnds(0, 4) = 0.5 * c(2);
dnds(0, 5) = 0.5 * (1 - c(1) - c(2));
dnds(1, 0) = 0.5 * (1 - c(0));
dnds(1, 1) = 0.0;
dnds(1, 2) = -0.5 * (1 - c(0));
dnds(1, 3) = 0.5 * (1 + c(0));
dnds(1, 4) = 0.0;
dnds(1, 5) = -0.5 * (1 + c(0));
dnds(2, 0) = 0.0;
dnds(2, 1) = 0.5 * (1 - c(0));
dnds(2, 2) = -0.5 * (1 - c(0));
dnds(2, 3) = 0.0;
dnds(2, 4) = 0.5 * (1 + c(0));
dnds(2, 5) = -0.5 * (1 + c(0));
}
/* -------------------------------------------------------------------------- */
template <>
template <class D>
inline Real GeometricalElement<_gt_pentahedron_6>::getInradius(
const Eigen::MatrixBase<D> &coord) {
auto &&u0 = coord.col(0);
auto &&u1 = coord.col(1);
auto &&u2 = coord.col(2);
auto &&u3 = coord.col(3);
auto &&u4 = coord.col(4);
auto &&u5 = coord.col(5);
auto inradius_triangle_1 = Math::triangle_inradius(u0, u1, u2);
auto inradius_triangle_2 = Math::triangle_inradius(u3, u4, u5);
auto d1 = (u3 - u0).norm() * 0.5;
auto d2 = (u5 - u2).norm() * 0.5;
auto d3 = (u4 - u1).norm() * 0.5;
auto p =
2. * std::min({inradius_triangle_1, inradius_triangle_2, d1, d2, d3});
return p;
}
} // namespace akantu

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