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element_class_segment_3_inline_impl.cc
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element_class_segment_3_inline_impl.cc
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/**
* @file element_class_segment_3_inline_impl.cc
*
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date creation: Fri Jul 16 2010
* @date last modification: Wed Oct 11 2017
*
* @brief Specialization of the element_class class for the type _segment_3
*
* @section LICENSE
*
* Copyright (©) 2010-2018 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/>.
*
* @section DESCRIPTION
*
* @verbatim
-1 0 1
-----x---------x---------x-----> x
1 3 2
@endverbatim
*
* @subsection coords Nodes coordinates
*
* @f[
* \begin{array}{lll}
* x_{1} = -1 & x_{2} = 1 & x_{3} = 0
* \end{array}
* @f]
*
* @subsection shapes Shape functions
* @f[
* \begin{array}{ll}
* w_1(x) = \frac{x}{2}(x - 1) & w'_1(x) = x - \frac{1}{2}\\
* w_2(x) = \frac{x}{2}(x + 1) & w'_2(x) = x + \frac{1}{2}\\
* w_3(x) = 1-x^2 & w'_3(x) = -2x
* \end{array}
* @f]
*
* @subsection quad_points Position of quadrature points
* @f[
* \begin{array}{ll}
* x_{q1} = -1/\sqrt{3} & x_{q2} = 1/\sqrt{3}
* \end{array}
* @f]
*/
/* -------------------------------------------------------------------------- */
AKANTU_DEFINE_ELEMENT_CLASS_PROPERTY(_segment_3, _gt_segment_3,
_itp_lagrange_segment_3, _ek_regular, 1,
_git_segment, 2);
/* -------------------------------------------------------------------------- */
template <>
inline void InterpolationElement<_itp_lagrange_segment_3>::computeShapes(
const Ref<const VectorXr> & natural_coords, Ref<VectorXr> N) {
Real c = natural_coords(0);
N(0) = (c - 1) * c / 2;
N(1) = (c + 1) * c / 2;
N(2) = 1 - c * c;
}
/* -------------------------------------------------------------------------- */
template <>
inline void InterpolationElement<_itp_lagrange_segment_3>::computeDNDS(
const Ref<const VectorXr> & natural_coords, Ref<MatrixXr> dnds) {
Real c = natural_coords(0);
dnds(0, 0) = c - .5;
dnds(0, 1) = c + .5;
dnds(0, 2) = -2 * c;
}
/* -------------------------------------------------------------------------- */
template <>
inline void
InterpolationElement<_itp_lagrange_segment_3>::computeSpecialJacobian(
const Ref<const MatrixXr> & dxds, Real & jac) {
jac = Math::norm2(dxds.data());
}
/* -------------------------------------------------------------------------- */
template <>
inline Real GeometricalElement<_gt_segment_3>::getInradius(
const Ref<const MatrixXr> & coord) {
Real dist1 = std::abs(coord(0, 0) - coord(0, 1));
Real dist2 = std::abs(coord(0, 1) - coord(0, 2));
return std::min(dist1, dist2);
}
/* -------------------------------------------------------------------------- */
template <>
inline void
GeometricalElement<_gt_segment_3>::getNormal(const Ref<const MatrixXr> & coord,
Ref<VectorXr> normal) {
Eigen::Matrix<Real, 1, 1> natural_coords;
natural_coords << 0;
ElementClass<_segment_3>::computeNormalsOnNaturalCoordinates(natural_coords,
coord, normal);
}

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