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rAKA/src/fe_engine/element_classes/element_class_hexahedron_20_inline_impl.cc
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/**
* @file element_class_hexahedron_20_inline_impl.cc
*
* @author Mauro Corrado <mauro.corrado@epfl.ch>
* @author Sacha Laffely <sacha.laffely@epfl.ch>
* @author Damien Scantamburlo <damien.scantamburlo@epfl.ch>
*
* @date creation: Tue Mar 31 2015
* @date last modification: Thu Jul 16 2015
*
* @brief Specialization of the element_class class for the type _hexahedron_20
*
* @section LICENSE
*
* Copyright (©) 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/>.
*
* @section DESCRIPTION
*
* @verbatim
\y
\z /
| /
7-----|18--------6
/| | / /|
/ | | / / |
19 | | / 17 |
/ 15 | / / 14
/ | | / / |
4-------16---/---5 |
| | +----|------------\x
| 3-------10-|-----2
| / | /
12 / 13 /
| 11 | 9
| / | /
|/ |/
0--------8-------1
x y z
* N0 -1 -1 -1
* N1 1 -1 -1
* N2 1 1 -1
* N3 -1 1 -1
* N4 -1 -1 1
* N5 1 -1 1
* N6 1 1 1
* N7 -1 1 1
* N8 0 -1 -1
* N9 1 0 -1
* N10 0 1 -1
* N11 -1 0 -1
* N12 -1 -1 0
* N13 1 -1 0
* N14 1 1 0
* N15 -1 1 0
* N16 0 -1 1
* N17 1 0 1
* N18 0 1 1
* N19 -1 0 1
*/
/* -------------------------------------------------------------------------- */
AKANTU_DEFINE_ELEMENT_CLASS_PROPERTY(_hexahedron_20,
_gt_hexahedron_20,
_itp_serendip_hexahedron_20,
_ek_regular,
3,
_git_segment,
3);
AKANTU_DEFINE_SHAPE(_gt_hexahedron_20, _gst_square);
/* -------------------------------------------------------------------------- */
template <>
template <class vector_type>
inline void
InterpolationElement<_itp_serendip_hexahedron_20>::computeShapes(const vector_type & c,
vector_type & N) {
// Shape function , Natural coordinates
N( 0) = 0.125 * (1 - c(0)) * (1 - c(1)) * (1 - c(2)) * (-2 - c(0) - c(1) - c(2));
N( 1) = 0.125 * (1 + c(0)) * (1 - c(1)) * (1 - c(2)) * (-2 + c(0) - c(1) - c(2));
N( 2) = 0.125 * (1 + c(0)) * (1 + c(1)) * (1 - c(2)) * (-2 + c(0) + c(1) - c(2));
N( 3) = 0.125 * (1 - c(0)) * (1 + c(1)) * (1 - c(2)) * (-2 - c(0) + c(1) - c(2));
N( 4) = 0.125 * (1 - c(0)) * (1 - c(1)) * (1 + c(2)) * (-2 - c(0) - c(1) + c(2));
N( 5) = 0.125 * (1 + c(0)) * (1 - c(1)) * (1 + c(2)) * (-2 + c(0) - c(1) + c(2));
N( 6) = 0.125 * (1 + c(0)) * (1 + c(1)) * (1 + c(2)) * (-2 + c(0) + c(1) + c(2));
N( 7) = 0.125 * (1 - c(0)) * (1 + c(1)) * (1 + c(2)) * (-2 - c(0) + c(1) + c(2));
N( 8) = 0.25 * (1 - c(0)*c(0)) * (1 - c(1)) * (1 - c(2));
N( 9) = 0.25 * (1 - c(1)*c(1)) * (1 + c(0)) * (1 - c(2));
N(10) = 0.25 * (1 - c(0)*c(0)) * (1 + c(1)) * (1 - c(2));
N(11) = 0.25 * (1 - c(1)*c(1)) * (1 - c(0)) * (1 - c(2));
N(12) = 0.25 * (1 - c(2)*c(2)) * (1 - c(0)) * (1 - c(1));
N(13) = 0.25 * (1 - c(2)*c(2)) * (1 + c(0)) * (1 - c(1));
N(14) = 0.25 * (1 - c(2)*c(2)) * (1 + c(0)) * (1 + c(1));
N(15) = 0.25 * (1 - c(2)*c(2)) * (1 - c(0)) * (1 + c(1));
N(16) = 0.25 * (1 - c(0)*c(0)) * (1 - c(1)) * (1 + c(2));
N(17) = 0.25 * (1 - c(1)*c(1)) * (1 + c(0)) * (1 + c(2));
N(18) = 0.25 * (1 - c(0)*c(0)) * (1 + c(1)) * (1 + c(2));
N(19) = 0.25 * (1 - c(1)*c(1)) * (1 - c(0)) * (1 + c(2));
}
/* -------------------------------------------------------------------------- */
template <>
template <class vector_type, class matrix_type>
inline void
InterpolationElement<_itp_serendip_hexahedron_20>::computeDNDS(const vector_type & c,
matrix_type & dnds) {
//derivatives
//ddx
dnds(0, 0) = 0.25 * (c(0) + 0.5 * (c(1) + c(2) + 1)) * (c(1) - 1) * (c(2) - 1);
dnds(0, 1) = 0.25 * (c(0) - 0.5 * (c(1) + c(2) + 1)) * (c(1) - 1) * (c(2) - 1);
dnds(0, 2) = -0.25 * (c(0) + 0.5 * (c(1) - c(2) - 1)) * (c(1) + 1) * (c(2) - 1);
dnds(0, 3) = -0.25 * (c(0) - 0.5 * (c(1) - c(2) - 1)) * (c(1) + 1) * (c(2) - 1);
dnds(0, 4) = -0.25 * (c(0) + 0.5 * (c(1) - c(2) + 1)) * (c(1) - 1) * (c(2) + 1);
dnds(0, 5) = -0.25 * (c(0) - 0.5 * (c(1) - c(2) + 1)) * (c(1) - 1) * (c(2) + 1);
dnds(0, 6) = 0.25 * (c(0) + 0.5 * (c(1) + c(2) - 1)) * (c(1) + 1) * (c(2) + 1);
dnds(0, 7) = 0.25 * (c(0) - 0.5 * (c(1) + c(2) - 1)) * (c(1) + 1) * (c(2) + 1);
dnds(0, 8) = -0.5 * c(0) * (c(1) - 1) * (c(2) - 1);
dnds(0, 9) = 0.25 * (c(1)*c(1) - 1) * (c(2) - 1);
dnds(0, 10) = 0.5 * c(0) * (c(1) + 1) * (c(2) - 1);
dnds(0, 11) = -0.25 * (c(1)*c(1) - 1) * (c(2) - 1);
dnds(0, 12) = -0.25 * (c(2)*c(2) - 1) * (c(1) - 1);
dnds(0, 13) = 0.25 * (c(1) - 1) * (c(2)*c(2) - 1);
dnds(0, 14) = -0.25 * (c(1) + 1) * (c(2)*c(2) - 1);
dnds(0, 15) = 0.25 * (c(1) + 1) * (c(2)*c(2) - 1);
dnds(0, 16) = 0.5 * c(0) * (c(1) - 1) * (c(2) + 1);
dnds(0, 17) = -0.25 * (c(2) + 1) * (c(1)*c(1) - 1);
dnds(0, 18) = -0.5 * c(0) * (c(1) + 1) * (c(2) + 1);
dnds(0, 19) = 0.25 * (c(2) + 1) * (c(1)*c(1) - 1);
//ddy
dnds(1, 0) = 0.25 * (c(1) + 0.5 * (c(0) + c(2) + 1)) * (c(0) - 1) * (c(2) - 1);
dnds(1, 1) = -0.25 * (c(1) - 0.5 * (c(0) - c(2) - 1)) * (c(0) + 1) * (c(2) - 1);
dnds(1, 2) = -0.25 * (c(1) + 0.5 * (c(0) - c(2) - 1)) * (c(0) + 1) * (c(2) - 1);
dnds(1, 3) = 0.25 * (c(1) - 0.5 * (c(0) + c(2) + 1)) * (c(0) - 1) * (c(2) - 1);
dnds(1, 4) = -0.25 * (c(1) + 0.5 * (c(0) - c(2) + 1)) * (c(0) - 1) * (c(2) + 1);
dnds(1, 5) = 0.25 * (c(1) - 0.5 * (c(0) + c(2) - 1)) * (c(0) + 1) * (c(2) + 1);
dnds(1, 6) = 0.25 * (c(1) + 0.5 * (c(0) + c(2) - 1)) * (c(0) + 1) * (c(2) + 1);
dnds(1, 7) = -0.25 * (c(1) - 0.5 * (c(0) - c(2) + 1)) * (c(0) - 1) * (c(2) + 1);
dnds(1, 8) = -0.25 * (c(0)*c(0) - 1) * (c(2) - 1);
dnds(1, 9) = 0.5 * c(1) * (c(0) + 1) * (c(2) - 1);
dnds(1, 10) = 0.25 * (c(0)*c(0) - 1) * (c(2) - 1);
dnds(1, 11) = -0.5 * c(1) * (c(0) - 1) * (c(2) - 1);
dnds(1, 12) = -0.25 * (c(2)*c(2) - 1) * (c(0) - 1);
dnds(1, 13) = 0.25 * (c(0) + 1) * (c(2)*c(2) - 1);
dnds(1, 14) = -0.25 * (c(0) + 1) * (c(2)*c(2) - 1);
dnds(1, 15) = 0.25 * (c(0) - 1) * (c(2)*c(2) - 1);
dnds(1, 16) = 0.25 * (c(2) + 1) * (c(0)*c(0) - 1);
dnds(1, 17) = -0.5 * c(1) * (c(0) + 1) * (c(2) + 1);
dnds(1, 18) = -0.25 * (c(2) + 1) * (c(0)*c(0) - 1);
dnds(1, 19) = 0.5 * c(1) * (c(0) - 1) * (c(2) + 1);
//ddz
dnds(2, 0) = 0.25 * (c(2) + 0.5 * (c(0) + c(1) + 1)) * (c(0) - 1) * (c(1) - 1);
dnds(2, 1) = -0.25 * (c(2) - 0.5 * (c(0) - c(1) - 1)) * (c(0) + 1) * (c(1) - 1);
dnds(2, 2) = 0.25 * (c(2) - 0.5 * (c(0) + c(1) - 1)) * (c(0) + 1) * (c(1) + 1);
dnds(2, 3) = -0.25 * (c(2) + 0.5 * (c(0) - c(1) + 1)) * (c(0) - 1) * (c(1) + 1);
dnds(2, 4) = 0.25 * (c(2) - 0.5 * (c(0) + c(1) + 1)) * (c(0) - 1) * (c(1) - 1);
dnds(2, 5) = -0.25 * (c(2) + 0.5 * (c(0) - c(1) - 1)) * (c(0) + 1) * (c(1) - 1);
dnds(2, 6) = 0.25 * (c(2) + 0.5 * (c(0) + c(1) - 1)) * (c(0) + 1) * (c(1) + 1);
dnds(2, 7) = -0.25 * (c(2) - 0.5 * (c(0) - c(1) + 1)) * (c(0) - 1) * (c(1) + 1);
dnds(2, 8) = -0.25 * (c(0)*c(0) - 1) * (c(1) - 1);
dnds(2, 9) = 0.25 * (c(1)*c(1) - 1) * (c(0) + 1);
dnds(2, 10) = 0.25 * (c(0)*c(0) - 1) * (c(1) + 1);
dnds(2, 11) = -0.25 * (c(1)*c(1) - 1) * (c(0) - 1);
dnds(2, 12) = -0.5 * c(2) * (c(1) - 1) * (c(0) - 1);
dnds(2, 13) = 0.5 * c(2) * (c(0) + 1) * (c(1) - 1);
dnds(2, 14) = -0.5 * c(2) * (c(0) + 1) * (c(1) + 1);
dnds(2, 15) = 0.5 * c(2) * (c(0) - 1) * (c(1) + 1);
dnds(2, 16) = 0.25 * (c(1) - 1) * (c(0)*c(0) - 1);
dnds(2, 17) = -0.25 * (c(0) + 1) * (c(1)*c(1) - 1);
dnds(2, 18) = -0.25 * (c(1) + 1) * (c(0)*c(0) - 1);
dnds(2, 19) = 0.25 * (c(0) - 1) * (c(1)*c(1) - 1);
}
/* -------------------------------------------------------------------------- */
template<>
inline Real
GeometricalElement<_gt_hexahedron_20>::getInradius(const Matrix<Real> & coord) {
Vector<Real> u0 = coord(0);
Vector<Real> u1 = coord(1);
Vector<Real> u2 = coord(2);
Vector<Real> u3 = coord(3);
Vector<Real> u4 = coord(4);
Vector<Real> u5 = coord(5);
Vector<Real> u6 = coord(6);
Vector<Real> u7 = coord(7);
Vector<Real> u8 = coord(8);
Vector<Real> u9 = coord(9);
Vector<Real> u10 = coord(10);
Vector<Real> u11= coord(11);
Vector<Real> u12 = coord(12);
Vector<Real> u13 = coord(13);
Vector<Real> u14 = coord(14);
Vector<Real> u15 = coord(15);
Vector<Real> u16 = coord(16);
Vector<Real> u17 = coord(17);
Vector<Real> u18 = coord(18);
Vector<Real> u19 = coord(19);
Real a = u0.distance(u1);
Real b = u1.distance(u2);
Real c = u2.distance(u3);
Real d = u3.distance(u0);
Real e = u0.distance(u4);
Real f = u1.distance(u5);
Real g = u2.distance(u6);
Real h = u3.distance(u7);
Real i = u4.distance(u5);
Real j = u5.distance(u6);
Real k = u6.distance(u7);
Real l = u7.distance(u4);
Real x = std::min(a, std::min(b, std::min(c, d)));
Real y = std::min(e, std::min(f, std::min(g, h)));
Real z = std::min(i, std::min(j, std::min(k, l)));
Real p = std::min(x, std::min(y, z));
return p;
}
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