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rAKA/fem/element_classes/element_class_triangle_3.cc
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element_class_triangle_3.cc
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/**
* @file element_class_triangle_3.cc
* @author Nicolas Richart <nicolas.richart@epfl.ch>
* @date Thu Jul 15 10:28:28 2010
*
* @brief Specialization of the element_class class for the type _triangle_3
*
* @section LICENSE
*
* Copyright (©) 2010-2011 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
\eta
^
|
x (0,0,1)
|`
| `
| q `
| ° `
x--------x-----> \xi
(1,0,0) (0,1,0)
@endverbatim
*
* @subsection shapes Shape functions
* @f{eqnarray*}{
* N1 &=& 1 - \xi - \eta \\
* N2 &=& \xi \\
* N3 &=& \eta
* @f}
*
* @subsection quad_points Position of quadrature points
* @f{eqnarray*}{
* \xi_{q0} &=& 1/3 \qquad \eta_{q0} = 1/3
* @f}
*/
// /// shape functions
// shape[0] = 1./3.; /// N1(q_0)
// shape[1] = 1./3.; /// N2(q_0)
// shape[2] = 1./3.; /// N3(q_0)
/* -------------------------------------------------------------------------- */
template<> UInt ElementClass<_triangle_3>::nb_nodes_per_element;
template<> UInt ElementClass<_triangle_3>::nb_quadrature_points;
template<> UInt ElementClass<_triangle_3>::spatial_dimension;
/* -------------------------------------------------------------------------- */
template <> inline void ElementClass<_triangle_3>::computeShapes(const Real * natural_coords,
Real * shapes){
/// Natural coordinates
Real c0 = 1 - natural_coords[0] - natural_coords[1]; /// @f$ c0 = 1 - \xi - \eta @f$
Real c1 = natural_coords[0]; /// @f$ c1 = \xi @f$
Real c2 = natural_coords[1]; /// @f$ c2 = \eta @f$
shapes[0] = c0; /// N1(q_0)
shapes[1] = c1; /// N2(q_0)
shapes[2] = c2; /// N3(q_0)
}
/* -------------------------------------------------------------------------- */
template <> inline void ElementClass<_triangle_3>::computeDNDS(__attribute__ ((unused)) const Real * natural_coords,
Real * dnds){
/**
* @f[
* dnds = \left(
* \begin{array}{cccccc}
* \frac{\partial N1}{\partial \xi} & \frac{\partial N2}{\partial \xi} & \frac{\partial N3}{\partial \xi} \\
* \frac{\partial N1}{\partial \eta} & \frac{\partial N2}{\partial \eta} & \frac{\partial N3}{\partial \eta}
* \end{array}
* \right)
* @f]
*/
dnds[0] = -1.; dnds[1] = 1.; dnds[2] = 0.;
dnds[3] = -1.; dnds[4] = 0.; dnds[5] = 1.;
}
/* -------------------------------------------------------------------------- */
template <> inline void ElementClass<_triangle_3>::computeJacobian(const Real * dxds,
const UInt dimension,
Real & jac){
const Real weight = .5;
if (dimension == spatial_dimension){
Real det_dxds = Math::det2(dxds);
jac = det_dxds;
}
else {
Real vprod[dimension];
Math::vectorProduct3(dxds,dxds+3,vprod);
jac = Math::norm3(vprod);
}
jac *= weight;
}
/* -------------------------------------------------------------------------- */
template<> inline Real ElementClass<_triangle_3>::getInradius(const Real * coord) {
return Math::triangle_inradius(coord, coord+2, coord+4);
}
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