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rAKA/src/fem/element_classes/element_class_segment_2_inline_impl.cc
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element_class_segment_2_inline_impl.cc
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/**
* @file element_class_segment_2.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 _segment_2
*
* @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
q
--x--------|--------x---> x
-1 0 1
@endverbatim
*
* @subsection shapes Shape functions
* @f{eqnarray*}{
* w_1(x) &=& 1/2(1 - x) \\
* w_2(x) &=& 1/2(1 + x)
* @f}
*
* @subsection quad_points Position of quadrature points
* @f{eqnarray*}{
* x_{q} &=& 0
* @f}
*/
/* -------------------------------------------------------------------------- */
template<> UInt ElementClass<_segment_2>::nb_nodes_per_element;
template<> UInt ElementClass<_segment_2>::nb_quadrature_points;
template<> UInt ElementClass<_segment_2>::spatial_dimension;
/* -------------------------------------------------------------------------- */
template <> inline void ElementClass<_segment_2>::computeShapes(const Real * natural_coords,
Real * shapes){
/// natural coordinate
Real c = natural_coords[0];
/// shape functions
shapes[0] = 0.5*(1-c);
shapes[1] =0.5*(1+c);
}
/* -------------------------------------------------------------------------- */
template <> inline void ElementClass<_segment_2>::computeDNDS(__attribute__ ((unused))
const Real * natural_coords,
Real * dnds){
/// dN1/de
dnds[0] = - .5;
/// dN2/de
dnds[1] = .5;
}
/* -------------------------------------------------------------------------- */
template <> inline void ElementClass<_segment_2>::computeJacobian(const Real * dxds,
const UInt dimension,
Real & jac){
if (dimension == spatial_dimension){
jac = dxds[0];
}
else {
jac = Math::norm2(dxds);
}
}
/* -------------------------------------------------------------------------- */
template<> inline Real ElementClass<_segment_2>::getInradius(const Real * coord) {
return sqrt((coord[0] - coord[1])*(coord[0] - coord[1]));
}
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