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rAKA/src/fem/element_class_structural.hh
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element_class_structural.hh
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/**
* @file element_class_structural.hh
*
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date Sat Nov 17 19:32:51 2012
*
* @brief Specialization for structural elements
*
* @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/>.
*
*/
/* -------------------------------------------------------------------------- */
template<InterpolationType interpolation_type>
class InterpolationElement<interpolation_type, _itk_structural> {
public:
typedef InterpolationPorperty<interpolation_type> interpolation_property;
/// compute the shape values for a given set of points in natural coordinates
static inline void computeShapes(const Matrix<Real> & natural_coord,
Matrix<Real> & N,
const Matrix<Real> & real_nodal_coord,
UInt n = 0) {
UInt nb_points = natural_coord.cols();
for (UInt p = 0; p < nb_points; ++p) {
Vector<Real> Np = N(p);
computeShapes(natural_coord(p), Np, real_nodal_coord, n);
}
}
/// compute the shape values for a given point in natural coordinates
static inline void computeShapes(const Vector<Real> & natural_coord,
Vector<Real> & N,
const Matrix<Real> & real_nodal_coord,
UInt n = 0);
/**
* compute @f$ B_{ij} = \frac{\partial N_j}{\partial S_i} @f$ the variation of
* shape functions along with variation of natural coordinates on a given set
* of points in natural coordinates
*/
static inline void computeDNDS(const Matrix<Real> & natural_coord,
Tensor3<Real> & dnds,
const Matrix<Real> & real_nodal_coord,
UInt n = 0) {
for (UInt i = 0; i < natural_coord.cols(); ++i) {
Matrix<Real> dnds_t = dnds(i);
computeDNDS(natural_coord(i), dnds_t, real_nodal_coord, n);
}
}
/**
* compute @f$ B_{ij} = \frac{\partial N_j}{\partial S_i} @f$ the variation of shape functions along with
* variation of natural coordinates on a given point in natural
* coordinates
*/
static inline void computeDNDS(const Vector<Real> & natural_coord,
Matrix<Real> & dnds,
const Matrix<Real> & real_nodal_coord,
UInt n = 0);
public:
static AKANTU_GET_MACRO_NOT_CONST(NbShapeFunctions, nb_shape_functions, UInt);
static AKANTU_GET_MACRO_NOT_CONST(ShapeSize, interpolation_property::nb_nodes_per_element, UInt);
static AKANTU_GET_MACRO_NOT_CONST(ShapeDerivativesSize, (interpolation_property::nb_nodes_per_element * interpolation_property::natural_space_dimension), UInt);
static AKANTU_GET_MACRO_NOT_CONST(NaturalSpaceDimension, interpolation_property::natural_space_dimension, UInt);
protected:
/// nb shape functions
static const UInt nb_shape_functions;
};
/* -------------------------------------------------------------------------- */
template<ElementType element_type>
class ElementClass<element_type, _ek_structural> :
public GeometricalElement<ElementClassProperty<element_type>::geometrical_type>,
public InterpolationElement<ElementClassProperty<element_type>::interpolation_type> {
protected:
typedef GeometricalElement<ElementClassProperty<element_type>::geometrical_type> geometrical_element;
typedef InterpolationElement<ElementClassProperty<element_type>::interpolation_type> interpolation_element;
public:
/// compute shape derivatives (input is dxds) for a set of points
static inline void computeShapeDerivatives(const Matrix<Real> & natural_coord,
Tensor3<Real> & shape_deriv,
const Matrix<Real> & real_nodal_coord,
UInt n = 0) {
UInt nb_points = natural_coord.cols();
for (UInt p = 0; p < nb_points; ++p) {
Matrix<Real> shape_deriv_p = shape_deriv(p);
interpolation_element::computeDNDS(natural_coord(p), shape_deriv_p, real_nodal_coord, n);
}
}
/// compute jacobian (or integration variable change factor) for a given point
static inline void computeJacobian(const Matrix<Real> & natural_coords,
const Matrix<Real> & nodal_coords,
Vector<Real> & jacobians);
public:
static AKANTU_GET_MACRO_NOT_CONST(Kind, _ek_structural, ElementKind);
static AKANTU_GET_MACRO_NOT_CONST(P1ElementType, _not_defined, const ElementType);
static AKANTU_GET_MACRO_NOT_CONST(FacetType, _not_defined, const ElementType);
static AKANTU_GET_MACRO_NOT_CONST(SpatialDimension, ElementClassProperty<element_type>::spatial_dimension, UInt);
};
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