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element_class_structural.hh
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rAKA akantu
element_class_structural.hh
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/**
* @file element_class_structural.hh
*
* @author Fabian Barras <fabian.barras@epfl.ch>
* @author Nicolas Richart <nicolas.richart@epfl.ch>
* @author Damien Spielmann <damien.spielmann@epfl.ch>
*
* @date creation: Thu Feb 21 2013
* @date last modification: Thu Oct 22 2015
*
* @brief Specialization of the element classes for structural elements
*
* @section LICENSE
*
* Copyright (©) 2014, 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/>.
*
*/
__BEGIN_AKANTU__
/* -------------------------------------------------------------------------- */
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(NbShapeDerivatives, nb_shape_derivatives, 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;
static const UInt nb_shape_derivatives;
};
/// Macro to generate the element class structures for different structural element types
/* -------------------------------------------------------------------------- */
#define AKANTU_DEFINE_STRUCTURAL_ELEMENT_CLASS_PROPERTY(elem_type, \
geom_type, \
interp_type, \
parent_el_type, \
elem_kind, \
sp, \
gauss_int_type, \
min_int_order) \
template<> \
struct ElementClassProperty<elem_type> { \
static const GeometricalType geometrical_type = geom_type; \
static const InterpolationType interpolation_type = interp_type; \
static const ElementType parent_element_type = parent_el_type; \
static const ElementKind element_kind = elem_kind; \
static const UInt spatial_dimension = sp; \
static const GaussIntergrationType gauss_integration_type = gauss_int_type; \
static const UInt minimal_integration_order = min_int_order; \
}
/* -------------------------------------------------------------------------- */
/* ElementClass for structural elements */
/* -------------------------------------------------------------------------- */
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;
typedef ElementClass<ElementClassProperty<element_type>::parent_element_type> parent_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();
if (element_type ==_kirchhoff_shell) {
/// TO BE CONTINUED and moved in a _tmpl.hh
UInt spatial_dimension = real_nodal_coord.cols();
UInt nb_nodes = real_nodal_coord.rows();
const UInt projected_dim = natural_coord.rows();
Matrix<Real> rotation_matrix(real_nodal_coord);
Matrix<Real> rotated_nodal_coord(real_nodal_coord);
Matrix<Real> projected_nodal_coord(natural_coord);
/* -------------------------------------------------------------------------- */
/* -------------------------------------------------------------------------- */
Matrix<Real> Pe (real_nodal_coord);
Matrix<Real> Pg (real_nodal_coord);
Matrix<Real> inv_Pg(real_nodal_coord);
/// compute matrix Pe
Pe.eye();
/// compute matrix Pg
Vector<Real> Pg_col_1(spatial_dimension);
Pg_col_1(0) = real_nodal_coord(0,1) - real_nodal_coord(0,0);
Pg_col_1(1) = real_nodal_coord(1,1) - real_nodal_coord(1,0);
Pg_col_1(2) = real_nodal_coord(2,1) - real_nodal_coord(2,0);
Vector<Real> Pg_col_2(spatial_dimension);
Pg_col_2(0) = real_nodal_coord(0,2) - real_nodal_coord(0,0);
Pg_col_2(1) = real_nodal_coord(1,2) - real_nodal_coord(1,0);
Pg_col_2(2) = real_nodal_coord(2,2) - real_nodal_coord(2,0);
Vector<Real> Pg_col_3(spatial_dimension);
Pg_col_3.crossProduct(Pg_col_1, Pg_col_2);
for (UInt i = 0; i < nb_points; ++i) {
Pg(i,0) = Pg_col_1(i);
Pg(i,1) = Pg_col_2(i);
Pg(i,2) = Pg_col_3(i);
}
/// compute inverse of Pg
inv_Pg.inverse(Pg);
/// compute rotation matrix
// rotation_matrix=Pe*inv_Pg;
rotation_matrix.eye();
/* -------------------------------------------------------------------------- */
/* -------------------------------------------------------------------------- */
rotated_nodal_coord.mul<false, false>(rotation_matrix, real_nodal_coord);
for (UInt i = 0; i < projected_dim ; ++i) {
for (UInt j = 0; j < nb_points; ++j) {
projected_nodal_coord(i,j) = rotated_nodal_coord(i,j);
}
}
Tensor3<Real> dnds(projected_dim, nb_nodes, natural_coord.cols());
Tensor3<Real> J (projected_dim, projected_dim, natural_coord.cols());
parent_element::computeDNDS(natural_coord, dnds);
parent_element::computeJMat(dnds, projected_nodal_coord, J);
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, projected_nodal_coord, n);
Matrix<Real> dNdS = shape_deriv_p;
Matrix<Real> inv_J(projected_dim, projected_dim);
inv_J.inverse(J(p));
shape_deriv_p.mul<false, false>(inv_J, dNdS);
}
}
else {
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) {
parent_element::computeJacobian(natural_coords, nodal_coords, jacobians);
}
public:
static AKANTU_GET_MACRO_NOT_CONST(Kind, _ek_structural, ElementKind);
static AKANTU_GET_MACRO_NOT_CONST(P1ElementType, _not_defined, ElementType);
static AKANTU_GET_MACRO_NOT_CONST(FacetType, _not_defined, ElementType);
static const ElementType getFacetType(UInt t = 0) { return _not_defined; }
static AKANTU_GET_MACRO_NOT_CONST(SpatialDimension, ElementClassProperty<element_type>::spatial_dimension, UInt);
static ElementType * getFacetTypeInternal() { return NULL; }
};
#include "element_classes/element_class_bernoulli_beam_inline_impl.cc"
#include "element_classes/element_class_kirchhoff_shell_inline_impl.cc"
__END_AKANTU__
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