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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/>.
*
*/
/* -------------------------------------------------------------------------- */
#include "element_class.hh"
/* -------------------------------------------------------------------------- */
#ifndef __AKANTU_ELEMENT_CLASS_STRUCTURAL_HH__
#define __AKANTU_ELEMENT_CLASS_STRUCTURAL_HH__
namespace
akantu
{
/// Macro to generate the InterpolationProperty structures for different
/// interpolation types
#define AKANTU_DEFINE_STRUCTURAL_INTERPOLATION_TYPE_PROPERTY( \
itp_type, itp_geom_type, ndof, nb_stress) \
template <> struct InterpolationProperty<itp_type> { \
static const InterpolationKind kind{_itk_structural}; \
static const UInt nb_nodes_per_element{ \
InterpolationProperty<itp_geom_type>::nb_nodes_per_element}; \
static const InterpolationType itp_geometry_type{itp_geom_type}; \
static const UInt natural_space_dimension{ \
InterpolationProperty<itp_geom_type>::natural_space_dimension}; \
static const UInt nb_degree_of_freedom{ndof}; \
static const UInt nb_stress_components{nb_stress}; \
}
/* -------------------------------------------------------------------------- */
template
<
InterpolationType
interpolation_type
>
class
InterpolationElement
<
interpolation_type
,
_itk_structural
>
{
public
:
using
interpolation_property
=
InterpolationProperty
<
interpolation_type
>
;
/// compute the shape values for a given set of points in natural coordinates
static
inline
void
computeShapes
(
const
Matrix
<
Real
>
&
natural_coord
,
const
Matrix
<
Real
>
&
real_coord
,
Tensor3
<
Real
>
&
N
)
{
for
(
UInt
i
=
0
;
i
<
natural_coord
.
cols
();
++
i
)
{
Matrix
<
Real
>
n_t
=
N
(
i
);
computeShapes
(
natural_coord
(
i
),
real_coord
,
n_t
);
}
}
/// compute the shape values for a given point in natural coordinates
static
inline
void
computeShapes
(
const
Vector
<
Real
>
&
natural_coord
,
const
Matrix
<
Real
>
&
real_coord
,
Matrix
<
Real
>
&
N
);
/// compute shape derivatives (input is dxds) for a set of points
static
inline
void
computeShapeDerivatives
(
const
Tensor3
<
Real
>
&
Js
,
const
Tensor3
<
Real
>
&
DNDSs
,
const
Matrix
<
Real
>
&
R
,
Tensor3
<
Real
>
&
Bs
)
{
for
(
UInt
i
=
0
;
i
<
Js
.
size
(
2
);
++
i
)
{
Matrix
<
Real
>
J
=
Js
(
i
);
Matrix
<
Real
>
DNDS
=
DNDSs
(
i
);
Matrix
<
Real
>
DNDS_R
(
DNDS
.
rows
(),
DNDS
.
cols
());
DNDS_R
.
mul
<
false
,
false
>
(
DNDS
,
R
);
Matrix
<
Real
>
B
=
Bs
(
i
);
auto
inv_J
=
J
.
inverse
();
Matrix
<
Real
>
inv_J_full
(
DNDS
.
rows
(),
DNDS
.
rows
());
// Gotta repeat J^-1 for each stress component
for
(
UInt
k
=
0
,
pos
=
0
;
k
<
getNbStressComponents
();
k
++
,
pos
+=
inv_J
.
rows
())
{
inv_J_full
.
block
(
inv_J
,
pos
,
pos
);
}
B
.
mul
<
false
,
false
>
(
inv_J_full
,
DNDS_R
);
}
}
/**
* 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
,
const
Matrix
<
Real
>
&
real_coord
,
Tensor3
<
Real
>
&
dnds
)
{
for
(
UInt
i
=
0
;
i
<
natural_coord
.
cols
();
++
i
)
{
Matrix
<
Real
>
dnds_t
=
dnds
(
i
);
computeDNDS
(
natural_coord
(
i
),
real_coord
,
dnds_t
);
}
}
/**
* 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
,
const
Matrix
<
Real
>
&
real_coord
,
Matrix
<
Real
>
&
dnds
);
public
:
static
AKANTU_GET_MACRO_NOT_CONST
(
NbNodesPerInterpolationElement
,
interpolation_property
::
nb_nodes_per_element
,
UInt
);
static
AKANTU_GET_MACRO_NOT_CONST
(
ShapeSize
,
(
interpolation_property
::
nb_nodes_per_element
*
interpolation_property
::
nb_degree_of_freedom
*
interpolation_property
::
nb_degree_of_freedom
),
UInt
);
static
AKANTU_GET_MACRO_NOT_CONST
(
ShapeDerivativesSize
,
(
interpolation_property
::
nb_nodes_per_element
*
interpolation_property
::
nb_degree_of_freedom
*
interpolation_property
::
nb_stress_components
),
UInt
);
static
AKANTU_GET_MACRO_NOT_CONST
(
NaturalSpaceDimension
,
interpolation_property
::
natural_space_dimension
,
UInt
);
static
AKANTU_GET_MACRO_NOT_CONST
(
NbDegreeOfFreedom
,
interpolation_property
::
nb_degree_of_freedom
,
UInt
);
static
AKANTU_GET_MACRO_NOT_CONST
(
NbStressComponents
,
interpolation_property
::
nb_stress_components
,
UInt
);
};
/// 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 GaussIntegrationType gauss_integration_type{gauss_int_type}; \
static const UInt polynomial_degree{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
:
using
geometrical_element
=
GeometricalElement
<
ElementClassProperty
<
element_type
>::
geometrical_type
>
;
using
interpolation_element
=
InterpolationElement
<
ElementClassProperty
<
element_type
>::
interpolation_type
>
;
using
parent_element
=
ElementClass
<
ElementClassProperty
<
element_type
>::
parent_element_type
>
;
public
:
static
inline
void
computeRotationMatrix
(
Matrix
<
Real
>
&
/*R*/
,
const
Matrix
<
Real
>
&
/*X*/
,
const
Vector
<
Real
>
&
/*extra_normal*/
)
{
AKANTU_DEBUG_TO_IMPLEMENT
();
}
/// compute jacobian (or integration variable change factor) for a given point
static
inline
void
computeJMat
(
const
Matrix
<
Real
>
&
DNDS
,
const
Matrix
<
Real
>
&
Xs
,
Matrix
<
Real
>
&
J
)
{
auto
nb_nodes
=
Xs
.
cols
();
auto
dim
=
Xs
.
rows
();
auto
nb_dof
=
interpolation_element
::
interpolation_property
::
nb_degree_of_freedom
;
Matrix
<
Real
>
B
(
dim
,
nb_nodes
);
for
(
UInt
s
=
0
;
s
<
dim
;
++
s
)
{
for
(
UInt
n
=
0
;
n
<
nb_nodes
;
++
n
)
{
B
(
s
,
n
)
=
DNDS
(
s
,
n
*
nb_dof
+
s
);
}
}
J
.
mul
<
false
,
true
>
(
B
,
Xs
);
}
static
inline
void
computeJMat
(
const
Tensor3
<
Real
>
&
DNDSs
,
const
Matrix
<
Real
>
&
Xs
,
Tensor3
<
Real
>
&
Js
)
{
using
itp
=
typename
interpolation_element
::
interpolation_property
;
auto
nb_nodes
=
Xs
.
cols
();
auto
dim
=
Xs
.
rows
();
auto
nb_dof
=
itp
::
nb_degree_of_freedom
;
Matrix
<
Real
>
B
(
dim
,
nb_nodes
);
for
(
UInt
i
=
0
;
i
<
Xs
.
cols
();
++
i
)
{
Matrix
<
Real
>
DNDS
=
DNDSs
(
i
);
Matrix
<
Real
>
J
=
Js
(
i
);
B
.
clear
();
for
(
UInt
s
=
0
;
s
<
dim
;
++
s
)
{
for
(
UInt
n
=
0
;
n
<
nb_nodes
;
++
n
)
{
B
(
s
,
n
)
=
DNDS
(
s
,
n
*
nb_dof
+
s
);
}
}
parent_element
::
computeJMat
(
B
,
Xs
,
J
);
// computeJMat(DNDS, Xs, J);
}
}
static
inline
void
computeJacobian
(
const
Matrix
<
Real
>
&
natural_coords
,
const
Matrix
<
Real
>
&
node_coords
,
Vector
<
Real
>
&
jacobians
)
{
using
itp
=
typename
interpolation_element
::
interpolation_property
;
UInt
nb_points
=
natural_coords
.
cols
();
Matrix
<
Real
>
dnds
(
itp
::
natural_space_dimension
,
itp
::
nb_nodes_per_element
);
Matrix
<
Real
>
J
(
natural_coords
.
rows
(),
itp
::
natural_space_dimension
);
// Extract relevant first lines
auto
x
=
node_coords
.
block
(
0
,
0
,
itp
::
natural_space_dimension
,
itp
::
nb_nodes_per_element
);
for
(
UInt
p
=
0
;
p
<
nb_points
;
++
p
)
{
Vector
<
Real
>
ncoord_p
(
natural_coords
(
p
));
parent_element
::
computeDNDS
(
ncoord_p
,
dnds
);
parent_element
::
computeJMat
(
dnds
,
x
,
J
);
jacobians
(
p
)
=
J
.
det
();
}
}
static
inline
void
computeRotation
(
const
Matrix
<
Real
>
&
node_coords
,
Matrix
<
Real
>
&
rotation
);
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
constexpr
auto
getFacetType
(
__attribute__
((
unused
))
UInt
t
=
0
)
{
return
_not_defined
;
}
static
constexpr
AKANTU_GET_MACRO_NOT_CONST
(
SpatialDimension
,
ElementClassProperty
<
element_type
>::
spatial_dimension
,
UInt
);
static
constexpr
auto
getFacetTypes
()
{
return
ElementClass
<
_not_defined
>::
getFacetTypes
();
}
};
}
// namespace akantu
/* -------------------------------------------------------------------------- */
#include "element_classes/element_class_hermite_inline_impl.cc"
/* keep order */
#include "element_classes/element_class_bernoulli_beam_inline_impl.cc"
#include "element_classes/element_class_kirchhoff_shell_inline_impl.cc"
/* -------------------------------------------------------------------------- */
#endif
/* __AKANTU_ELEMENT_CLASS_STRUCTURAL_HH__ */
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