Page Menu
Home
c4science
Search
Configure Global Search
Log In
Files
F78001585
element_class_structural.hh
No One
Temporary
Actions
Download File
Edit File
Delete File
View Transforms
Subscribe
Mute Notifications
Award Token
Subscribers
None
File Metadata
Details
File Info
Storage
Attached
Created
Sat, Aug 17, 18:50
Size
10 KB
Mime Type
text/x-c++
Expires
Mon, Aug 19, 18:50 (2 d)
Engine
blob
Format
Raw Data
Handle
19113190
Attached To
rAKA akantu
element_class_structural.hh
View Options
/**
* @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
ElementType
getFacetType
(
__attribute__
((
unused
))
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__
Event Timeline
Log In to Comment