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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 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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