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test_solid_mechanics_model_igfem.cc
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text/x-c++
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rAKA akantu
test_solid_mechanics_model_igfem.cc
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/**
* @file test_solid_mechanics_model_igfem.cc
*
* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
*
*
* @brief test the solidmechancis model for IGFEM analysis
*
* @section LICENSE
*
* Copyright (©) 2010-2012, 2014 EPFL (Ecole Polytechnique Fédérale de Lausanne)
* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
*
*/
/* -------------------------------------------------------------------------- */
#include "solid_mechanics_model_igfem.hh"
#include "material_elastic.hh"
#include "aka_common.hh"
#include <cstdlib>
#include <fstream>
#include <iostream>
#include <cmath>
#include <math.h>
#include "dumper_paraview.hh"
#include "mesh_geom_common.hh"
/* -------------------------------------------------------------------------- */
using
namespace
akantu
;
/* -------------------------------------------------------------------------- */
void
outputArray
(
const
Mesh
&
mesh
,
const
Array
<
Real
>
&
array
)
{
StaticCommunicator
&
comm
=
StaticCommunicator
::
getStaticCommunicator
();
Int
prank
=
comm
.
whoAmI
();
UInt
spatial_dimension
=
mesh
.
getSpatialDimension
();
UInt
nb_global_nodes
=
mesh
.
getNbGlobalNodes
();
Array
<
Real
>
solution
(
nb_global_nodes
,
spatial_dimension
,
0.
);
Array
<
Real
>::
vector_iterator
solution_begin
=
solution
.
begin
(
spatial_dimension
);
Array
<
Real
>::
const_vector_iterator
array_it
=
array
.
begin
(
spatial_dimension
);
for
(
UInt
n
=
0
;
n
<
mesh
.
getNbNodes
();
++
n
,
++
array_it
)
{
if
(
mesh
.
isLocalOrMasterNode
(
n
))
solution_begin
[
mesh
.
getNodeGlobalId
(
n
)]
=
*
array_it
;
}
comm
.
allReduce
(
solution
.
storage
(),
solution
.
getSize
()
*
solution
.
getNbComponent
(),
_so_sum
);
std
::
cout
<<
std
::
fixed
;
std
::
cout
<<
std
::
setprecision
(
6
);
if
(
prank
==
0
)
{
Array
<
Real
>::
const_vector_iterator
sol_it
=
solution
.
begin
(
spatial_dimension
);
for
(
UInt
n
=
0
;
n
<
nb_global_nodes
;
++
n
,
++
sol_it
)
// Print absolute values to avoid parasite negative sign in machine precision zeros
std
::
cout
<<
std
::
abs
((
*
sol_it
)(
0
))
<<
","
<<
std
::
abs
((
*
sol_it
)(
1
))
<<
std
::
endl
;
}
}
/* -------------------------------------------------------------------------- */
class
Sphere
{
public
:
Sphere
(
const
Vector
<
Real
>
&
center
,
Real
radius
,
Real
tolerance
=
0.
)
:
center
(
center
),
radius
(
radius
),
tolerance
(
tolerance
)
{
}
bool
isInside
(
const
Vector
<
Real
>
&
point
)
const
{
return
(
point
.
distance
(
center
)
<
radius
+
tolerance
);
}
const
Vector
<
Real
>
&
getCenter
()
const
{
return
center
;
}
Real
&
getRadius
()
{
return
radius
;
}
protected
:
Vector
<
Real
>
center
;
Real
radius
,
tolerance
;
};
void
growGel
(
std
::
list
<
SK
::
Sphere_3
>
&
query_list
,
Real
new_radius
)
{
std
::
list
<
SK
::
Sphere_3
>::
const_iterator
query_it
=
query_list
.
begin
(),
query_end
=
query_list
.
end
();
std
::
list
<
SK
::
Sphere_3
>
sphere_list
;
for
(;
query_it
!=
query_end
;
++
query_it
)
{
SK
::
Sphere_3
sphere
(
query_it
->
center
(),
new_radius
*
new_radius
);
sphere_list
.
push_back
(
sphere
);
}
query_list
.
clear
();
query_list
=
sphere_list
;
}
Real
computeAlpha
(
Real
inner_radius
,
Real
outer_radius
,
const
Vector
<
Real
>
&
lambda
,
const
Vector
<
Real
>
&
mu
)
{
Real
alpha
=
(
lambda
(
1
)
+
mu
(
1
)
+
mu
(
0
))
*
outer_radius
*
outer_radius
/
((
lambda
(
0
)
+
mu
(
0
))
*
inner_radius
*
inner_radius
+
(
lambda
(
1
)
+
mu
(
1
))
*
(
outer_radius
*
outer_radius
-
inner_radius
*
inner_radius
)
+
(
mu
(
0
)
*
outer_radius
*
outer_radius
));
return
alpha
;
}
void
applyBoundaryConditions
(
SolidMechanicsModelIGFEM
&
model
,
Real
inner_radius
,
Real
outer_radius
,
const
Vector
<
Real
>
&
lambda
,
const
Vector
<
Real
>
&
mu
)
{
/// boundary conditions for circular inclusion:
Real
alpha
=
computeAlpha
(
inner_radius
,
outer_radius
,
lambda
,
mu
);
Mesh
&
mesh
=
model
.
getMesh
();
mesh
.
computeBoundingBox
();
const
Vector
<
Real
>
&
lowerBounds
=
mesh
.
getLowerBounds
();
const
Vector
<
Real
>
&
upperBounds
=
mesh
.
getUpperBounds
();
Real
bottom
=
lowerBounds
(
1
);
Real
top
=
upperBounds
(
1
);
Real
left
=
lowerBounds
(
0
);
Real
right
=
upperBounds
(
0
);
Real
eps
=
std
::
abs
((
top
-
bottom
)
*
1e-12
);
const
Array
<
Real
>
&
pos
=
mesh
.
getNodes
();
Array
<
Real
>
&
disp
=
model
.
getDisplacement
();
Array
<
bool
>
&
boun
=
model
.
getBlockedDOFs
();
Real
radius
=
0
;
Real
phi
=
0
;
disp
.
clear
();
boun
.
clear
();
/// absolute confinement
for
(
UInt
i
=
0
;
i
<
mesh
.
getNbNodes
();
++
i
)
{
if
(
std
::
abs
(
pos
(
i
,
0
)
-
left
)
<
eps
)
{
radius
=
std
::
sqrt
(
pos
(
i
,
0
)
*
pos
(
i
,
0
)
+
pos
(
i
,
1
)
*
pos
(
i
,
1
));
phi
=
std
::
atan2
(
pos
(
i
,
1
),
pos
(
i
,
0
));
boun
(
i
,
0
)
=
true
;
disp
(
i
,
0
)
=
cos
(
phi
)
*
(
(
radius
-
4.
/
radius
)
*
alpha
+
4.
/
radius
);
boun
(
i
,
1
)
=
true
;
disp
(
i
,
1
)
=
sin
(
phi
)
*
(
(
radius
-
4.
/
radius
)
*
alpha
+
4.
/
radius
);
}
if
(
std
::
abs
(
pos
(
i
,
0
)
-
right
)
<
eps
)
{
radius
=
std
::
sqrt
(
pos
(
i
,
0
)
*
pos
(
i
,
0
)
+
pos
(
i
,
1
)
*
pos
(
i
,
1
));
phi
=
std
::
atan2
(
pos
(
i
,
1
),
pos
(
i
,
0
));
boun
(
i
,
0
)
=
true
;
disp
(
i
,
0
)
=
cos
(
phi
)
*
(
(
radius
-
4.
/
radius
)
*
alpha
+
4.
/
radius
);
boun
(
i
,
1
)
=
true
;
disp
(
i
,
1
)
=
sin
(
phi
)
*
(
(
radius
-
4.
/
radius
)
*
alpha
+
4.
/
radius
);
}
if
(
std
::
abs
(
pos
(
i
,
1
)
-
top
)
<
eps
)
{
radius
=
std
::
sqrt
(
pos
(
i
,
0
)
*
pos
(
i
,
0
)
+
pos
(
i
,
1
)
*
pos
(
i
,
1
));
phi
=
std
::
atan2
(
pos
(
i
,
1
),
pos
(
i
,
0
));
boun
(
i
,
0
)
=
true
;
disp
(
i
,
0
)
=
cos
(
phi
)
*
(
(
radius
-
4.
/
radius
)
*
alpha
+
4.
/
radius
);
boun
(
i
,
1
)
=
true
;
disp
(
i
,
1
)
=
sin
(
phi
)
*
(
(
radius
-
4.
/
radius
)
*
alpha
+
4.
/
radius
);
}
if
(
std
::
abs
(
pos
(
i
,
1
)
-
bottom
)
<
eps
)
{
radius
=
std
::
sqrt
(
pos
(
i
,
0
)
*
pos
(
i
,
0
)
+
pos
(
i
,
1
)
*
pos
(
i
,
1
));
phi
=
std
::
atan2
(
pos
(
i
,
1
),
pos
(
i
,
0
));
boun
(
i
,
0
)
=
true
;
disp
(
i
,
0
)
=
cos
(
phi
)
*
(
(
radius
-
4.
/
radius
)
*
alpha
+
4.
/
radius
);
boun
(
i
,
1
)
=
true
;
disp
(
i
,
1
)
=
sin
(
phi
)
*
(
(
radius
-
4.
/
radius
)
*
alpha
+
4.
/
radius
);
}
}
}
class
SphereMaterialSelector
:
public
DefaultMaterialIGFEMSelector
{
public
:
SphereMaterialSelector
(
std
::
vector
<
Sphere
>
&
sphere_list
,
SolidMechanicsModelIGFEM
&
model
)
:
DefaultMaterialIGFEMSelector
(
model
),
model
(
model
),
spheres
(
sphere_list
)
{
}
UInt
operator
()(
const
Element
&
elem
)
{
if
(
Mesh
::
getKind
(
elem
.
type
)
==
_ek_igfem
)
return
this
->
fallback_value_igfem
;
// return 2;//2model.getMaterialIndex(2);
const
Mesh
&
mesh
=
model
.
getMesh
();
UInt
spatial_dimension
=
model
.
getSpatialDimension
();
Vector
<
Real
>
barycenter
(
spatial_dimension
);
mesh
.
getBarycenter
(
elem
,
barycenter
);
std
::
vector
<
Sphere
>::
const_iterator
iit
=
spheres
.
begin
();
std
::
vector
<
Sphere
>::
const_iterator
eit
=
spheres
.
end
();
for
(;
iit
!=
eit
;
++
iit
)
{
const
Sphere
&
sp
=
*
iit
;
if
(
sp
.
isInside
(
barycenter
))
{
return
1
;
//model.getMaterialIndex("inside");;
}
}
return
0
;
//return DefaultMaterialSelector::operator()(elem);
}
void
update
(
Real
new_radius
)
{
std
::
vector
<
Sphere
>::
iterator
iit
=
spheres
.
begin
();
std
::
vector
<
Sphere
>::
iterator
eit
=
spheres
.
end
();
for
(;
iit
!=
eit
;
++
iit
)
{
Real
&
radius
=
iit
->
getRadius
();
radius
=
new_radius
;
}
}
protected
:
SolidMechanicsModelIGFEM
&
model
;
std
::
vector
<
Sphere
>
spheres
;
};
typedef
Spherical
SK
;
/// the following modeling problem is explained in:
/// T.-P. Fries "A corrected XFEM approximation without problems in blending elements", 2008
int
main
(
int
argc
,
char
*
argv
[])
{
initialize
(
"material.dat"
,
argc
,
argv
);
/// problem dimension
const
UInt
spatial_dimension
=
2
;
StaticCommunicator
&
comm
=
StaticCommunicator
::
getStaticCommunicator
();
Int
psize
=
comm
.
getNbProc
();
Int
prank
=
comm
.
whoAmI
();
/// mesh creation
Mesh
mesh
(
spatial_dimension
);
akantu
::
MeshPartition
*
partition
=
NULL
;
if
(
prank
==
0
)
{
mesh
.
read
(
"plate.msh"
);
partition
=
new
MeshPartitionScotch
(
mesh
,
spatial_dimension
);
partition
->
partitionate
(
psize
);
}
/// model creation
SolidMechanicsModelIGFEM
model
(
mesh
);
model
.
initParallel
(
partition
);
delete
partition
;
Math
::
setTolerance
(
1e-14
);
/// geometry of IGFEM interface: circular inclusion
Real
radius_inclusion
=
0.401
;
Vector
<
Real
>
center
(
spatial_dimension
,
0.
);
/// @todo: Simplify this: need to create two type of spheres:
/// one for the geometry and one for the material selector
SK
::
Sphere_3
sphere
(
SK
::
Point_3
(
center
(
0
),
center
(
1
),
0
),
radius_inclusion
*
radius_inclusion
);
std
::
list
<
SK
::
Sphere_3
>
sphere_list
;
sphere_list
.
push_back
(
sphere
);
ID
domain_name
=
"gel"
;
SphereMaterialSelector
*
mat_selector
;
/// set material selector and initialize the model completely
std
::
vector
<
Sphere
>
spheres
;
spheres
.
push_back
(
Sphere
(
center
,
radius_inclusion
,
1.e-12
));
mat_selector
=
new
SphereMaterialSelector
(
spheres
,
model
);
model
.
setMaterialSelector
(
*
mat_selector
);
model
.
initFull
();
/// register the sphere list in the model
model
.
registerGeometryObject
(
sphere_list
,
domain_name
);
/// add fields that should be dumped
model
.
setBaseName
(
"regular_elements"
);
model
.
setBaseNameToDumper
(
"igfem elements"
,
"igfem elements"
);
model
.
addDumpField
(
"material_index"
);
model
.
addDumpField
(
"partitions"
);
model
.
addDumpFieldVector
(
"displacement"
);
model
.
addDumpField
(
"blocked_dofs"
);
model
.
addDumpField
(
"stress"
);
model
.
addDumpFieldToDumper
(
"igfem elements"
,
"lambda"
);
model
.
addDumpFieldVectorToDumper
(
"igfem elements"
,
"real_displacement"
);
model
.
addDumpFieldVectorToDumper
(
"igfem elements"
,
"displacement"
);
model
.
addDumpFieldToDumper
(
"igfem elements"
,
"material_index"
);
model
.
addDumpFieldToDumper
(
"igfem elements"
,
"stress"
);
model
.
addDumpFieldToDumper
(
"igfem elements"
,
"partitions"
);
/// dump mesh before the IGFEM interface is created
model
.
dump
();
model
.
dump
(
"igfem elements"
);
/// create the interface
model
.
update
(
domain_name
);
/* -------------------------------------------------------------------------- */
/// apply exact solution for the displacement along the outer boundary
Real
outer_radius
=
2.0
;
/// get the Lame constants for the two non-igfem materials (frist two materials in the material file):
/// Needed for compuation of boundary conditions
Vector
<
Real
>
lambda
(
2
);
Vector
<
Real
>
mu
(
2
);
for
(
UInt
m
=
0
;
m
<
2
;
++
m
)
{
MaterialElastic
<
spatial_dimension
>
&
mat
=
dynamic_cast
<
MaterialElastic
<
spatial_dimension
>
&
>
(
model
.
getMaterial
(
m
));
lambda
(
m
)
=
mat
.
getLambda
();
mu
(
m
)
=
mat
.
getMu
();
}
applyBoundaryConditions
(
model
,
radius_inclusion
,
outer_radius
,
lambda
,
mu
);
/// dump the mesh after the IGFEM interface has been created
model
.
dump
();
model
.
dump
(
"igfem elements"
);
/// solve the system
bool
factorize
=
false
;
bool
converged
=
false
;
Real
error
;
converged
=
model
.
solveStep
<
_scm_newton_raphson_tangent
,
_scc_increment
>
(
1e-12
,
error
,
2
,
factorize
);
if
(
!
converged
)
{
std
::
cout
<<
"Solving step did not yield a converged solution, error: "
<<
error
<<
std
::
endl
;
return
EXIT_FAILURE
;
}
/// dump the solution
model
.
dump
();
model
.
dump
(
"igfem elements"
);
/// output the displacement in parallel
outputArray
(
mesh
,
model
.
getDisplacement
());
finalize
();
return
EXIT_SUCCESS
;
}
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