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test_bem_grid.py
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rTAMAAS tamaas
test_bem_grid.py
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#!/usr/bin/env python
# coding: utf-8
# -----------------------------------------------------------------------------
# @author Lucas Frérot <lucas.frerot@epfl.ch>
#
# @section LICENSE
#
# Copyright (©) 2016 EPFL (Ecole Polytechnique Fédérale de
# Lausanne) Laboratory (LSMS - Laboratoire de Simulation en Mécanique des
# Solides)
#
# Tamaas 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.
#
# Tamaas 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 Tamaas. If not, see <http://www.gnu.org/licenses/>.
# -----------------------------------------------------------------------------
from
__future__
import
print_function
import
tamaas
as
tm
import
numpy
as
np
from
numpy.linalg
import
norm
from
numpy.fft
import
fft2
,
ifft2
def
make_profile
(
f
,
profile
,
k
):
x
=
np
.
linspace
(
0
,
1
,
profile
.
shape
[
0
],
endpoint
=
False
)
y
=
np
.
linspace
(
0
,
1
,
profile
.
shape
[
1
],
endpoint
=
False
)
x
,
y
=
np
.
meshgrid
(
x
,
y
)
profile
[:,
:]
=
f
(
2
*
k
*
np
.
pi
*
y
)
def
sin_profile
(
profile
,
k
):
make_profile
(
np
.
sin
,
profile
,
k
)
def
cos_profile
(
profile
,
k
):
make_profile
(
np
.
cos
,
profile
,
k
)
def
test_bem_grid
():
"""Checking that all the pipes are clean"""
tm
.
initialize
(
1
)
size
=
128
k
=
1
E
=
0.91
nu
=
0.3
mu
=
E
/
(
2
*
(
1
+
nu
))
pressure
=
np
.
zeros
((
size
,
size
))
surface
=
np
.
zeros
((
size
,
size
))
westergaard_disp
=
np
.
zeros
((
size
,
size
))
cos_profile
(
pressure
,
k
)
cos_profile
(
surface
,
k
)
bem
=
tm
.
BemGridPolonski
(
surface
)
bem
.
setElasticity
(
E
,
nu
)
bem
.
computeInfluence
()
bem
.
getTractions
()[:,
:,
2
]
=
pressure
[:,
:]
bem
.
computeDisplacementsFromTractions
()
displacements
=
bem
.
getDisplacements
()
# Constructing vertical displacement solution
cos_profile
(
westergaard_disp
,
k
)
westergaard_disp
*=
(
1
-
nu
**
2
)
/
(
E
*
np
.
pi
*
k
)
westergaard_norm
=
(
1
-
nu
**
2
)
/
(
E
*
np
.
pi
*
k
)
*
np
.
sqrt
(
0.5
)
*
size
# Computing error
error
=
norm
(
displacements
[:,
:,
2
]
-
westergaard_disp
)
/
westergaard_norm
assert
error
<
1e-10
,
"Error in normal displacement"
# Constructing horizontal displacement solution
sin_profile
(
westergaard_disp
,
k
)
westergaard_disp
*=
(
2
*
nu
-
1
)
/
(
4
*
np
.
pi
*
k
*
mu
)
westergaard_norm
=
np
.
abs
(
2
*
nu
-
1
)
/
(
4
*
np
.
pi
*
k
*
mu
)
*
np
.
sqrt
(
0.5
)
*
size
error
=
norm
(
displacements
[:,
:,
1
]
-
westergaard_disp
)
/
westergaard_norm
assert
error
<
1e-10
,
"Error in horizontal displacement"
# Looking at normal vectors
normals
=
np
.
zeros
((
size
,
size
,
3
))
normals_norm
=
np
.
zeros
((
size
,
size
,
3
))
sin_profile
(
normals
[:,
:,
1
],
k
)
normals
[:,
:,
1
]
*=
2
*
np
.
pi
*
k
normals
[:,
:,
2
]
=
1
x
=
np
.
linspace
(
0
,
1
,
size
,
endpoint
=
False
)
y
=
np
.
linspace
(
0
,
1
,
size
,
endpoint
=
False
)
x
,
y
=
np
.
meshgrid
(
x
,
y
)
normals_norm
[:,
:,
0
]
=
np
.
sqrt
(
1
+
4
*
np
.
pi
**
2
*
k
**
2
*
np
.
sin
(
2
*
np
.
pi
*
k
*
y
)
**
2
)
normals_norm
[:,
:,
1
]
=
np
.
sqrt
(
1
+
4
*
np
.
pi
**
2
*
k
**
2
*
np
.
sin
(
2
*
np
.
pi
*
k
*
y
)
**
2
)
normals_norm
[:,
:,
2
]
=
np
.
sqrt
(
1
+
4
*
np
.
pi
**
2
*
k
**
2
*
np
.
sin
(
2
*
np
.
pi
*
k
*
y
)
**
2
)
normals
/=
normals_norm
bem
.
computeSurfaceNormals
()
bem_normals
=
bem
.
getSurfaceNormals
()
error
=
norm
(
bem_normals
-
normals
)
assert
error
<
1e-9
,
"Error in surface normals"
tm
.
finalize
()
if
__name__
==
"__main__"
:
test_bem_grid
()
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