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hertz.py
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Sun, Sep 22, 11:22
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text/x-python
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Tue, Sep 24, 11:22 (1 d, 23 h)
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rTAMAAS tamaas
hertz.py
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#!/usr/bin/env python
# @file
# @section LICENSE
#
# Copyright (©) 2016-19 EPFL (École Polytechnique Fédérale de Lausanne),
# Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU Affero General Public License as published
# by the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program 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 Affero General Public License for more details.
#
# You should have received a copy of the GNU Affero General Public License
# along with this program. If not, see <https://www.gnu.org/licenses/>.
import
tamaas
def
dumpHertzPrediction
(
file
,
bem
,
pressure
,
r
,
E
):
A
=
tamaas
.
SurfaceStatistics
.
computeContactArea
(
bem
.
getTractions
())
Aratio
=
tamaas
.
SurfaceStatistics
.
computeContactAreaRatio
(
bem
.
getTractions
())
radius
=
np
.
sqrt
(
A
/
np
.
pi
)
#L = bem.getSurface().getL()
L
=
1.
load
=
pressure
*
L
*
L
radius_hertz
=
pow
(
0.75
*
load
*
r
/
E
,
1.
/
3.
)
p0_hertz
=
1.
/
np
.
pi
*
pow
(
6.
*
E
*
E
*
load
/
r
/
r
,
1.
/
3.
)
p0
=
tamaas
.
SurfaceStatistics
.
computeMaximum
(
bem
.
getTractions
())
n
=
bem
.
getTractions
()
.
shape
[
0
]
computed_load
=
bem
.
getTractions
()
.
sum
()
/
n
/
n
*
L
*
L
file
.
write
(
"{0}
\t
{1}
\t
{2}
\t
{3}
\t
{4}
\t
{5}
\t
{6}
\t
{7}
\t
{8}
\t
{9}
\n
"
.
format
(
pressure
,
load
,
computed_load
,
Aratio
,
A
,
radius
,
radius_hertz
,
radius_hertz
/
radius
,
p0
,
p0_hertz
))
################################################################
def
main
(
argv
):
parser
=
argparse
.
ArgumentParser
(
description
=
'Hertz test for the Boundary element method of Stanley and Kato'
)
parser
.
add_argument
(
"--N"
,
type
=
int
,
help
=
"Surface size"
,
required
=
True
)
parser
.
add_argument
(
"--r"
,
type
=
float
,
help
=
"radius of hertz sphere"
,
required
=
True
)
parser
.
add_argument
(
"--steps"
,
type
=
int
,
help
=
"number of steps within which the pressure is applied."
,
required
=
True
)
parser
.
add_argument
(
"--precision"
,
type
=
float
,
help
=
"relative precision, convergence if | (f_i - f_{i-1})/f_i | < Precision."
,
required
=
True
)
parser
.
add_argument
(
"--e_star"
,
type
=
float
,
help
=
"effective elastic modulus"
,
required
=
True
)
parser
.
add_argument
(
"--L"
,
type
=
float
,
help
=
"size of the surface"
,
required
=
True
)
parser
.
add_argument
(
"--max_pressure"
,
type
=
float
,
help
=
"maximal load requested"
,
required
=
True
)
parser
.
add_argument
(
"--plot_surface"
,
type
=
bool
,
help
=
"request output of text files containing the contact pressures on the surface"
,
default
=
False
)
parser
.
add_argument
(
"--nthreads"
,
type
=
int
,
help
=
"request a number of threads to use via openmp to compute"
,
default
=
1
)
args
=
parser
.
parse_args
()
arguments
=
vars
(
args
)
n
=
arguments
[
"N"
]
r
=
arguments
[
"r"
]
max_pressure
=
arguments
[
"max_pressure"
]
Ninc
=
arguments
[
"steps"
]
epsilon
=
arguments
[
"precision"
]
Estar
=
arguments
[
"e_star"
]
L
=
arguments
[
"L"
]
plot_surface
=
arguments
[
"plot_surface"
]
nthreads
=
arguments
[
"nthreads"
]
pressure
=
0.
dp
=
max_pressure
/
float
(
Ninc
)
s
=
np
.
zeros
((
n
,
n
))
print
s
.
shape
for
i
in
range
(
0
,
n
):
for
j
in
range
(
0
,
n
):
x
=
1.
*
i
-
n
/
2
y
=
1.
*
j
-
n
/
2
d
=
(
x
*
x
+
y
*
y
)
*
1.
/
n
/
n
*
L
*
L
if
d
<
r
*
r
:
s
[
i
,
j
]
=
-
r
+
np
.
sqrt
(
r
*
r
-
d
)
else
:
s
[
i
,
j
]
=
-
r
print
"
\n
::: DATA ::::::::::::::::::::::::::::::
\n
"
print
" [N] {0}
\n
"
.
format
(
n
)
print
" [r] {0}
\n
"
.
format
(
r
)
print
" [Pext] {0}
\n
"
.
format
(
max_pressure
)
print
" [Steps] {0}
\n
"
.
format
(
Ninc
)
print
" [Precision] {0}
\n
"
.
format
(
epsilon
)
bem
=
tamaas
.
BemPolonski
(
s
)
bem
.
setEffectiveModulus
(
Estar
)
file
=
open
(
"hertz-prediction"
,
'w'
)
file
.
write
(
"#pressure
\t
load
\t
computed-load
\t
area_ratio
\t
area
\t
radius
\t
radius-hertz
\t
radius/radius-hertz
\t
p0
\t
p0-hertz
\n
"
)
for
i
in
range
(
0
,
Ninc
):
pressure
+=
dp
bem
.
computeEquilibrium
(
epsilon
,
pressure
)
A
=
tamaas
.
SurfaceStatistics
.
computeContactAreaRatio
(
bem
.
getTractions
())
dumpHertzPrediction
(
file
,
bem
,
pressure
,
r
,
Estar
)
if
A
==
1.0
:
file
.
close
()
break
tamaas
.
dumpTimes
()
################################################################
import
sys
import
argparse
import
numpy
as
np
main
(
sys
.
argv
)
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