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from __future__ import division
##############################################################################
#
# Copyright (c) 2003-2018 by The University of Queensland
# http://www.uq.edu.au
#
# Primary Business: Queensland, Australia
# Licensed under the Apache License, version 2.0
# http://www.apache.org/licenses/LICENSE-2.0
#
# Development until 2012 by Earth Systems Science Computational Center (ESSCC)
# Development 2012-2013 by School of Earth Sciences
# Development from 2014 by Centre for Geoscience Computing (GeoComp)
#
##############################################################################
__copyright__="""Copyright (c) 2003-2018 by The University of Queensland
http://www.uq.edu.au
Primary Business: Queensland, Australia"""
__license__="""Licensed under the Apache License, version 2.0
http://www.apache.org/licenses/LICENSE-2.0"""
__url__="https://launchpad.net/escript-finley"
from esys.escript import *
from esys.escript.linearPDEs import LinearPDE
from esys.weipa import saveVTK
try:
from esys.finley import Brick
HAVE_FINLEY = True
except ImportError:
print("Finley module required but not available")
HAVE_FINLEY = False
if HAVE_FINLEY:
#... set some parameters ...
lam=1.
mu=0.1
alpha=1.e-6
xc=[0.3,0.3,1.]
beta=8.
T_ref=0.
T_0=1.
#... generate domain ...
mydomain = Brick(l0=1.,l1=1., l2=1.,n0=10, n1=10, n2=10)
x=mydomain.getX()
#... set temperature ...
T=T_0*exp(-beta*length(x-xc))
#... open symmetric PDE ...
mypde=LinearPDE(mydomain)
mypde.setSymmetryOn()
#... set coefficients ...
C=Tensor4(0.,Function(mydomain))
for i in range(mydomain.getDim()):
for j in range(mydomain.getDim()):
C[i,i,j,j]+=lam
C[i,j,i,j]+=mu
C[i,j,j,i]+=mu
msk=whereZero(x[0])*[1.,0.,0.] \
+whereZero(x[1])*[0.,1.,0.] \
+whereZero(x[2])*[0.,0.,1.]
sigma0=(lam+2./3.*mu)*alpha*(T-T_ref)*kronecker(mydomain)
mypde.setValue(A=C,X=sigma0,q=msk)
mypde.getSolverOptions().setVerbosityOn()
#... solve pde ...
u=mypde.getSolution()
#... calculate von-Misses
g=grad(u)
sigma=mu*(g+transpose(g))+lam*trace(g)*kronecker(mydomain)-sigma0
sigma_mises=sqrt(((sigma[0,0]-sigma[1,1])**2+(sigma[1,1]-sigma[2,2])**2+ \
(sigma[2,2]-sigma[0,0])**2)/2. \
+3*(sigma[0,1]**2 + sigma[1,2]**2 + sigma[2,0]**2))
#... output ...
saveVTK("deform.vtu",disp=u,stress=sigma_mises)
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