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
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
