/[escript]/trunk/doc/examples/usersguide/lame.py
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Contents of /trunk/doc/examples/usersguide/lame.py

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Revision 5213 - (show annotations)
Wed Oct 22 05:59:37 2014 UTC (5 years ago) by jduplessis
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nlpde example for user guide
1 #set up domain and symbols
2 from esys.escript import *
3 from esys.finley import Rectangle
4 from esys.weipa import saveSilo
5 mydomain = Rectangle(l0=1.,l1=1.,n0=10, n1=10)
6 u = Symbol('u',(2,), dim=2)
7 q = Symbol('q', (2,2))
8 sigma=Symbol('sigma',(2,2))
9 theta = Symbol('theta')
10 # q is a rotation matrix represented by a Symbol. Values can be substituted for
11 # theta.
12 q[0,0]=cos(theta)
13 q[0,1]=-sin(theta)
14 q[1,0]=sin(theta)
15 q[1,1]=cos(theta)
16 # Theta gets substituted by pi/4 and masked to lie between .3 and .7 in the
17 # vertical direction. Using this masking means that when q is used it will apply
18 # only to the specified area of the domain.
19 x = Function(mydomain).getX()
20 q=q.subs(theta,(symconstants.pi/4)*whereNonNegative(x[1]-.30)*whereNegative(x[1]-.70))
21 # epsilon is defined in terms of u and has the rotation applied.
22 epsilon0 = symmetric(grad(u))
23 epsilon = matrixmult(matrixmult(q,epsilon0),q.transpose(1))
24 # For the purposes of demonstration, an arbitrary c with isotropic constraints
25 # is chosen here. In order to act as an isotropic material c is chosen such that
26 # c00 = c11 = c01+c1+2*c55
27 c00 = 10
28 c01 = 8; c11 = 10
29 c05 = 0; c15 = 0; c55 = 1
30 # sigma is defined in terms of epsilon
31 sigma[0,0] = c00*epsilon[0,0]+c01*epsilon[1,1]+c05*2*epsilon[1,0]
32 sigma[1,1] = c01*epsilon[0,0]+c11*epsilon[1,1]+c15*2*epsilon[1,0]
33 sigma[0,1] = c05*epsilon[0,0]+c15*epsilon[1,1]+c55*2*epsilon[1,0]
34 sigma[1,0] = sigma[0,1]
35 sigma0=matrixmult(matrixmult(q.transpose(1),sigma),q)
36 # set up boundary conditions
37 x=mydomain.getX()
38 gammaD=whereZero(x[1])*[1,1]
39 yconstraint = FunctionOnBoundary(mydomain).getX()[1]
40 # The nonlinear PDE is set up, the values are substituted in and the solution is
41 # calculated y represents an external shearing force acting on the domain.
42 # In this case a force of magnitude 50 acting in the x[0] direction.
43 p = NonlinearPDE(mydomain, u, debug=NonlinearPDE.DEBUG0)
44 p.setValue(X=sigma0,q=gammaD,y=[-50,0]*whereZero(yconstraint-1),r=[1,1])
45 v = p.getSolution(u=[0,0])
46 saveSilo("solution",solution=v)

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