[Getfem-users] about dirichlet boundary conditions

[Michel Dupront]

Hello,
 I am a new user.
 I attached a small python script that I am using
to understand how getfem++ works.
 Here I am trying to cruch a cube.
 In this case the three components of the displacement are imposed at each node
of the boundary.
 For example at the top surface the imposed displacement is such that  u_x = 0,
u_y = 0 and u_z =-0.3.
 Is it possible (and how?) to impose only one component of the displacement
at only one point?
 For example I would like to impose only ux=0,uy=0 and let uz free
at a corner point.

Thank in advance


script
====


import getfem as gf
import numpy as np

tol = 1.e-6

mesh = gf.Mesh('regular_simplices', np.arange(0,1.1,0.1), np.arange(0,1.1,0.1), np.arange(0,1.1,0.1))

mfu = gf.MeshFem(mesh,3)
mfu.set_fem(gf.Fem('FEM_PK(3,1)'))

mim = gf.MeshIm(mesh, gf.Integ('IM_TETRAHEDRON(1)'))

Points = mesh.pts()
ctop     = (abs(Points[2,:] - 1) < tol)
cbot     = (abs(Points[2,:]    ) < tol);

pidtop=np.compress(ctop, range(0, mesh.nbpts()))
pidbot=np.compress(cbot, range(0, mesh.nbpts()))

ftop     = mesh.faces_from_pid(pidtop)   
fbot     = mesh.faces_from_pid(pidbot)

BD_TOP = 1
BD_BOT = 2

mesh.set_region(BD_TOP,ftop)
mesh.set_region(BD_BOT,fbot)

md = gf.Model('real')
md.add_fem_variable('u', mfu)

E=1e5
Nu=0.3
Lambda = E*Nu/((1+Nu)*(1-2*Nu))
Mu =E/(2*(1+Nu))
md.add_initialized_data('lambda', [Lambda])
md.add_initialized_data('mu', [Mu])

md.add_isotropic_linearized_elasticity_brick(mim,'u','lambda','mu')

deltaZ = -0.3
md.add_initialized_data('bd_top', [0.,0.,deltaZ])
md.add_Dirichlet_condition_with_multipliers(mim, 'u', mfu, BD_TOP, 'bd_top')
md.add_initialized_data('bd_bot', [0.,0.,0.])
md.add_Dirichlet_condition_with_multipliers(mim, 'u', mfu, BD_BOT, 'bd_bot')

md.solve()

u = md.variable('u')
mfu.export_to_pos('u.pos',u,'Computed solution')