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variational formulation
11

As you have not supplied to mesh, I’ve changed the problem to a 2D problem.
If you would like to to the point force (or any pointwise boundary condition), you need to remove the on_boundary argument from your topbc function, and add pointwise to the topbc. I’ve illustrated how to use a pointforce in the code below:

from dolfin import *
mesh = UnitSquareMesh(10,10)
E = Constant(1e5)
nu = Constant(0.3)

mu = E/2/(1+nu)
lmbda = E*nu/(1+nu)/(1-2*nu)

def eps(v):
    return sym(grad(v))

def sigma(v):
    return lmbda*tr(eps(v))*Identity(2) + 2*mu*eps(v)

V = VectorFunctionSpace(mesh, 'Lagrange', degree=2)
f = Function(V)
du = TrialFunction(V)
u_ = TestFunction(V)
a = inner(sigma(du),eps(u_))*dx
l = inner(f, u_)*dx

def basebc(x, on_boundary):
    return near(x[1],0.) and on_boundary

X = 0.5
desloc_top = -1e6
def topbc(x,on_boundary):
    return near(x[1],1) and near(x[0], X)

bc_base = DirichletBC(V.sub(1), Constant(0.), basebc)
bc_top = DirichletBC(V.sub(1), Constant(desloc_top), topbc,"pointwise")
bc_top.apply(f.vector())
File("f.pvd") << f
u = Function(V, name='Displacement')
solve(a == l, u, bcs=[bc_base])
File("uh.pvd") << u

To use a point deformation, change the size of desloc_top to something reasonable (like 0.05), and add the bc back into the solve command:

V = VectorFunctionSpace(mesh, 'Lagrange', degree=2)
f = Constant((0,0))
du = TrialFunction(V)
u_ = TestFunction(V)
a = inner(sigma(du),eps(u_))*dx
l = inner(f, u_)*dx

def basebc(x, on_boundary):
    return near(x[1],0.) and on_boundary

X = 0.5
desloc_top = -0.05
def topbc(x,on_boundary):
    return near(x[1],1) and near(x[0], X)

bc_base = DirichletBC(V.sub(1), Constant(0.), basebc)
bc_top = DirichletBC(V.sub(1), Constant(desloc_top), topbc,"pointwise")

u = Function(V, name='Displacement')
solve(a == l, u, bcs=[bc_base, bc_top])
File("uh.pvd") << u