How extract the displacement field on the boundary?

1

I got the displacement field as solution. I then create a deformed mesh with the displacement field. Now I want to use the displacement in the reverse direction as displacement boundary condition to get back to the original shape. I tired Mesh.Domainboundar(). but I couldn’t find it in my library so I am unable to use it.

  1. How to get the displacement field on the boundary alone.
  2. How to apply it in the deformed mesh without projecting the displacement field onto a deformed mesh:
    import numpy as np
mesh = df.UnitSquareMesh(36,36)
V = df.VectorFunctionSpace(mesh, "Lagrange",2,dim=2)
u=df.project(df.Expression(("x[0]", "x[1]"), degree= 1),df. VectorFunctionSpace(mesh, "CG", 1))
def boundary(x,on_boundary):
    return on_boundary
u_bndry="function to get the displacement on the boundary"
DeformedMesh = df.Mesh(mesh)
X = DeformedMesh.coordinates()
X+=np.vstack(map(u,X))
V_1= df.VectorFunctionSpace(DeformedMesh, "Lagrange",2,dim=2)
D_bc=df.DirichletBC(V_1,-u_bndry,boundary)
2

The following code does exactly what you would like to do without defining a new mesh:

import numpy as np
import dolfin as df
mesh = df.UnitSquareMesh(36,36)
V = df.VectorFunctionSpace(mesh, "Lagrange",2,dim=2)
u=df.project(df.Expression(("2*x[0]", "x[1]"), degree= 1),df. VectorFunctionSpace(mesh, "CG", 1))
def boundary(x,on_boundary):
    return on_boundary
df.ALE.move(mesh, u)
u_out = df.Function(V)
D_bc=df.DirichletBC(V,-u,boundary)
# Add boundary condition to new function to visualize its effect
D_bc.apply(u_out.vector())
df.File("u_on_deformed.pvd") << u_out
3

Does ALE change the vectorFunctionSpace V along with mesh?

4

I’d like to compress the object.

5

The function space is dependent of the mesh, as you are implicitly changing the mesh, you are also changing the function space with this command.

I am not sure what you mean by your last remark:

6

is mesh and function space V are maintained by some call by reference kind of method?

7

The function space contains a reference to the mesh, print for instance V.mesh() and mesh, or the id V.mesh().id() and mesh.id(), or mesh==V.mesh().
ALE.move is an implicit operation that changes the coordinates of your mesh (similar to what you did manually on your deformed mesh).

8

I’d like to solve the problem by defining (sigma:epsilon) in LHS and RHS =0 with the BCS as mentioned above. just changing the displacement field u_out.vector will not ensure what I want, isn’t it?

9

I am not sure what you are asking for now.
What I have shown above is the following:

  1. Deform your mesh with a displacement u
  2. Create a Dirichlet-condition on the deformed mesh which enforces -u on the boundary.

The variable u_out is simply there as a helper for you to see that the boundary condition is applied on the deformed mesh, in the direction opposite to the initial deformation. This is why I apply the boundary condition to u_out and save it to file, so you can visualize it in Paraview.

1 Like
10

Thanks, I see what you mean. It worked well .