Area weighted average

General
1

Hello,

I have carried out a linear elastic simulation in 2D and calculated the stresses. Now I want to average the stresses over the area according to this rule:

1p0n9

With:
A_i : Area of element i
Sigma_x,i : Stress xx at the middel of element i
A_total: total Area of the domain

I created the mesh in Gmsh, wrote an msh file, which I then imported with meshio to create an xdmf file. Here is the code:

with XDMFFile(MPI.COMM_WORLD, "/home/fenics/shared/my_mesh.xdmf", "r") as xdmf:
    domain = xdmf.read_mesh(name="Grid")
    ct = xdmf.read_meshtags(domain, name="Grid")
domain.topology.create_connectivity(domain.topology.dim, domain.topology.dim - 1)
with XDMFFile(MPI.COMM_WORLD, "/home/fenics/shared/my_mesh.xdmf", "r") as xdmf:
    ft = xdmf.read_meshtags(domain, name="Grid")

As you can see the mesh is very irregular in shape and size of the elements:

Bildschirmfoto vom 2023-12-14 20-04-02
Bildschirmfoto vom 2023-12-14 20-04-021535×783 124 KB

I suspected that there was something like a cell index that could be used to directly access the area of the element and the global coordinates of the center point, but I couldn’t find anything.

I would be very grateful for any help

2

Isn’t that just the domain integration (surface integration)?

\bar\sigma = \frac{\int \sigma dS}{\int dS}

i.e. (not exact syntax, but similar to)

area = scalar_assemble(Constant(1)*dx)  #  note this is not the correct syntax for Constant
stress = assemble(sigma*dx)
average_stress = stress / area
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