Plotting 3D elastic model in paraview

1

Hi I am a new user to with fenics. I have a stupid question. I tried to solve a 3D elasticity problem, and my code runs okay. It’s a cantilever beam problem with force applied. I wanted to plot its bending figure. But when I tried to plot it in my spyder on anaconda, it failed. Also, I tried to save it and plotted it with paraview. It failed too. The displacement in the function is “u”. The code is show below:

from __future__ import print_function
from dolfin import *
from fenics import *
import matplotlib.pyplot as plt
import math
import ufl
from mpl_toolkits import mplot3d
import numpy as np
from mpl_toolkits.mplot3d import Axes3D


L = 25.
H = 1.
T = 1.
Nx = 25
Ny = 5
Nz = 5
mesh = BoxMesh(Point(0., 0., 0.), Point(L, H, T), Nx, Ny, Nz)


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

E = Constant(1e5)
nu = Constant(0.3)

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


def sigma(v):
    return lmbda*tr(eps(v))*Identity(3) + 2.0*mu*eps(v)

rho_g = 1e-3
f = Constant((0, -rho_g, 0))
V = VectorFunctionSpace(mesh, "CG", degree = 1)


du = TrialFunction(V)
u_ = TestFunction(V)
a = inner(sigma(du), eps(u_))*dx
l = inner(f, u_)*dx

def left(x, on_boundary):
    return near(x[0], 0.)

bc = DirichletBC(V, Constant((0., 0., 0.)), left)


u = Function(V, name="Displacement")
solve(a == l, u, bc) 

plot(u)

The saving codes are:

file = XDMFFile("output.xdmf")
file.write(u, 0)

I also tried .pvd, but it failed too. I hope someone could help me out with this hard problem. Thanks a lot.

2

Could you post the error you get while plotting, and which version of dolfin are you using? Your code runs fine and simply doing

XDMFFile("test.xdmf").write(u)

works just fine in paraview !

displacement
displacement1242×535 14.8 KB

3

Also, for simple 3D problems you could also use vtkplotter, namely, for your example

from dolfin import *
from vtkplotter.dolfin import plot as vplot
# code here to write solution in the function `u`
vplot(u)

There is an extensive set of examples in vtkplotter and specifically in vtkplotter.dolfin. But for larger, more complicated problems paraview would be better.

4

Thanks a lot for your help. Sorry for the late reply. My dolfin version is 2019.1.0. And my paraview is 5.8.0. Is that okay to do the plot?

5

Hi I just made it out! the vtkplot works for me! Thank you so much!

6

There is a bug in Paraview 5.8.0, see: Error in opening 3D plots in fenics and .pvd files in Paraview 5.8.0 in Ubuntu 19.04

7

Yes this should work. I have paraview 5.6 on my windows machine but I expect this to work on 5.8 too unless it didn’t install properly.
Edit: Dokken already posted the link to the discussion I was about to post.
Also just for completeness:

from dolfin import *

is the same as

from fenics import *

and you may need to explicitly import ufl only in very selected cases. For the most part importing dolfin with wildcards should work. Also, dolfin's plot would work fine for 2D functions as is but not 3D.

8

I see. Thank you for your help!