Incompatible constructor arguments for inner product

Linear Algebra
1

Hello community,

I’m working on elastic deformation of rotational symmetric cases. Therefore somebody gave me an example which I try to adapt.

The code of this example is:

from __future__ import print_function
from dolfin import *
from mshr import *
import matplotlib.pyplot as plt
#get_ipython().run_line_magic('matplotlib', 'notebook')

Re = 11.
Ri = 9.
rect = Rectangle(Point(0., 0.), Point(Re, Re))
domain = Circle(Point(0., 0.), Re, 100) - Circle(Point(0., 0.), Ri, 100)
domain = domain - Rectangle(Point(0., -Re), Point(-Re, Re))                 - Rectangle(Point(0., 0.), Point(Re, -Re))

mesh = generate_mesh(domain, 40)
plot(mesh)

class Bottom(SubDomain):
    def inside(self, x, on_boundary):
        return near(x[1], 0) and on_boundary
class Left(SubDomain):
    def inside(self, x, on_boundary):
        return near(x[0], 0) and on_boundary
class Outer(SubDomain):
    def inside(self, x, on_boundary):
        return near(sqrt(x[0]**2+x[1]**2), Re, 1e-1) and on_boundary  
    
facets = MeshFunction("size_t", mesh, 1)
facets.set_all(0)
Bottom().mark(facets, 1)
Left().mark(facets, 2)
Outer().mark(facets, 3)
ds = Measure("ds", subdomain_data=facets)

x = SpatialCoordinate(mesh)

def eps(v):
    return sym(as_tensor([[v[0].dx(0), 0, v[0].dx(1)],
                          [0, v[0]/x[0], 0],
                          [v[1].dx(0), 0, v[1].dx(1)]]))

E = Constant(1e5)
nu = Constant(0.3)
mu = E/2/(1+nu)
lmbda = E*nu/(1+nu)/(1-2*nu)
def sigma(v):
    return lmbda*tr(eps(v))*Identity(3) + 2.0*mu*eps(v)

n = FacetNormal(mesh)
p = Constant(10.)

V = VectorFunctionSpace(mesh, 'CG', degree=1)
du = TrialFunction(V)
u_ = TestFunction(V)
a = inner(sigma(du), eps(u_))*x[0]*dx

At first I tried to change the geometry and run the script until that point is reached.

from __future__ import print_function
from dolfin import *
from mshr import *
import matplotlib.pyplot as plt
#get_ipython().run_line_magic('matplotlib', 'notebook')
Ra=11
Ri=9
lz=2
#-----------------------------------------------------------------------------2D-domain and mesh
domain= Rectangle(Point(Ri, 0), Point(Ra, lz))
mesh = generate_mesh(domain, 10)

#-----------------------------------------------------------------------------2D-Boundarydefinition
class house(SubDomain):
    def inside(self, x, on_boundary):
        return near(x[0], Ra, 1e-1) and on_boundary
class rod(SubDomain):
    def inside(self, x, on_boundary):
        return near(x[0], Ri, 1e-1) and on_boundary
class outer(SubDomain):
    def inside(self, x, on_boundary):
        return near(x[1], lz, 1e-1) and on_boundary
class inner(SubDomain):
    def inside(self, x, on_boundary):
        return near(x[1], 0, 1e-1) and on_boundary

facets = MeshFunction("size_t", mesh, 1)
facets.set_all(0)
inner().mark(facets, 1)
house().mark(facets, 2)
outer().mark(facets, 3)
rod().mark(facets, 4)
ds = Measure("ds", subdomain_data=facets)

x = SpatialCoordinate(mesh) 
def eps(v):
    return sym(as_tensor([[v[0].dx(0), 0, 0.5*(v[1].dx(0)+v[0].dx(1))],
                          [0, v[0]/x[0], 0],
			   [0.5*(v[1].dx(0)+v[0].dx(1)), 0, v[1].dx(1)]]))
                         
E = Constant(1e5)
nu = Constant(0.3)
mu = E/2/(1+nu)
lmbda = E * nu/(1+nu)/(1-2 * nu)
def sigma(v):
return lmbda * tr(eps(v)) * Identity(3) + 2.0 * mu * eps(v)    

n = FacetNormal(mesh)
p = Constant(10.)

V = VectorFunctionSpace(mesh, 'CG', degree=1)
du = TrialFunction(V)
u_ = TestFunction(V)
a = inner(sigma(du), eps(u_))*x[0]*dx

Now, I get the error, that eps and sigma are not compatible for the inner product. And exactly, by printing both, there is a clear difference between them. But I don’t get why. Sigma is computed from eps in exactly the same way in both codes? Or not?

Thank you very much for any help.

Florian

2

Please reformat the code such that indentation is preserved.

This should be the case if you encapsulate your code with 3x` after copy pasting it from a text editor

3

what do you mean with that? “3x`” and “```” both do not work.

4

3x` as in ``` should render code as follows:

def test(x):
    return x[0]
1 Like
5

:slight_smile: :slight_smile: like that? :slight_smile: :slight_smile:

6

This is because you have overloaded the function inner with this class. Change the name of this class.

2 Likes