On 01/12/08 09:33 AM, Garth N. Wells wrote:
Bartosz Sawicki wrote:
On 01/12/08 09:07 AM, Garth N. Wells wrote:
Bartosz Sawicki wrote:
Hi all,
I can't find anything in the manuals, any example in the demo
directory and even google is silent like a grave, when asked for
"anisotropy site:fenics.org".
Does it mean that anisotropy is not supported by FEniCS?
Can you be more specific on what you have in mind?
My question is, if anyone has already tried to solve any anisotropic
problem with fenics?
One of the problems, which come to my mind is that for anisotropic
material I need at tensor function for material property. Can FFC
handle this?
Just define the equation you want to solve and try compiling it with
FFC. For an anisotropic solid, part of this will involve defining the
constitutive model. The DOLFIN library shouldn't need to be (nor
should it be) aware of the details of the constitutive model.
Yes, I know that, but there is a problem with anisotropic material
property which is in general case described by tensor.
Let's look on example. Simple Poisson equation form:
element = FiniteElement("Lagrange", "tetrahedron", 1)
v = TestFunction(element)
u = TrialFunction(element)
f = Function(element)
g = Function(element)
k = Constant("tetrahedron")
a = k*dot(grad(v), grad(u))*dx
L = v*f*dx + v*g*ds
In case of anisotropy, k (material property) shouldn't be "scalar
constant", but rather "tensor constant" over the element.
For Poisson I can manage with "vector constant", but that's definitely
not a general approach:
k = VectorConstant("tetrahedron")
a = (k[0]*D(v,0)*D(u,0) + k[1]*D(v,1)*D(u,1) + k[2]*D(v,2)*D(u,2))*dx
How would you advice to describe tensor function or tensor constant in
the form? Is it possible?
