dolfin team mailing list archive

[Catherine Micek <mice0012@xxxxxxx>]

Hi,

I'm a (relatively) new user to the Fenics system and have a  
question.  I'm not sure if this is the correct place to send this,  
but I couldn't find anything
in the repository or the manuals (perhaps there's a relevant example  
somewhere I missed ... ?), so I ended up here.

I'm using Fenics to study the equations of linear elasticity (in a  
mixed Stokes formulation), which allows me to directly compute a  
displacement U and
pressure P.  In addition to these two variables, I am interested in  
the stress of the system. I have been able to obtain the stress by  
defining a suitable
projection:

	stresselement = VectorElement("Discontinuous Lagrange", "triangle",  
1, 9)
	S = TrialFunction(stresselement)
   	T = TestFunction(stresselement)

	a = dot(S, T)*dx
	# Sigma is the symmetric stress computed from the displacement, U
   	L = dot(Sigma, t)*dx

and then solving the resulting linear system for S.  Next, I would  
like to do some calculations with the stresses; for example,  
integrate the stress along a boundary.
To do this, I need the stress vector, s = Sn, where n is the normal  
on the boundary.  However, I am unclear how to do this, as I have  
defined the stress as a 9-component
vector instead of a 3x3 matrix (and n will be defined as a 3  
component vector if I use the FacetNormal function).

Any suggestions on how to handle this?  Thanks!

Katy