Question:
I am a graduate student at Ohio University, Athens. I am working on a
software called Alpid 2-D. I am planning to implement error estimation
in stress calculations. I have a small problem here. The stress output
given out by the software is at the centroid at each element and I need
the stresses at each node.
Answer:
I'd be interested in how you actually do the error estimate.
Ansys calculates a percentage error in a global energy norm.
I think that it calculates the strain energy in two ways and
compares the two results. The first estimate is obtained with
the element by element stress solution. The second estimate
is obtained after "nodal stress averaging." This makes it
possible for the program to determine how to adapt a finite
element mesh, i.e., alter the mesh on the basis of the local
error norm calculation. But the error estimate is not an
accurate measure of the actual error in a solution. I've
done enough numerical experiments with ansys to convice
myself of this. In fact, the supplier of ansys warns users
to not use the error norm calculation as an error estimate.
The supplier suggests that that particular error norm
should be used only to QUALITATIVELY compare multiple
finite element meshes. For most engineers, that is pretty
useless, since we usually are interested only in the accuracy
of the solution at a point, say, at a fillet or small hole.
Error calculations on the basis of some global energy norm
just don't cut it, in my opinion. I have a model with which
I've shown that the actual error increases at the same time
that the percentage error in the energy norm decreases.
The problem solved is that of a nearly infinite rectangular
plate with a centrally located hole. The plate is subjected
to a uniform tension in one direction. The peak tensile
stress, which occurs at the top and bottom of the hole, is
three times the uniform stress. With the model I can
calculate just about any value of error in the energy norm,
with no correlation to the actual error. In my opinion,
that is not only useless but dangerous, particularly in
the hands of trusting individuals.
For my research, I am using spectral super elements to compute
dynamic stress concentration factors and dynamic stress intensity
factors. Here I use simple constant strain plane stress triangular
elements. I obtained the the nodal stresses by averaging the
stresses of all the elements connected to the node in question.
I compared this solution with my spectral element solution.
