Stress and strains at integration points vs. at the nodes

[Gandhara]

Hi eng-tips community,

In which applications or scenarios would you be interested in using...
1) the stresses/strains at the Gauss Integration points?
2) the unaveraged stresses/strains at the nodes?
3) the averaged stresses/strains at the nodes?

When do you consider it important to discern between the above 3 cases? Any tips or experiences from your own career?

Feel free to share!

 

[FEA way]

1 - when checking stress at particular locations
2 - when verifying the correctness of the results and looking for suspiciously large differences between elements
3 - when checking overall results for the model

 

[centondollar]

FEA way already gave a good description.

Here are my tips:

A) The so-called "superconvergence" of results at integration points is valid only for certain element types and integration schemes. In practice, with a reasonable mesh density, it does not matter if you inspect the stresses mid-element or at integration points

B) Do not use averaged stresses (or so-called "isolines" or "averaged stress countours" or whatever other name the software applies to their method of "averaging") for any analyses which may be considered detailed, e.g., for elastic-plastic analysis with solid or shell elements involving contact (bolt bearing against bolt holes etc.). If you wish to find bending moments of a beam with a "height/2" or similar discretization accuracy, averaging should be less of an issue.

C) Use nodal values of stresses whenever possible, because results will always be most accurate at those points - anything shown inside an element is produced by interpolating the solved nodal degrees of freedom.

Finally, the difficulty in FE analysis is usually not choosing the post-processing, but rather ensuring that everything (geometry, material model, dimension reduction model (beam, plate, shell), kinematic assumptions (moderate rotations or infinitesimal rotations), boundary conditions, non-linearities, loads) is realistically modelled and solved with a robust and reliable solver (Arc length method for snap-through problems, for example) if any non-linearities are present.

The problem is seldom in the numerics, but rather in what you as the user command the FE program to do.