Integration points 2

[waterice]

Hi experts,

Could someone tell me where are stresses and displacements calculated? Are they calculated at the nodes or at the integration points?

Thanks and regards,
Siddharth Premkumar.

 

[Drej]

In linear implicit FE, the fundamental quantity calculated is displacement, which is derived from the relationship F=K.x (F=nodal force, K=stiffness, x=displacement). The stiffness (matrix) is obtained from the structure, whilst the nodal forces can be obtained separately from the loading and model boundary conditions. The stiffness matrix K can then be inverted to find displacement at the nodes. Once this is known, the strains are obtained across the element and are calculated at the element integration points from which the stresses are then derived (also at the IPs).

In FE post-processing packages, the stresses can be listed/contoured at the integration points or can be extrapolated to the nodes. Most packages show stresses as contour plots, and by default these are either a pure extrapolation at the nodes, or an extrapolation PLUS averaging across elements.


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[waterice]

Thank you!......that was very helpful.....

 

[aeroafrix2]

check previous eng-tips post for detailed discussion on this issue. I can't remember the link but you might want to do a good search.

Alternatively you might want to consult Robert D Cook's book on "Finite Element Modelling for Stress Analysis" page 60 under 'Plane Stress'. Very informative and practical explaination/discussion on this issue.