MET 415 Notes / Singularity

Prof. Dave Johnson, psuprofdj@psu.edu, Penn State - Erie, The Behrend College

SINGULARITY:
 

2D Beam, Fixed At Left End, With Mid-Span (knife-edge) Support and Tip Load (knife-edge)

Evaluating: the Normal Stress on Outermost Fibers, SX

Case 1: Singularity at Point Support (knife-edge)

Case 2: Singularity at Excessive Constraint (fixed condition on entire end – prevents Poisson’s contraction)

Case 3: Singularity at Point Load

Stress at a singularity is artificially high (and always increases even higher with mesh refinement).  Recognize conditions of singularity and ignore results local to the singularity point.

  Irregular (esp. jagged contours) usually indicate a problem – stress results should be smooth, if they are not, we should understand why not.

  Often decisions/assumptions we make to simplify our models cause these effects

 

[Not Shown: Singularity also occurs at an inside, sharp corner]