Analysis tipsTips-Tricks

Analysis of re-entrant stresses in Finite Element Analysis (FEA)

This tip relates to analysis of re-entrant stresses in Finite Element Analysis (FEA). Consider a tee bracket subjected to a horizontal force. This is just a simple example, but as the mesh refinement increases the corner stress is shown to be diverging - not converging! How do you know what the actual stress will be?

The corner stress can be calculated easily by hand, but this example shows one of the challenges of using FEA accurately.

mesh stress1

The hand calculated stress at the joint is 60MPa (calculated from first principles here). So initially the stress is underestimated, then apparently over estimated, with the expected stress lying somewhere between.

This is a classic FEA problem, and in short, the actual corner stress cannot be determined from this FE model. The stresses will not converge because of the re-entrant corner (crack). If this part was made of glass (or another brittle material) it would break. But because most materials yield, this part would live fine for ductile materials and static loads. However, for a fatigue load case, even metals would fail due to this kind of stress concentration. Some simple redesign would address this issue by adding fillets etc. The FEA is correct in highlighting the location of stress concentration, but the magnitude of the stress at the crack is completely unreliable and purely dependant on the mesh size used.

For complex problems where the stresses are difficult to derive accurately, there are a number of approximate methods available to the advanced analyst - give Greg a call on 03 382 5282 or email him to discuss further training or analysis options.