1.4: Stress Concentration in Plate with Hole¶
Geometry and Boundary Conditions¶
Loading: A uniform unit pressure load
Material¶
Isotropic (stress will be the same irrespective of material)
Results¶
From reference [6]
Stress concentration factor \(K_t = 2.233\) based on equation below (where \(d\) is hole diameter and \(W\) is plate width):
\[K_t = 3 - 3.14 \left( \frac{d}{W} \right) + 3.667 \left( \frac{d}{W} \right)^2 - 1.527 \left( \frac{d}{W} \right)^3\]
Theoretical stress concentration value using the formula in [6] = 3.72 Pa
Stress Concentration ( \(\sigma_{xx}\), in Pa)¶
Resolution |
Theory [6] |
Intact Direct Solver [%Error] |
Intact Iterative Solver [%Error] |
Time (s) to solve with <3% error |
|---|---|---|---|---|
10,000 |
3.72 |
3.34 [10.09%] |
3.34 [10.09%] |
|
50,000 |
3.72 |
3.55 [4.47%] |
3.55 [4.47%] |
|
100,000s |
3.72 |
3.62 [2.61%] |
3.69 [2.56%] |
Direct: 7.8 / Iterative: 66 |