1.4: Stress Concentration in Plate with Hole

Geometry and Boundary Conditions

Loading: A uniform unit pressure load

../../../_images/benchmark1-5-setup.png

Material

Isotropic (stress will be the same irrespective of material)

Results

From reference [6]

Stress concentration factor Kt = 2.233 based on equation below (d is hole diameter and W is plate width):

../../../_images/benchmark1-5-eqn.png

Theoretical stress concentration value using the formula in [6] = 3.72 Pa

Stress Concentration (Sigma_xx, in Pa)

Num of Elements

Theory [6]

Intact Direct Solver [%Error]

Intact Iterative Solver [%Error]

Time (s) to solve with <3% error

10K

3.72

3.34 [10.09%]

3.34 [10.09%]

50K

3.72

3.55 [4.47%]

3.55 [4.47%]

100K

3.72

3.62 [2.61%]

3.69 [2.56%]

Direct: 7.8 / Iterative: 66