Tools › Structures › Stress Concentrations › Drawn Cutout › Example
Two drawn equal holes with centres three radii apart under tension across the line: boundary-element 3.266 against the two-hole series 3.264
| Tool | Drawn Cutout |
| Source | Ling, C.-B. (1948). "On the Stresses in a Plate Containing Two Circular Holes." Journal of Applied Physics, Vol. 19, No. 1, pp. 77–82; Haddon, R. A. W. (1967). "Stresses in an Infinite Plate with Two Unequal Circular Holes." Quarterly Journal of Mechanics and Applied Mathematics, Vol. 20, No. 3, pp. 277–291 (3.264 at a gap of one radius). |
| Level | Graduate |
Problem
Two round cutouts of unit radius are drawn with centres 3 radii apart on the x axis (a gap of one radius) in a plate under unit tension along y. Find the peak hoop stress and the stresses at the point (1.5, 1) between the holes, and compare with the two-hole series solution.
Inputs to Enter
- Tension along y, σ = 1
- Two circle templates of radius 1 at (0, 0) and (3, 0) (test script: 120 points each, 480 elements)
- Corner radius 0
Answers
- Max hoop / σ on hole 1 = 3.2657 against the Two Holes tool's series 3.2641 (Haddon 3.264)
- Point (1.5, 1): σ_yy 1.5947 / σ_xx −0.1058 against the series 1.595 / −0.1051
- Far point (40, 10): σ_yy 1.0011, σ_xx 0.0011 (the far field recovered)
Notes
Values from test-scripts/test_bem_cutout.php (tolerance 1.5 %). The test's comment calls the spacing a one-diameter gap; with centres three radii apart the gap is one radius, which is the geometry the 3.264 belongs to. 480 elements take about 7 s; the tool caps the mesh at 320 elements, so draw the holes with fewer points.