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Drawn obround slot 4:1 across the load: boundary-element K_t = 5.09 against Inglis's tip-radius estimate 5.0

ToolDrawn Cutout
SourceInglis, C. E. (1913). "Stresses in a Plate Due to the Presence of Cracks and Sharp Corners." Transactions of the Institution of Naval Architects, Vol. 55, pp. 219–241 (K_t = 1 + 2√(a/ρ)); Brebbia, C. A., Telles, J. C. F., and Wrobel, L. C. (1984). Boundary Element Techniques: Theory and Applications in Engineering. Springer-Verlag, Berlin.
LevelGraduate

Problem

A 0.1 in plate carries 10,000 lb/in in y and contains a 4 in long, 1 in wide slot with semicircular ends lying along x. Find the peak hoop stress on the slot and the stress concentration factor, and compare with Inglis's estimate for an ellipse of the same half-length and tip radius.

Inputs to Enter

  • N_xx = 0, N_yy = 10000 lb/in, N_xy = 0, t = 0.1 in (σ = 100 ksi)
  • Cutout: the default obround slot, 4 in × 1 in (half-length a = 2 in, end radius ρ = 0.5 in), drawing grid 0.25 in
  • Corner radius r_c = 0.5 in (equal to the end radius, so the facets carry no kinks)
Open the Drawn Cutout tool (loaded with this example)

Answers

  • K_t = 5.09 at the slot ends: σ_edge,max = 509 ksi
  • Inglis 1 + 2√(a/ρ) = 1 + 2√(2/0.5) = 5.0 for an ellipse of the same half-length and tip radius
  • Slots of 2:1 and 8:1 give 3.86 and 6.85 (changelog harness values)

Notes

The tool's default inputs are this case. Enter a corner radius at least equal to a template arc's radius; below it the polygon keeps kinks and the peak rises (5.99 for the default slot at a smaller radius). The solver caps the mesh at 320 elements.

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