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Drawn elliptic cutout, a/b = 2 across the load: boundary-element K_t = 4.984 against Inglis's 5

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.
LevelUndergraduate

Problem

An elliptic cutout with semi-axes 2 along x and 1 along y is drawn in a plate under unit tension along y. Find the extreme hoop stresses on the edge and σ_yy at the point (3, 0) on the major axis, and compare with Inglis.

Inputs to Enter

  • Tension along y, σ = 1 (any N_yy / t pair)
  • Ellipse template a = 2 along x, b = 1 along y (test script: 160-point ellipse, 304 elements)
  • Corner radius 0
Open the Drawn Cutout tool

Answers

  • Max hoop / σ = 4.9839 (Inglis 1 + 2a/b = 5), min hoop / σ = −0.9973 (−1)
  • σ_yy at (3, 0) = 1.4082 against the Inglis series 1.4082
  • 304 constant elements, solve about 1.9 s in the test script

Notes

Values from test-scripts/test_bem_cutout.php (tolerance 2 %). The ellipse template is an n-gon; keep the corner radius at zero for it.

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