Tools › Structures › Stress Concentrations › Drawn Cutout

Drawn Cutout in Infinite Plate under General In-plane Load

Stresses around one or more cutouts of any shape drawn on the screen, in an infinite plate under a uniform far-field state given as the resultants Nxx, Nyy, Nxy and the thickness t. The plate is solved by the boundary element method (Kelvin's fundamental solution, constant elements on the cutout edges, the far field superposed), so no formula for the particular shape is needed: slots, rounded squares, D-holes, keyholes, clusters of holes. Sharp corners are rounded with the entered corner radius, because a sharp re-entrant corner has an infinite elastic stress. The tool reports the hoop-stress extremes on every cutout edge with their positions, Kt referred to the maximum far-field principal stress, the stress field as fringe plots, and the hoop stress around each edge.

  • Draw the cutouts by clicking points or from the templates (circle, ellipse, slot, rounded rectangle); several cutouts interact

  • Boundary element solution with Kelvin's fundamental solution: checked against Kirsch (circle), Inglis (ellipse) and the two-hole series

  • Hoop-stress extremes and Kt = σedge,max / S1 for every cutout; fringe plots of the tangential and maximum principal stress

  • Corner radius applied to every drawn corner; a sharp corner is singular and must not be analysed as drawn

Loads and Cutout Geometry

Unit System: /

Far-field Loads and Thickness





Draw the Cutouts


Click on the grid to add points. Drag a point to move it; right-click (or select + delete point) to remove it. A selected point makes the next click insert after it.
Template:

Solution Settings





References

Brebbia, C. A., Telles, J. C. F., and Wrobel, L. C. (1984). Boundary Element Techniques: Theory and Applications in Engineering. Springer-Verlag, Berlin.

Kelvin, Lord (Thomson, W.) (1848). "Note on the Integration of the Equations of Equilibrium of an Elastic Solid." Cambridge and Dublin Mathematical Journal, Vol. 3, pp. 87–89.

Michell, J. H. (1899). "On the Direct Determination of Stress in an Elastic Solid, with Application to the Theory of Plates." Proceedings of the London Mathematical Society, Vol. 31, pp. 100–124.

Kirsch, G. (1898). "Die Theorie der Elastizität und die Bedürfnisse der Festigkeitslehre." Zeitschrift des Vereines deutscher Ingenieure, Vol. 42, No. 29, pp. 797–807.

Inglis, 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.

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.

Pilkey, W. D., and Pilkey, D. F. (2008). Peterson's Stress Concentration Factors, 3rd ed. John Wiley and Sons, Hoboken, NJ.

Worked Examples

Published examples this tool reproduces; each page lists the inputs to enter and the printed answers.

All worked examples

DISCLAIMER: The methods and calculation on aNOWysis.com are provided as means to educate the reader. There is no warranty, expessed or implied, as to the relevance or accuracy of the methods or calculations. All calculations should be checked by a qualified analyst for appropriateness and accuracy. We will not be held liable for any damages, injuries or deaths caused by using methods or calculations from this site.