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I have written my own finite element code for a linear elastic (plane stress) problem consisting of a plate with a circular hole in the middle, fixed on one side, having a tensile force acting on the other side.

I have obtained displacements and calculated the stresses and strains at the nodes. I want to calculate the stress concentration factor numerically and compare it with theoretical values for the same case.

I understand that the stress concentration factor $K_{t}$ is given by

$$ K_t = \frac{\sigma_{max}}{\sigma_{nom}} $$

$\sigma_{max}$ is very easy to find but I have trouble understanding how to calculate $\sigma_{nom}$ for my problem.

Any help would be appreciated!

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$\sigma_{\text{nom}}$ is the stress in the component without a hole.

You should be able to calculate that by hand, without needing to create another FE model ;)

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  • $\begingroup$ Thanks for the answer! This may seem like a silly follow up question but my plate also has some fillets with stresses concentrated near them in addition to the central hole. Do I have to consider a plate without holes and fillets to calculate the nominal stress? $\endgroup$ – Anirudh N Jun 22 at 9:39
  • $\begingroup$ Link to diagram: imgur.com/gxiY5VG $\endgroup$ – Anirudh N Jun 22 at 9:47
  • $\begingroup$ Since you have large holes and large fillets compared with the size of the plate, all the features will interact with each other and it's not very obvious what a single "stress concentration factor" would mean anyway. If you make the plate longer (theoretically, infinitely long) with no fillets and only one hole, this will give you theoretical solutions: amesweb.info/StressConcentrationFactor/…. For a very small hole, the stress concentration factor is exactly 3 For bigger holes, it is less. $\endgroup$ – alephzero Jun 22 at 18:30

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