A hole in a plate -- Sigma_rr magnitude 1

[FEAppp]

It's a very basic problem in order to know how the stress distribute around the hole.
After the analysis, in the visualization, I created a cylindrical coordinate system in order to visualize the stress sigma_rr, sigma_tt.
In principal, the sigma_rr around the hole need to be zero because it’s a free surface.
So I extract the value around the circumference of the hole. However, the result shows otherwise. We could see that the sigma_rr acts as a sine wave.
I get it that the sigma_rr cannot be exactly zero, but I am confused where the sine wave pattern comes from.
As for the sigma_tt, it’s correct. Because as for the analytical solution, the sigma_tt around the hole should be like a sine wave

Did I do something wrong?
Thanks a lot.

Wenjing

 

[FEA way]

Kirsch’s problem assumes infinite plate. Try with larger plate (compared with the size of the hole). You can use symmetry to solve it faster.

Also refine the mesh, especially around the hole. Bias is the best choice here.