(1) Stress Concentration or Singularity
For linear elastic analysis, there is no converged stress at the areas with stress concentration. The maximum stress is infinite just as the theory predicts. Thus, if there is stress concentration, the maximum stress in a linear elastic analysis is not a useful criterion to validate the structure.
(2) A Beam Example of Stress Concentration
The same beam example in Shear Locking is used here. Fully integrated 20-node elements are used to avoid shear locking. No stress convergence is observed with finer and finer meshes.
(a) Meshing: W x H x L = 4 x 1 x 10. Maximum normal stress in Z = 293 MPa.
(b) Meshing: W x H x L = 16 x 4 x 100. Maximum normal stress in Z = 328 MPa.
(c) Meshing: W x H x L = 32 x 8 x 200. Maximum normal stress in Z = 328 MPa.
(d) Meshing: W x H x L = 64 x 16 x 400. Maximum normal stress in Z = 429 MPa.
(3) A Real-life Example without Consideration of Stress Concentration
This is a shipping frame for SHMS HB magnet manufactured by a vendor. The HB magnet is a baby one, about 2000 lbs. However, a super strong frame was made to ship it to JLab. An educated guess is that solid elements, not beam elements, were used during finite element analysis. With high local stresses due to stress concentration from FEA, very beefy beams had to be used. If beam elements were used, the maximum stress should be much low under any circumstance.
