Semester of Graduation
Master of Science in Mechanical Engineering (MSME)
Mechanical and Industrial Engineering
Accurately determining stresses at re-entrant corners using finite element analysis (FEA) is challenging due to the high stresses produced at the corner. Indeed, FEA is unable to obtain quantitatively accurate peak stresses at mathematically sharp re-entrant corners with traditional boundary conditions because these stresses are singular. Imposing a local corner radius by rounding the sharp corner to remove the singular result is an appropriate technique for large radii, but as the corner radius tends to zero and the notch is close to being sharp, we expect there are radii that yield quantitatively inaccurate results with traditional FEA. We seek to determine a range of radii that are solved accurately with traditional boundary conditions and determine a finite stress result for a sharp re-entrant corner.
Here, we improve upon traditional boundary conditions by employing cohesive stress-separation laws in an elastic plate for a series of 90-degree V-notches with radii. We use convergence checks and construct test problems to verify our FEA. Then, we determine a range of radii for which traditional FEA is appropriate and accurate. Further, we obtain results for radii which are beyond the applicability of traditional FEA.
Through our analysis, we find that traditional FEA is appropriate for a broad range of notch radii. In addition, we find that the maximum peak stress does not occur for a sharp corner, but rather for a V-notch with a small radius.
Andrus, Trent Mattieu, "On the Stress Concentration at Sharp V-Notches Under Tension" (2020). LSU Master's Theses. 5218.