STRESS CONCENTRATION OF A CIRCULAR HOLE

In this section, we consider the stress concentration factor (SCF) for a centrally-located circular hole in a finite-width plate subjected to a "uniform" uniaxial tension load. Figure 9 shows the plates as defined and Figure 10 shows the refined mesh of triangular elements, consisting of 2732 nodes, which is the mesh that is actually used to solve for the stresses around the hole. For this problem, the ratio of the hole diameter, $D$, to the plate width, $W$, is $D/W=$ 0.131. The uniaxial tension load is applied to the left edge of the model, while the right edge of the model is restrained. The total load that is applied is 1200 kips, and this produces a nominal tension stress of $\sigma_\textrm{t}=$ 3.33 ksi based on the gross cross-sectional area.

Figure 9: Plate with Hole – Original Mesh

Figure 10: Plate with Hole – Refined Computational Mesh

Figure 11 shows the computed stress distribution around the hole. The maximum stress that is obtained here is $\sigma_{\textrm{max}}=$ 9.43 ksi, giving an estimate for the SCF value of 2.83. This compares quite favourably with the SCF value of 3.06 at the edge of the hole that is obtained using the formula provided in Chart 4.1 in Pilkey (1997). In comparison, for a uniaxially-loaded infinite plate with a circular hole, the theoretical SCF is 3. As shown by Howland (1930), the tension stress decays rapidly away from the edge of the circular hole. Thus, the maximum stress computed in the present finite element analysis is commensurate with that behavior, as it is about 7.5% less than the peak tensile stress that occurs at the edge of the hole.

Figure 11: Plate with Hole with Refined Mesh – Stress Around Hole