Question 17.CS.3: Stress Concentration in a Plate with a Hole in Uniaxial Tens......
Stress Concentration in a Plate with a Hole in Uniaxial Tension
A thin plate containing a small circular hole of radius a is subjected to uniform tensile load of intensity \sigma _0 at its edges, as shown in Figure 17.16(a). Apply the FEA to determine the theoretical stress-concentration factor.
Given: L=24 \text { in., } a=2 \text { in., } h=20 \text { in., } \sigma_0=6 ksi , E=10 \times 10^6 \text { psi, } \nu=0.3 .
Owing to the symmetry, only any one-quarter of the plate needs to be analyzed (Figure 17.16(b)). The solution for the case in which the quarter plate discretized to contain 202 CST elements is given in [1]. The roller boundary conditions are also indicated in the figure. The values of the normal edge stress \sigma _x obtained by the FEM and the theory of elasticity are plotted in Figure 17.16(c) for comparison. We see from the figure that the agreement is reasonably good. The stress-concentration factor for \sigma _x is K_t \approx 3 \sigma_0 / \sigma_0=3 .