Consider the problem of a stress-free hole in an infinite domain under equal and uniform farfield loading T, as shown in Fig. 8.11 . The plane strain radial displacement solution for this problem is found to be:

where r₁ is the hole radius. Using the appropriate transformation relations from Table7.1 , determine the corresponding displacement for the plane stress case. Next develop a comparison plot for each case of the radial displacement versus radial distance r with Poisson’s ratio v = 0.4 . Use dimensionless variables and plot u_r/(Tr₁/E) versus r/r₁ over the range 0 ≤ r/r₁ ≤10. Which displacement is larger and what happens as Poisson’s ratio goes to zero? Finally plot the dimensionless radial displacement on the hole boundary r = r₁ versus Poisson’s ratio over the range 0 ≤v≤ 0.5 .

Fig 8.11

Table 7.1

Transcribed Image Text:

Ur v) 2 T(1+1) [(1 E (12v)r + r