Consider the elliptical hole problem in Example 11.7. By letting a→0, determine the stress field for the case where the hole reduces to a line crack of length 2b. Demonstrate the nature of the singularity for this case.

Data from example 11.7

Table 11.2

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Consider next an infinite anisotropic plate with a stress-free elliptical hole. The plate is loaded in the x direction, as shown in Fig. 11.10. Recall that the isotropic case was previously solved in Example 10.7. The potentials for this problem can be determined by our previously developed conformal mapping procedures from Example 11.6. The details for this and other cases are given in Savin (1961), and the final result may be written as 01 (21) = A121 iSb 2(4-4) iSb 2(-1) P2 (22) = A222 +: a - iub 21+2 - (a + ub) a- iub 22+2(a + 1b) - (11.5.48) The first term in each expression corresponds to the uniform tension case discussed in Example 11.3. For tension in the x direction, the constants become