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Exercise 4. Consider an antiplane problem with an elliptical cylindrical hole with vertex a, co-vertex b, and traction applied at infinity til Figure 1: Antiplane problem 1
+ (a) What is the solution for the displacement component u3(x) for this problem in terms of the complex potential o(2) given by it(a + b) 6() - + Cos 24 where H, Cos are material constants, and 2 = x; + ixis a complex number. (b) Derive an expression for uz () in terms of *; and 22. (c) Explain how we can use the solution to derive the solution of an antiplane problem with a symmetric crack (15 marks