Following similar procedures as in Section 10.9, establish a Westergaard stress function method for skew-symmetric crack problems.

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Following similar procedures as in Section 10.9, establish a Westergaard stress function method for skew-symmetric crack problems. For this case, assume that loadings are applied skew-symmetrically with respect to the crack, thereby establishing that the normal stress σy vanishes along y = 0. Show that this leads to the following relations:

x = 2ReZ(z)  ylmz' (z) %y = ylmz' (z) Txy=-ImZ(z) - YRez' (2)-B where Z(z) = 2y' (2) and B is a real constant.

Data from section 10.9

10.9 Westergaard method for crack analysis As mentioned, Westergaard (1937) developed a specialized complex

Using the stress combination definitions (10.2.11), we eliminate the potential and find ox2 Re[y' (2)] -

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