Abstract
Taking the crack opening displacement (COD) as the unknown function and the resultant force as the right hand term (RHD) in the resulting integral equation, a singular integral equation for the circular arc crack problem is formulated. Similarly, taking the jump of the resultant force along the circular arc rigid line as the unknown function and the prescribed displacement as the RHD, a singular integral equation for the circular arc rigid line problem is obtainable. It is proved that Vekua's regularization is possible for the proposed singular integral equations. In the case of remote stress, solutions in a closed form are derived.
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