The second mixed boundary value problem is solved by the classical theory of thin plate bending. The mixed boundary consists of a boundary (M) on which one respective component of external force and deflective angle are given, and on the remaining boundary the external forces are given. The boundary (M) is straight and the remaining boundary is arbitrary configuration. A closed solution is obtained. Complex stress functions and a rational mapping function are used. A half-plane with a crack is analyzed under a concentrated torsional moment. Stress distributions before and after the crack initiation, and stress intensity factors are obtained for from short to long cracks and for some Poisson’s ratio.

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