A general scheme for the solution of linear elastic quasi-periodic fracture problems is presented. The simplest type of such problems is characterized by a nonperiodic stress state in a domain with translational symmetry. Employing the discrete Fourier transform reduces the initial problem to a problem of a representative cell with speci®c boundary conditions which may be solved analytically or numerically. The procedure for solving the problem by the ®nite element method is developed. The suggested technique is employed for the solution of the problem of antiplane deformation of a strip weakened by a periodic array of arbitrary loaded cracks.

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