Abstract: In this paper, the least square method of determination of the perturbation parameter is presented when the perturbation technique is used in the solution of large deflection of axisymmetrical plates and shallow shells. The examples of circular plates are calculated and compared with the exact solution and other perturbation solutions. The results show the best agreement with the exact solution among those perturbation solutions.

Key words: periodical crack, interfacial crack, anisotropic elastoplastic fracture of bi-rnaterial, antiplane problem, Dugdale-Barenblatt (D-B ) model, crack openning displacement (COD)