The evaluation of stress intensity factors for surface flaw problems and, in particular, semi-elliptical surface cracks in cylindrical pressure vessels has been well developed using the finite element alternating method. Some of the examples presented here include the interaction effects due to multiple internal longitudinal surface cracks in cylinders as recommended for analysis in the ASME Boiler and Pressure Vessel Code (Section XI). For each crack geometry, several loading cases are considered including internal pressure and polynomial pressure loadings from constant to fourth order. By the method of superposition, the magnification factors for internally pressurized cylinders are rederived using the polynomial influence functions. These influence functions give useful information for design purposes such as in the analysis of a thermally shocked cylinder. The problem of a single circumferential crack in a cylinder is also investigated using the finite element alternating method, and a number of results for such problems are also presented here.

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