Abstract: Based on the general formulas of N.I.Muskhelishvili about a plate under concentrated loads, the more generalized formulas with arbitrary transform function, Z = ω(ξ), were derived. By these formulas and a few terms of the transform function,the problems of infinite plate with a hole and finite plate with arbitrary outside bounds were solved in closed form. These results were applied to analysing the problem of the damaged plate reinforced by all kinds of glued patchs.

Key words: conformal mapping, damage, crack, stress intensity factor