Effective solution of the fundamental quasi-periodic problems of the theory of elasticity for a plane with cuts distributed along a straight line (Q1314185)

The method of the Riemann boundary value problem for a denumerable set of contours is used to solve the fundamental quasi-periodic problems of the theory of elasticity for a plane with cuts distributed along a straight line. The solutions are obtained in explicit form as ``ordinary'' ``corrected'' Cauchy-type integrals along a denumerable set of segments of the real axis, and uniformly converging series of simple fractions whose coefficients are found from an infinite system of linear algebraic equations. Formulae are obtained for the stress intensity factors and their asymptotic expressions for the cuts situated near infinity. Numerical examples are given for the quasi-linear problem of the theory of cracks.