Makhorkin M. 2 D elasticity theory problems for a wedge system with thin radially located defects

Using the method of generalized conjugation problems the antiplane and plane elasticity theory problems (concerning the study of the stress-strain state in a system consisting of arbitrary number of wedges and thin radially oriented defects) is reduced to seeking the solution to the boundary-value problem for one and two partially degenerated differential equations. The structure of singular components of general solutions to such problems is determined under all possible boundary conditions. Their Mellin-representation (the reccurent dependences for a plane elasticity theory problem and that explicit - for the antiplane one ) is constructed. The characteristic equations are written. For some configurations of the system under longitudinal shear the formulas are found to calculate their roots. The notion of generalized stress-intensity factors of a wedge system is introduced and the procedure for calculation of their values is developed. The analogy between the asymptotic solutions of boundary-value problems in the vicinity of salient points of the surfaces of materials with linearly and bilinearly elastic behaviour (or material with linear strengthening) is found. For particular boundary conditions, configurations and ways of loading the system the singularities of stress fields, the values of generalized stress-intensity factors of a wedge system and distributions of stress fields and specific potential strain energy in the vicinity of two or three wedges meeting are studied analytically and numerically