Journal of Theoretical
and Applied Mechanics

37, 1, pp. 47-63, Warsaw 1999

Antiplane problems for anisotropic layered media with thin elastic inclusions under concentrated forces and screw dislocations

Georgiy Sulym, Sava Shevchuk
The antiplane problem of elasticity theory for a layered anisotropic medium containing the plane ribbon inhomogeneities is solved using the jump function method. The external load is determined by the boundary conditions, concentrated forces and screw dislocations inside layers. The inclusions are modelled by jumps of the stress and displacement vectors on the middle surfaces. Using the Fourier integral transform we obtain the relation between the stress tensor and displacement vector components and the external load and unknown functions of jumps. Taking into account the conditions interaction of between thin inclusion and anisotropic environment, the problem is reduced to a system of singular integral eÄ…uations in the functions of jumps. In a general case the last is solved by means the collocation method. Some example is considered to illustrate the method.
Keywords: elastic inclusion; antiplane state of strain; concentrated force; dislocation