Antonenko N. The solution of elasticity theory boundary problems for layered media with elastic connections between the layers

The study suggests the method of quadrature solution of basic elasticity theory boundary problems for multilayer bases with elastic connections between layers. The spatial, flat and axisymmetric deformations of bases of this type are considered. The technique is based on Fourier integral transformation and Hankel integral transformation. The influence of coefficients of elastic connections on the distribution of stresses and displacements in the layers of one-layer and two-layer bases is researched. The solution for the problem of unilateral contact between a smooth strip and a multilayer basis with normal elastic connections on their common border is offered. This problem is a generalization of the classical problem of unilateral contact between a strip and a semi-plane. The research dwells on normal fracture interface cracks with adhesive filler. The integro-differential equations for the problem of a crack with filler between an elastic multilayer stack and a semi-plane are created. Тhe problem of a penny-shaped crack with filler between an elastic layer and a semi-space is solved for the case of axisymmetric deformation. The solutions for all types of integral and integro-differential equations which were derived in the work are offered. The computer programs for the solution of all problems which were considered in work are developed. Numerical computations were carried out. The mechanic effects are offered.