Chornenkyi A. Plane problems of the theory of elasticity for a quasi-orthotropic body with holes, notches and cracks

In the thesis the main relations of the plane problem of the theory of elasticity for a quasi-orthotropic body are obtained. The first basic problem for the plane with cracks is reduced to singular integral equations on curvilinear contours in the auxiliary mathematical plane of a complex variable which depends on the basic mechanical orthotropic parameter (the ratio of the basic modulus of elasticity of the material). An analogy between the problems of elasticity theory for isotropic and quasi-orthotropic bodies is established for the first time. This analogy is that the singular integral equations in a quasi-orthotropic body are the same as in an isotropic one, only written in the auxiliary plane of a complex variable. Solutions of eigenvalue problem for the quasi-orthotropic wedge are found. The similar solutions are obtained for a quasi-orthotropic plane with a semi-infinite rounded V-notch by the use of the method of singular integral equations. Based on these solutions the relationships between the stress intensity and concentration factors of the sharp and rounded vertices of the angular notch in the quasi-orthotropic plane are established. On this basis, in a similar way to the corresponding problems for the isotropic body, the unified approach to defining the stress concentration in sharp or rounded notches is developed. The method of singular integral equations is also used to construct the solution of the first main problem of the theory of elasticity for the quasi-orthotropic half-plane with a periodic curvilinear edge, and the integral equation is obtained from a periodic system of curvilinear cracks, which are joined together.