Pasternak I. Two dimensional stress state of solids containing thin structural components

The thesis considers the development of mathematical models and methods for numeric-analytical and numerical analysis of two-dimensional (plane, antiplane and axisymmetric) stress-strain and limit state of elastic solids containing thin shapes. The numeric-analytical method is developed for determination of the stress-strain state of solids containing inclusions, in particular thin ones. The stress field induced by thin rectangular inclusion is studied. Basing on the results of this method different implementations of ordinary BEM are analysed as applied to the inclusion problem. It is shown that the most efficient is the usage of regularized equations and quadratic or cubic boundary elements. The regularization approach is developed and applied to the integral equations of antiplane anisotropic and plane isotropic elasticity. Thus, both singular and nearly-singular integrals are regularized and the boundary layer effect is completely eliminated. This approach shows high efficiency for the analysis of solids containing thin shapes, especially for the anisotropic solids, where the error of nonlinear transformation technique for nearly-singular integral evaluation is significant. Singular and hypersingular integral equations of axisymmetric elasticity are completely regularized and the continuous to the boundary equations are obtained. Thus, stresses and displacements can be evaluated in the whole domain continuously up to the boundary. These equations are applied to the analysis of axisymmetric solids containing thin inclusions and thread connections. For the determination of limit state estimation parameters, in particular generalized SIF, several methods are developed. The dependence between M- and J-integral and GSIF is obtained. The physical sense of the J-integral for elastic inclusion is considered. The dominant GSIF and mutual integral approaches are developed for GSIF decomposition. Another approach for determination of GSIF is developed basing on the least square method and generalized asymptotic expansion approximation. Considered are the two-dimensional problems for the bounded and unbounded solids with thin linear and curved inclusions. The polynomial conservation principle is studied as applied for bounded solids. Stress concentration in the hydroturbine unit thread connections is considered. Basing on the numerical results simple formula for determination of the maximal stress concentration is obtained. Basing on the correlation function approach the SIF of surface cracks in the thread connection is estimated.