Dmytriieva I. The stress state of isotropic elastic-plastic shell with cracks, with regard for material hardening

The thesis is devoted to the investigation of the new research problems of stressed state of elastic-plastic isotropic shells of double curvature, the material of the plastic zones of which are hardened in the process of deformation. One through, surface or internal crack and a system of two collinear through or non-through cracks, located along the lines of one of the principal curvatures of the shell are considered. The method based on the use of two-dimensional integral Fourier transformation within the theory of generalized functions has been used at the construction of integral expression of strengths and moments. The use of this method, combined with generalized to materials with hardening analog of Leonov-Panasyuk-Dugdale model, makes it possible to get a system of singular integral equations for study the stress state of shells of dual curvature with through, surface and internal cracks, oriented along the lines of shell's principal curvatures. The linear law of stress distribution in plastic zones has been used in this problem. Fundamental solution of problems for a plate with one through and one nonthrough crack, with system of two collinear through or nonthrough cracks has been achieved. The influence of plastic zone's material hardening, shell's curvature, external load, crack depth and length and distance between them on plastic zone length and crack opening has been found.