STRESSED STATE OF A TRANSVERSALLY ISOTROPIC MEDIUM WITH NON-CANONICAL CAVITIES

A spatial boundary value problem is considered for a transversely isotropic medium bounded by closed non-canonical surfaces obtained by rotating regular hexagons with rounded corners around one of their axes, with comprehensive stretching and compression. One of the effective approximate methods for studying the stress state of a deformable body with different boundary surfaces is a variant of the approximate method of boundary shape perturbation, developed and tested in the works of O. Guz and Yu. Nemish. In this case, boundary problems for an infinite medium bounded in the middle by non-canonical surfaces of revolution are formally reduced to a sequence of boundary problems for a medium with spherical surfaces. Articles [2, 3] are devoted to the use of the approximate method of boundary shape perturbation in solving boundary problems of mathematical elasticity theory. Numerical results are obtained for some transversely isotropic materials. The influence of material anisotropy on the stress concentration factor is analyzed. The boundary shape perturbation method was used to obtain solutions to the problem of the stress-strain state of thick layered shells of revolution [10]. In this case, the general solution of the equilibrium equations for an isotropic medium in a spherical coordinate system was used. The calculations allowed us to analyze the stress-strain state of shells under the action of internal and external pressure. The numerical results of the analysis of the stress-strain state of the shells can be added to the works of M. Leonov and K. Rusynka, V. Panasyuk, L. Berezhnytsky, S. Yarema, L. Ratych, and M. Stashchuk. [13-15], who evaluate the stress-strain state of composite materials with various defects. The latter use various criteria for the limit assessment of composites.