Boundary value problems of elasticity theory in areas with thin inclusions

The report will provide a brief overview of the author's results in the field of boundary value problems of elasticity theory. Various mathematical models describing the behavior of bodies with thin inclusions (cracks, beams, rods, etc.) will be considered. The issues of solvability of the corresponding boundary value and variational problems, the asymptotic properties of their solutions, the construction of numerical algorithms, as well as applications to problems of fracture mechanics, mechanics of composites and optimal control of the shape of the area will be discussed. In particular, the problem of averaging the dynamic model of a thermoelastic composite reinforced with thin thermoelastic fibers will be considered.