Berchun Y. Mathematical and experimental modeling of extended systems

The dissertation carried out mathematical modeling and experimental studies of the stress-strain state of extended systems in the field of mass and surface forces. For the first time: a physically and geometrically nonlinear hyperbolic four-mode mathematical model of the ES was developed and its correctness was proved for individual cases. A method, algorithm, and program for parallelizing computations by the propagation velocities of the waves of the dynamics of extended systems have been developed, and their effectiveness has been proved. It was further developed: mathematical modeling of the stress-strain state of reinforced concrete piles and anti-landslide structures under the conditions of distributed and concentrated dynamic effects of various intensities and magnitudes; experimental monitoring studies of the construction of reinforced concrete piles 40 m long at a landslide hazardous construction site in Kyiv and experimental vibration studies of anti-landslide structures of the Lviv Railway. The results of mathematical modeling of anti-landslide structures showed their own 20 oscillation frequency - 9.46 Hz, and the experimentally recorded natural oscillation frequency is 10.2 Hz. Differences in the vast majority of calculated and experimental indicators did not exceed 18% - 15%. The results of monitoring studies of building structures are summarized in the form of a new regulatory document of Ukraine DSTUN B V.1.2-17: 2016, which has been put in force since April 2017.