Перегляд за Автор "Kostyushko, I."

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    Semi-analytical implicit direct time integration method for 1-D gas dynamic problem
    (Igor Sikorsky Kyiv Polytechnic Institute, 2023) Orynyak, I.; Kostyushko, I.; Mazuryk, R.
    Sharp wave treatment for 1-D gas dynamic problem is still a challenge for modern numerical methods. They often require too many space and time steps, produce spurious oscillation of solution, exhibit a strong numerical dissipation or divergence of results. This paper is further extension of authors’ idea of employment the analytical solution for space coordinate, where time step is a parameter which used in the space solution. Its peculiarity consists in development of additional linearization procedure of dependence between the pressure and density. It is performed in premise that actual pressure for each space element is close to the basic pressure, attained at previous moment of time. The efficiency of method is tested on the very popular task of Sod, where two different ideal gases in a tube are separated by diaphragm, which is suddenly broken. The problem considered in Lagrangian coordinates formulation. The results obtained show the very good method efficiency, which requires the essentially lesser time and space steps, leads to no spurious oscillation and give consistent and predictable results with respect to meshing. The accuracy of method is mostly controlled by time step, which should be larger than clearly stated theoretical lower limit. Other advantage of method is that it can calculate the process to any desired time moment, and space meshing can be variable in time and space and can be easily adapted during the process of calculation.
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    Study of motion stability of a viscoelastic rod
    (Igor Sikorsky Kyiv Polytechnic Institute, 2024) Kostyushko, I.; Shapovalov, H.
    Abstract. Stability of non-conservatively loaded elastic and inelastic bodies - a classic section of deformable solid mechanics that has been of interest for many years. In this paper, we study the motion stability of a free rod subjected to a constant tracking force on one of its ends. The problem is interesting in practical application, as it can be viewed as a simplified model of a rocket moving under the action of a jet force. The defining ratio of the rod material is the Kelvin-Voigt model. The solution to the problem is presented as a decomposition of the beam function. The number of terms of this expansion is substantiated. The critical load values in the presence and absence of viscosity are determined. It is established that the existence of a non-zero value of the internal viscosity coefficient in the Kelvin-Voigt model leads to a significant reduction in the critical load value compared to the elastic rod model. The given analytical results are confirmed by numerical calculations.