Математичне моделювання імпульсної взаємодії з наскрізним отвором у товстому шарі (кососиметричний випадок)

• Datum: 2025
• Hauptverfasser: Kovalev , Yuriy, Panchenko , Borys, Severyn , Mykola, Perekrestov , Ihor
• Format: Artikel
• Sprache: Ukrainian
• Veröffentlicht: V.M. Glushkov Institute of Cybernetics of NAS of Ukraine 2025
• Schlagworte: тривимірні динамічні крайові задачі; сингулярні інтегральні рівняння; чисельний експеримент; імпульсний вплив
• Online Zugang: https://jais.net.ua/index.php/files/article/view/513
• Назва журналу: Problems of Control and Informatics

This paper presents a new mathematical model for solving a dynamic (impact) skew-symmetric boundary value problem for a layer weakened by a through hole, with sliding clamping of the edges. In industry, especially in heavy machinery and transport (rolling mills or heavy-duty vehicles), structural elements such as roller bearings are widely used. The load-bearing element here is the roller. It represents a cylinder whose ends operate under conditions of sliding clamping. Both solid hollow rollers (to reduce weight) and rollers with fillers (for reinforcement) are utilized. Problems modeling the stress state of the roller under conditions of impulse or impact loading are particularly relevant. This paper models the stress state of a layer (skew-symmetric case) weakened by a cylindrical hole under conditions of impulse or impact loading. Such an external boundary value problem is reduced to a system consisting of 3k (k = 1, 2,…) singular integral equations (SIE) of the 2nd kind. The algorithm for modeling the stress-strain state (SSS) of a solid roller (internal problem) is similar to the algorithm for solving the external problem. For such modeling, it is only necessary to reverse the signs of the extra-integral terms. Similar problems under static or dynamic loading have been con-sidered in many studies. The result is the characterization of the SSS of a layer weakened by a through hole under impact or impulse loading. In this work, a comparison with results obtained by the series method for a similar problem showed satisfactory convergence. A new method based on a system of three singular integral equations was developed and numerically tested. As a result of high-precision numerical investigation, it was revealed that with an increase in the impulse length, there is an increase in the relative circumferential stress. With short impulses, a wave-like damping process occurs in the ε-neighborhood of the origin, due to the inertia of the system, a zone of negative stresses appears, which, interacting with a positive impulse, generates this process. A similar situation also occurs when the impulse is removed. Corresponding graphs are provided.