PLASTINKANING ELASTIK HOLATINI KANTOROVICH-VLASOV VA DIFFERENSIAL HAYDASH USULLARI YORDAMIDA MATEMATIK MODELLASHTIRISH
DOI:
https://doi.org/10.5281/zenodo.20524366Keywords:
Kirchhoff-Love nazariyasi, Kantorovich-Vlasov usuli, differensial haydash usuli, Koshi masalasi, Runge-Kutta usuli, egilish funksiyasi, matematik modellashtirish.Abstract
Mazkur tadqiqot yupqa plastinkalarning egilish va deformatsiya holatini baholash uchun Kirchhoff-Love nazariyasiga asoslangan yangi avtomatlashtirilgan hisoblash algoritmini taqdim etadi. Ikki o'lchovli xususiy hosilali differensial tenglamalarni yechishdagi hisoblash murakkabliklarini bartaraf etish maqsadida Kantorovich-Vlasov variatsion usuli qo'llanilib, masala bir o'lchovli to'rtinchi tartibli oddiy differensial tenglamalar sistemasiga keltirildi. Olingan chegaraviy masala differensial haydash (progonka) usuli orqali boshlang'ich shartli Koshi masalasiga transformatsiya qilindi va to'rtinchi tartibli Runge-Kutta usulida sonli integrallandi. Ishlab chiqilgan algoritm Python dasturlash muhitida to'liq avtomatlashtirildi. Sonli natijalarning analitik yechimlar bilan qiyosiy tahlili shuni ko'rsatdiki, lokal xatolik kompensatsiyasi hisobiga markaziy nuqtalardagi maksimal tafovut 0.51% dan oshmaydi. Bu esa taklif etilayotgan yondashuvning yuqori variatsion barqarorligini tasdiqlaydi.References
Timoshenko S.P., Voynovskiy-Kriger S. Пластинкы и оболочки. M.:Nauka 1966.
L.V. Kantorovich, V.I. Krilov. Priblijennie metodi visshego analiza. M.: Fiziko-matematicheskoy literaturi, 1962.
Samarskiy A.A., Gulin A.V. Chislennie metodi. – M: Nauka, 1989. – 432 s.
Zienkiewicz, O. C., Taylor, R. L., Zhu, J. Z. (2013). The Finite Element Method: Its Basis and Fundamentals. 7-nashr. Butterworth-Heinemann, 756 b.
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2026-06-03
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M.Olimov, M., & E.T.Ismoilov, E. (2026). PLASTINKANING ELASTIK HOLATINI KANTOROVICH-VLASOV VA DIFFERENSIAL HAYDASH USULLARI YORDAMIDA MATEMATIK MODELLASHTIRISH. Science and Innovation, 4(51), 48-50. https://doi.org/10.5281/zenodo.20524366
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