Розрахунок локально навантажених тонких ортотропних замкнених конічних оболонок на основі класичної та деяких уточнених теорій

M. V. Marchuk, R. I. Tuchapskyi

Анотація


Реалізовано напіваналітичні алгоритми розв’язування задач про напружено-деформований стан тонких ортотропних зрізаних замкнених конічних оболонок під дією локальних навантажень, для моделювання яких використано дельтоподібні функції. Алгоритми використовують системи рівнянь теорій оболонок Кірхгоффа–Лява, типу Тимошенка та методу {m,n}-апроксимації, розв’язаних відносно частинних похідних першого порядку за координатою вздовж меридіана (при цьому всі невідомі функції, що в них входять, виражено через компоненти векторів розв’язків і частинні похідні за кільцевою координатою від них). Ці системи рівнянь записано в спеціальній формі і з використанням тригонометричних рядів Фур’є за кільцевою координатою зведено до послідовностей незв’язаних нормальних систем звичайних диференціальних рівнянь, які можна розв’язувати за допомогою методу ортогональної прогонки С. К. Годунова. Отримані результати свідчать про надійність реалізованих алгоритмів і важливість уточнених теорій оболонок для адекватного опису тривимірного напруженого стану.

 

Зразок для цитування: М. В. Марчук, Р. І. Тучапський, “Розрахунок локально навантажених тонких ортотропних замкнених конічних оболонок на основі класичної та деяких уточнених теорій”, Мат. методи та фіз.-мех. поля, 67, №3-4, 172-194 (2024), https://doi.org/10.15407/mmpmf2024.67.3-4.172-194


Ключові слова


конічна оболонка, локальне навантаження, теорія Кірхгоффа–Лява, теорія типу Тимошенка, метод {m,n}-апроксимації, тригонометричний ряд, метод ортогональної прогонки С. К. Годунова

Посилання


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