Фундаментальні розв’язки для кусково-однорідного трансверсально-ізотропного пружного простору

O. F. Kryvyi, Yu. O. Morozov

Анотація


Проблема побудови фундаментальних розв’язків для кусково-однорідного трансверсально-ізотропного простору зведена до матричної задачі Рімана в просторі узагальнених функцій повільного зростання, для якої запропоновано метод розв’язування. В результаті отримано в явному вигляді вирази для компонент вектора фундаментального розв’язку, а також прості подання для компонент тензора напружень і вектора переміщень у площині з’єднання трансверсально-ізотропних пружних півпросторів, які знаходяться під дією зосереджених нормальних і дотичних сил. Досліджено поля напружень і переміщень у площині з’єднання півпросторів. Зокрема, для деяких комбінацій матеріалів наведено числові значення коефіцієнтів впливу зосереджених сил на напруження і переміщення. Встановлено також умови, при яких відсутні нормальні переміщення в площині з’єднання трансверсально-ізотропних пружних півпросторів.

 

Зразок для цитування: О. Ф. Кривий, Ю. O. Морозов, “Фундаментальні розв’язки для кусково-однорідного трансверсально-ізотропного пружного простору,” Мат. методи та фіз.-мех. поля, 63, No. 1, 122–132 (2020).


Ключові слова


фундаментальні розв’язки, матрична задача Рімана, трансвер- сально-ізотропний неоднорідний простір, узагальнені функції

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