INVESTIGATION OF INFLUENCE OF LOCAL LOADING ON THE STRESSED STATE OF HOLLOW CYLINDERS WITH CONCAVE CORRUGATED CROSS SECTIONS

  • Ya. M. Grigorenko S.P. Timoshenko Institute of mechanics, NAS of Ukraine
  • L. S. Rozhok National transport university, MEC of Ukraine
Keywords: noncircular hollow cylinders, concave semi-corrugations, discrete Fourier series, discrete-orthogonalization method, local loading, stress state

Abstract

The paper considers solving the problem on equilibrium of noncircular hollow cylinders is performed in spatial formulation at certain boundary conditions at the ends. There were considered hollow cylinders which cross sections are concave semi-corrugations. The paper presents a nontraditional approach to solving boundary-value problems on stress state of spatial bodies. The approach is based on the reduction of two-dimensional problems to one-dimensional one using the discrete Fourier series. The two-dimensional problem contains the geometrical and mechanical parameters as the multipliers on solving functions what makes it impossible to separate variables. Introduction of additional functions, which include resolving functions, and their derivatives together with indicated multipliers, allows to reduce the problem to one-dimensional one through expansion of all the functions into the Fourier series in one coordinate direction. In integrating the one-dimensional boundary-value problem, the amplitude values of additional functions are determined through the Fourier series of functions which are specified at the discrete set of points. The one-dimensional boundary-value problem is solved by the stable numerical method of discrete orthogonalization. The results can be used for calculation of construction elements and details of machines of this type. The results of the paper can be used when selecting the cross section of the cylinders of a similar type.

References

1. Lugovoi P. Z., Sirenko V. N., Skosarenko Yu. V., Batutina T. Ya. Lugovoi P. Z. Dynamics of a Discretely Reinforced Cylindrical Shell Under a Local Impulsive Load. Int. Appl. Mech. 2017. Vol. 52, No 2. Р. 173–180.
2. Kwanghyun Ahn. Lim In-Gyu, Yoon Jonghun, Huh Hoon. A simplified prediction method for the local buckling load of cylindrical tubes. Int. J. of Precision Eng. and Manufacturing. 2016. Vol. 17, No 9. Р. 1149–1156.
3. Marchuk A. V., Gnidash S. V. Analysis of the Effect of Local Loads on Thick-Walled Cylindrical Shells with Different Boundary Conditions. Int. Appl. Mech. 2016. Vol. 52, No 4. Р. 368–377.
4. Даревский В. М. Контактные задачи теории оболочек (действие локальных нагрузок на оболочки). В: Труды VI Всес. конф. по теории оболочек и пластин, Баку. Москва: Наука, 1966.
С. 115–119.
5. Жигалко Ю. П. Расчет тонких упругих цилиндрических оболочек на локальные нагрузки (обзор литературы, метод и результаты). Исследования по теории пластин и оболочек. Вып. IV. Казань: Изд-во Казанского универ-та, 1966. С. 3–41.
6. Даревский В. М. Оболочки под действием локальных нагрузок. Справочник «Прочность, устойчивость, колебания». Москва: Машиностроение, 1968. С. 49–96.
7. Григоренко Я. М. Изотропные и анизотропные слоистые оболочки вращения переменной жесткости. Киев: Наук. думка, 1973. 228 с.
8. Тимошенко С. П. Курс теории упругости. Киев: Наук. думка, 1975. 564 с.
9. Григоренко Я. М., Рожок Л. С. Влияние изменения параметров кривизны на напряженное состояние полых цилиндров с поперечным сечением в виде вогнутых полугофров. Прикл. механика. 2018. Т. 54, № 3. С. 27 – 35.
10. Григоренко Я. М., Рожок Л. С. Застосування дискретних рядів Фур’є до розв’язання крайових задач статики пружних тіл неканонічної форми. Мат. методи та фіз.-мех. поля. 2005. Т. 48, № 2. С. 79–100.
Published
2020-03-02
How to Cite
Grigorenko, Y. M., & Rozhok, L. S. (2020). INVESTIGATION OF INFLUENCE OF LOCAL LOADING ON THE STRESSED STATE OF HOLLOW CYLINDERS WITH CONCAVE CORRUGATED CROSS SECTIONS. Bulletin of Zaporizhzhia National University. Physical and Mathematical Sciences, (2), 38-47. Retrieved from http://journalsofznu.zp.ua/index.php/phys-math/article/view/224