Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


For citation:

Mirsalimov V. M., Rustamov B. E. Simulation of Partial Closure Crack-Visible Cavities in Burning Solid Fuel Under the Influence of Body Forces. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2011, vol. 11, iss. 1, pp. 70-77. DOI: 10.18500/1816-9791-2011-11-1-70-77

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
15.01.2011
Full text:
(downloads: 124)
Language: 
Russian
Heading: 
UDC: 
539.375

Simulation of Partial Closure Crack-Visible Cavities in Burning Solid Fuel Under the Influence of Body Forces

Autors: 
Mirsalimov Vagif M, Azerbaijan Technical University, Baku, Azerbaijan
Rustamov B. E., Azerbaijan Technical University, Baku, Azerbaijan
Abstract: 

On the basis of the theory of elasticity mathematical description of the model for the covering crack-visible cavities with end zones in which cohesive forces of material act, in the burning solid-fuel has been performed. It is accepted that the interaction of crack-visible cavity surfaces under the influence of body and surface loads leads to the appearance of overlap zones of their surfaces. The determination of the unknown parameters that characterize the closure crack- visible cavities, is reduced to the solving of the system of singular integrodifferential equations. Using the procedure of algebraization integral equations are reduced to the system of nonlinear algebraic equations which is solved by successive approximations. Normal and tangential contact stresses, the tractions in the bonds, the values of the size of the end contact zones, where the faces of the crack-visible cavities are closed, have been found.

References: 
  1. Соркин, Р.Е. Газотермодинамика ракетных двигателей на твердом топливе / Р.Е. Соркин. М.: Наука, 1967. 319 с.
  2. Шапиро, Я.М. Основы проектирования ракет на твердом топливе/ Я.М. Шапиро, Г.Ю. Мазинг, Н.Е. Прудников. М.: Военное изд-во, 1978. 621 с.
  3. Budianscky, B. Fiber-matrix de bonding effects on cracking in aligned fiber ceramic composites / B. Budianscky, A.G. Evans, J.W. Hutchinson // Intern. J. Solid Structures. 1995. Vol. 32, No 3–4. P. 315–328.
  4. Ji, H. Adhesion via Connector Molecules: The Many-stitch Problem / H. Ji, P.G. de Gennes // Macromolecules. 1993. Vol. 26. P. 520–525.
  5. Cox, B.N. Concepts for bridged cracks fracture and fatigue / B.N. Cox, D.B. Marshall // Acta Met. Mat. 1994. Vol. 42, No 2. P. 341–363.
  6. Goldstein, R.V. Modelling of the adhesion strength and fracture kinetics of the microelectronic package polymer-polymer joints / R.V. Goldstein, V.F. Bakirov, M.N. Perelmuter // Proc. Inst. Phys. Technol. Russian Ac. of Sci. 1997. Vol. 13. P. 115–125.
  7. Черепанов, Г.П. Механика хрупкого разрушения / Г.П. Черепанов. М.: Наука, 1974. 640 с.
  8. Мусхелишвили, Н.И. Некоторые основные задачи математической теории упругости / Н.И. Мусхелишвили. М.: Наука, 1966.
  9. Панасюк, В.В. Распределение напряжений около трещин в пластинках, оболочках / В.В. Панасюк, М.П. Саврук, А.П. Дацышин. Киев: Наук. думка, 1976. 443 с.
  10. Мирсалимов, В.М. Неодномерные упругопластические задачи / В.М. Мирсалимов. М.: Наука, 1987. 256 с.
  11. Ильюшин, А.А. Пластичность / А.А. Ильюшин. М.; Л.: Гостехиздат, 1948.
  12. Гольдштейн, Р.В. Рост трещин по границе соединения материалов / Р.В. Гольдштейн, М.Н. Перельмутер // Проблемы механики: сб. статей к 90-летию со дня рождения А.Ю. Ишлинского / под ред. Д.М. Климова. М.: Физматлит, 2003. С. 221–238.