Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

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

For citation:

Ilyukhin A. A., Timoshenko D. V. The One-Dimensional Micropolar Theory of Elastic Rods Basic Parities Construction. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2008, vol. 8, iss. 4, pp. 52-61. DOI: 10.18500/1816-9791-2008-8-4-52-61

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
17.11.2008
Full text:
download
(downloads: 214)
Language: 
Russian
Heading: 
Mechanics
UDC: 
531.38, 575
DOI: 
10.18500/1816-9791-2008-8-4-52-61

The One-Dimensional Micropolar Theory of Elastic Rods Basic Parities Construction

Autors: 
Ilyukhin Aleksandr Alekseevich, Taganrog State Pedagogical Institute, Russia
Timoshenko Dmitrii Vladimirovich, Taganrog State Pedagogical Institute, Russia
Abstract: 

The reduction from a three-dimensional problem of the asymmetrical theory of elasticity to one-dimensional by means of splitting a three-dimensional problem on set of two-dimentional and one-dimensional problems is carried out. Kinematic parameters with which it is necessary to involve are specified that together with system Kirchoff differential equations to receive the closed system of the equations of the one-dimensional micropolar theory of cores. Other geometrical sizes are found from parities defining them. Conditions with which should satisfy factors in closing parities are received. The contribution to these parities which introduces the account moment pressure is estimated. For the one-dimensional theory the common decision at presence stiffnesse is specified to symmetry.

Key words: 
elastic rod
asymmetrical theory of elasticity
reduction
closing parities
moment pressures
References: 
  1. Аэро Э.Л., Кувшинский Е.В. Основные уравнения теории упругости сред с вращательным взаимодействием частиц // ФТТ. 1960. Т. 2, № 7. С. 1399–1409.
  2. Кувшинский Е.В., Аэро Э.Л. Континуальная теория асимметрической упругости // ФТТ. 1969. Т. 5, № 9. С. 2591–2598.
  3. Cosserat E., Cosserat F. Theorie des corps deformables. Paris, 1909. vi+226 p. (Appendix, p. 953–1173 of Chwolson’s Traite de Physicue. 2nd ed., Paris).
  4. Koiter W.T. Couple-stresses in the theory of elasticity. Pt. I–II // Proc. Koninkl. Neterland. Akad. Wetensh. 1964. V. B67, № 1. P. 17–44.
  5. Новацкий В. Теория упругости. М.: Мир, 1975. 872 с.
  6. Пальмов В.А. Основные уравнения теории несимметричной упругости // ПММ. 1964. Т. 28, вып. 3. С. 401–408.
  7. Nowacki W. Theory of Asymmetric Elasticity. Oxford, N.Y., Toronto et al: Pergamon-Press, 1986. 383 p.
  8. Toupin R.A. Theories of elasticity with couple-stress // Arch. Ration. Mech. Anal. 1964. V. 17, № 2. P. 85–112.
  9. Eringen A.C. Nonlocal polar field theories // Continuum Physics. V. 4. N.Y.: Academic Press, 1976. P. 205–268.
  10. Eringen A.C. Microcontinuum Field Theories. I. Foundations and Solids. Berlin, Heidelberg, N.Y. et al: Springer-Verlag. 1999. 325 p.
  11. Eringen A.C. Microcontinuum Field Theories. II. Fluent Media. Berlin, Heidelberg, N.Y. et al: SpringerVerlag. 2001. 342 p.
  12. Иванова Е.А. и др. Учет моментного взаимодействия при расчете изгибной жесткости наноструктур // Докл. РАН. 2003. Т. 391, № 6. С. 764–768.
  13. Китайгородский А.И. Невалентные взаимодействия атомов в органических кристаллах и молекулах // УФН. 1979. Т. 127, вып. 3. С. 391–419.
  14. Лурье А.И. Нелинейная теория упругости. М.: Наука, 1980. 920 с.
  15. Илюхин А.А., Щепин Н.Н. К моментной теории упругих стержней // Изв. вузов. Северо-Кавказский регион. Естественные науки. 2001. Спецвыпуск. С. 92–94.
  • 1119 reads