Skip to main content
SpringerLink
Log in

General Theorems of Linear Micropolar Elasticity

  • Chapter
Theory of Micropolar Elasticity

Part of the book series: International Centre for Mechanical Sciences ((CISM,volume 25))

  • 220 Accesses

Abstract

The classical theory of elasticity is based on an ideal model of an elastic, continuous medium in which the loadings are transmitted through an area element αA in the body by means of the stress vector only.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 16.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Voigt, W.: Theoretische Studien liber die Elastizitätsverhfflt nisse der Kristalle. Abh. Ges. Wiss. Göttingen, 34 (1887)

    Google Scholar 

  2. Cosserat, E., and F. Cosserat: Théorie des corps déformables. A. Hermann, Paris, 1909.

    Google Scholar 

  3. Truesdell, C., and R.A. Toupin: The classical field theories. Encyclopedia of Physics, 3, No 1, Springer Verlag, Berlin, 1960.

    Google Scholar 

  4. Grioli, G.: Elasticità asimmetrica. Ann. di Mat. pura ed appl. Ser. IV. 50, (1960).

    Google Scholar 

  5. Mindlin, R.D. and H.F. Tiersten: Effects of couple-stresses in linear elasticity. Arch. Mech. Analysis, 11, (1962), 385.

    Article  MathSciNet  Google Scholar 

  6. Toupin, R.A.: Theories of elasticity with couple-stresses. Arch. Mech. Analysis. 17, (1964), 85.

    MATH  MathSciNet  Google Scholar 

  7. Eringen, A.C., and E.S. Suhubi: Non linear theory of micro elastic solids. Int. J. Eng. Sci. 2 (1964), 189, 389.

    MathSciNet  Google Scholar 

  8. Gilnther, W.: Zur Statik und Kinematik des Cosseratschen Kon tinuum. Abh. Braunschweig. Wiss. Ges 10, (1958), 85.

    Google Scholar 

  9. Schaefer, H.: Versuch einer Elastizitätstheorie des zweidi mensionalen Cosserat-Kontinuum, Misz. Angew. Math. Festschrift Tollmien, Berlin, 1962, Akademie Verlag.

    Google Scholar 

  10. Kuvshinskii, E.V., and A.L. Aero: Continuum theory of asym metric elasticity, (in Russian). Fizika Tverdogo Tela 5, (1963), 2592.

    Google Scholar 

  11. Palmov, N.A.: Fundamental equations of the theory of asymmetric elasticity (in Russian). Prikl. Mat. Mekh. 28 (1964), 401.

    MathSciNet  Google Scholar 

  12. Nowacki W.: Couple-stresses in the theory of thermoelasticity. Proc. of the IUTAM symposia, Vienna, June 22–28 1966. Springer Verlag, Wien, 1968.

    Google Scholar 

  13. Schaefer, H.: Das Cosserat-Kontinuum. Z.A.M.M. 47 (1967), 485

    MATH  Google Scholar 

  14. Kaliski, S.: On a model of the continuum with an essentially non-symmetric tensor of mechanical stress. Arch. Mech. Stos. 15, 1 (1963), 33.

    MATH  MathSciNet  Google Scholar 

  15. Askar, A. and A.S. Cakmak: A structural model of a micro-polar continuum. Int. J. Eng. Sci. 6, 10 (1968), 583.

    Article  MATH  Google Scholar 

  16. The considerations presented here are more extensively treated (in connection with the classical elastic continuum) by this author in the monograph “Dynamical Problems of Thermoelasticity” (in Polish) Warsaw, PWN. 1968.

    Google Scholar 

  17. W. Nowacki: “Couple-stresses in the theory of thermoelasticity”, Proc. of the IUTAM-Symposium on Irreversible Aspects in Con tinuum Mechanics, Vienna,1966, Springer Verlag,Wien-New York,1968

    Google Scholar 

  18. Lamé G.: Leçons sur la théorie mathématique de l’élasticité des corps solides. Paris, Bachelier, 1852.

    Google Scholar 

  19. Palmov W.A.: Fundamental equations of non-symmetric elastici ty (in Russian), Prikl.Mat.Mech. 28 (1964), p. 401.

    MathSciNet  Google Scholar 

  20. Galerkin, B.: “Contributions à la solution générale du problème de la théorie de l’élasticité dans le cas de trois dimension”, C.R.Acad. Sci. Paris, 190 (1930), p. 1047.

    MATH  Google Scholar 

  21. Iacovache, M.: “O extindere a metodei lui Galerkin pentru sistemul ecuatiilor elasticitâii”, Bull. Stiint. Acad. Rep. Pop. Romane, Ser. A. 1 (1949), 593.

    MathSciNet  Google Scholar 

  22. Sandru, N.: “On some problems of the linear theory of asym metric elasticity” Int. J. Engng. Sci. 4, 1, (1966), 81.

    Article  Google Scholar 

  23. Moisil, Gr. C.: “Aspura sistemelor de equaii cu derivata partiale lineare si cu coeficien i constanti”. Bull.§tiint.Acad. Rep. Pop. Romane, Ser. A., (1949), p. 341.

    Google Scholar 

  24. Nowacki, W.: “On the completeness of stress functions in asymmetric elasticity”, Bull. Acad. Polon. Sci., Sér. Sci. Techn. 14, No 7 (1968), p. 309.

    Google Scholar 

  25. N. Sandru, op. cit. p.53.

    Google Scholar 

  26. Stefaniak, J.:“A generalization of Galerkin’s functions for asymmetric thermoelasticity”, Bull.Acad. Polon.Sci., Série Sci. Tech., 8, 14, (1968), p. 391.

    Google Scholar 

  27. Boggio, T.:“Sull’integrazione di alcune equazioni lineari alle derivate parziali”, Ann. Mat., Ser. III (1903), 181.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Warsaw, Poland

    Witold Nowacki

Authors
  1. Witold Nowacki
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1970 Springer-Verlag Wien

About this chapter

Cite this chapter

Nowacki, W. (1970). General Theorems of Linear Micropolar Elasticity. In: Theory of Micropolar Elasticity. International Centre for Mechanical Sciences, vol 25. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2720-9_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-7091-2720-9_1

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-81078-1

  • Online ISBN: 978-3-7091-2720-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation