Journal of Elasticity

, Volume 81, Issue 2, pp 159–177 | Cite as

A Generalized Fourier Approximation in Anti-plane Cosserat Elasticity

Article
First Online:
Received:
Accepted:

Abstract

In the present paper we use the modification of Kupradze’s method of generalized Fourier series for the treatment of interior and exterior Dirichlet and Neumann boundary-value problems arising in a linear theory of anti-plane elasticity which includes the effects of material microstructure.

Mathematics Subject Classifications (2000)

74A99 74E99 45E05 42B05 

Key words

micropolar elasticity boundary integral equation method generalized Fourier series 
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A.C. Eringen, Linear theory of micropolar elasticity. J. Math. Mech. 15 (1966) 909–923.MATHMathSciNetGoogle Scholar
  2. 2.
    W. Nowacki, Theory of Asymmetric Elasticity. Polish Scientific Publishers, Warszawa (1986).MATHGoogle Scholar
  3. 3.
    R. Lakes, Experimental methods for study of Cosserat elastic solids and other generalized elastic continua. In: H.B. Muhlhaus (ed.), Continuum Models for Materials with Microstructure. Wiley (1995).Google Scholar
  4. 4.
    R. Lakes, Experimental micromechanics methods for conventional and negative Poisson’s ratio cellular solids as Cosserat continua. J. Eng. Mater. Technol. 113 (1991) 148–155.Google Scholar
  5. 5.
    R. Lakes, Foam structures with a negative Poisson’s ratio. Science 235 (1987) 1038–1040.CrossRefADSGoogle Scholar
  6. 6.
    R. Lakes, Experimental microelasticity of two porous solids. Int. J. Sol. Struct. 22 (1986) 55–63.CrossRefGoogle Scholar
  7. 7.
    V.D. Kupradze, et al. Three-Dimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity. North-Holland, Amsterdam (1979).MATHGoogle Scholar
  8. 8.
    D. Iesan, Torsion of micropolar elastic beams. Int. J. Eng. Sci. 9 (1971) 1047–1060.CrossRefGoogle Scholar
  9. 9.
    S. Potapenko, P. Schiavone, A. Mioduchowski, On the solution of torsion of cylindrical beams with microstructure. Math. Mech. Solids (2005) doi:  10.1177/1081286504040399.
  10. 10.
    C.O. Horgan, Anti-plane shear deformations in linear and nonlinear solid mechanics, SIAM Rev. 37 (1995) 53–81.CrossRefMATHMathSciNetGoogle Scholar
  11. 11.
    S. Potapenko, P. Schiavone and A. Mioduchowski, Antiplane shear deformations in a linear theory of elasticity with microstructure, ZAMP 56(3) (2005) 516–528.CrossRefMATHADSMathSciNetGoogle Scholar
  12. 12.
    S. Potapenko, P. Schiavone and A. Mioduchowski, On the solution of mixed problems in antiplane micropolar elasticity. Math. Mech. Solids 8 (2003) 151–160.CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    C. Constanda, A Mathematical Analysis of Bending of Plates with Transverse Shear Deformation. Longman Scientific & Technical, Harlow (1990).MATHGoogle Scholar
  14. 14.
    P. Schiavone and C. Constanda, Existence theorems in the theory of thin micropolar plates. Int. J. Eng. Sci. 27 (1989) 463–468.CrossRefMATHMathSciNetGoogle Scholar
  15. 15.
    P. Schiavone and C. Constanda, Uniqueness in the elastostatic problem of bending of thin micropolar plates. Arch. Mech. 41(5) (1989) 785–791.MATHMathSciNetGoogle Scholar
  16. 16.
    P. Schiavone, On existence theorems in the theory of extensional motions of thin micropolar plates. Int. J. Eng. Sci. 27 (1989) 1129–1133.CrossRefMATHMathSciNetGoogle Scholar
  17. 17.
    P. Schiavone, Fundamental sequences of functions in the approximation of solutions to exterior problems in the bending of thin micropolar plates. Appl. Anal. 35 (1990) 263–274.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Department of Civil EngineeringUniversity of WaterlooWaterlooCanada

Personalised recommendations