Advertisement

Anisotropic Elastic Beams With Axially Distributed Loads

  • Omri RandEmail author
  • Vladimir Rovenski
Chapter
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 168)

Abstract

The paper provides a recurrenceexact formulation for homogeneous elastic beams of generic Cartesian anisotropy under axially polynomial loading distributions. The model is derived by solution levels that consistently reduce the problem to a recurrence sequence of two-dimensional boundary value problems. It therefore represents a generalization of Lekhnitskii’s model, and supplies a comprehensive solution methodology for homogeneous anisotropic beams.

Keywords

Boundary Value Problem Stress Component Stress Function Recurrence Sequence Rigid Body Displacement 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Almansi E (1901) Sopra la deformazione dei cilindri sollecitati lateralmente. Atti della Acad Naz dei Lincei Rend 10, I: 333–338, II: 400–408Google Scholar
  2. 2.
    Lekhnitskii SG (1981) Theory of elasticity of an anisotropic body. Mir Publ., Moscow, USSRGoogle Scholar
  3. 3.
    Rand O, Rovenski V (2005) Analytical methods in anisotropic elasticity with symbolic computational tools. Birkhäuser, BostonGoogle Scholar
  4. 4.
    Rovenski V, Rand O (2001) Analysis of anisotropic beams: an analytic approach. J Appl Mech, ASME 68 (4):674–678CrossRefGoogle Scholar
  5. 5.
    Rovenski V, Rand O (2003) Beams of general anisotropy with axially distributed loads. TAE Report 945. Haifa, Israel: TechnionGoogle Scholar
  6. 6.
    Rovenski V, et al (2007) Saint-Venant’s problem for homogeneous piezoelectric beams. J Appl Mech, ASME 74(6):1095–1103CrossRefGoogle Scholar
  7. 7.
    Rovenski V, Abramovich H (2007) Behavior of piezoelastic beams under axially non-uniform distributed loads. J Elast 88(3):223–253CrossRefGoogle Scholar
  8. 8.
    Ruchadze AK (1975) On one problem of elastic equilibrium of homogeneous isotropic prismatic bar. Tr Gruz Politech Inst 3(176):208–218 (in Russian)Google Scholar
  9. 9.
    Zivsivadse RT, Berekashvili RA (1984) Generalization of Almansi problem for compaund anisotropic cylindrical beams. Georg Polytech Inst 9 (279):130–135 (in Russian)Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Faculty of Aerospace Engineering, TechnionIsrael Institute of TechnologyHaifaIsrael

Personalised recommendations