Anisotropic Elastic Beams With Axially Distributed Loads

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


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.


Boundary Value Problem Stress Component Stress Function Recurrence Sequence Rigid Body Displacement 
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  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

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