Materials Science

, Volume 40, Issue 2, pp 215–222 | Cite as

Three-dimensional problem of the theory of elasticity for orthotropic cantilevers and plates subjected to bending by transverse forces

  • V. P. Revenko


The exact solution of the problem of bending of an orthotropic composite cantilever (plate) with rectangular cross section loaded by transverse forces at the end is found within the framework of the three-dimensional theory of elasticity. The explicit expressions are presented for stresses and displacements. The numerical analysis of the distributions of tangential stresses is performed for the cantilever and the plate. New qualitative features of the distributions of tangential stresses in the three-dimensional case are established. The strength of the plate is evaluated.


Exact Solution Structural Material Explicit Expression Tangential Stress Qualitative Feature 
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  1. 1.
    Timoshenko, S. P., Woinowski-Krieger, S. 1963Theory of Plates and ShellsFizmatgizMoscow[Russian translation]Google Scholar
  2. 2.
    Ambartsumyan, S. A. 1987Theory of Anisotropic PlatesNaukaMoscow[in Russian]Google Scholar
  3. 3.
    Timoshenko, S. P., Goodier, G. N. 1975Theory of ElasticityNaukaMoscow[Russian translation]Google Scholar
  4. 4.
    Lekhnitskii, S. G. 1977Theory of Elasticity for Anisotropic BodiesNaukaMoscow[in Russian]Google Scholar
  5. 5.
    Saint–Vénant, B. 1961Mémoire sur la Torsion des Prismes. Mémoire sur la Flexion des PrismesFizmatgizMoscow[Russian translation]Google Scholar
  6. 6.
    V. P. Revenko and A. V. Revenko, “Bending of a cantilever by transverse forces within the framework of three-dimensional elasticity theory,” Prikl. Probl. Mekh. Matem., Issue 1, 96–100 (2003).Google Scholar
  7. 7.
    Lomakin, V. A. 1976Theory of Elasticity for Inhomogeneous BodiesIzd. Mosk. Univ.Moscow[in Russian]Google Scholar
  8. 8.
    Lekhnitskii, S. G. 1972The Saint-Venant problem for a continuously nonuniform anisotropic beamContinuum Mechanics and Related Problems of AnalysisNaukaMoscow[in Russian]Google Scholar
  9. 9.
    Antsiferov, V. N., Sokolkin, Yu. V., Tashkinov, A. A.,  et al. 1990Fibrous Composite Materials Based on TitaniumNaukaMoscow[in Russian]Google Scholar
  10. 10.
    Lubin, G. eds. 1988Handbook of CompositesMashinostroenieMoscow[Russian translation]Google Scholar
  11. 11.
    Tolstov, G. P. 1980Fourier SeriesNaukaMoscow[in Russian]Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2004

Authors and Affiliations

  • V. P. Revenko
    • 1
  1. 1.Pidstryhach Institute for Applied Problems in Mechanics and MathematicsUkrainian Academy of SciencesLviv

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