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The saint-venant torsion of a cartesian orthotropic bar with an isosceles right-angled triangle cross-section

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Języki publikacji
EN
Abstrakty
EN
The Saint-Venant torsion of the Cartesian orthotropic homogeneous linearly elastic bar is considered. The cross-section of the prismatic bar is an isosceles right-angled triangular plane domain. An approximate analytical method is presented to obtain Prandtl’s stress function, shearing stresses, and torsional rigidity. Upper and lower bounds for the torsional rigidity are provided. The obtained results for shearing stresses are verified through FEM computation.
Rocznik
Strony
81--94
Opis fizyczny
Bibliogr. 22 poz., rys., tab., wykr.
Twórcy
  • Institute of Applied Mechanics, University of Miskolc Miskolc Egyetemv´aros, Hungary H-5315
autor
  • Institute of Applied Mechanics, University of Miskolc Miskolc Egyetemv´aros, Hungary H-5315
Bibliografia
  • 1. Jog C.S., Continuum Mechanics. Volume I: Foundations and Applications of Mechanics, Cambridge University Press, 2015.
  • 2. Sokolnikoff I.S., Mathematical Theory of Elasticity, 2nd ed., Robert E. Krieger Publishing Company, Malabar, Florida, 1987.
  • 3. Sparrow E.M., Laminar flow in isosceles triangular ducts, AIChE Journal, 8(5): 599–604, 1962, doi: 10.1002/aic.690080507.
  • 4. Kolossoff M.C., Sur la torsion des primes ayant pour base un triangle rectangle [in French], Comptes Rendus, 178: 2057–2060, 1924.
  • 5. Hay G.E., The method of images applied to the problem of torsion, Proceedings of the London Mathematical Society, s2-45(1): 382–397, 1939, doi: 10.1112/plms/s2-45.1.382.
  • 6. Leknitskii S.G., Theory of Elasticity of an Anisotropic Body, Holden-Day Inc., San Francisco, 1963.
  • 7. Leknitskii S.G., Torsion of Anisotropic and Non-homogeneous Beams [in Russian], Nauka, Moscow, 1971.
  • 8. Milne-Thomson L.M., Antiplane Elastic Systems, Springer, Berlin, 1962.
  • 9. Sadd M.H., Elasticity. Theory, Applications and Numerics, Elsevier, London, 2005.
  • 10. Rand O., Rovenski W., Analytical Methods in Anisotropic Elasticity with Symbolic Computational Tools, Birkh¨aser, Boston, 2005, doi: 10.1007/b138765.
  • 11. Ecsedi I., Baksa A., Saint-Venant torsion of anisotropic bar, International Journal of Mechanical Engineering Education, 45(3): 286–294, 2017, doi: 10.1177/0306419017708642.
  • 12. Ecsedi I., Baksa A., A method for the solution of uniform torsion of Cartesian orthotropic bar, Journal of Theoretical and Applied Mechanics, 52(2): 129–143, 2022, doi: 10.55787/jtams.22.52.2.129.
  • 13. Sarkisian V.S., Some Problems of the Mathematical Theory of Elasticity of Anisotropic Body [in Russian], Izd. Erevan University Press, Erevan, 1976.
  • 14. Sarkisian V.S., Some Problems of Anisotropic Elastic Bodies [in Russian], Izd. Erevan University Press, Erevan, 1970.
  • 15. Ecsedi I., Baksa A., Estimation of the torsional rigidity of orthotropic solid cross-section, Engineering Transactions, 69(2): 211–221, 2021, doi: 10.24423/EngTrans.1294.20210607.
  • 16. Swider P., Briot J., Estival´ezes E., A solution of torsional problem by energy method in the case of anisotropic cross-section, Archives of Applied Mechanics, 81: 801–808, 2011, doi: 10.1007/s00419-010-0450-7.
  • 17. Chen T., Wei C.J., Saint-Venant torsion of anisotropic shafts: Theoretical frameworks, external bounds and affine transformations, Quarterly Journal of Mechanics and Applied Mathematics, 58(2): 269–287, 2005, doi: 10.1093/qjmamj/hbi013.
  • 18. Chen T., A homogeneous elliptical shaft may not warp under torsion, Acta Mechanica, 169(1): 221–224, 2004, doi: 10.1007/s00707-004-0093-2.
  • 19. Ecsedi I., Elliptic cross-section without warping under torsion,Mechanics Research Communications, 31(2): 147–150, 2004, doi: 10.1016/S0093-6413(03)00098-3.
  • 20. Horgan C.O., On the torsion of functionally graded anisotropic linearly elastic bars, IMA Journal of Applied Mathematics, 72(5): 556–562, 2007, doi: 10.1093/imamat/hxm027.
  • 21. Nowinski J.L., Cauchy-Schwarz inequality and the evaluation of torsional rigidity of anisotropic bars, SIAM Journal of Applied Mathematics, 24(3): 324–331, 1973, doi: 10.1137/0124034, https://www.jstor.org/stable/2099768.
  • 22. Lurie A.I., Theory of Elasticity, Springer, Berlin, 2005.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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