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The torsional rigidity of anisotropic prisms

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Summary

Upper and lower bounds are obtained for the torsional rigidity of a prismatic cylinder of non-homogeneous anisotropic elastic material. Improvement in the bounds is obtained by expressing each bound as the quotient of two bordered determinants. Some analytical and numerical results are also presented.

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References

  1. Yu Chen, Torsion of non-homogeneous bars,J. Frank. Inst., 277 (1964) 50–54.

    Google Scholar 

  2. R. K. Brown and E. E. Jones, On the torsion of a curvilinearly aeolotropic cylinder,Quart. App. Math., 26 (1968) 273–275.

    Google Scholar 

  3. W. Prager,Introduction to mechanics of continua, Ginn and Company, Boston (1961).

    Google Scholar 

  4. J. B. Diaz, On the estimation of torsional rigidity and other physical constants,Proc. First Nat. Congress App. Mechs., (1951) 259–263.

  5. A. E. H. Love,The mathematical theory of elasticity, Dover Publications, New York (1944).

    Google Scholar 

  6. S. G. Lekhnitskii,Theory of elasticity of an anisotropic elastic body (translated by P. Fern), Holden-Day, San Fransisco (1963).

    Google Scholar 

  7. J. N. Flavin, Bounds for the torsional rigidity of orthotropic cylinders,ZAMP, 18 (1967) 694–704.

    Google Scholar 

  8. R. Dourant, Variational methods for the solution of problems of equilibrium and vibrations,Bull. Am. Math. Soc., 49 (1943) 1–23.

    Google Scholar 

  9. T. J. Higgins, The approximate mathematical methods of applied physics as exemplified by application to Saint-Venant's torsion problem,J. App. Phys., 14 (1943) 469–480.

    Google Scholar 

  10. W. L. Ferrar,Algebra, Oxford University Press, (1941).

  11. A. C. Aitken,Determinants and matrices, Oliver and Boyd, Edinburgh (1964).

    Google Scholar 

  12. H. Levine and J. Schwinger, On the theory of electromagnetic wave diffraction by an aperture in an infinite plane conducting screen,The theory of electromagnetic waves, Ed. M. Kline, Dover Publications, New York (1951).

    Google Scholar 

  13. E. Nicolai, Über die Drillungssteifigkeit zylindrischer Stabe,ZAMM 4 (1923) 181–182.

    Google Scholar 

  14. B. R. Seth, Torsion of beams whose cross-section is a regular polygon ofn sides,Proc. Camb. Phil. Soc., 30 (1934) 139–149.

    Google Scholar 

  15. G. Polya and G. Szego,Isoperimetric inequalities in mathematical physics, Princeton University Press (1951).

  16. I. M. Kabaza,Matrix computations, Lecture notes, Queen Mary College, University of London, (1963).

  17. J. L. Synge,The hypercircle in mathematical physics, Cambridge University Press, (1957).

  18. G. E. Hay, The method of images applied to the problem of torsion,Proc. London Math. Soc., 45 (1939) 382–397.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Wales Institute of Science and Technology, Cardiff, Wales

    E. E. Jones

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  1. E. E. Jones
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Jones, E.E. The torsional rigidity of anisotropic prisms. J Eng Math 9, 39–51 (1975). https://doi.org/10.1007/BF01535496

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  • DOI: https://doi.org/10.1007/BF01535496

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