Torsional instabilities of Greenhill type in elastic rods

Franco Pastrone

Rendiconti del Seminario Matematico della Università di Padova (1992)

  • Volume: 87, page 77-91
  • ISSN: 0041-8994

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Pastrone, Franco. "Torsional instabilities of Greenhill type in elastic rods." Rendiconti del Seminario Matematico della Università di Padova 87 (1992): 77-91. <http://eudml.org/doc/108260>.

@article{Pastrone1992,
author = {Pastrone, Franco},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {equilibrium; wrench; helical and straight solutions},
language = {eng},
pages = {77-91},
publisher = {Seminario Matematico of the University of Padua},
title = {Torsional instabilities of Greenhill type in elastic rods},
url = {http://eudml.org/doc/108260},
volume = {87},
year = {1992},
}

TY - JOUR
AU - Pastrone, Franco
TI - Torsional instabilities of Greenhill type in elastic rods
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1992
PB - Seminario Matematico of the University of Padua
VL - 87
SP - 77
EP - 91
LA - eng
KW - equilibrium; wrench; helical and straight solutions
UR - http://eudml.org/doc/108260
ER -

References

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  1. [1] S.S. Antman, Nonuniqueness of equilibrium states for bars in tension, J. Math. Anal. Appl., 44, 2 (1973), p. 333. Zbl0267.73031MR334637
  2. [2] S.S. Antman, Kirchhoff's problem for nonlinearly elastic rods, Quart. Appl. Math., 32, 3 (1974), p. 221. Zbl0302.73031MR667026
  3. [3] S.S. Antmann - C.S. Kenney, Large buckled states of nonlinearly elastic rods under torsion, thrust and gravity, Arch. Ratl. Mech. Anal., 76 (1981), p. 289. Zbl0472.73036MR628172
  4. [4] J.L. Ericksen, Simpler static problems in nonlinear theories of rods, Intl. J. Solids Structures, 6 (1970), p. 371. Zbl0213.26805
  5. [5] J.L. Ericksen, Bending a prism of helical form, Arch. Ratl. Mech. Anal., 66 (1977), p. 1. Zbl0364.73038MR459169
  6. [6] J.L. Ericksen, Special Topics in Elastostatics, Advances in Applied Mechanics, Vol. 17, Academic Press (1977), p. 189. Zbl0475.73017
  7. [7] A.G. Greenhill, On the strength of shafting when exposed both to torsion and to end thrust, Proc. Inst. Mech. Eng. (1883). 
  8. [8] A E.H. LovE, A Treatise on the Mathematical Theory of Elasticity, 4th ed., Cambridge Univ. Press (1927) (reprinted by Dover Publ., New York (1944)). Zbl53.0752.01MR10851JFM53.0752.01
  9. [9] F. Pastrone, Sulla stabilità nelle verghe iperelastiche, Atti Accad. Sci. Torino, 114 (1980). Zbl0495.73048
  10. [10] H. Cohen - A.B. Whitman, Waves in elastic rods, J. Sound Vibrn., 51 (2) (1977), p. 283. Zbl0366.73018

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