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Reach of an inclined cantilever with a tip load

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We investigate the problem of determining the reach of an inclined cantilever for a given point load suspended from its tip. Two situations are considered. Firstly, we find the maximum reach of the cantilever by varying its angle of inclination. Secondly, we find the reach of the cantilever subject to the condition that its tip is at some specified height, above or below, the level of the clamped end. In the second case, the reach of the cantilever is maximised by shortening its physical length whilst keeping the physical load and physical height of load deployment constant. All of our solutions representing various reaches of an inclined cantilever for a given point load suspended from its tip are shown to be stable to the snap-back instability.
Słowa kluczowe
Rocznik
Strony
595--614
Opis fizyczny
Bibliogr. 15 poz., rys.
Twórcy
autor
  • School of Engineering, London South Bank University, London SE1 OAA, UK
  • School of Engineering, London South Bank University, London SE1 OAA, UK
Bibliografia
  • 1. K.E. Bisshopp, D.C. Drucker, Large deflection of cantilever beams, Quarterly of Applied Mathematics, 3, 272–275, 1945.
  • 2. C.Y. Wang, Large deflections of an inclined cantilever with an end load, International Journal of Non-Linear Mechanics, 16, 2, 155–164, 1981.
  • 3. S. Navaee, R.E. Elling, Equilibrium configurations of cantilever beams subjected to inclined end loads, Journal of Applied Mechanics, 59, 3, 572–579, 1992.
  • 4. S. Navaee, R.E. Elling, Possible ranges of end slope for cantilever beams, Journal of Engineering Mechanics, 119, 3, 630–635, 1993.
  • 5. M. Batista, Analytical treatment of equilibrium configurations of cantilever under terminal loads using Jacobi elliptical functions, International Journal of Solids and Structures, 51, 13, 2308–2326, 2014.
  • 6. C.Y. Wang, Longest reach of a cantilever with a tip load, European Journal of Physics, 37, 1, 012001, 2016.
  • 7. M. Batista, Comment on ‘Longest reach of a cantilever with a tip load’, European Journal of Physics, 37, 5, 058004, 2016.
  • 8. R.H. Plaut, L.N. Virgin, Furthest reach of a uniform cantilevered elastica, Mechanics Research Communications, 83, 18–21, 2017.
  • 9. C. Armanini, F. Dal Corso, D. Misseroni, D. Bigoni, From the elastica compass to the elastica catapult: an essay on the mechanics of soft robot arm, Proceedings of the Royal Society A, 473, 20160870, 2017.
  • 10. M. Kaneko, N. Kanayama, T. Tsuji, Active antenna for contact sensing, IEEE Transactions on Robotics and Automation, 14, 2, 278–291, 1998.
  • 11. T. Michels, I.W. Rangelow, Review of scanning probe micromachining and its applications within nanoscience, Microelectronic Engineering, 126, 191–203, 2014.
  • 12. G. Gao, H. Wang, Q. Xia, M. Song, H. Ren, Study on the load capacity of a single section continuum manipulator, Mechanism and Machine Theory, 104, 313–326, 2016.
  • 13. R. Frisch-Fay, Flexible Bars, Butterworths, London, pp. 33–64, 1962.
  • 14. C.L. Dym, I.H. Shames, Solid Mechanics: A Variational Approach, augmented Edition, Springer, New York, pp. 516–521, 2013.
  • 15. I.S. Gradshteyn, I.M. Ryzhik, Table of Integrals, Series, and Products, 7th Edition, Elsevier Academic Press, San Diego, pp. 859–883, 2007.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-5540c07e-f9a6-4139-acb4-f477fd9a3558
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