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TECHNICAL PAPERS

The Elastic Stability of Twisted Plates

[+] Author and Article Information
E. M. Mockensturm

Department of Mechanical and Nuclear Engineering, Pennsylvania State University, University Park, PA 16802 Mem. ASME

J. Appl. Mech 68(4), 561-567 (Oct 18, 2000) (7 pages) doi:10.1115/1.1357517 History: Received April 12, 2000; Revised October 18, 2000
Copyright © 2001 by ASME
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References

Thomson, W. (Lord Kelvin) and Tait, P. G., 1883, Treatise on Natural Philosophy, Cambridge University Press, London.
de Saint-Venant, A., 1855, “De la Torsion des Prismes, avec des considérations sur leur Flexion,” Mémoires des Savants Étrangers.
Green,  A. E., 1936, “The Equilibrium and Elastic Stability of a Thin Twisted Strip,” Proc. R. Soc. London, A125, pp. 430–455.
Green,  A. E., 1937, “The Elastic Stability of a Thin Twisted Strip—II,” Proc. R. Soc. London, A161, pp. 197–220.
Crispino,  D. J., and Benson,  R. C., 1986, “Stability of Twisted Orthotropic Plates,” Int. J. Solids Struct., 28, No. 6, pp. 371–379.
Mockensturm,  E. M., and Mote,  C. D., 1999, “Steady Motions of Translating, Twisted Webs,” Int. J. Non-Linear Mech., 34, No. 2, pp. 247–257.
Mockensturm, E. M., 1998, “On the Finite Twisting of Translating Plates,” Ph.D. thesis, University of California, Berkeley, CA.
Naghdi, P. M., 1972, “The Theory of Shells and Plates,” S. Flügge’s Handbuch der Physik, Vol. VIa/2, C. Truesdell, ed., Springer-Verlag, Berlin, pp. 425–633.
Naghdi, P. M., 1980, “Finite Deformation of Elastic Rods and Shells,” Proceedings of the IUTAM Symposium on Finite Elasticity, D. E. Carlson and R. T. Shield, eds., Martinus Nijhoff, Dordrecht, The Netherlands, pp. 47–103.

Figures

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The initial, X0α), unbuckled, Xα), and buckled, xα), configurations of the plate
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Illustration of the difference between the case with fixed support separation and the case with fixed support force
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Dependence of critical twist on longitudinal mode number and aspect ratio for an initially untensioned plate and fixed support separation. Insets show lateral mode shapes for various aspect ratios.
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Dependence of critical twist on longitudinal mode number and aspect ratio for a plate initially strained 0.5 percent and fixed support separation. Insets show lateral mode shapes for various aspect ratios.
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Critical twist as a function of initial strain and thickness for a square plate and fixed support separation
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Critical twist as a function of initial strain for various aspect ratios and fixed support separation
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Dependence of critical twist on longitudinal mode number and aspect ratio for a plates with various fixed support forces
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Dependence of critical twist on fixed support force for α=1/2,1,2
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Critical twist normalized by plate thickness as a function of plate thickness for various aspect ratios and no support force

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