Structural Engineering and Mechanics

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Large deflection behavior of a flexible circular cantilever arc device subjected to inward or outward polar force

  • Al-Sadder, Samir Z. (Department of Civil Engineering, Faculty of Engineering, Hashemite University)
  • Received : 2005.07.26
  • Accepted : 2005.11.28
  • Published : 2006.03.10
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Abstract

The problem of very large deflection of a circular cantilever arc device subjected to inward or outward polar force is studied. An exact elliptic integral solution is derived for the two cases and the results are checked using large displacement finite element analysis via the ANSYS package by performing a new novel modeling simulation technique for this problem. Excellent agreements have been obtained between the exact analytical solution and the numerical approach. From this study, a design chart for engineers is developed to predict the required value for the inward polar force for the device to switch on for a given angle forming the circular arc (${\theta}_o$). This study has several interesting applications in mechanical engineering, integrated circuit technology, nanotechnology and especially in microelectromechanical systems (MEMs) such as a MEM circular device switch subjected to attractive or repulsive magnetic forces due to the attachments of two magnetic poles at the fixed and at the free end of the circular cantilever arc switch device.

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References

  1. Anderson, N.A. and Done, G.T. (1971), 'On the partial simulation of a nonconservative system by a conservative system', Int. J. Solids Struct., 7, 183-191 https://doi.org/10.1016/0020-7683(71)90042-4
  2. Aristizabal-Ochoa, J.D. (2004), 'Large deflection stability of slender beam-columns with semirigid connections: Elastica approach', J. Engng. Mech., 130, 274-282 https://doi.org/10.1061/(ASCE)0733-9399(2004)130:3(274)
  3. Barten, H.J. (1945), 'On the deflection of a cantilever beam', Quart. of Appl. Math., 4, 275
  4. Bisshopp, K.E. and Drucker, D.C. (1945), 'Large deflections of cantilever beams', Quart. of Appl. Math., 3, 272 https://doi.org/10.1090/qam/13360
  5. Chucheepsakul, S., Buncharoen, S. and Wang, C.M. (1994), 'Large deflection of beam under moment gradient', J. Engng. Mech., 120, 1848-1860 https://doi.org/10.1061/(ASCE)0733-9399(1994)120:9(1848)
  6. Chucheepsakul, S., Buncharoenm, S. and Huang, T. (1995), 'Elastica of simple variable-are-length beam subjected to end moment', J. Engng. Mech., 121, 767-772 https://doi.org/10.1061/(ASCE)0733-9399(1995)121:7(767)
  7. Chucheepsakul, S., Thepphitak, G. and Wang, C.M. (1996), 'Large deflection of simple variable-are-length beam subjected to apoint load', Struct. Eng. Mech., 4, 49-59 https://doi.org/10.12989/sem.1996.4.1.049
  8. Chucheepsakul, S., Wang, C.M., He, X. and Monprapussom, T. (1999), 'Double curvature bending of variablearc- length elastica', J. Appl. Mech., 66, 87-94 https://doi.org/10.1115/1.2789173
  9. Chucheepsakul, S. and Phungpaigram, B. (2004), 'Elliptical integral solutions of variable-arc-Iength elastica under an inclined follower force', ZAMM Z. Angew. Math. Mech., 84, 29-38 https://doi.org/10.1002/zamm.200410076
  10. Farshad, M. (1973), 'On general conservative end loading of pretwisted rods', Int. J. Solids Struct., 9, 1361-1371 https://doi.org/10.1016/0020-7683(73)90044-9
  11. Frisch-Fay, R. (1962), Flexible Bars, Butterworths, London
  12. Hartono, W. (1997), 'Elastic nonlinear behavior of truss system under follower and non-follower forces', J. Comput. Struct., 63, 939-949 https://doi.org/10.1016/S0045-7949(96)00386-0
  13. Hartono, W. (2000), 'Behavior of variable length elastica with frictional support under follower force', Mech. Research Communications, 27, 653-658 https://doi.org/10.1016/S0093-6413(00)00142-7
  14. Hartono, W. (2001), 'On the post-buckling behavior of elastica fixed-end column with central brace', ZAMM Z. Angew. Math., 81, 605-611 https://doi.org/10.1002/1521-4001(200109)81:9<605::AID-ZAMM605>3.0.CO;2-1
  15. Lau, J.H. (1974), 'Large deflections of beams with combined loads', J. of the Engng. Mech. Div., ASCE, 12, 140
  16. Mattiasson, K. (1981), 'Numerical results from large deflection beam and frame problems analysis by means of elliptic integrals', Int. J. Num. Meth. Engng., 16, 145
  17. Mladenov, K.A. and Sugiyama, Y. (1983), 'Buckling of elastic cantilevers subjected to a polar force: Exact solution', Transactions JSASS, 26, 80-90
  18. Ohtsuki, A. and Tsurumi, T. (1996), 'Analysis of large deflections in a cantilever beam with low support stiffhess', Transactions of the JSME, 60, 493-499
  19. Timoshenko S.P. and Gere J.M. (1961), Theory of Elastic Stability, NY, McGraw-Hill
  20. Tse, P.C. and Lung, C,T, (2000), 'Large deflections of elastic composite circular springs under uniaxial tension', Int. J. Non-Linear Mech., 35, 293-307 https://doi.org/10.1016/S0020-7462(99)00015-3
  21. Wang, C.M., Lam, K.L. and He, X.Q. (1998), 'Instability of variable arc-length elastica under follower force', Mech. Res. Commun., 25, 189-194 https://doi.org/10.1016/S0093-6413(98)00024-X
  22. Willem, N. (1966), 'Experimental verification of the dynamic stability of a tangentially loaded cantilevered column', J. Appl. Mech., 33, 460-471 https://doi.org/10.1115/1.3625073

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