'American Institute of Aeronautics and Astronautics (AIAA)'
Doi
Abstract
A study was conducted to address the problem of building a simple dynamic model of a long beam deformed by a tip pulling cable. The exact static deformation shape of a long beam was obtained through the solution of the nonlinear beam governing differential equations. The exact deformed configuration for beams with a uniform cross section and transversal end load was found through the recursive solution of elliptic integrals. The deformed configuration of beams with an inclined pulling force was found via numerical approximations, using adequate methods such as the Runge-Kutta method, the finite element method, and the quasi-linearization finite difference method. A strategy to calculate the static deformation of a long beam pulled by a tip cable was also proposed in the study.52715591563Puig, L., Barton, A., Rando, N., A review on large deployable structures for astrophysics missions (2010) Acta Astronautica, 67 (1-2), pp. 12-26. , July-Aug. doi:10.1016/j.actaastro.2010.02.021Tibert, G., (2002) Deployable Tensegrity Structures for Space Applications, pp. 9-30. , Royal Inst, of Technology, StockholmPellegrino, S., (2001) Deployable Structures, pp. 1-35. , Springer MilanFrisch-Fay, R., (1962) Flexible Bars, pp. 33-64. , Butterworths LondonTimoshenko, S., Gere, J., (1961) Theory of Elastic Stability, pp. 66-70. , 2nd ed. McGraw-Hill New YorkOhtsuki, A., Analysis of the characteristics of fishing rods based on the large-deformation theory (2001) Materials and Science in Sports, pp. 161-170. , edited by Sam, F.H. , Minerals, Metals and Materials Society , Warrendale, PAShvartsman, B., Large deflections of a cantilever beam subjected to a follower force (2007) Journal of Sound and Vibration, 304 (3-5), pp. 969-973. , doi:10.1016/j.jsv.2007.03.010Holland, D., Stanciulescu, I., Virgin, L., Plaut, R., Vibration and large deflection of cantilevered elastica compressed by angled cable (2006) AIAA Journal, 44 (7), pp. 1468-1476. , doi:10.2514/1.18000Howell, L.L., (2001) Compliant Mechanisms, pp. 42-55. , Wiley , New YorkAl-Sadder, S., Al-Rawi, R., Finite difference scheme for large-deflection analysis of non-prismatic cantilever beams subjected to different types of continuous and discontinuous loadings (2006) Applied Mechanics, 75 (8-9), pp. 459-473. , doi:10.1007/s00419-005-0422-5Yau, J., Close-form solutions of large deflections for a guyed cantilever column pulled by an inclinations cable (2010) Journal of Marine Science and Technology, 18 (1), pp. 130-136Ferris, D., Afonia, A., Small vibrations of flexible bars by using the finite element method with equivalent uniform stiffness and mass methodology (1993) Journal of Sound and Vibration, 163 (2), pp. 343-358. , doi:10.1006/jsvi.1993.1170Sallstrom, J., Poelaert, D., Janssens, F., Small displacements about equilibrium of a beam subjected to large static loads (1996) AIAA Journal, 34 (11), pp. 2384-2391. , Nov. doi: 10.2514/3.13405Santillan, S., Virgin, L., Plaut, R., Post-buckling and vibration of heavy beam on horizontal or inclined rigid foundation (2006) Journal of Applied Mechanics, 73 (4), pp. 664-671. , July doi: 10.1115/1.2165237Santillan, S., Virgin, L., Plaut, R., Equilibria and vibration of a heavy pinched loop (2005) Journal of Sound and Vibration, 288 (1-2), pp. 81-90. , Nov. doi:10.1016/j.jsv.2004.12.016Santillan, S., Virgin, L., Plaut, R., Static and dynamic behavior of highly deformed risers and pipelines (2010) Journal of Offshore Mechanics and Arctic Engineering, 132 (2). , Paper 021401. doi:10.1115/1.4000555Petyt, M., (2010) Introduction to Finite Element Vibration Analysis, pp. 45-115. , 2nd ed. Cambridge Univ. Press New YorkCraig, R., Kurdila, A., (2006) Fundamentals of Structural Dynamics, pp. 417-453. , 2nd ed. Wiley New YorkKwon, Y., Bang, H., (1997) The Finite Element Method Using Matlab, pp. 197-304. , CRC Press Boca Raton, FLCook, R., Malkus, D., Plesha, M., (1989) Concepts and Applications of Finite Element Method, pp. 31-57. , 3rd ed., Wiley, New Yor
