Browse > Article
http://dx.doi.org/10.12989/sem.2002.13.1.103

Analysis of transversely isotropic hollow toroids using the semi-analytical DQM  

Jiang, W. (Department of Mechanical Engineering, University of Ottawa)
Redekop, D. (Department of Mechanical Engineering, University of Ottawa)
Publication Information
Structural Engineering and Mechanics / v.13, no.1, 2002 , pp. 103-116 More about this Journal
Abstract
A solution based on the linear three-dimensional theory of elasticity is developed for vibration and elastostatic problems of hollow toroids. The theory is developed for transversely isotropic toroids of arbitrary thickness, and has the potential to validate some vehicle and aircraft tire models in the linear range. In the semi-analytical method that is adopted Fourier series are written in the circumferential direction, forming a set of two-dimensional problems. These problems are solved using the differential quadrature method. A commercial finite element program is used to determine alternative solutions. For validation both problems of vibration and elastostatics are considered. Finally results are determined for local surface loading problems, and conclusions are drawn.
Keywords
toroids; differential quadrature; finite elements;
Citations & Related Records

Times Cited By Web Of Science : 3  (Related Records In Web of Science)
Times Cited By SCOPUS : 2
연도 인용수 순위
1 ADINA, User's Manual, 7.4, ADINA R & D Inc., Waterdown, Mass. (2000).
2 Chandrashekhara, K., and Nanjunda Rao, K.S. (1997), "Approximate elasticity solution for a long and thick laminated circular cylindrical shell of revolution," Int. J. Solids Struct., 34, 1327-1341.   DOI   ScienceOn
3 Grigorenko, A. Ya., Dyak, I.I., and Makar, V.M. (1998), "Three-dimensional dynamic elasticity-theory problem for anisotropic bodies," Int. Appl. Mech., 34(5), 424-430.
4 Jiang, W., and Redekop, D. (2002), "Polar axisymmetric vibration of a hollow toroid using the differential quadrature method," J. Sound Vibr., accepted for publication.
5 McGill, D.J., and Lenzen, K.H. (1967), "Polar axisymmetric free oscillations of thick hollowed tori," SIAM Journal, 15, 678-692.
6 Shu, C. (2000), Differential Quadrature and its Application in Engineering, Springer, New York.
7 Zhu, Y., and Redekop, D. (1995), "Band loading of a thick-walled toroidal shell," Int. J. Pres. Vess. & Piping, 61, 99-109.   DOI   ScienceOn
8 Redekop, D. (1992), "A displacement solution in toroidal elasticity," Int. J. Pres. Vess. & Piping, 51, 189-209.   DOI   ScienceOn
9 Naboulsi, S.K., Palazotto, A.N., and Greer, J.M. (2000), "Static-dynamic analyses of toroidal shells," J. Aero. Eng., ASCE, 13, 110-121.   DOI   ScienceOn
10 Darnell, I., Hulbert, G.M., and Mousseau, C.W. (1997), "An efficient three-dimensional tire model for vehicle dynamics simulations," Mech. Struct. & Mach., 25, 1-19.   DOI   ScienceOn
11 Zhang, Y., Palmer, T., and Farahani, A. (1997), "A finite element tire model and vibration analysis: a new approach," Tire Sci. Technol., 26, 149-172.   DOI
12 Redekop, D., and Xu, B. (2000), "Dynamic buckling of toroidal shells subject to impulsive local loading," Proc. ICPVT-9 Conference, Sydney, 1, 685-692.
13 Gall, R., Tabaddor, F., Robbins, D., Majors, P., Sheperd, W., and Johnson, S. (1995), "Some notes on the finite element analysis of tires," Tire Sci. Technol., 23, 175-188.   DOI   ScienceOn
14 Kim, D.O., Noor, A.K., and Tanner, J.A. (1990), "Modeling and analysis of the space shuttle nose-gear tire with semianalytic finite elements," NASA TP 2977, 33 pages.
15 Leung, A.Y.T., and Kwok, N.T.C. (1994), "Free vibration analysis of a toroidal shell," Thin-Walled Struct., 18, 317-332.   DOI   ScienceOn
16 Bathe, K.J. (1996), Finite Element Procedures, Prentice Hall, Englewood Cliffs.
17 Redekop, D. (1994), "Natural frequencies of a short curved pipe," Trans CSME, 18, 35-45.
18 Balderes, T., and Armenakas, A.E. (1973), "Free vibrations of ring-stiffended toroidal shells," AIAA J., 11, 1637- 1644.   DOI   ScienceOn
19 Redekop, D., and Zhang, F. (1992), "Local loads on a toroidal shell," J. Strain Analy., 27, 59-66.   DOI