Tire Contact Using Two-Dimensional Finite Elements
Publication: Journal of Engineering Mechanics
Volume 124, Issue 3
Abstract
The problem of static contact between a tire and a nondeformable surface is explored with two-dimensional shell finite elements. The tire is treated as a composite shell, due to its nylon-corded rubber ply (laminated) construction. In the actual tire, the ply orientation angles, numbers of plies, ply thicknesses, and even the ply moduli change in the meridional direction (the direction perpendicular to the “rolling” direction). Moreover, the moduli of the materials used in construction span several orders of magnitude (isotropic rubber tread, nylon-corded rubber plies, and steel bead wires). These features present a formidable challenge to analyzing the tire with two-dimensional finite element codes. In the current work, quasi-three-dimensional behavior of the tire in static contact with a flat surface is generated through the finite element technique. The two-dimensional finite elements include the effects of transverse shear warping and thickness stretching, and use the Jaumann (local engineering) stress measures. A local and layer-wise displacement field is used to describe the behavior of the shell away from the reference surface. In contrast to stress-resultant models, this technique allows estimation of stresses and strains in individual plies, including interlaminar shear and peeling stresses.
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References
1.
Atluri, S. N.(1984). “Alternate stress and conjugate strain measures, and mixed variational formulations involving rigid rotations, for computational analyses of finitely deformed solids, with applications to plates and shells—I, theory.”Comp. and Struct., 18(1), 93–116.
2.
Atluri, S. N., and Murakawa, H. (1977). “On hybrid finite element models in nonlinear mechanics.”Finite elements in nonlinear mechanics: Papers presented at the International Conference on Finite Elements in Nonlinear Solid and Structural Mechanics, P. G. Bergan et al., eds., Tapir, Trondheim, Norway, 3–41.
3.
Brockman, R. A., Braisted, W. R., J. Padovan, Tabaddor, F., and Clark, S. K. (1992). “Design and analysis of aircraft tires.”Final Rep. WL-TR-91-3060, Flight Dyn. Directorate, Wright Lab., Air Force Sys. Command, Wright-Patterson Air Force Base, Ohio; Univ. of Dayton Res. Inst. Rep. UDR-TR-91-41, Dayton, Ohio.
4.
Cook, R. D., Malkus, D. S., and Plesha, M. E. (1989). Concepts and applications of finite element analysis. John Wiley & Sons, Inc., New York, N.Y.
5.
Danielson, D. A., and Hodges, D. H.(1987). “Nonlinear beam kinematics by decomposition of the rotation tensor.”J. Engrg. Mech., ASCE, 54(2), 258–262.
6.
DeEskinazi, J., Yang, T. Y., and Soedel, W.(1978). “Displacements and stresses resulting from contact of a steel belted radial tire with a flat surface.”Tire Sci. & Technol., 11(1), 48–70.
7.
Epstein, M., and Glockner, P. G.(1977). “Nonlinear analysis of multilayered shells.”Int. J. Solids and Struct., 13, 1081–1089.
8.
Epstein, M., and Huttelmaier, H.-P.(1983). “A finite element formulation for multilayered and thick plates.”Comp. and Struct., 16(6), 645–650.
9.
Fraeijs de Veubeke, B.(1972). “A new variational principle for finite elastic displacements.”Int. J. Engrg. Sci., 10(9), 745–763.
10.
Greer, J. M. Jr. (1996). “Non-linear finite element analyses of composite shells by total Lagrangian decomposition with application to the aircraft tire,” PhD dissertation, AFIT/DS/ENY/96-1, Grad. School of Engrg., The Air Force Inst. of Technol., Wright-Patterson Air Force Base, Ohio.
11.
Greer, J. M. Jr., and Palazotto, A. N.(1996). “Nonlinear finite element analysis of isotropic and composite shells by a total Lagrangian decomposition scheme.”Mech. of Compos. Mat. and Struct., 3, 241–271.
12.
Greer, J. M. Jr., and Palazotto, A. N.(1997). “Application of a total lagrangian corotational finite element scheme to the inflation of a tire.”Int. J. Solids Struct., 34(27), 3541–3570.
13.
Hinrichsen, R. L., and Palazotto, A. N.(1986). “Nonlinear finite element analysis of thick composite plates using cubic spline functions.”AIAA J., 24(11), 1836–1842.
14.
Hornbeck, R. W. (1975). Numerical methods. Quantum Publishers, Inc., New York, N.Y.
15.
Kennedy, R., and Padovan, J.(1987). “Finite element analysis of steady and transiently moving/rolling nonlinear viscoelastic structure—II. Shell and three-dimensional simulations.”Comp. and Struct., 27(2), 259–273.
16.
Kim, K. O., and Noor, A. K. (1990). “Modeling and analysis of the space shuttle nose-gear tire with semianalytic finite elements.”NASA Tech. Paper TP-2977, Nat. Aeronautics and Space Admin., Washington, D.C.
17.
Malvern, L. E. (1969). Introduction to the mechanics of a continuous medium. Prentice-Hall, Inc., Englewood Cliffs, N.J.
18.
Meirovitch, L. (1967). Analytical methods in vibrations. Macmillan, New York, N.Y.
19.
Murakami, H. (1984). “Laminated composite plate theories with improved inplane responses.”ASME Pressure Vessels and Piping Conf., ASME, New York, N.Y., 257–263.
20.
Owen, D. R. J., and Hinton, E. (1980). Finite elements in plasticity: Theory and practice. Pineridge Press, Ltd., Swansea, U.K.
21.
Padovan, J.(1975). “Traveling waves vibrations and buckling of rotating anisotropic shells of revolution by finite elements.”Int. J. Solids and Struct., 11, 1367–1380.
22.
Padovan, J.(1976). “On viscoelasticity and standing waves in tires.”Tire Sci. & Technol., 4(4), 233–246.
23.
Padovan, J.(1977). “Circumferentially traveling radial loads on rings and cylinders.”Int. J. Non-Linear Mech., 12, 241–250.
24.
Pai, P. F., and Nayfeh, A. H.(1992). “A nonlinear composite shell theory.”Nonlinear Dyn., 3, 431–463.
25.
Pai, P. F., and Nayfeh, A. H.(1994). “A new method for the modeling of geometric nonlinearities in structures.”Comp. and Struct., 53(4), 877–895.
26.
Pai, P. F., Nayfeh, A. H., Oh, K., and Mook, D. T.(1993). “A refined nonlinear model of composite plates with integrated piezoelectric actuators and sensors.” Int. J. Solids and Struct., 30(12), 1603–1630.
27.
Pai, P. F., and Palazotto, A. N.(1995). “Nonlinear displacement-based finite-element analyses of composite shells—A new total Lagrangian formulation.”Int. J. Solids and Struct., 32(20), 3047–3073.
28.
Palazotto, A. N., and Dennis, S. T. (1992). Nonlinear analysis of shell structures, AIAA Educational Ser. Am. Inst. of Aeronautics and Astronautics, Inc., Washington, D.C.
29.
Reddy, J. N.(1989). “On refined computational models of composite laminates.”Int. J. for Numer. Methods in Engrg., 27, 361–382.
30.
Renka, R. J.(1987). “Interpolatory tension splines with automatic selection of tension factors.”Siam J. on Scientific and Statistical Computing, 8(3), 393–415.
31.
Schweizerhof, K., and Ramm, E.(1984). “Displacement dependent pressure loads in nonlinear finite element analyses.”Comp. and Struct., 18(6), 1099–1114.
32.
Simo, J. C., Fox, D. D., and Rifai, M. S.(1990). “On a stress resultant geometrically exact shell model, part III. Computational aspects of the nonlinear theory.”Comp. Methods in Appl. Mech. and Engrg., 79(1), 21–70.
33.
Sve, C., and Herrmann, G.(1974). “Moving load on a laminated composite.”J. Appl. Mech., 41(3), 663–667.
34.
Washizu, K. (1982). Variational methods in elasticity and plasticity, 3rd Ed., Pergamon Press, Inc., Tarrytown, N.Y.
35.
Whitney, J. M. (1987). Structural analysis of laminated anisotropic plates. Technomic Publishing Inc., Lancaster, Pa.
36.
Wolfram, S. (1991). Mathematica: A system for doing mathematics by computer, 2nd Ed., Addison-Wesley, Redwood City, Calif.
37.
Wu, B., and Du, X.(1995). “Finite element formulation of radial tires with variables constraint conditions.”Comp. and Struct., 55(5), 871–875.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 124 • Issue 3 • March 1998
Pages: 348 - 357
Copyright
Copyright © 1998 American Society of Civil Engineers.
History
Published online: Mar 1, 1998
Published in print: Mar 1998
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