Nonlinear three-dimensional finite element analysis of contact problem of statically loaded tires

Publisher Summary This chapter presents a general and efficient 3D finite element (FE) model capable of analyzing and predicting the nonlinear response of statically loaded tires in contact with a rigid surface. The FEM is used to construct the discretized model of the problem. Both geometrical and material nonlinearities are accounted for. Lagrangian description with the composite material theories is adopted to model the nonlinear behavior of the tire structure. The mathematical programming (MP) technique is adopted to present a general model to analyze both frictionless and frictional tires contacts. With frictional contact, Coulomb's law of friction is modified to be applied nonlocally. This, logically, eliminates the difficulties that have been encountered with the direct application of the classical Coulomb's law. A typical radial tire is taken as a case study to which the model is applied. The defined tire shape, the contact patch, and both normal and tangential contact stresses are predicted in the chapter. The results demonstrate the efficient applicability of the developed model to analyze the nonlinear contact problem of the loaded tires.

[1]  J. R. Stafford,et al.  Nonlinear vibration of cord-reinforced composite shells , 1981 .

[2]  H. Rothert,et al.  On the finite element solution of the three-dimensional tire contact problem , 1984 .

[3]  T. Y. Yang,et al.  Inflation and Contact Predictions of Composite Tire Shell Carcass , 1987 .

[4]  Ahmed K. Noor,et al.  Exploiting symmetries in the modeling and analysis of tires , 1987 .

[5]  J T Tielking,et al.  INVESTIGATION OF TIRE-PAVEMENT INTERACTION DURING MANEUVERING , 1977 .

[6]  J. T. Tielking.  A Finite Element Tire Model , 1983 .

[7]  Y. Tozawa,et al.  Stress Analysis of a Tire Under Vertical Load by a Finite Element Method , 1977 .

[8]  John Thomas Tielking.  Analytic tire model. Phase I: the statically loaded toroidal membrane. Final report , 1975 .

[9]  J. Lions,et al.  Inequalities in mechanics and physics , 1976 .

[10]  Joseph D. Walter,et al.  Radial Tire Cord-Rubber Composites , 1976 .

[11]  J. Oden,et al.  Algorithms and numerical results for finite element approximations of contact problems with non-classical friction laws , 1984 .

[12]  H. Rothert,et al.  On the Three‐Dimensional Computation of Steel‐Belted Tires , 1986 .

[13]  John T. Tielking.  Aircraft Tire/Pavement Pressure Distributions , 1989 .

[14]  M. J. Trinko.  Ply and Rubber Stresses and Contact Forces for a Loaded Radial Tire , 1983 .

[15]  T. Y. Yang,et al.  Displacements and Stresses Resulting from Contact of a Steel Belted Radial Tire with a Flat Surface , 1978 .

[16]  S. K. Clark,et al.  MECHANICS OF PNEUMATIC TIRES , 1971 .

[17]  Anil Chaudhary,et al.  A solution method for static and dynamic analysis of three-dimensional contact problems with friction , 1986 .

[18]  K. Bathe,et al.  FINITE ELEMENT FORMULATIONS FOR LARGE DEFORMATION DYNAMIC ANALYSIS , 1975 .

[19]  Ahmed K. Noor,et al.  Advances and trends in the development of computational models for tires , 1985 .

[20]  Joseph D. Walter.  Cord—Rubber Tire Composites: Theory and Applications , 1978 .

[21]  W. Hofferberth,et al.  Mechanics of the Pneumatic Tire , 1967 .

[22]  Paul S. Shoemaker.  Tire Engineering by Finite Element Modeling , 1984 .

[23]  T. Y. Yang,et al.  Contact of an Inflated Toroidal Membrane with a Flat Surface as an Approach to the Tire Deflection Problem , 1975 .

[24]  J. Oden,et al.  Nonlocal and Nonlinear Friction Laws and Variational Principles for Contact Problems in Elasticity , 1983 .

[25]  J. T. Oden,et al.  Numerical analysis of certain contact problems in elasticity with non-classical friction laws , 1983 .

[26]  J. R. Luchini,et al.  A Laminated Composite Solid Element and its Application to Tire Analysis , 1987 .

[27]  G. R. Potts,et al.  Advances in Tire Composite Theory , 1973 .

[28]  H. Rothert,et al.  On geometrically nonlinear contact problems with friction , 1985 .

[29]  H. K. Brewer.  Tire Stress and Deformation from Composite Theory , 1973 .

[30]  Ahmed K. Noor,et al.  Frictionless contact of aircraft tires , 1989 .

[31]  H. Rothert,et al.  Numerical Results of Tire‐Test Drum Interaction , 1986 .

[32]  W. Jacobi,et al.  On the Contact Problem of Tires, Including Friction , 1985 .

[33]  Edoardo Robecchi.  MECHANICS OF THE PNEUMATIC TIRE: PART II: THE LAMINAR MODEL UNDER INFLATION AND IN ROTATION , 1973 .

[34]  Ahmed K. Noor,et al.  Mixed Models and Reduction Techniques for Large-Rotation, Nonlinear Analysis of Shells of Revolution with Application to Tires , 1984 .

[35]  J. Oden,et al.  Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods , 1987 .

[36]  David J. Benson,et al.  Sliding interfaces with contact-impact in large-scale Lagrangian computations , 1985 .