Computation of Stresses, Strains, and Deformations of Tires

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Abstract
The pneumatic tire is often taken for granted as a simple and reliable component of the vehicle. A closer look, however, shows that the tire in service is subjected to severe stresses and deformations whose quantities must be determined in order to accurately predict tire performance. Modern tire structures have evolved through a series of modifications of the original pneumatic rubber tire. These modifications were based on field experiences and on mostly experimental studies of tire behavior. The use of analytical techniques to calculate tire stresses and deformations remained limited in scope for a long time because the complexity of the tire structure placed it beyond the domain of available methods of analysis. The recent emphasis on analytical techniques is due, at least partly, to their potential for becoming less time consuming and less expensive than experimental methods, the need for predicting a tire's behavior before its manufacture, and the notable advances in computational and structural analysis methods. In this paper, these methods are described and applied to the calculation of tire stresses and deformations. Structural analysis is the analytical determination of structural responses to a prescribed set of applied loads. The responses may be displacements or distortions if force loads are known, or forces if displacement or distortions are known. Given the geometry of a structure (shape, dimensions), the relevant properties of its component materials, the magnitude and distribution of applied loads, and any constraints from boundary conditions, then structural analysis is used to calculate displacements, strains, or stresses at any chosen location in or on the structure. These calculated values may be compared to those required for functionality of the structure. Although structural analysis is not directly applicable to determining the most efficient configuration of the structural components, the analysis of successive well chosen modifications can often optimize compositions or geometries. The application of structural analysis to a tire requires (a) knowledge of the relevant physical properties of the component materials, and their configuration in the tire, (b) complete characterization of the applied loads, and (c) an analytical technique (i.e. theory) for calculating the required responses. These requirements are explained in the following sections.

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