In this paper, we use an approach which involves 3D finite elements and a contact algorithm. For a given deflection of the hub, the algorithm computes the nodes that come into contact with a predefined contact plane, and the magnitudes of the contact forces at the nodes. Thus, the algorithm computes the size and shape of the footprint, and the contact forces at the FE nodes. To illustrate the technique, we analyze a homogeneous tire subjected to footprint loading. The computed shapes and sizes of the footprint area at different levels of rim deflection are shown to be in good agreement with experimental results. The computed tire profiles and the load‐deflection response of the tire are also in good agreement with experimental results. The computed results include the distribution of stress, strain, and strain energy density within the tire, and the changes in this distribution with applied footprint loadings.
A computational method is described for the analysis of deformable bodies loaded against rigid surfaces. The deformable body is modeled by three‐dimensional isoparametric elements. A contact algorithm determines the nodes that come into contact with each loading step; the finite element analysis computes the size and shape of the footprint and the distribution of contact pressure in the footprint. The procedure is illustrated by analysis of the contact of a rubber disk. The close agreement, shown between the computed and measured results for the rubber disk, demonstrates the potential of the technique for 3D contact analysis of pneumatic tires.
An analysis is presented for determining tire deformation due to shrinkage. The analysis uses composite theory and the finite element technique in modeling the material properties and the structural behavior. The constant strain toroidal shell element developed by Wilson for small displacement and isotropic properties is modified for orthotropic properties which depend on the element location. Temperature history and the buildup of shrink forces during cure are determined experimentally. The shrink forces are represented by a set of equivalent loads applied at the nodes. Good correlation is obtained between calculated and experimental displacements. The analysis is applied in relating the mold shape to the final shape of the tire.