Realistic computation of automobile tires is best achieved by modeling the whole tire with finite element methods. A numerical solution of the quasi‐static contact problem for the whole tire requires a refined mesh of elements with redundant degrees of freedom when nonlinear material assumptions are considered. Both laminated shell elements and incompressible continuum elements are used here. The stiffness matrix of a shell element is determined by numerically integrating all layers within the thickness of each element. Numerical studies have been made by a finite element technique that includes shell elements and Swanson's material model, which covers large deformations. The major contribution of this paper is implementation of a composite theory that includes effects of large displacements on the stiffness into an existing element. Swanson's material law was also simplified and implemented.

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