A finite element analysis of the static and dynamic behavior of the automobile tire

A mathematical model to represent a radial ply passenger car tire has been developed for axisymmetric and asymmetric static and dynamic eigenvalue analysis by the use of a direct stiffness finite element method. Linear analysis is performed. The tire is considered as a thin shell of revolution. The finite element chosen has a shape of a conical frustrum with five degrees of freedom at each node in the local coordinate system of the element. The tire properties have been derived by assuming the tire to be composed of thin layers of composite materials, linearly orthotropic in nature. Hamilton's principle has been applied to derive the equation of motion of the element.

In the case of asymmetric static analysis, fifteen Fourier harmonic terms have been used to represent the as)TTimetric loading and deformation. The equation for the static case has been solved by employing the Gauss elimination method. Three different types of pressure distributions have been assumed to simulate the actual pressure distribution in the tire footprint area. The natural frequencies and the associated set of mode shapes have been evaluated by employing a method based on a modified version of Lanczos' n-step iteration procedure.

The analysis predicts experimentally verifiable deformed shapes under static loading, and natural frequencies of vibration and associated mode shapes with good accuracy.